HIGH DIELECTRIC CONSTANT 0-3 CERAMIC-POLYMER COMPOSITES  
 
 
Except where reference is made to the work of others, the work described in this 
dissertation is my own or was done in collaboration with my advisory committee. This 
dissertation does not include proprietary or classified information. 
 
 
 
 
Xiaobing Shan 
 
 
 
 
 
Certificate of Approval: 
 
 
 
Dong-Joo Kim                                                                    Zhongyang  Cheng, Chair 
Associate Professor                                                            Associate Professor 
Materials Engineering                                                        Materials Engineering 
 
 
 
Jeffrey Fergus                                                                     Maria Lujan Auad 
Associate Professor                                                            Assistant Professor 
Materials Engineering                                                        Polymer and Fiber Engineering 
 
 
 
 
George T. Flowers 
Dean 
Graduate School 
 
 
 
  
 
HIGH DIELECTRIC CONSTANT 0-3 CERAMIC-POLYMER COMPOSITES 
 
Xiaobing Shan 
 
A Dissertation 
Submitted to  
the Graduate Faculty of  
Auburn University 
in Partial Fulfillment of the 
 Requirements for the  
Degree of  
Doctor of Philosophy 
 
 
Auburn, Alabama 
August 10, 2009
iii 
 
HIGH DIELECTRIC CONSTANT 0-3 CERAMIC-POLYMER COMPOSITES 
 
 
 
Xiaobing Shan 
 
 
 
Permission is granted to Auburn University to make copies of this dissertation at its 
discretion, upon the request of individuals or institutions and at their expense.  
The author reserves all publication rights. 
 
 
 
 
 
                                                                         Signature of Author 
 
 
 
 
                                                                         Date of Graduation 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
iv 
 
VITA 
 
 
Xiaobing Shan, son of Dexi Shan and Fengling Lu, was born on July 17, 1977, in 
the city of Nanjing, China. He entered Yancheng Institute of Technology in August 1996 
and graduated in June 2000 with Bachelor degree in Materials Engineering. He joined the 
graduate program in Nanjing University of Technology in August 2000 and graduated 
with Master degree in Materials Science in June 2003.  He then got involved with 
fundamental research in Shanghai Institute of Ceramics, Chinese Academy of Sciences 
(CAS) to work as a research assistant until July 2004. He joined the graduate program at 
Auburn University in August 2004 to pursue his Ph.D degree in Materials Engineering. 
v 
 
 
 
 
 
 
DISSERTATION ABSTRACT 
 
 
HIGH DIELECTRIC CONSTANT 0-3 CERAMIC-POLYMER COMPOSITES 
 
 
Xiaobing Shan 
 
Doctor of Philosophy, August 10, 2009 
(M.S., Nanjing University of Technology, 2003) 
(B.S., Yancheng Institute of Technology, 2000) 
 
327 Typed Pages 
Directed by Zhongyang Cheng 
 
0-3 ceramic-polymer composites using both nano-size and micro-size 
CaCu
3
Ti
4
O
12
 ceramic particles were studied.  
            The micro-size ceramic particles were prepared from the CaCu
3
Ti
4
O
12
 pellets by 
milling. The CaCu
3
Ti
4
O
12
 ceramics were prepared using conventional solid-state reaction 
under different conditions, such as molding pressure, milling media and time, and 
calcination temperature and time. Based on the analysis of the dielectric spectrum, it was 
found that the dielectric responses of CaCu
3
Ti
4
O
12
 ceramics are determined by three 
different processes. The effect of thickness of the ceramics on the dielectric properties 
was observed and studied. Although the dielectric response at low frequency increases 
with decreasing thickness, the dielectric behavior for the high frequency relaxation 
process is weakly dependent on thickness. 
            0-3 composites with different concentrations (0-50 vo% CaCu
3
Ti
4
O
12
 ceramics) 
were prepared using solution casting. However, a clear polymer-rich layer was found in 
vi 
 
as-cast film due to the poor wettability between ceramic and polymer matrix. The HP was 
used to modify the morphology of the composites. Different configurations were studied 
for the HP process. Composites with a dielectric constant of 510 at 1 kHz were obtained 
in 50vol% CaCu
3
Ti
4
O
12 
composite with CC HP at room temperature. It was found that 
the relaxation time of the major relaxation process obtained in the composite changes 
with processing condition, such as annealing, HP and concentration. It indicates that the 
interfacial layers between ceramic particles and polymer matrix play an important role on 
the dielectric response of the composite. As for the HP samples, it was interestingly 
observed that as HP time changes, there is a critical HP time at which the composite 
exhibits a much higher dielectric constant. Based on the dielectric spectrum of the 
composites at different temperatures, it was concluded that the loss of the composites at 
low frequency is controlled by a relaxation process.  
            For the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite, the dielectric response is strongly 
dependent on temperature due to the fact that the dielectric constant of P(VDF-TrFE) is 
strongly dependent of temperature. However, as for the CaCu
3
Ti
4
O
12
/P(VDF-CTFE) 
composites, the dielectric constant of the composite is almost independent of temperature 
and the composite has a small loss. For example, composites with a dielectric constant of 
151 and loss of 0.14 at 1 kHz were obtained at room temperature. A clear difference 
between nano-size and micro-size CaCu
3
Ti
4
O
12 
composite was observed. Moreover, It 
was also found that the difference of dielectric constant between nano-size and micro-size 
particles in P(VDF-CTFE) copolymer is much smaller than that in P(VDF-TrFE) 
copolymer. 
 
 
vii 
 
ACKNOWLEDGEMENTS 
 
  I would like to give my gratitude to my advisor, Dr. Zhongyang Cheng, who has 
guided my thinking to reach my full potential through the completion of my research and 
dissertation in the past years. He has provided solid support and motivation in helping me 
reach my goals, both professionally and personally during my every bit of stay in 
Auburn.  
  I would like to express my sincere thanks to all my committee members, Dr. 
Maria Lujan Auad, Dr. Jeffrey Fergus and Dr. Dong-Joo Kim for their kind support and 
valuable suggestions in making my dream come true. Thanks to Mr. Roy Howard, Mr. 
L.C. Mathison and Mr. Levar Odum for providing continuous support for all these years.         
  I would like to gratefully acknowledge all my group members, Dr. Zhimin Li, Dr. 
Suiqiong Li, Lisa Orona, Yuhong Wang, Xin Yang, Liling Fu, Kewei Zhang, Levar 
Odum, Peixuan Wu, Lin Zhang, Zack Lamb, David Busby for all their supports and help 
to my research. Especially many thanks to Dr. Suiqiong Li, Levar Odum, Zack Lamb, 
Lin Zhang, Peixuan Wu, and Houmin Li for their kind generous help to my project. I 
appreciate the encouragement of all my friends and I would like to mention Dr. Nofrijon 
Sofyan, Dr. Li Chen and many more.  
  I am indebted to my family, especially my mother for her encouragement and 
support throughout my entire education. Without her support and encouragement, it is 
hard to imagine how much I can complete. Finally, I would like to acknowledge the 
financial support for this work from an Auburn University Competitive Research Grant 
and 3M Non-Tenured Faculty Grant. I also appreciated the support and research work at 
Pacific Northwest National Lab (PNNL). 
 
viii 
 
 
 
 
 
 
 
 
 
 
 
 
Dedicated to my wonderful mother, who was not well 
educated, but gave me so much courage, strength and 
faith to complete my Doctor of Philosophy degree. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ix 
 
 
 
 
 
Style manual or journal used: Macromolecules 
 
Computer software used: Microsoft Word, Excel, PowerPoint 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
x 
 
 
 
 
 
TABLE OF CONTENTS 
 
?
LIST OF FIGURES ......................................................................................................... xiv?
LIST OF TABLES ........................................................................................................ xxxii 
 
CHAPTER 1?
INTRODUCTION AND RESEARCH OBJECTIVES ...................................................... 1?
1.1 Theory of Dielectric Materials .............................................................................. 2?
1.1.1 Permittivity ................................................................................................ 2?
1.1.2 Origins of Permittivity ............................................................................... 3?
1.1.3 Dielectric Relaxation ................................................................................. 7?
1.1.4 Cole and Cole plot ..................................................................................... 9?
1.2 Classification of Dielectric Materials ................................................................. 10?
1.2.1 Nonpolar Materials .................................................................................. 10?
1.2.2 Polar Materials ......................................................................................... 10?
1.2.2.1 Ferroelectric Ceramic and Polymer ................................................... 11?
1.2.2.2 Ferroelectric Polymers ...................................................................... 16?
1.3 Energy Storage Density ...................................................................................... 17?
1.4 Applications of Dielectric Materials ................................................................... 18?
1.5 Calcium Copper Titanate CaCu
3
Ti
4
O
12
 .............................................................. 20?
1.5.1 Crystallographic Structure of CaCu
3
Ti
4
O
12
 ............................................. 21?
1.5.2 Origin of Colossal Dielectric Response ................................................... 23?
1.6 Ceramic-Polymer Composites ............................................................................ 27?
1.6.1 General Concepts for Composites ........................................................... 27?
1.6.2 Mixing Rule for Permittivity in Two-Phase Composites ........................ 29?
1.7 Current Developments of Polymer-Matrix Composite ....................................... 32?
1.7.1 Ferroelectric Ceramic/Polymer Composite .............................................. 32?
1.7.2 Conductive Filler/Polymer Composites ................................................... 34?
xi 
 
1.8 Interface Effect in Composites ............................................................................ 35?
1.8.1 Interfacial Forces ..................................................................................... 38?
1.8.2 Dielectric Properties................................................................................. 39?
1.9 Objectives of This Research ............................................................................... 44?
References ................................................................................................................. 45 
 
CHAPTER 2?
MATERIALS PREPARATION AND CHARACTERIZATION METHODS ................ 53?
2.1 Ceramic Synthesis ............................................................................................... 53?
2.2 Ceramic-Polymer 0-3 Composite Fabrication .................................................... 56?
2.2.1 Ceramic-Polymer 0-3 Composite Casting Procedure .............................. 56?
2.2.2 Optimization of Ceramic-Polymer 0-3 Composite .................................. 58?
2.2.2.1 Hot Pressing Process ......................................................................... 58?
2.2.2.2 Silane Coupling Process .................................................................... 60?
2.2.2.3 Annealing Process ............................................................................. 61?
2.3 Materials Characterization Methods ................................................................... 61?
2.3.1 Crystalline Structure Determination Using Wide Angle X-ray Diffraction
........................................................................................................................... 61?
2.3.2 Microstructure Analysis Using SEM ....................................................... 61?
2.3.3 Dielectric Analysis Using Impedane Analyzer ........................................ 64?
References ................................................................................................................. 66 
 
CHAPTER 3?
PROCESSING AND CHARACTERIZATION OF CaCu
3
Ti
4
O
12
 CERAMIC ................ 67?
3.1 Introduction ......................................................................................................... 67?
3.2 Experimental ....................................................................................................... 67?
3.3 Results and Discussion ....................................................................................... 68?
3.3.1 Solid State Synthesis ................................................................................ 68?
3.3.2 Effect of Processing On Dielectric Properties ......................................... 71?
3.3.2.1 Effect of Molding Pressure ................................................................ 71?
3.3.2.2 Effect of Ball Milling Time and Sintering time ................................ 76?
3.3.2.3 Effect of Calcination Temperature and Milling Solvent ................... 82?
xii 
 
3.3.2.4 Effect of Thickness on Dielectric Properties ..................................... 89?
3.3.2.4 Effect of CuO Doping on Dielectric Properties ................................ 98?
3.3.2.5 Effect of the Annealing Time on Dielectric Properties ................... 112?
3.3.2.6 Impedance Analysis ........................................................................ 115?
3.4 Summary ........................................................................................................... 118?
References ............................................................................................................... 119 
 
CHAPTER 4?
PROCESS INFLUENCE ON THE DIELECTRIC PROPERTIES OF 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) COMPOSITES .................................................................. 120?
4.1 Introduction ....................................................................................................... 120?
4.2 Experimental ..................................................................................................... 120?
4.3 Results and Discussion ..................................................................................... 121?
4.3.1 Dielectric Behavior and Annealing Effect ............................................. 121?
4.3.2 Hot Pressing Effect ................................................................................ 129?
4.3.3 Multiple-Layer Configuration ................................................................ 140?
4.3.3.1 Dielectric Response using PC Hot Pressing .................................... 140?
4.3.3.2 Dielectric Response using CC Hot Pressing ................................... 147?
4.3.3.3 Uniformity of 0-3 Composite under CC Hot Pressing .................... 162?
4.3.3.4 Temperature Dependent of Dielectric Response ............................. 171?
4.3.3.5 Impedance Analysis ........................................................................ 191?
4.3.4 P-E Hysteresis Loop .............................................................................. 199?
4.3.5 Polymer Matrix Effect on Dielectric Behavior ...................................... 205?
4.3.5.1 Dielectric Behavior .......................................................................... 205?
4.3.5.2 Hot Pressing Effect .......................................................................... 210?
4.3.5.3 Temperature Dependent of Dielectric Response ............................. 216?
4.4 Summary ........................................................................................................... 224?
References ............................................................................................................... 226 
 
 
 
 
 
xiii 
 
CHAPTER 5?
STUDY OF DIELECTRIC BEHAVIOR ON THE CaCu
3
Ti
4
O
12
-BASED COMPOSITES
......................................................................................................................................... 227?
5.1 Introduction ....................................................................................................... 227?
5.2 Experimental ..................................................................................................... 228?
5.3 Results and Discussion ..................................................................................... 228?
5.3.1 Size Effect on Dielectric Behavior ........................................................ 228?
5.3.1.1 Dielectric Behavior .......................................................................... 229?
5.3.1.2 Hot Pressing Effect .......................................................................... 233?
5.3.1.3 Hot Pressing Time on Dielectric Properties .................................... 239?
5.3.1.4 Temperature Dependent of Dielectric Response ............................. 249?
5.3.1.5 P-E Hysteresis Loop ........................................................................ 253?
5.3.1.6 Polymer Matrix Effect on Dielectric Behavior ............................... 262?
5.3.2 Silane Coupling Effect on Dielectric Behavior ..................................... 268?
5.3.2.1 Theoretical Calculation for Silane Coupling Agent ........................ 268?
5.3.3.1 Dielectric Behavior .......................................................................... 271?
5.3.3.3 Silane Concentration Effect on Dielectric Behavior ....................... 278?
5.3.3.4 Temperature Dependent of Dielectric Response ............................. 282?
5.3.3.5 Size Effect on Dielectric Behavior .................................................. 285?
5.4 Summary ........................................................................................................... 290?
References ............................................................................................................... 291 
 
CHAPTER 6?
CONCLUSION AND FUTURE WORKS ..................................................................... 292?
6.1 Summary of Results and Conclusions .............................................................. 292?
6.2 Future Works .................................................................................................... 293?
 
 
xiv 
 
 
 
 
 
LIST OF FIGURES 
 
 
Figure 1-1 Schematics of (a) electron polarization, (b) ionic polarization, (c) orientational 
polarization, (d) space charge polarization. ........................................................................ 5 
 
Figure 1-2 The influence of the polarization: (a) real part of relative permittivity and (b) 
imaginary part of relative permittivity with frequency. ...................................................... 6 
 
Figure 1-3 Argand diagram for dielectric material with only one relaxation time based on 
Debye equation. .................................................................................................................. 8 
 
Figure 1-4 The schematic of 
r
'? , 
r
"? and ?tan as functions of ?  based on Debye 
equation. .............................................................................................................................. 8 
 
Figure 1-5 The Cole-Cole plot for dielectric material with a set of relaxation time based 
on Cole-cole equation. ...................................................................................................... 10 
 
Figure 1-6 P-E loop of ferroelectric. ................................................................................. 13 
 
Figure 1-7 Effect of grain size on permittivity of BaTiO
3
4
. (Relative permittivity is 
represented by 
r
'?  which is described in Section 1.1). ..................................................... 13 
 
Figure 1-8 Dielectric permittivity of PMN: (a) at various amplitudes, Em (1-0.01, 2-0.5, 
3-1, 4-1.5, 5-2 kV/cm), and (b) various frequencies, ?  (1-1 kHz, 2-100 Hz, 3-20 Hz) of 
the ac field
34
. ( '?  is equivalent to 
r
'? which is described in  Section 1.1). ....................... 14 
 
Figure 1-9 Relationship of electric displacement D  vs. electric field E : (a) linear; (b) 
nonlinear with positive curvature; (c) nonlinear with negative curvature. ....................... 17 
 
Figure 1-10  The classified categories of dielectric materials
56
. ( '? is equivalent to 
r
'?  
which is described in  Section 1.1). .................................................................................. 19 
 
Figure 1-11 The temperature dependence of dielectric constant and loss ........................ 20 
 
Figure 1-12  The structure of CaCu
3
Ti
4
O
12
 (Cu-blue, Oxygen-red, Ca-yellow)
61
. .......... 22 
 
Figure 1-13 The schematic of twin boundary in CaCu
3
Ti
4
O
12
72
. ..................................... 24 
 
 
xv 
 
Figure 1-14  (a) Temperature-dependent dielectric constants and (b) conductivities of 
single-crystalline CaCu
3
Ti
4
O
12
 with sputter gold (solid lines) and silver-paint contacts 
(symbols) at various frequencies
78
. The dashed and dashed-dotted lines in (b) show an 
estimate of the intrinsic bulk dc conductivity and the contribution of the insulating layer. 
( '?  is equivalent to 
r
'? which is described in Section 1.1). .............................................. 25 
 
Figure 1-15  (a) Frequency-dependent dielectric constants, (b) loss, and (c) conductivities 
of single crystalline CaCu
3
Ti
4
O
12
 with silver-paint contacts at various temperatures
78
. ( '?  
and "? are equivalent to 
r
'? and 
r
"? respectively, which are described in  Section 1.1). .. 26 
 
Figure 1-16 Ten dimension patterns in diphasic composites
79
. ........................................ 28 
 
Figure 1-17 Schematic of (a) parallel and (b) series connections. .................................... 29 
 
Figure 1-18 Schematic of dielectric constant of two phases 1 and 2 vs. their volume 
fraction in the mixture: 1, parallel connection; 2, series connection; 3, real composite. .. 30 
 
Figure 1-19  (a) percentage volume of interface as function of interface thickness d for 
particle sizes 10, 1 and 0.5 nm. (b) Schematic of particle A from micrometric to 
nanometric and then to sub-nanometric size. The interface increasingly dominates
103
. .. 36 
 
Figure 1-20 Interfacial regions as a function of filler particle size. The filler is shown in 
red, the interfacial region in dark blue and bulk polymer in pale blue. (a) Large particle 
produce low radius of curvature and relative less polymer in the interfacial regions. (b) 
The same volume of filler broken into small particles creates a high radius of curvature 
and more polymer in the interfacial region
104
. .................................................................. 37 
 
Figure 1-21 Schematic of electrical layers of extended interface
103
. ................................ 39 
 
Figure 1-22 The dielectric response vs. alumina volume fraction at 100 kHz and 25
o
C
112
. 
(?  is equivalent to 
r
'? which is described in  Section 1.1). .............................................. 42 
 
Figure 1-23 The correlation between the interfacial area and the dielectric enhancement 
in PI-alumina nanocomposite
112
. (?  is equivalent to 
r
'? which is described in  Section 
1.1). ................................................................................................................................... 42 
 
Figure 1-24 Comparison of the Vo-Shi model prediction with experimental results on PI-
alumina nanocomposites and epoxy-(PMN-PT) composites, respectively. Also shown are 
the prediction by Maxwell-wagner rule for both systems
112
. (?  is equivalent to 
r
'? which 
is described in  Section 1.1. K is a constant that is dependent on the degree of particle 
clustering influencing the surface area and the thickness of the interface region between 
the nanoparticles.). ............................................................................................................ 43?
 
Figure 2-1 Image of 48000 Barnstead Thermolyne furnace. ............................................ 54 
 
xvi 
 
Figure 2-2 Image of Al
2
O
3
 crucible and sintered ceramic pellet. ..................................... 55 
 
Figure 2-3 SEM image of milled CaCu
3
Ti
4
O
12
 powder. .................................................. 56 
 
Figure 2-4  Particle size distribution of milled CaCu
3
Ti
4
O
12
 powder. ............................. 57 
 
Figure 2-5 Image of flexible CaCu
3
Ti
4
O
12
- P(VDF-TrFE) 0-3 composite. ...................... 57 
 
Figure 2-6 Process flowchart for CaCu
3
Ti
4
O
12
-P(VDF-TrFE) 0-3 composite fabrication.
........................................................................................................................................... 58 
 
Figure 2-7 The schematic of (a) PC hot pressing and (b) CC hot pressing. ..................... 59 
 
Figure 2-8 The schematic of silane coupling agent reaction process with P(VDF-TrFE) 
and CaCu
3
Ti
4
O
12
. .............................................................................................................. 60 
 
Figure 2-9 Image of Pelco SC-6 sputter coater. ................................................................ 63 
 
Figure 2-10 Measurement setup of Scanning Electron Microscopy (SEM). .................... 63 
 
Figure 2-11 Image of mask with diameter of 1.7 millimeter. ........................................... 65 
 
Figure 2-12 Image of Agilent 4294A impedance analyzer. .............................................. 65 
 
Figure 2-13 Setup of home-made probe for temperature dependence measurement. ...... 66?
 
Figure 3-1 XRD patterns on the CaCu
3
Ti
4
O
12
: (a) calcination at 1075
o
C after 48, 72 and 
96 hrs milling; (b) calcination at 900
o
C after 48, 72 and 96 hrs milling according to the 
procedure #1 and 2 in table 3-1. ........................................................................................ 70 
 
Figure 3-2 Dielectric response vs. frequency for CaCu
3
Ti
4
O
12
 samples with 24 hrs D.I 
water ball milling, calcinated at 1075 
o
C, and then sintered at 1075 
o
C for 1 hr, 24 hrs, 48 
hrs and 72 hrs using  (a) 2500 PSI, and (b) 3000 PSI  pellet molding pressure. .............. 73 
 
Figure 3-3  SEM fractographs of CaCu
3
Ti
4
O
12
 after 24 hrs D.I water ball milling, 
calcinated at 1075 
o
C, sintered at 1075 
o
C for (a) 1 hrs, (b) 24 hrs, (c) 48 hrs (d) 72 hr 
using 2500 PSI pellet molding pressure. ........................................................................... 74 
 
Figure 3-4  SEM fractographs of CaCu
3
Ti
4
O
12
 after 24 hrs D.I water ball milling, 
calcinated at 1075 
o
C, sintered at 1075 
o
C for (a) 1 hr, (b 24 hrs, (c) 48 hrs (d) 72 hrs by 
3000 PSI pellet molding pressure. .................................................................................... 75 
 
Figure 3-5 Dielectric response vs. frequency for samples: (a), (b) and (c) after 48, 72 and 
96 hrs milling respectively,  calcining at 1075
 o
C for 12 hrs,  then sintering at 1075 
o
C for 
24, 48, and 72 hrs according to procedure #1 in table 3-1. ............................................... 78 
 
xvii 
 
Figure 3-6 SEM fractographs of CaCu
3
Ti
4
O
12
 for 48 hrs D.I water ball milling, calcining 
at 1075
 o
C for 12 hrs, then sintering at 1075
o
C for (a) 24 hrs, (b) 48 hrs, (c) 72 hrs. ....... 79 
 
Figure 3-7 SEM fractographs of CaCu
3
Ti
4
O
12
 for 72 hrs D.I water ball milling, calcining 
at 1075
 o
C for 12 hrs, then sintering at 1075
o
C for (a) 24 hrs, (b) 48 hrs, (c) 72 hrs. ....... 80 
 
Figure 3-8 SEM fractographs of CaCu
3
Ti
4
O
12
 for 96 hrs D.I water ball milling, calcining 
at 1075
 o
C for 12 hrs, then sintering at 1075 
o
C for (a) 24 hrs, (b) 48 hrs, (c) 72 hrs. ...... 81 
 
Figure 3-9 Dielectric response vs. frequency for samples: (a), (b) and (c) after 48, 72 and 
96 hrs milling respectively, then sintering for 24, 48, and 72 hrs according to procedure 
#2 in Table 3-1. ................................................................................................................. 84 
 
Figure 3-10 SEM fractographs of CaCu
3
Ti
4
O
12
 for 48 hrs D.I water ball milling, 
calcinated at 900
 o
C, then sintering at 1075
 o
C for (a) 24 hrs, (b) 48 hrs, (c) 72 hrs. ....... 85 
 
Figure 3-11 Dielectric response vs. frequency for samples: (a) after 72 hrs milling 
according to procedure #3 in Table 3-1; (b) after 72 hrs milling according to procedure #4 
in Table 3-1. ...................................................................................................................... 88 
 
Figure 3-12 Dielectric response vs. frequency for samples with different sample thickness 
(1.60 mm, 0.78 mm, 0.60 mm and 0.36 mm, respectively) after 96 hrs milling and then 
24 hrs sintering according to procedure #2 in Table 3-1. ................................................. 91 
 
Figure 3-13 Dielectric response vs. frequency for samples with different sample thickness 
(1.25 mm, 0.79 mm, 0.60 mm and 0.39 mm, respectively) after 96 hrs milling and then 
48 hrs sintering according to procedure #2 in Table 3-1. ................................................. 91 
 
Figure 3-14 Dielectric response vs. frequency for samples with different sample thickness 
(1.13 mm, 0.81 mm, 0.60 mm and 0.38 mm, respectively) after 96 hrs milling and then 
72 hrs sintering according to procedure #2 in Table 3-1. ................................................. 92 
 
Figure 3-15 Illustration of edge, middle, core areas in CaCu
3
Ti
4
O
12
 ceramic pellet for 
SEM fractographs. ............................................................................................................ 92 
 
Figure 3-16 SEM fractographs of CaCu
3
Ti
4
O
12
 after 96 hrs milling and then 24 hrs 
sintering according to procedure #2 in Table 3-1: (a) edge area, (b) middle area, (c) core 
area. ................................................................................................................................... 93 
 
Figure 3-17 SEM fractographs of CaCu
3
Ti
4
O
12
 after 96 hrs milling and then 48 hrs 
sintering according to procedure #2 in Table 3-1: (a) edge area, (b) middle area, (c) core 
area. ................................................................................................................................... 94 
 
Figure 3-18 SEM fractographs of CaCu
3
Ti
4
O
12
 after 96 hrs milling and then 72 hrs 
sintering according to procedure #2 in Table 3-1: (a) edge area, (b) middle area, (c) core 
area. ................................................................................................................................... 95?
xviii 
 
Figure 3-19  Cole-cole plot of the dielectric data of samples with different sample 
thickness (0.78 mm, 0.60 mm and 0.36 mm, respectively) after 96 hrs milling and then 24 
hrs sintering according to procedure #2 in Table 3-1. ...................................................... 96 
 
Figure 3-20 Cole-cole plot of the dielectric data of samples with different sample 
thickness (0.79 mm, 0.60 mm and 0.39 mm, respectively) after 96 hrs milling and then 48 
hrs sintering according to procedure #2 in Table 3-1. ...................................................... 96 
 
Figure 3-21 Cole-cole plot of the dielectric data of samples with different sample 
thickness (0.81 mm, 0.60 mm and 0.38 mm, respectively) after 96 hrs milling and then 72 
hrs sintering according to procedure #2 in Table 3-1. ...................................................... 97 
 
Figure 3-22 The relationship of ?? (?
rs
-?
r?
) vs. sample thickness after 96 hrs milling and 
then 24, 48 and 72 hrs sintering according to procedure #2 in Table 3-1. ........................ 97 
 
Figure 3-23 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
 after 72 hrs D.I water 
ball milling according to procedure #1 in table 3-1 with (a) 5 % CuO doping; (b) 10 % 
CuO doping ....................................................................................................................... 99 
 
Figure 3-24 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 24 hrs at site #1. .............................................................................. 100 
 
Figure 3-25 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 24 hrs at site #2. .............................................................................. 101 
 
Figure 3-26 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 48 hrs at site #1. .............................................................................. 102 
 
Figure 3-27 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 48 hrs at site #2. .............................................................................. 103 
 
Figure 3-28 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 72 hrs at site #1. .............................................................................. 104 
 
Figure 3-29 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 72 hrs at site #2. .............................................................................. 105 
 
Figure 3-30 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 24 hrs at site #1. .............................................................................. 106 
 
Figure 3-31 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 24 hrs at site #2. .............................................................................. 107 
 
Figure 3-32 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 48 hrs at site #1. .............................................................................. 108 
 
xix 
 
Figure 3-33 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 48 hrs at site #2. .............................................................................. 109 
 
Figure 3-34 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 72 hrs at site #1. .............................................................................. 110 
 
Figure 3-35 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 72 hrs at site #2. .............................................................................. 111 
 
Figure 3-36 Dielectric response vs. frequency for CaCu
3
Ti
4
O
12
 samples with initial 48 hrs 
milling according to procedure #1 in table 3-1: (a) post annealing in vacuum for different 
time at 1000 
o
C; (b) post annealing in flowing argon for different time at 1000 
o
C; (c) 
post annealing in flowing argon at different temperature for 1 hr. ................................. 113 
 
Figure 3-37 SEM fractographs of CaCu
3
Ti
4
O
12
 with post annealing in flowing argon at 
1000 
o
C for 10 hrs with magnification of : (a)-1 X150, (a)-2 X450, (a)-3 X450; for 24 hr: 
(b)-1 X150, (b)-2 X450, (b)-3 X450. .............................................................................. 114 
 
Figure 3-38 Impedance plot of CaCu
3
Ti
4
O
12
 calcinating at 1075 ?C and then sintering at 
1075 ?C for 24, 48 and 72 hrs after (a) 48 hrs D.I water ball milling; (b) 72 hrs D.I water 
ball milling; (c) 96 hrs D.I water ball milling. ................................................................ 116 
 
Figure 3-39 Impedance plot of CaCu
3
Ti
4
O
12
 calcinating at 900 ?C and then sintering at 
1075 ?C for 24, 48 and 72 hrs after (a) 48 hrs D.I water ball milling; (b) 72 hrs D.I water 
ball milling; (c) 96 hrs D.I water ball milling. ................................................................ 117?
 
Figure 4-1 Dielectric response vs. frequency of pure P(VDF-TrFE) film: (a) casting at 123 
 
Figure 4-2 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (10 vol% CCTO) without annealing,  with annealing in comparison with 
P(VDF-TrFE). ................................................................................................................. 123 
 
Figure 4-3 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (20 vol% CCTO) without annealing,  with annealing in comparison with 
P(VDF-TrFE). ................................................................................................................. 124 
 
Figure 4-4 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (30 vol% CCTO) without annealing,  with annealing in comparison with 
P(VDF-TrFE). ................................................................................................................. 124 
 
Figure 4-5 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (40 vol% CaCu
3
Ti
4
O
12
) without annealing,  with annealing in comparison with 
P(VDF-TrFE). ................................................................................................................. 125 
 
xx 
 
Figure 4-6 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% CaCu
3
Ti
4
O
12
) without annealing,  with annealing in comparison with 
P(VDF-TrFE). ................................................................................................................. 125 
 
Figure 4-7 Dependence of dielectric response (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite at room temperature without annealing 
and with annealing respectively. ..................................................................................... 126 
 
Figure 4-8 Cole-cole plot of the dielectric data of (a) 1 layer and (b) 1 annealed layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 10 to 50 vol% CaCu
3
Ti
4
O
12
 powder at RT.
......................................................................................................................................... 127 
 
Figure 4-9 The relationship of relaxation time and   CaCu
3
Ti
4
O
12
 volume concentration 
between 1 layer and 1 annealed layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite samples 
with 10 to 50 vol% CaCu
3
Ti
4
O
12
 powder. ...................................................................... 128 
 
Figure 4-10 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 10 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 131 
 
Figure 4-11 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 20 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 132 
 
Figure 4-12 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 30 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 133 
 
Figure 4-13 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 40 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 134 
 
Figure 4-14 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 135 
 
Figure 4-15 Dependence of dielectric constant (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
using 1 layers hot pressing (HP) at room temperature: (a) without annealing; (b) with 
annealing. ........................................................................................................................ 136 
 
Figure 4-16 Cole-cole plot of the dielectric data of 1 layer HP annealed 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 10 to 50 vol% CaCu
3
Ti
4
O
12
 powder. ....... 137 
 
Figure 4-17  Comparison of the present model predictions with experimental data for 1 
HP layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. ............................................................... 138?
xxi 
 
Figure 4-18 Comparison of the present model predictions with experimental data for 1 
layer HP annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. ................................................ 138 
 
Figure 4-19 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 141 
 
Figure 4-20 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 20 vol% CaCu
3
Ti
4
O
12 
powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 142 
 
Figure 4-21 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 30 vol% CaCu
3
Ti
4
O
12 
powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 143 
 
Figure 4-22 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12 
powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 144 
 
Figure 4-23 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12 
powder: (a) without annealing; (b) with annealing.
......................................................................................................................................... 145 
 
Figure 4-24 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% 
CaCu
3
Ti
4
O
12
 powder using hot pressing for 10 seconds, (a) 1 layer without hot pressing, 
(b) 2 layer PC pressing,  (c) 3 layer PC pressing, (d) 4 layer PC pressing, (e) 5 layer PC 
pressing, (f) 6 layer PC pressing respectively. ................................................................ 146 
 
Figure 4-25 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10~50 vol% CaCu
3
Ti
4
O
12 
powder: (a) 2 layer; (b) 4 layer; (c) 6 layer 
after 10s CC HP. ............................................................................................................. 150 
 
Figure 4-26 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10~50 vol% CaCu
3
Ti
4
O
12 
powder: (a) 2 layer; (b) 4 layer; (c) 6 layer 
after 20s CC HP. ............................................................................................................. 151?
Figure 4-27 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10~50 vol% CaCu
3
Ti
4
O
12 
powder: (a) 2 layer; (b) 4 layer; (c) 6 layer 
after 30s CC HP. ............................................................................................................. 152 
 
Figure 4-28 Dependence of dielectric response (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
using 2 layer CC hot pressing (HP) for 10, 20, and 30s at room temperature. ............... 154 
 
Figure 4-29 Dependence of dielectric response (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
using 4 layer CC hot pressing (HP) for 10, 20, and 30s at room temperature. ............... 154 
 
xxii 
 
Figure 4-30 Dependence of dielectric response (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
using 4 layer CC hot pressing (HP) for 10, 20, and 30s at room temperature. ............... 155 
 
Figure 4-31 Comparison of the present model predictions with experimental data for 2 
layer 30s CC-HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. .................................................. 156 
 
Figure 4-32 Comparison of the present model predictions with experimental data for 4 
layer 30s CC-HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. .................................................. 156 
 
Figure 4-33 Comparison of the present model predictions with experimental data for 6 
layer 30s CC-HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. .................................................. 157 
 
Figure 4-34 Comparison of the present model predictions with highest experimental data 
for 10, 20, 30, 40 and 50 vol% CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample in this work.......... 157 
 
Figure 4-35 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% 
CCTO powder using 2 layer CC hot pressing for: (a) 10s; (b) 20s; and (c) 30s 
respectively. .................................................................................................................... 159 
 
Figure 4-36 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% 
CCTO powder using 4 layer CC hot pressing for: (a) 10s; (b) 20s; and (c) 30s 
respectively. .................................................................................................................... 160 
 
Figure 4-37 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% 
CCTO powder using 6 layer CC hot pressing for: (a) 10s; (b) 20s; and (c) 30s 
respectively. .................................................................................................................... 161 
 
Figure 4-38 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 10s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). ............. 163 
 
Figure 4-39 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 20s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). ............. 164 
 
Figure 4-40 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 30s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). ............. 165 
 
Figure 4-41 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 10s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). ............. 166 
 
Figure 4-42 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 20s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). ............. 167?
xxiii 
 
Figure 4-43 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 30s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). ............. 168 
 
Figure 4-44 Temperature dependence of the 2, 4, 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder for: (a) 10s CC HP, (b) 20s CC HP, and 
(c) 30s CC HP, repectivley. ............................................................................................ 175 
 
Figure 4-45  Temperature dependence of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites 
with 50 vol% CaCu
3
Ti
4
O
12
 powder using: (a) 2 layer CC HP, (b) 4 layer CC HP, and (c) 
6 layer CC HP for 10, 20, and 30s, respectively. ............................................................ 176 
 
Figure 4-46 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 2 layer 10s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. .............................................................. 177 
 
Figure 4-47 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 2 layer 20s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. .............................................................. 178 
 
Figure 4-48 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 2 layer 30s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. .............................................................. 179 
 
Figure 4-49 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 4 layer 10s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. .............................................................. 180 
 
Figure 4-50 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 4 layer 20s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. .............................................................. 181 
 
Figure 4-51 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 4 layer 30s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. .............................................................. 182 
 
Figure 4-52 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 6 layer 10s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. .............................................................. 183 
 
Figure 4-53 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 6 layer 20s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. .............................................................. 184?
xxiv 
 
Figure 4-54 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 6 layer 30s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. .............................................................. 185 
 
Figure 4-55 The relationship of )"(
r
Ln ?  vs. )( fLn of 6 layer 10s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. ................ 186 
 
Figure 4-56 The relationship of )"(
r
Ln ?  vs. )( fLn of 6 layer 20s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. ................ 186 
 
Figure 4-57 The relationship of )"(
r
Ln ?  vs. )( fLn of 6 layer 30s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. ................ 187 
 
Figure 4-58 The relationship of )"(
r
Ln ?  vs. temperature of 6 layer 10s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. ................ 189 
 
Figure 4-59 The relationship of )"(
r
Ln ?  vs. temperature of 6 layer 20s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. ................ 189 
 
Figure 4-60 The relationship of )"(
r
Ln ?  vs. temperature of 6 layer 30s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. ................ 190 
 
Figure 4-61 Cole-cole plot of the dielectric data of 2, 4 and 6 layer CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder and HP for (a) 10s, (b) 20s and (c) 
30s, respectively. ............................................................................................................. 193 
 
Figure 4-62 Cole-cole plot of the dielectric data of (a) 2 layer, (b) 4 layer and (c) 6 layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50vol% CaCu
3
Ti
4
O
12
 powder and HP for 10s, 
20s and 30s, respectively. ............................................................................................... 194 
 
Figure 4-63 Cole-cole plot of the dielectric data of 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 10 to 50vol% CaCu
3
Ti
4
O
12
 powder and HP for (a) 10s, (b) 20s and (c) 
30s, respectively. ............................................................................................................. 195 
 
Figure 4-64 Polarization electric hysteresis loop for pure P(VDF-TrFE). ..................... 200 
 
Figure 4-65 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 200 
 
Figure 4-66 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 20 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 201 
 
Figure 4-67 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 30 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 201?
xxv 
 
Figure 4-68 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 202 
 
Figure 4-69 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 202 
 
Figure 4-70  Polarization electric hysteresis loop for 2 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder using CC HP for 10s. .......................... 203 
 
Figure 4-71 Polarization electric hysteresis loop for 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder using CC HP for 10s. .......................... 203 
 
Figure 4-72 Polarization electric hysteresis loop for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder using CC HP for 10s ........................... 204 
 
Figure 4-73 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(10 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. .......................... 206 
 
Figure 4-74 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(20 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. .......................... 206 
 
Figure 4-75 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(30 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. .......................... 207 
 
Figure 4-76 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(40 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. .......................... 207 
 
Figure 4-77 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. .......................... 208 
 
Figure 4-78 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration (?-size 
CaCu
3
Ti
4
O
12
) for 1 layer CaCu
3
Ti
4
O
12
/VC88 composite at room temperature. ............ 209 
 
Figure 4-79 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (10 vol% ?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C.
......................................................................................................................................... 211 
 
Figure 4-80 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (20 vol% ?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C.
......................................................................................................................................... 211 
 
Figure 4-81 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (30 vol%?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C.
......................................................................................................................................... 212?
xxvi 
 
Figure 4-82 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (40 vol% ?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C.
......................................................................................................................................... 212 
 
Figure 4-83 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (50 vol% ?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C.
......................................................................................................................................... 213 
 
Figure 4-84 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration for 
CaCu
3
Ti
4
O
12
/VC88 composite (?-size CaCu
3
Ti
4
O
12
) using 10s CC HP for 2, 4, and 6 
layer respectively at room temperature. .......................................................................... 214 
 
Figure 4-85 SEM fractographs of 1 layer annealed CaCu
3
Ti
4
O
12
/VC88 composite (50 
vol% ?-size CaCu
3
Ti
4
O
12
). ............................................................................................. 214 
 
Figure 4-86 SEM fractographs of CaCu
3
Ti
4
O
12
/VC88 composites (50 vol% ?-size 
CaCu
3
Ti
4
O
12
)  using 10s CC HP for (a) 2 layer, (b) 4 layer and (c) 6 layers, respecvtigely.
......................................................................................................................................... 215 
 
Figure 4-87 Temperature dependence of pure VC88. .................................................... 217 
 
Figure 4-88 Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (10 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. ........................ 218 
 
Figure 4-89 Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (20 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. ........................ 219 
 
Figure 4-90 Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (30 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. ........................ 220 
 
Figure 4-91Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (40 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. ........................ 221 
 
Figure 4-92 Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (50 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. ........................ 222?
 
Figure 5-1  Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (10, 20, 30, 40, and 50 vol% nano-size CaCu
3
Ti
4
O
12
)  with annealing in 
comparison with P(VDF-TrFE): (a) Dielectric constant vs. frequency; (b) Dielectric loss 
vs. frequency. .................................................................................................................. 230 
 
Figure 5-2  Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration for 1 layer  
CaCu
3
Ti
4
O
12
/ P(VDF-TrFE) composite (nano-size /?-size CaCu
3
Ti
4
O
12
) at room 
temperature with annealing at 125 
o
C for 8 hr. ............................................................... 231 
 
xxvii 
 
Figure 5-3 SEM fractographs of annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 
50 vol%: (a) nano-size; (b) ?-size CaCu
3
Ti
4
O
12
 ceramic powder. ................................. 232 
 
Figure 5-4  Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (10 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C.............................................................................................................................. 234 
 
Figure 5-5 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (20 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C.............................................................................................................................. 234 
 
Figure 5-6  Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (30 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C.............................................................................................................................. 235 
 
Figure 5-7 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (40 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C.............................................................................................................................. 235 
 
Figure 5-8 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (20 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C.............................................................................................................................. 236 
 
Figure 5-9 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration (nano-size 
CaCu
3
Ti
4
O
12
) using 10s CC HP for 2, 4, and 6 layers respectively at room temperature.
......................................................................................................................................... 237 
 
Figure 5-10 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites  (50vol% nano-
size CaCu
3
Ti
4
O
12
) using 10s CC HP for (a) 2 layer, (b) 4 layer and (c) 6 layers, 
respecvtigely. .................................................................................................................. 238 
 
Figure 5-11 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (10 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C.............................................................................................................................. 241 
 
Figure 5-12 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (20 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C.............................................................................................................................. 241 
 
Figure 5-13 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (30 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C.............................................................................................................................. 242 
 
Figure 5-14 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (40 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C.............................................................................................................................. 242?
xxviii 
 
Figure 5-15 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (50 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C.............................................................................................................................. 243 
 
Figure 5-16 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration (nano-size 
CaCu
3
Ti
4
O
12
) using 30s CC HP for 2, 4, and 6 layers respectively at room temperature.
......................................................................................................................................... 244 
 
Figure 5-17 Comparison of the present model predictions with experimental data for 2 
layer CC HP 30s annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. ................................... 244 
 
Figure 5-18 Comparison of the present model predictions with experimental data for 4 
layer CC HP 30s annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. ................................... 245 
 
Figure 5-19 Comparison of the present model predictions with experimental data for 6 
layer CC HP 30s annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. ................................... 245 
 
Figure 5-20 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (50 vol% nano-size CaCu
3
Ti
4
O
12
): (a) 2 layer CC HP, (b) 4 layer CC 
HP, (c) 6 layer CC HP for 10, 20, 30 and 40s................................................................. 247 
 
Figure 5-21 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration (50 vol% 
nano-size CaCu
3
Ti
4
O
12
) of 2, 4 and 6 layers CC HP for 10, 20, 30 and 40s at room 
temperature, respectively. ............................................................................................... 248 
 
Figure 5-22 Temperature dependence of the 2 layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (50 vol% nano-size CaCu
3
Ti
4
O
12
) for: (a) 10s, and (b) 30s CC HP............. 250 
 
Figure 5-23 Temperature dependence of the 4 layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (50 vol% nano-size CaCu
3
Ti
4
O
12
) for: (a) 10s, and (b) 30s CC HP............. 251 
 
Figure 5-24 Temperature dependence of the 6 layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% nano-size CaCu
3
Ti
4
O
12
) for: (a) 10s, and (b) 30s CC HP.............. 252 
 
Figure 5-25 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 254 
 
Figure 5-26 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 20 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 254 
 
Figure 5-27  Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 30 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 255 
 
Figure 5-28 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 255 
 
xxix 
 
Figure 5-29 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 256 
 
Figure 5-30 Polarization electric hysteresis loop for two layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 256 
 
Figure 5-31 Polarization electric hysteresis loop for two layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 257 
 
Figure 5-32 Polarization electric hysteresis loop for two layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. ............................................................ 257 
 
Figure 5-33 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. .............................................. 258 
 
Figure 5-34 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 20 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. .............................................. 258 
 
Figure 5-35 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 30 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. .............................................. 259 
 
Figure 5-36 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. .............................................. 259 
 
Figure 5-37 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. .............................................. 260 
 
Figure 5-38 Dielectric response vs. frequency of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(10 vol% nano-size CaCu
3
Ti
4
O
12
) : (a) as-casted 1 layer vs. as annealed 1 layer, (b) 2, 4, 
and 6 layers CC HP for 10s............................................................................................. 263 
 
Figure 5-39 SEM fractographs of 1 layer annealed CaCu
3
Ti
4
O
12
/VC88 composite (50 
vol% nano-size CaCu
3
Ti
4
O
12
). ........................................................................................ 264 
 
Figure 5-40 SEM fractographs of CaCu
3
Ti
4
O
12
/VC88 composites (50 vol% nano-size 
CaCu
3
Ti
4
O
12
)  using 10s CC HP for (a) 2 layer, (b) 4 layer and (c) 6 layers, respectively.
......................................................................................................................................... 265 
 
Figure 5-41 Temperature dependence of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite (50 vol% 
nano-size CaCu
3
Ti
4
O
12
). ................................................................................................. 266 
 
Figure 5-42 Temperature dependence of 2 layer CaCu
3
Ti
4
O
12
/VC88 composite for 10s 
CC HP (50 vol% nano-size CaCu
3
Ti
4
O
12
). ..................................................................... 266 
 
Figure 5-43 Temperature dependence of 4 layer CaCu
3
Ti
4
O
12
/VC88 composite for 10s 
CC HP (50 vol% nano-size CaCu
3
Ti
4
O
12
). ..................................................................... 267?
xxx 
 
Figure 5-44 Temperature dependence of 6 layer CaCu
3
Ti
4
O
12
/VC88 composite for 10s 
CC HP (50 vol% nano-size CaCu
3
Ti
4
O
12
). ..................................................................... 267 
 
Figure 5-45  The molecule structure of the silane coupling agent (C
8
H
4
Cl
3
F
13
Si). ....... 269 
 
Figure 5-46 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (10 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. ...... 272 
 
Figure 5-47 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (20 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. ...... 273 
 
Figure 5-48 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (30 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. ...... 274 
 
Figure 5-49 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (40 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. ...... 275 
 
Figure 5-50 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. ...... 276 
 
Figure 5-51 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 0.3, (b) 0. 5 and (c) 0.75 wt% silane.
......................................................................................................................................... 279 
 
Figure 5-52 Dependence of dielectric response vs. silane coupling concentration in 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (?-size CaCu
3
Ti
4
O
12
): (a) 1 layer vs. 1 annealed 
layer, (b) multiple layers using 10s CC HP at room temperature. .................................. 280 
 
Figure 5-53 SEM fractographs of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites  
(50vol% ?-size CaCu
3
Ti
4
O
12
) with:  (a) 0.3 wt%, (b) 0.5 wt%, (c) 0.75 wt%, (d) 1 wt%, 
(e) 5 wt% and (f) 10 wt% silane,  respectively. .............................................................. 281 
 
Figure 5-54 Temperature dependence of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) with 0.75 wt% silane. .................................................... 283 
 
Figure 5-55 Temperature dependence of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) with 0.75 wt% silane. .................................................... 283 
 
Figure 5-56 Temperature dependence of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) with 1 wt% silane. ......................................................... 284 
 
Figure 5-57 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% nano-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5 and (c) 10 wt% silane. .. 286 
 
xxxi 
 
Figure 5-58 SEM fractographs of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites  
(50vol% nano-size CaCu
3
Ti
4
O
12
) with: (a) 1, (b) 5 and (c) 10 wt% silane, respectively.
......................................................................................................................................... 288 
 
Figure 5-59 Temperature dependence of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) with 1 wt% silane. ......................................................... 289?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
xxxii 
 
 
 
 
 
LIST OF TABLES 
 
 
Table 1-1 Summery of dielectric data for FE ceramics and polymers. ............................ 15 
 
Table 1-2 Mechanical and dielectric properties for FE ceramics ..................................... 15 
 
Table 1-3 Dielectric constant 
r
'? & dielectric strength bE
 
of some current ..................... 18 
 
Table 1-4 Dielectric and cell edge data for ACu
3
Ti
4
O
12
 (at 25 
o
C)
58
. .............................. 22 
 
Table 1-5 Dielectric property of some commercial composite products
93
. ...................... 33 
 
Table 1-6 Dielectric properties of some current ceramic-polymer composites at RT. ..... 33?
 
Table 2-1 The CaCu
3
Ti
4
O
12
 processing conditions. ......................................................... 55 
 
Table 2-2 Volumetric ratio table for CaCu
3
Ti
4
O
12
- P(VDF-TrFE) composite samples. .. 59 
 
Table 2-3 Physical and chemical properties of silane coupling agent. ............................. 60?
 
Table 3-1 The CaCu
3
Ti
4
O
12
 processing conditions. ......................................................... 69 
 
Table 3-2  Shrinking rate of the pellet. ............................................................................. 86 
 
Table 3-3  Density of the pellet: g/cm
3
. ............................................................................ 86?
 
Table 4-1 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(?-size CaCu
3
Ti
4
O
12
) (1 kHz). ........................................................................................ 126 
 
Table 4-2 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(?-size CaCu
3
Ti
4
O
12
) with hot pressing (1 kHz). ........................................................... 137 
 
Table 4-3 Summary of fitted dielectric data for CaCu
3
Ti
4
O
12 
in1 layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (?-size CaCu
3
Ti
4
O
12
) with hot pressing (1 kHz).
......................................................................................................................................... 139 
 
Table 4-4  Summary of dielectric data for multiple layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 10s (1 kHz). ....................... 153 
 
Table 4-5 Summary of dielectric data for multiple layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 20s (1 kHz). ....................... 153?
xxxiii 
 
Table 4-6 Summary of dielectric data for multiple layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 30s (1 kHz). ....................... 153 
 
Table 4-7 Summary of fitted dielectric data for CaCu
3
Ti
4
O
12 
multiple layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 
30s (1 kHz). ..................................................................................................................... 158 
 
Table 4-8 Summary of reliability measurements of 4 layer CC HP CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite with 40 vol% ?-size CaCu
3
Ti
4
O
12
 powder (1 kHz). ........................... 169 
 
Table 4-9 Summary of reliability measurements of 4 layer CC HP CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder (1 kHz). ........................... 170 
 
Table 4-10 Summary of fitting results for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder after 10s CC HP. ......................................... 187 
 
Table 4-11 Summary of fitting results for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder after 20s CC HP. ......................................... 188 
 
Table 4-12 Summary of fitting results for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder after 30s CC HP. ......................................... 188 
 
Table 4-13 Summary of activation energy for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder after 10s, 20s, and 30s CC HP. .. 190?
Table 4-14 Fitting results for 1 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
with 10 to 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder. ........................................................... 196 
 
Table 4-15 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 10 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. ......... 196 
 
Table 4-16 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 20 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. ......... 197 
 
Table 4-17 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 30 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. ......... 197 
 
Table 4-18 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 40 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. ......... 198 
 
Table 4-19 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. ......... 198 
 
Table 4-20 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/VC88 composite (?-size 
CaCu
3
Ti
4
O
12
) (1 kHz). .................................................................................................... 208?
xxxiv 
 
Table 4-21 Summary of dielectric data for multiple layers CaCu
3
Ti
4
O
12
/VC88 composite  
in contrast to CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (?-size CaCu
3
Ti
4
O
12
) with CC hot 
pressing for 10s (1 kHz). ................................................................................................. 213 
 
Table 4-22 Summary of dielectric constant for multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s at different temperature (1 kHz). 223?
 
Table 5-1  Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(nano-size /?-size CaCu
3
Ti
4
O
12
) annealed at 125 
o
C (1 kHz). ....................................... 231 
 
Table 5-2 Summary of dielectric data for multiple layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (nano-size/?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 10s (1 kHz). ...... 236 
 
Table 5-3  Summary of dielectric data for multiple layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (nano-size/?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 30s (1 kHz). ...... 243 
 
Table 5-4 Summary of fitted dielectric data for CaCu
3
Ti
4
O
12 
multiple layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (nano-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 
30s (1 kHz). ..................................................................................................................... 246 
 
Table 5-5 Summary of dielectric data for multiple layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (50vol% nano-size CaCu
3
Ti
4
O
12
)  with CC hot pressing for 10, 20, 30 and 40s 
(1 kHz). ........................................................................................................................... 248 
 
Table 5-6 Summary of P-E results for one layer 10 to 50 vol% CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite at 95 
o
C. .............................................................................................. 261 
 
Table 5-7  Summary of dielectric data for multiple layers CaCu
3
Ti
4
O
12
/VC88 composite 
(nano-size /?-size CaCu
3
Ti
4
O
12
) annealed at 125 
o
C (1 kHz). ....................................... 264 
 
Table 5-8 Physical properties of silane coupling agent (C
8
H
4
Cl
3
F
13
Si) and ceramic 
(CaCu
3
Ti
4
O
12
). ................................................................................................................ 268 
 
Table 5-9 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(?-size CaCu
3
Ti
4
O
12
) with 0, 1, 5 and 10 wt% silane with annealed at 125 
o
C (1 kHz). 277 
 
Table 5-10 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(?-size CaCu
3
Ti
4
O
12
) with 0.3, 0.5, 0.75, 1, 5 and 10 wt% silane with annealed at 125
o
C 
(1 kHz). ........................................................................................................................... 280 
 
Table 5-11 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(nano-size and ?-size CaCu
3
Ti
4
O
12
) with 1, 5 and 10 wt% silane with annealed at 125 
o
C 
(1 kHz). ........................................................................................................................... 287?
 
 
1 
 
 
 
 
 
CHAPTER 1 
 
INTRODUCTION AND RESEARCH OBJECTIVES 
 
 
Dielectrics, which are materials responding to an external electric stimulation 
with a polarization, have been widely used in industries such as capacitors, insulation 
layer and energy storage devices.  
From manufacture and device reliability point of view, dielectrics, which are 
flexible, easy to process, and can stand with high mechanical impact, are highly desirable. 
Conversely, from property point of view, dielectrics with high dielectric constant and 
high dielectric strength (or breakdown field E
b
) are required for applications, such as high 
charge-storage density capacitor in IC due to the needs for miniaturizing devices
1-3
.  
The dielectrics can be inorganic materials, such as Ta
5
O
2
, BaTiO
3
 (BT), PbTiO
3
 
(PT), Pb(Mg
1/3
Nb
2/3
)O
3
 (PMN) etc, or organic materials such as polypropylene, 
polysulfone, polyester etc. Inorganic materials usually exhibit a high dielectric constant 
(10
2
~10
4
), but a low breakdown field and require a high processing temperature
4-6
. 
Conversely, organic materials can be processed at low temperature and exhibit high 
breakdown field (up to more than 500 MV/m), but very small dielectric constant (mostly 
less than 5)
7-18
. Therefore, a great deal of effort has gone into developing ceramic- 
polymer composites, such as Pb(Mg
1/3
Nb
2/3
)O
3
-epoxy composite and PbZrO
3
-P(VDF-
TrFE) composite, which are polymer matrix filled with high dielectric constant inorganic 
powders to create a new type of dielectric that is flexible and easy to process, and is of 
relative high dielectric constant and high breakdown strength
19-22
. 
 
 
 
 
2 
 
1.1 Theory of Dielectric Materials  
1.1.1 Permittivity  
Dielectrics respond to an electric field E  with polarization P , which reflects the 
induced dipole moments p .  That is
23, 24
:  
dv
p
P
N
i
?
=
=
1
                                                                                      (1-1) 
  The permittivity ?  is used to measure the polarization response of a material to 
the external electric field. Its definition in DC condition is shown as following
4, 25
: 
PED +=
0
?                                                                                    (1-2) 
EED
r 0
' ??? ==                                                                           (1-3)                   
where D  is named as electric displacement, 
0
?  is the permittivity in vacuum 
(8.8541878176 ? 10
?12
 C
2
/J?m), ?  is permittivity of the material between the plates, 
r
'? is 
the relative permittivity (or dielectric constant) of a material. 
  Based on the equation (1-2) and (1-3), it can be transformed as: 
                            EEP
r 00
)1'( ???? =?=                                                                    (1-4) 
                            1' ?=
r
??                                                                                           (1-5) 
where?  is the dielectric susceptibility of the material. 
 If a time-varying electric field is applied on a dielectric material, the relative 
permittivity changes with frequency and becomes complex: 
rrr
j "'* ??? ?=                                                                                   (1-6) 
in which j is the imaginary unit,  
r
'? and 
r
"? are the real and imaginary part of relative 
permittivity respectively. The loss angle ? is defined as: 
r
r
'
"
tan
?
?
? =                                                                                         (1-7) 
where ?tan is also named as loss factor.  
 The relationship between 
r
'? and 
r
"? can be described with the Kramers-Krong 
relations 
25
: 
3 
 
du
u
uu
rr
?
?
?
?
+=
0
22
)("2
)('
?
?
?
???                                                          (1-8) 
du
u
u
rrr
22
0
])('[
2
)("
?
?
??
?
??
?
?=
?
?
?
                                          (1-9) 
where 
?r
? is the permittivity at high frequency limit and ? is the angular frequency. 
If let ?=0, the above Equation (1-8) becomes:  
u
du
u
rrrsr
?
?
?
+==
0
)("
2
)0(' ?
?
???  
           Therefore 
?
?
??
?
?
?
??
d
u
du
u
rrrrs
??
??
?
==?
00
)("
2
)("
2
 
)(ln)("
2
0
???
?
d
r
?
?
=  
Or            )(
2
)(ln)("
0
?
?
?=
?
rrsr
d ??
?
???                                                     (1-10) 
where 
rs
? is also named as the static permittivity. Equation (1-10) implies that in order to 
obtain a higher 
?
?
rrs
?? , then a higher 
r
"? is required.  
 
1.1.2 Origins of Permittivity  
  The polarization P  or the induced dipole moment in a dielectric material can 
originate from different mechanisms. In general, there are four mechanisms for a 
dielectric material (as illustrated in Figure 1-1)
4, 25
.  
(1) Electronic polarization: The electric field causes the displacement of the outer 
electron cloud from the inner positive nucleus in Figure 1-1(a). The response time 
is about 10
-14
~10
-16
 s. 
(2) Ionic polarization: Ionic responds to an electric field with a change in the relative 
distance in between them in Figure 1-1(b) and the response time is varying from 
10
-12
~10
-13
s.  
(3) Orientational Polarization: If there are dipoles in a material, the electric field 
generates a torque on each dipole, which causes dipoles aligned along the electric 
field direction. This is called orientational polarization, as shown in Figure 1-1(c). 
4 
 
The response time is strongly dependent on T and ranges over approximately 10
0
 
~10
-9
s.  
(4) Space charge polarization: When the space charge appears in the dielectric, the 
electric field generates a force on the charge carriers, which separates the positive 
and negative charges as shown in Figure 1-1(d). The response time which is 
strongly dependent on T is approximately 10
-4
s. 
  If the frequency << 1/t (t: the response time) in a polarization, the corresponding 
polarization mechanism would result in a ??
r
?0 and a ??
r
 that is the static permittivity (as 
shown in Figure 1-2).  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
5 
 
 
 
 
 
 
 
 
                                                                     (a) 
 
                                                                            
 (b) 
 
 
 
                                                                       (c) 
 
 
 
                                                               
                                                            (d) 
Figure 1-1 Schematics of (a) electron polarization, (b) ionic polarization, (c) orientational 
polarization, (d) space charge polarization. 
 
 
 
No Field  Field Applied  
                    E 
Nucleus 
Electrons 
6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1-2 The influence of the polarization: (a) real part of relative permittivity and (b) 
imaginary part of relative permittivity with frequency. 
 
 
 
 
 
 
?
?
r
 
10
0
 
10
4
 10
8
 10
12
 10
16
 
10
4
 
10
9
 10
13
 10
16
 
?
?
r
 
Electronic 
Ionic 
Orientation 
Space Charge 
7 
 
1.1.3 Dielectric Relaxation  
  Dielectric relaxation refers to the relaxation response of a dielectric material to an 
external electric field, which exhibits a momentary delay in the dielectric response of a 
material. Dielectric theories for relaxation were developed and virtually have been 
applied in different systems. 
  Debye relaxation is the dielectric relaxation response of an ideal, non-interacting 
population of dipoles to an alternating external electric field. The Debye equation 
assumes that the conductivity of the material is zero, free orientation of non-interacting 
dipoles and all dipoles exhibit only one relaxation time. Thus, its dielectric permittivity 
can be written as
25
: 
                            
0
1
)(*
??
??
???
j
rrs
rr
+
?
+=
?
?
                                                               (1-11) 
               Or         
2
0
2
1
'
??
??
??
+
?
+=
?
?
rrs
rr
                                                                       (1-12) 
                            
2
0
2
0
1
)(
"
??
????
?
+
?
=
?rrs
r
                                                                        (1-13) 
                            
2
0
2
0
)(
'
"
tan
????
????
?
?
?
?
?
+
?
==
rrs
rrs
r
r
                                                           (1-14) 
where 
rs
? is the static permittivity, 
?r
? is the permittivity at high frequency limit, 
0
?  is the 
characteristic relaxation time and 
?
?
rrs
??  reflects the strength of the relaxation process. 
  By combing the Equation (1-12) and (1-13), the equation without 
0
?? can be 
written as: 
222
)
2
(")
2
'(
??
?
=+
+
?
rrs
r
rrs
r
??
?
??
?                                                (1-15) 
  The schematic of 
r
'? - 
r
"? relation is shown in Figure 1-3 and 1-4. The maximum 
value of 
r
"? occurs at 
0
? when: 
                               1
00
=??                                                                                          (1-16) 
The ?tan reaches its maximum at
?
? : 
2/1
)(2
tan
?
?
=
?
=
rrs
rrs
??
??
?
?
??
                                                                (1-17) 
8 
 
 
?
r?
?
rs
?
?
?
?=1/?
0
?"
r
?'
r
???
?=0
0
?
(?
rs
+?
r?
)/2
(?
rs
-?
r?
)/2
?
 
Figure 1-3 Argand diagram for dielectric material with only one relaxation time based on 
Debye equation. 
?
?=1/? ?=(?
rs
/?
r?
)
1/2
(?
0
)
-1
?
r?
?
rs
(?
rs
+?
r?
)/2
(?
rs
-?
r?
)/2
?
'
r
?
"
r
ta
n(
?
)
 
Figure 1-4 The schematic of 
r
'? , 
r
"? and ?tan as functions of ?  based on Debye 
equation. 
 
9 
 
1.1.4 Cole and Cole plot 
  Debye equation does not fit the experimental results for most dielectric materials 
that have a set of relaxation time. Therefore, there are many empirical relaxation 
equations that have been introduced to describe the relaxation phenomena. For example, 
Cole and Cole equation  is shown as
25, 26
:  
                             
?
??
??
???
?
?
?
+
?
+=
1
0
)(1
)(*
j
rrs
rr
                                                     (1-18) 
where ? varies 0<?<1, and the maximum loss occurs at ??
0
=1. Some experimental results 
agree well with Cole-Cole equation with ? >0. After eliminating ??
0 
from the equation 
(1-18), it is an equation of a circle with center at ]
2
tan
2
)(
,
2
[
??????
??
?
?
?
rrsrrs
and 
radius of ]
2
sec
2
[
????
?
?
rrs
as shown in Figure 1-5. This is written as following: 
222
]
2
sec
2
[]
2
tan
2
)(
"[]
2
)(
'[
????????
?
??
?
???
?
=
?
++
+
?
rrsrrs
r
rrs
r
   (1-19) 
  The Davidson-Cole and Havriliak-Negami equations are given by
25
:  
                        
?
??
??
??
)1(
*
0
j
rrs
rr
+
?
=?
?
?
                                                                      (1-20) 
                        
??
??
??
??
])(1[
*
1
0
?
?
?
+
?
=?
j
rrs
rr
                                                               (1-21) 
where 0<?<1 and 0<?<1. If choosing the proper parameters ? and ?, the modification of 
the Cole-Cole equation can better fit experimental results. It has been found that several 
materials obey the Davidson-Cole equation, such as glycerol triacetate and pyralene. 
However, in other conditions, the Havriliak-Negami equation results a much better fit to 
most experimental results.  
 
 
 
 
 
 
 
10 
 
?"
r
?'
r
?
?
(?
rs
+?
r?
)/2
(?
rs
-?
r?
)tan(??/2)/2
??/2 ??/2
?
rs
?
r ?
0
? "
r (max)
 
Figure 1-5 The Cole-Cole plot for dielectric material with a set of relaxation time based 
on Cole-cole equation. 
 
1.2 Classification of Dielectric Materials  
  Dielectric materials can be classified into two major categories: nonpolar 
materials and polar materials
25
.  
1.2.1 Nonpolar Materials  
  A nonpolar material is defined as a material obtaining no permanent dipole 
moments. Their dielectric constants are relatively small, such as silicon?3.7, 
diamonds?5.5~10, parfin?1.9~2.5, and carbon tetrachloride?2.0.  
1.2.2 Polar Materials  
  A polar material is defined as a material possessing a permanent dipole moment 
which is associated with molecule or unit cell. Among those materials, if crystals have 
spontaneous polarization, then it is called Pyroelectric crystals. The ferroelectric crystals 
are categorized into Pyroelectric crystals, but they also have reversible polarization
4, 27
. 
There is a critical temperature, called the Curie temperature, which marks the dramatic 
change from the ordered to the disordered in phase. At this temperature, the dielectric 
constant can reach values three to four orders of magnitude higher than that in the 
11 
 
disordered phase. Among polar materials, the ferroelectrics, due to their dielectric 
constants as high as 5,000~18,000, have attracted a lot of attention and will be discussed 
later in detail. 
1.2.2.1 Ferroelectric Ceramic and Polymer 
  A ferroelectric crystal exhibits a reversible spontaneous electric polarization and a 
hysteresis loop. As the electric field E increases, the polarization will reach its saturation 
value. Ferroelectric (FE) behaves uniquely and is characterized by a P
s
 which can be 
switched by an electric field E. Saturated polarization P
s 
is the state when the increase of 
electric field cannot lead to an increase on the polarization, such that an increase of 
electric field produces no significant change in energy density. Coercive field E
c
 is the 
applied electric field required to reduce the polarization to zero. After the removal of the 
applied field, polarization is not zero but a finite value called as the remnant polarization 
P
r
25, 28-30
.  The basic feature of a FE is shown in Figure 1-6.  
  FE goes through a phase transition from a FE phase to a PE phase (paraelectrics) 
at a temperature T
c
 (Curie temperature) at which its dielectric constant reaches its 
maximum value
4, 25, 27
 as shown in Figure 1-7. When above curie temperature T
c
, the 
dielectric constant of ferroelectric materials obey closely the Curie-Weiss relation
4, 25
: 
                              
c
r
TT
C
?
='?                                                                                    (1-22) 
  where C is the Curie constant. 
   FE can be inorganic materials such as BaTiO
3
 (BT), PbTiO
3
 (PT), or organic 
materials such as P(VDF-TrFE), nylon
30
. Although FE exhibited high dielectric constant, 
the dielectric constant is strongly dependent on temperature. There are a lot of research 
works to broaden the permittivity versus temperature. By substituting Ti with other 
cations such as Sr etc, T
c
 can be reduced. At the same time, by using La
3+
, Nb
5+
 doping in 
BaTiO
3
, it can inhibit grain growth and then has the effect of enhancing the permittivity 
below T
c
. For example, with 1.5 wt% Nb oxide doping, it can result in a dielectric 
constant of 5000~18,000 below T
c
 (~130 ?C)
31
.  Besides BaTiO
3
, Lead magnesium 
niobate (PMN) is another important ferroelectric material. For pure PMN, the dielectric 
12 
 
constant is about 16,000
32-34
 and the relaxation phenomena between permittivity and 
temperature is shown in Figure 1-8
34
.  
  As shown in Table 1-2, FE ceramics have high dielectric constant, but they 
exhibit low dielectric strength, tend to be brittle and generally need high processing 
temperature. Despite the low dielectric constant in FE polymers, FE polymers display 
high dielectric strength, relative flexibility and require low processing temperature in 
contrast with FE ceramics. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
13 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1-6 P-E loop of ferroelectric. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1-7 Effect of grain size on permittivity of BaTiO
3
4
. (Relative permittivity is 
represented by 
r
'?  which is described in Section 1.1). 
 
P
s
P
E
C
P
r
E 
 
 
14 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1-8 Dielectric permittivity of PMN: (a) at various amplitudes, Em (1-0.01, 2-0.5, 
3-1, 4-1.5, 5-2 kV/cm), and (b) various frequencies, ?  (1-1 kHz, 2-100 Hz, 3-20 Hz) of 
the ac field
34
. ( '?  is equivalent to 
r
'? which is described in  Section 1.1). 
 
(a) 
(b) 
15 
 
 
 
 
 
 
 
Table 1-1 Summery of dielectric data for FE ceramics and polymers. 
Materials T
c
, ?C ??
r
 at T
c
 P
s
, C/m
2
 Ref. 
Rochelle salt 24 5,000 0.25 (RT) 
4
 
BaTiO
3
 120 1,600 0.26 (RT) 
4
 
KNbO
3
 434 4,200 0.26 (RT) 
4
 
P(VDF-TrFE) 65 70 0.10 (RT) 
12, 30
 
 
 
Table 1-2 Mechanical and dielectric properties for FE ceramics 
and polymers at RT and T
c
. 
 Density (g/cc) Y (GPa) ?'
r(max)
/loss (1 kHz) T
c
,?C Ref.
BT (BaTiO
3
) >5.55 67 1,450/0.008 120 
35
 
PMN (Pb(Mg
1/3 
Nb
2/3
)O
3
) >6.1 61 5,500/0.05 -15 
36
 
PZT (Pb(Zr
0.52 
Ti
0.48
)O
3
) >7.55 63 1,340/0.004 300 
37, 38
PNN (Pb(Ni
1/3
Nb
2/3
)O
3
) >7.8 55 5,500/0.023 150 
36
 
PVDF 1.76 2.0 5.6/0.05 80
39
 
P(VDF-TrFE) 50/50mol% 1.8 2.3 15/0.075 70 
12, 40
            
 
 
 
 
 
 
16 
 
x
y
n
CH
2
-CF
2
CF-CF
2
H
x
y
n
CH
2
-CF
2
CF-CF
2
Cl
1.2.2.2 Ferroelectric Polymers 
  Poly(vinylidene fluoride) (PVDF) exhibits the high dielectric constant (?11), as 
well as better piezoelectricity and ferroelectricity
41-43
. PVDF was the first polymer that 
exhibits both significant piezoelectric and ferroelectric properties. The high 
electronegative fluorine atom with a  van der waals radius of 1.5 ?, is slightly larger than 
that of hydrogen about 1.2 ?, so the monomer unit has a net dipole moment of about 
7.06?10
-30
 Cm
25, 30
. The monomer unit is -CH
2
-CF
2
-.  
 Among electroactive polymers, poly(vinylidene fluoride-trifluoroethylene) 
P(VDF-TrFE) copolymer has been widely studied 
7, 44-46
. With increasing film thickness 
and for longer annealing times, the dielectric constant for P(VDF-TrFE) was found to 
reach 10 after it was deposited on different substrates, such as Si and SiO
2
47
.  After 
irradiation with 4?10
5
 Gy at 120 
o
C, it was found that a dielectric constant of 28 at 1 kHz 
was reached in P(VDF-TrFE) 50/50 copolymer
7
. Moreover, its dielectric properties are 
dependent on composition: the higher ?VDF, then the higher piezoelectric coefficients. 
Therefore, P(VDF-TrFE) 55/45 copolymer exhibits higher dielectric constant, but low 
piezoelectric coefficients. The chemical structure of P(VDF-TrFE) is shown as following: 
 
 
 
 
Recently, it was found that a new copolymer P(VDF-CTFE) can withstand high 
electric field
8, 48
, as well as exhibiting a high dielectric constant (?10). The chemical 
structure of P(VDF-CTFE) is shown as following: 
 
 
 
 
17 
 
1.3 Energy Storage Density   
  The energy stored in a dielectric material under an electric field E  can be 
expressed by the shadow area in Figure 1-9 in which different relationships between E  
and D  are presented
8, 49
: 
                               DdEW
E
?
?=                                                                                (1-23) 
where W
E
 is energy storage density defined as the energy stored in a unit volume (J/m
3
).  
(a)
(b) (c)
E E E
E
W
E
W
E
W
D
D
D
 
Figure 1-9 Relationship of electric displacement D  vs. electric field E : (a) linear; (b) 
nonlinear with positive curvature; (c) nonlinear with negative curvature. 
 
  Based on Figure 1-9 and Equation (1-23), it can be concluded that a higher D  and 
a higher E  are very important to achieve a higher energy density. Additionally, the 
curvature of D  vs. E  is also very critical to the W
E
.  
  For linear dielectrics, the W
E
 can be simplified as
8
: 
                               
2
0
'
2
1
EW
rE
??=                                                                              (1-24)      
  According to Equation (1-24), a higher dielectric strength, which would allow a 
high electric field to be applied and a higher permittivity, are highly desirable for the 
dielectrics used in energy storage devices. The dielectric constant and strength of some 
inorganic and organic materials are given in Table 1-3.  As shown in Table 1-3, inorganic 
materials usually exhibit high dielectric constants, however, their dielectric strengths bE  
are very low. On the other hand, organic materials have very high dielectric strengths bE , 
18 
 
but low dielectric constants.  Due to inorganic materials? low bE , inorganic materials 
usually have small energy densities, whereas organic materials have higher energy 
densities due to their high dielectric strengths which have been shown in Table 1-3. 
Therefore, there is a great need to develop a new hybrid ceramic-polymer composite 
which exhibits high dielectric constant, as well as high dielectric strength.  
Table 1-3 Dielectric constant 
r
'? & dielectric strength bE
 
of some current 
dielectric materials. 
 
Materials ?'
r
 
bE  (MV/m) 
W
E
 at ? bE  
(kJ/m
3
) 
Ref. 
Inorganic 
Air 1.007 3 0.01 
50
 
Tantalum oxide 11 4 0.20 
6
 
Quartz, fused 3.85 20 1.70 
51
 
Reconstitute mica 7.8 64 17.67 
52, 53
High-Voltage ceramic 500~6000 2 27 
54, 55
Organic 
Epoxy 4 16 1.10 
36
 
Polyester 3.4 28 2.90 
36
 
Polysulfone 3.2 100 35 
36
 
Polypropylene 2.3 140 49 
36
 
Kapton (Polyimide) 3.6 339 312 
36
 
 
1.4 Applications of Dielectric Materials  
  Dielectric materials have many applications, such as capacitors and electronic 
package. For dielectric materials used in capacitors, they have two primary functions: (a) 
energy storage, (b) capacitive coupling in electrical circuit. For electronic package 
purpose, dielectric materials are used to enclose and protect an electronic device in order 
to reduce the overall noise between operating supplies such as power and ground. Based 
on the application, the dielectrics used in capacitors have been categorized into three 
classes by the Electronic Industries Association (EIA)
4, 25
: 
            Class I: Dielectric materials with a relatively low permittivity (15~500) and a 
dielectric loss ? 0.003 over a working temperature range from -55 ?C to +85 ?C. 
            Class II: Dielectric materials based on ferroelectrics with high permittivity 
(500~20,000).  
19 
 
            Class III: Dielectric materials based on conductive phase with very high 
capacitances and very low breakdown field. 
 Those materials are presented in Figure 1-10 with their 
r
'?  and ?tan . Dielectric 
materials for temperature compensating capacitor ( %5??? ) are mainly based on 
barium titanate with titanium dioxide and calcium titanate in order to increase the 
dielectric constant or to get desired temperature curve. Those materials are presented in 
lower-left corner of Figure 1-10
56
.  
 
 
 
             
 
 
 
 
 
 
 
Figure 1-10  The classified categories of dielectric materials
56
. ( '? is equivalent to 
r
'?  
which is described in  Section 1.1). 
            
 High dielectric constant capacitor category can be mainly classified into X5R, 
X7R, Z5U and Y5U based on temperature coefficient of capacitance (TCC) by the 
Electronic Industries Association (EIA) standards. Those materials are presented in high-
right corner of Figure 1-10
25
.  
I. For X5R, %15' ??
r
? from -55 ?C to +85 ?C.  
                For X7R, %15' ??
r
? from -55 ?C to +125 ?C.  
II. For Z5U, %22'%55 ????
r
? from +10 ?C to +85 ?C.  
III. For Y5V, %22'%82 ????
r
? from -30 ?C to +85 ?C.  
20 
 
1.5 Calcium Copper Titanate CaCu
3
Ti
4
O
12
 
            Recently, a new material CaCu
3
Ti
4
O
12
 with perovskite-related structure and very 
different dielectric properties has been reported by M.A.Subramanian
57, 58
. In order to 
grow CaCu
3
Ti
4
O
12
 phase, both conventional powder-sintering techniques and mechanical 
alloying have been used
57, 59-61
. By calcining at 900-1,000 ?C, a high dielectric constant 
of 12,000 was reported, and it is found that by decreasing the calcination temperature to 
around 800 ?C, the dielectric constant has been improved to 10
5
 and remains almost 
constant at temperature between 100 and 600 K (Figure 1-11). In Figure 1-11, the 
dielectric response is around 100 fold drop around 100 k. However, no detectable 
crystallographic structure change has been probed
61
. A dielectric constant for 
CaCu
3
Ti
4
O
12 
as high as 20,000 for ceramics and 300,000 for single crystals at 1 kHz and 
room temperature has been reported
59, 61
. 
 
Figure 1-11 The temperature dependence of dielectric constant and loss 
in CaCu
3
Ti
4
O
12
61
. (
1
?  is equivalent to 
r
'? which is described in  Section 1.1). 
21 
 
1.5.1 Crystallographic Structure of CaCu
3
Ti
4
O
12
 
            The ACu
3
Ti
4
O
12
 (A=trivalent rare earth or Bi) family of compound was found in 
1967 and accurate structure was determined in 1979. The dielectric constant and loss of 
ACu
3
Ti
4
O
12
 family are shown in Table 1-4.  
            Neutron powder diffraction of CaCu
3
Ti
4
O
12 
indicates a cubic-perovskite structure 
with Im3 group symmetry and cubic lattice parameter a=7.391 ?
61
. Figure 1-12 shows 
the structure of CaCu
3
Ti
4
O
12
. In comparison with ferroelectrics, the high dielectric 
constant originates from the rattling of Ti
4+
 within the TiO
6
 octahedron. Moreover, the 
CaCu
3
Ti
4
O
12
 exhibits more constraint than ferroelectrics. The TiO
6
 octahedra tilt and 
form a square planar arrangement around Cu
2+
. Based on structure calculations, it is 
found that the Ti-O bonds are under tension and increase the polarization of the TiO
6
 
octahedra
57
. 
 Due to fact that CaCu
3
Ti
4
O
12
 is weak scatter, there are only five predicted modes 
around 444, 453,510, 576 and 761 cm
-1
 in raman scattering. Among those modes, 444, 
453 and 510 cm
-1
 are related to TiO
6
 rotationlike modes, 576 cm
-1
 is due to Ti-O-Ti anti-
streching and 761 cm
-1
 is assigned to TiO
6
 octahedra
62, 63
. Moreover, based on raman 
spectra and XRD diffraction, there is no evidence found to prove any structure phase 
transformation up to 46 GPa
64
. However, Fagan et al. reported that when pressure is > 3.0 
GPa, the stable structure is rhombohedra (R3) instead of cubic (Im3)
65
. Besides high 
pressure influence, the gain size effects on the dielectric constant of the CaCu
3
Ti
4
O
12 
have been studied
66
. It was observed that the dielectric constant became four times higher 
varying 2,000 to 8,000 as the grain size increased from 1.3 ?m to 4.1 ?m.  
 
 
 
 
 
 
 
 
 
22 
 
Table 1-4 Dielectric and cell edge data for ACu
3
Ti
4
O
12
 (at 25 
o
C)
58
. 
Compound Relative dielectric constant (?'
r
) Loss tangent (tg?) a ( ? at 25 
o
C)
CaCu
3
Ti
4
O
12
 10286 0.067 7.391 
CdCu
3
Ti
4
O
12
 409 0.093 7.384 
La
2/3
Cu
3
Ti
4
O
12
 418 0.060 7.427 
Sm
2/3
Cu
3
Ti
4
O
12
 1665 0.048 7.400 
Dy
2/3
Cu
3
Ti
4
O
12
 1633 0.040 7.386 
YCu
3
Ti
3
FeO
12
 33 0.308 7.383 
Bi
2/3
Cu
3
Ti
4
O
12
 1871 0.065 7.413 
BiCu
3
Ti
3
FeO
12
 692 0.082 7.445 
LaCu
3
Ti
3
FeO
12
 44 0.339 7.454 
NdCu
3
Ti
3
FeO
12
 52 0.325 7.426 
 
Figure 1-12  The structure of CaCu
3
Ti
4
O
12
 (Cu-blue, Oxygen-red, Ca-yellow)
61
. 
 
23 
 
1.5.2 Origin of Colossal Dielectric Response  
  A few explanations on the colossal dielectric response of CaCu
3
Ti
4
O
12 
have been 
proposed. After having studied by x-ray, optical-, and neutron-diffraction techniques, 
impedance spectroscopy, and theoretical electronic structure calculations, it is unlikely 
that the large dielectric response is related with intrinsic properties
58, 59, 61, 67-72
. Intrinsic 
means CaCu
3
Ti
4
O
12
 is a perfectly stoichiometric, defect free single-domain crystal. Based 
on experimental results, different explanations have been proposed: 
1. Subramanian et al. thought the high dielectric constant originates from the 
creation of internal barrier layer capacitances (IBLC)
57, 58
, presumably at twin boundaries 
(Figure 1-13) which has been detected by Wu et al. in high-resolution TEM
72
. In 
boundary layer dielectrics, an effective circuit of parallel capacitors formed from 
microcrystalline grains is thought to give rise to high dielectric response.  
2. Wu et al. pointed out for polycrystalline samples, the main defects lie at grain 
boundary, while for a single crystal, they will be the dislocations and planar defects. 
Since the disorder-induced lattice discontinuity or displacement will result in IBLC and 
change the dielectric response of the material, this cation disorder could have significant 
implications on the origin of the colossal dielectric responses.  
3. Lunkenheimer et al. suggested it might be due to Maxwell-Wagner-type 
contribution of depletion layers at the interface between sample and contacts
71
.  
4. Cohen et al. thought the high dielectric constant originates from the 
inhomogeneity of local dielectric boundaries where twin, Ca ordering, and antiphase 
boundaries exist
69
.  
5. Adams et al. suggested due to the limited reoxidation in the furnace, there is the 
formation of semiconducting grains and insulating grain boundaries
59
. Sinclair et al. also 
thought the semiconductivity of grain is because of the oxygen loss at high temperature
67
.     
6. Besides those explanations, other theories such as the electrode/sample effects, 
doping effect etc, have been proposed
73-77
. Broadband dielectric spectroscopy studies up 
to 1.3 GHz by Krohns et al. have been carried out
78
. Temperature dependent results based 
on two different types of contacts (silver-paint and sputtered gold) exhibited significant 
difference which proved the surface-related origin of the high permittivity value in Figure 
1-14.  At the same time in broadband frequency studies, besides the Maxwell-Wagner 
24 
 
Twin
Boundary
Tw
i
n
B
o
undar
y
a
c
relaxation, a second relaxation mode showed up as T>180 K for 5 Hz in Figure 1-15. 
Krohns et al. further confirmed that the second relaxation should be caused by a second 
surface layer. Thus based on experimental results, Krohns et al. suggested that two 
relaxations existed: one is related with the internal barrier layer capacitor (IBLC) and the 
other with surface barrier layer capacitor (SBLC).  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1-13 The schematic of twin boundary in CaCu
3
Ti
4
O
12
72
. 
 
 
 
 
 
 
 
 
 
25 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1-14  (a) Temperature-dependent dielectric constants and (b) conductivities of 
single-crystalline CaCu
3
Ti
4
O
12
 with sputter gold (solid lines) and silver-paint contacts 
(symbols) at various frequencies
78
. The dashed and dashed-dotted lines in (b) show an 
estimate of the intrinsic bulk dc conductivity and the contribution of the insulating layer. 
('?  is equivalent to 
r
'? which is described in Section 1.1). 
 
 
 
26 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1-15  (a) Frequency-dependent dielectric constants, (b) loss, and (c) conductivities 
of single crystalline CaCu
3
Ti
4
O
12
 with silver-paint contacts at various temperatures
78
. ( '?  
and "? are equivalent to 
r
'? and 
r
"? respectively, which are described in  Section 1.1). 
 
 
 
 
 
 
27 
 
1.6 Ceramic-Polymer Composites 
            Both advantages and disadvantages of ceramic and polymer have been well 
discussed in previous sections. In order to combine superior properties of both polymer 
and ceramics which result in far better performance than those constituent materials, 
ceramic-polymer composites have been studied as dielectric materials in order to 
fabricate a flexible hybrid material with better dielectric properties, such as high 
dielectric constant ??
r
 and high dielectric strength bE .  
 
1.6.1 General Concepts for Composites 
            The physical properties of composites can be the sum, combination, and product 
of properties of its constituents based on the properties or connectivity. For example, the 
total mass is simply the sum of their individual ones. The connectivity was first classified 
by Newnham et al
79
. Based on their connectivity and morphology of each phase, the 
dimension is defined as 0-0, 1-0, 2-0, 3-0, 1-1, 2-1, 3-1, 2-2, 3-2, and 3-3 for a 2-phase 
composite as shown in Figure 1-16, where 0/1/2/3 represent the number of dimensions 
for each component in the composite
30, 79
. For example, for 0-3 composite it is defined as 
0-dimension particle (usually the ceramic particle) and is embedded inside 3-dimensions 
polymer matrix as shown in Figure 1-16 (blue color: polymer matrix, white color: 
ceramic particle). 
 
 
 
 
 
 
 
 
 
 
 
 
28 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1-16 Ten dimension patterns in diphasic composites
79
. 
 
 
 
 
 
 
 
 
 
29 
 
1.6.2 Mixing Rule for Permittivity in Two-Phase Composites 
 
 
 
 
 
 
 
 
 
 
 
 
 
 (a)                                                                          (b) 
Figure 1-17 Schematic of (a) parallel and (b) series connections. 
 
 It is known that the dielectric property of the composite is a function of many 
factors: 1) size and shape of ceramic particles; 2) dielectric constants of ceramic particles 
and polymer respectively; 3) morphology distribution of ceramic in the polymer matrix; 4) 
volume fraction of ceramic in the composite; 5) the appearance of interfacial layer 
between ceramic and polymer.  
            For a 2-phase composite, the parallel and series connectivity as shown in Figure 
1-17 are two simple cases. The effective dielectric constant ??
 
is
30
: 
                              
nnn
vv '''
2211
??? +=                                                                          (1-25) 
where: v
1
 and v
2
 are the volume fraction of the ceramic particles and polymer matrix 
respectively (
A
A
v
1
1
= and
A
A
v
2
2
=  in parallel case; 
21
1
1
dd
d
v
+
= and
21
2
2
dd
d
v
+
=  in 
series case), ??
1
 and ??
2
 are the dielectric constant of the ceramic particles and polymer 
matrix respectively, and  n is +1 and -1 for parallel and series connection, respectively. 
            In most cases, ceramic-polymer 2-phase composites are statistical mixtures of its 
components, so the effective dielectric constant of the composite should lie between the 
values determined by Equation (1-25) for n=-1 and n=1 as is illustrated in the shadow 
area in Figure 1-18. 
 
 
??
2
 
??
1
 
A
1
 
A
2
 
d 
??
1
 ??
2
 
A 
d
1
 d
2
 
30 
 
             
 
 
 
 
 
 
 
Figure 1-18 Schematic of dielectric constant of two phases 1 and 2 vs. their volume 
fraction in the mixture: 1, parallel connection; 2, series connection; 3, real composite. 
 
  Ceramic-polymer 0-3 composites are widely used due to the fact that it is flexible 
and easy to fabricate. Different models have been introduced to simulate the effective 
dielectric constant of these composites.  
  For a random ceramic-polymer 0-3 composite, Lichtenecker?s logarithmic law of 
mixing is shown as following
30
: 
                              
2211
'log'log'log ????? +=                                                             (1-26) 
            Lichtenecker?s equation is modified as: 
  )
'
'
log()1('log'log
2
1
12
?
?
??? k?+=                                                  (1-27) 
where k is a fitting constant for composite material. The value for k is around 0.3 for most 
well dispersed ceramic-polymer composites.  
            Das-Gupta et al. also suggested
80
: 
                              
1121
1121
2
')1(')2(
')21(')1(2
''
??
??
??
vv
vv
?++
++?
=                                                       (1-28) 
            If ceramic particles are sphere in shape, then the Maxwell-Wagner mixing rule is 
used
81, 82
: 
                              
)''(''2
)''(2''2
''
21112
21112
2
????
????
??
??+
?++
=
v
v
                                                      (1-29) 
3 
1 
2 
100% phase 2 
 
100% phase 1 
 
?
2
?
1
 
?
? 
31 
 
Maxwell-Wagner mixing rule is effective for infinite dilution of the dispersed phase that 
the spherical ceramic particles are separated by distances greater than their characteristic 
size.  
            If ellipsoidal ceramic particles are randomly distributed into an a polymer matrix, 
the effective dielectric constant ?? is
83
: 
                              
11
2111
1
')1('
'
vv
vv
?+
?+
=
?
???
?                                                                   (1-30) 
where ? is the field factor (
)1'/'(1
1
21
??+
=
??
?
L
) and L is defined as the ?equivalent? 
depolarization coefficient of the particles in the direction of the applied field (0<L<1). 
            Regarding ellipsoid ceramic particles in polymer matrix, another estimation 
equation is given by Yamada et al.: 
                              
( )
()()
?
?
?
?
?
?
??+
?
+=
1212
211
2
1'''
''
1''
vn
nv
???
??
??                                                  (1-31) 
where n is a constant related to geometry of ceramic particles. 
  Based on the percolation theory, the Bruggeman model was developed
30, 84
: 
                              0
'2'
''
)1(
'2'
''
2
2
1
1
1
1
=
?
?
?
?
?
?
?
?
+
?
?+
?
?
?
?
?
?
?
?
+
?
??
??
??
??
vv                                               (1-32) 
 
 
 
 
 
 
 
 
 
 
 
32 
 
1.7 Current Developments of Polymer-Matrix Composite 
1.7.1 Ferroelectric Ceramic/Polymer Composite           
  Composites based on ferroelectric fillers, such as BaTiO
3
 (BT), PbZrO
3
 (PZT), 
Ba
0.65
Sr
0.35
TiO
3
 (BST) and Pb(Mg
1/3 
Nb
2/3
)O
3
 (PMN), have been studied and the 
dielectric properties in some commercial products are shown in Table 1-5. Most of the 
research has focused on polymer matrices, such as PMMA, Epoxy, and recently more on 
PVDF-based polymers due to their high dielectric constant.  
  Composites with PMMA and BT have been fabricated without any considerable 
gradient in ceramic powder concentration
85-87
. A linear relationship between BT volume 
fraction and the effective dielectric constant was observed in PMMA and BT composite 
and as there are 60 vol.% BT, the dielectric constant is about 40
30
. If replacing PMMA 
with Epoxy, a dielectric constant of 44 with 40 vol.% BT was reported by Kuo et al
88
,  
while the dielectric constant of composite with 40 vol.% PMN in Epoxy is 24.  
  As mentioned above, in order to improve the dielectric constant, composite with 
P(VDF-TrFE) and PMN-PT (PMN and PT based solid solution) was prepared and a 
dielectric constant of 200 at 1 kHz was reached
22
. By combining P(VDF-TrFE) and BST 
with irradiation, a dielectric constant  as high as 150 at 1 kHz (RT)  and 200 at 1 kHz 
(curie temperature) was achieved
89
. Beside a two components composite, a three phase 
composite with carbon fiber (CF), BT and PVDF has been successfully fabricated with 
dielectric constant of 100 with 15 vol. % CF
90
. Moreover, another important 
ferroelectrics is PZT, which has been widely studied by using different polymer matrices, 
such as PU, PVDF etc.  When there are 30 vol.% PZT, the dielectric constant of 24 has 
been reported in 0-3 composite with PU as matrix, while in PVDF matrix, a dielectric 
constant of 40 was achieved
91, 92
. The summary for ceramic-polymer composite is shown 
in Table 1-6. 
 
 
 
 
 
 
33 
 
 
 
 
 
 
 Table 1-5 Dielectric property of some commercial composite products
93
. 
 
 
Table 1-6 Dielectric properties of some current ceramic-polymer composites at RT. 
  
 
 
 
 
 
 
 
 
 
 
Company 
name 
Product name 
Product thickness 
(?m) 
?'
r?max?
 
Capacitance 
density 
(nF/in
2
) 
Motorola 
Labs and 
Vantico AG 
CFP (Ceramic-filled  
BaTiO
3
 
photodielectric 
liquid) 
12 20-22 10 
3M 
C-Ply (BaTiO
3
 in 
epoxy matrix) 
4~25 14~18 5~30 
Sanmina 
BC 2000 and 
EmCap (BaTiO
3
 in 
epoxy matrix) 
50~100 4-36 0.5~2.1 
DuPont 
Ferroelectric 
materials in glass 
powder 
? ? 100-180 
Ceramic-polymer Composite 
?'
r
 /
loss
 (1 kHz) 
Ref. 
Ceramic Polymer 
BT PMMA 40/0.012~0.016 
30
 
BT Epoxy resin 44/0.2 
88
 
BT Polystyrene 100/0.5 
94
 
CF+BT PVDF 100/0.06 
90
 
PMN Epoxy resin 24/0.05 
88
 
PMN-PT Irradiated P(VDF-TrFE) 200/0.25 
22
 
PZT PU 24/0.8 
92
 
PZT PVDF 40/0.08 
91
 
PZT PVDF+PANI 100/0.04 
95
 
PZT PVC+graphite 360/0.34 
96
 
BST P(VDF-TrFE) 200/0.03 
89
 
34 
 
1.7.2 Conductive Filler/Polymer Composites            
 Conductive filler/polymer composites are another approach towards high 
dielectric constant materials, which belong to conductor-insulator composite based on 
percolation theory
97-101
. The percolative equation is given as following: 
                               
q
c
c
m
f
ff
?
?
= )('' ??                                                                         (1-33) 
where ?? is the effective dielectric constant, ??
m 
is the dielectric constant of the matrix, f
c
 is 
the percolation threshold, q is the critical exponent (~1 for three-dimensional composites). 
Ultra high dielectric constant can be expected with conductive filler/polymer composites 
when the concentration of the conductive filler is approaching the percolation threshold 
due to the fact that the percolative approach requires much lower volume concentration 
of the filler compared to traditional approach of high dielectric constant particle in a 
polymer matrix. Therefore, this material option provides advantageous characteristics 
over the conventional ceramic/polymer composites, especially ultra high dielectric 
constant with balanced mechanical performance. A polymer matrix composite based on 
metal powers such as Ni, Cu, Al etc has been fabricated with a high dielectric constant, 
and better flexibility. Dang et al. has proposed a new composite based on LTNO (Li and 
Ti doped NiO) and PVDF in which the dielectric constant can be optimized to 400 at 
room temperature at 1 kHz with 30 vol.% LTNO
97
. By doping with multiwalled carbon 
nanotube (MWNT), it is reported a dielectric constant of about 900 at RT has been 
achieved in PVDF monopolymer as the MWNT volume fraction increasing to 0.08
98
. 
Furthermore, the interfacial effect on the percolative behavior was studied and it was 
found that the percolation threshold varied from 7 vol% to 10 vol% as the filler size 
increased from 3.5 ?m to 5 ?m
101
. Up to now, more efforts were focused on developing a 
material which could fulfill the ultimate goal between high dielectric constant and low 
dielectric loss.  
 
 
 
 
 
 
 
35 
 
1.8 Interface Effect in Composites 
  In the previous modeling studied on ceramic-polymer 0-3 composites, the 
effective dielectric constant was only dependent on the dielectric constant of the ceramic 
particles and polymer matrix. However, accurately predicting the effective dielectric 
constant has proven to be difficult. More recently, many researchers working on 
dielectric behavior have been focusing on the interface effect at the atomic or molecular 
level of materials
102-104
.  
  By considering the interface between two uniform materials phases, there are 
interactions between those atoms and its surroundings via a combination of both short or 
long-rang forces. Although the forces change over atomic distances and fluctuate because 
of thermal activity, there will be mean properties characteristic of the bulk phase. As 
approaching the interface or the boundary, those forces will become increasingly 
modified. The effective thickness may be less than 1 nm if there are only short-range 
forces, or 10 nm if the interface is electrically charged. It is well known that interfaces 
have played an important role in controlling electron and ion transportation in composite 
systems
103
. In a composite system, as the phase A which is a finite-size particle is 
surrounded by a phase B, then the interface between A and B phases will exhibit 
significant dominance as the particle size decreases. It is clear that the interface volume 
exceeds 50 vol% of the particle volume when the particle diameter is less than 5 nm as 
shown in Figure 1-20. The interfacial layer even constitutes at low filler concentration 
and shows different properties from the bulks as shown in Figure 1-21. The interfacial 
properties may begin to vary when the bulk phase disappears. For example, with atomic 
doping of a semiconductor crystal, even though the dopant has small influence on 
structure, it can cause a remarkable change of the electrical properties of the 
?composites?. Especially, the influence of interfaces with nanometric size particles is 
highly significant.  
 
 
 
 
 
36 
 
 
 
 
Interface 
volume %
0.5 nm
1.0 nm
10 nm
1
100
80
60
40
20
0
10 100 300
d/nm
(a)
 
B
A
(b)
 
Figure 1-19  (a) percentage volume of interface as function of interface thickness d for 
particle sizes 10, 1 and 0.5 nm. (b) Schematic of particle A from micrometric to 
nanometric and then to sub-nanometric size. The interface increasingly dominates
103
. 
 
 
 
 
 
37 
 
 
 
 
 
(a)
 
 
(b)
 
Figure 1-20 Interfacial regions as a function of filler particle size. The filler is shown in 
red, the interfacial region in dark blue and bulk polymer in pale blue. (a) Large particle 
produce low radius of curvature and relative less polymer in the interfacial regions. (b) 
The same volume of filler broken into small particles creates a high radius of curvature 
and more polymer in the interfacial region
104
. 
 
 
38 
 
1.8.1 Interfacial Forces 
   As the atoms are close to each other, there are repulsive short-range forces, which 
originate from quantum mechanical overlap interactions between the electron clouds of 
the atoms, and are responsible for covalent bonding, charge-transfer reactions and steric 
interactions. Besides the short-range forces, the others are electrostatic forces. Those 
forces usually involve negative electrons and positive nuclei of the system and then lead 
to dipole moments. All the dipole-related polarization forces are confined in moderate 
range, which exhibit attractive in nature known as Waals forces. 
  The term quasi-planar interface has been applied to describe the interfaces in 
many composite situations as shown in Figure 1-22, where in general three layers can be 
distinguished. On the left side of the interface, there is a double layer in A related with 
surface states and arising from immobile charged impurities, trapped carriers and mobile 
electrons and holes in A phase. In particular, the corresponding strength and extent of the 
A layer will only depend on the value of conductivity. Next to the double layer, is the 
Stern or Helmholtz double layer, which is about 1 nm and may exhibit high charge 
density. The Helmholtz double layer consists of dipoles in left side and the outer 
Helmholtz plane (OHP) in right side, as shown in Figure 1-22. Extending beyond the 
OHP into phase B is the so-called Gouy-Chapman layer. Due to the fact that this is region 
of mobile charge, it will have a significant role in influencing the dispersion of the A 
particles in the B matrix and secondly in determining the dielectric and conductive 
properties of the resulting composite
103
.  
 
 
 
 
 
 
 
 
 
 
39 
 
 
AB
Double layer
in A
Surface states 
of A
Adsorbed ions/dipoles
Stern/Helmholtz
Double layer
Gouy-Chapman
Diffusion double 
Layer in B
Out
Helmholtz
Plane (OHP)
>100 nm 1 ~100 nm
 
Figure 1-21 Schematic of electrical layers of extended interface
103
. 
 
1.8.2 Dielectric Properties 
  It is well known that the dielectric properties will be increasingly dominated by 
their interfacial interactions with their environment, whose outcome is frequently a 
degree of polarization and charge separation. Based on the influence of interfaces to 
dielectrics, they can have both passive and active roles, although the distinction is not so 
clear. 
 
Passive Interfaces 
  Since last century, the determination of satisfactory models for the effective 
macroscopic dielectric function, ??, of the composite materials has received extensive 
attention
105
. In the beginning, the Maxwell-Wagner model, in which spherical non-
interacting particles, A with permittivity ??
A
 are dispersed in matrix B, of permittivity ??
B , 
has been applied
 
81, 82
. Many methods are related to the analysis by Maxwell-Garnett
106
. It 
is noted that the effective macroscopic dielectric function, ??, is not solely determined by 
40 
 
the volume fraction and permittivity of the A and B phases but also by the shape of the A 
particles, their orientation and their interaction, which have been well discussed
83
.  
  As mentioned before, none of these models take into account the existence of 
finite interface between A and B phases. The experimental results of Bowler on particles 
with coatings marked a transition towards employing more realistic interfaces. Bowler 
indicated that the thickness and uniformity of the coating can have a significant effect on 
the frequency-dependence of effective macroscopic dielectric function, ??
A
107
. 
Furthermore, the work of Xue on loss-free two-component composites further 
demonstrates that the important role played by interfaces on dielectric properties
108
. In 
some special situation, the interface has become inevitably a large part of the device 
volume in the development of nanometric devices. For instance, in order to reduce the 
transistor size, it requires a reduction of gate area and SiO
2
 gate thickness to maintain its 
capacitance. However, it is found that a lesser thickness will cause interfaces deficient in 
oxygen and less insulating to dominate the gate properties, so a fully insulating gate of 
SiO
2
 requires a minimal thickness of 0.4 nm. In order to solve the problem, alternative 
dielectrics with higher permittivity and better interfaces are being pursued
109
.  
 
Active Interfaces 
  In the above discussion, so far interfaces are considered as passive dielectrics, but 
they can often take on an active role. O?Konski has confirmed the effect of interfacial 
conduction on the overall dielectric properties of a random suspension of spherical 
particles in a dielectric medium
110
. At low frequencies or high conductivity, charge 
carriers can be efficiently transferred by the applied field around the particle interface, 
which induce polarization at opposite ends of the particle and creates a large dipole. 
Therefore, the effective dielectric constant of the system ??, can then exceed ??
A
. 
Reversely, the polarization is reduced at high frequency due to their less transferring 
efficiency around interface. The permittivity ?? is then determined by ??
A
, ??
B
 and their 
corresponding volume concentration of particles.  
  Moreover, this model has been developed further by Chew and Sen
111
. This 
modified model emphasized the importance of the counter-ion component of the diffuse 
double layer on the A particle. Besides the polarization charge in the double layer, it 
41 
 
indicated that a neutral cloud of charge developed outside it and then it is followed by a 
charge transferring into and across B phase by diffusion. The consequence of this 
modified model shows that at low frequencies, an out of phase dipole moment forms due 
to an out of phase and large diffusion cloud. Therefore, it substantially weakens the 
dipole moment as the frequency increases and then leads to a broader frequency response 
of the permittivity than the Debye response and similar to the empirical Cole-Cole 
function frequency employed.  
  Murugaraj et al have reported the results about dielectric enhance in polymer-
nanoparticle composites through interphase polarization
112
. As shown Figure 1-23, it was 
found in this study that the dielectric constant increased monotonically with increasing 
polyimide (PI)-alumina volume concentration well above the predicted value by 
Maxwell?s rule below the percolation threshold. More studies have proved that the 
measured ?
composite
 values were found to exceed the corresponding nanoparticle such as 
?
polymer< 
?
particle
< ?
composite
, which is in contrast to the conventiol composite where ?
polymer< 
?
composite
< ?
particle
. The observed dielectric enhancement (?
composite
-?
Maxwell
) exhibited a 
correlation with the total surface area of the nanoparticle as shown in 1-24 and 1-25, 
which supported that the enhanced dielectric behavior originated from interfacial 
interaction and then demonstrated the critical role of the interfacial regions within the 
nanocomposites in enhancing their dielectric characteristics. 
  Quantitative studies on the interfacial layer using model nanocomposites have 
been carried out
104, 113, 114
. Work such as mixing nanosized silica into polystyrene matrix 
indicated that suppressing T
g
 occurred. Based on this finding, quantitative mimicking of 
T
g
 shifting pursued
104
. This is the first time that this behavior has been quantitatively 
studied in a controlled nanocomposite system, and quantitative correlation between thin-
film thickness and effective interparticle spacing was established. Experimental results 
showed that a measurable change in T
g
 can occur at effective interfacial spacing, which is 
about 500 nm. These results were larger than the expected theoretical value
115
, but 
correlate with other studies that exhibited large change in T
g
 at nanoparticle loading as 
low as 1 vol%
116
. In addition, using modeling, it would be possible to alter interfacial 
interaction energy between the silica and polymer using surface modification. Therefore, 
the results provided a framework for understanding and designing new nanocomposite 
42 
 
materials and also could lend insight on the glass-transition phenomenon for polymer in 
confined geometries.  
 
Figure 1-22 The dielectric response vs. alumina volume fraction at 100 kHz and 25
o
C
112
. 
(?  is equivalent to 
r
'? which is described in  Section 1.1). 
 
 
Figure 1-23 The correlation between the interfacial area and the dielectric enhancement 
in PI-alumina nanocomposite
112
. (?  is equivalent to 
r
'? which is described in  Section 
1.1). 
 
 
43 
 
 
 
 
 
 
 
 
Figure 1-24 Comparison of the Vo-Shi model prediction with experimental results on PI-
alumina nanocomposites and epoxy-(PMN-PT) composites, respectively. Also shown are 
the prediction by Maxwell-wagner rule for both systems
112
. (?  is equivalent to 
r
'? which 
is described in  Section 1.1. K is a constant that is dependent on the degree of particle 
clustering influencing the surface area and the thickness of the interface region between 
the nanoparticles.). 
 
 
 
 
 
 
 
 
44 
 
1.9 Objectives of This Research 
  In this work, ceramic-polymer 0-3 composites based on CaCu
3
Ti
4
O
12
 ceramic 
particles as filler are studied. Two different polymer matrices will be employed as 
matrices in this work: 1). P(VDF-TrFE) 55/45 mol% copolymer which exhibits a high 
dielectric constant and a weak piezoelectric effect, 2). P(VDF-CTFE)  88/12 mol% 
(VC88) which exhibits high a dielectric constant and no piezoelectric effect with weak 
temperature dependence. The goal for this work is to develop 0-3 composite with high 
dielectric constant. In order to achieve the goal, the following objectives are designed: 
1. Preparation of CaCu
3
Ti
4
O
12
 ceramic with high dielectric constant and low dielectric 
loss; 
2. Investigation of  the polarization mechanism in CaCu
3
Ti
4
O
12
 ceramic; 
3. Fabrication of micro-size CaCu
3
Ti
4
O
12
-based composite with different processes, 
such as as-casing, annealing, hot pressing and hot pressing time; 
4. Determination of the origin of the loss observed in the composite at low frequency; 
5. Fabrication of nano-size CaCu
3
Ti
4
O
12
-based composite with different processes, 
such as as-casing, annealing, hot pressing and hot pressing time; 
6. Property characterization and microstructure study on CaCu
3
Ti
4
O
12
-based composite.  
 
 
 
 
 
 
 
 
 
 
 
 
 
45 
 
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53 
 
 
 
 
 
CHAPTER 2 
 
MATERIALS PREPARATION AND CHARACTERIZATION 
METHODS 
 
 
In this chapter, several experimental preparation and characterization methods 
will be addressed. Materials preparation methods, such as CaCu
3
Ti
4
O
12
 ceramic synthesis 
and ceramic-polymer 0-3 composite fabrication, are presented in this work. At the same 
time, several materials characterization methods, such as X-ray diffraction (XRD), 
Scanning Electron Microscopy (SEM), Impedance analyzer, Polarization Measurement, 
are explained in detail. 
2.1 Ceramic Synthesis 
  Polycrystalline samples of CaCu
3
Ti
4
O
12
 were prepared by solid-state reaction. 
High purity metal oxide powders of calcium carbonate (CaCO
3
, 99.5 %, Alfa Aesar), 
copper oxide (CuO, 99.7 %, Alfa Aesar) and titanium dioxide (TiO
2
, 99.8 %, Alfa Aesar) 
were used to prepare the ceramics. The raw materials were weighted according to the 
stoichiometric ratio based on the following reaction
1, 2
: 
                                  CaCO
3
 + 3CuO +4TiO
2
 = CaCu
3
Ti
4
O
12
 + CO
2
?
 
  The mixture of raw materials was grinded in a polyethylene bottle with zirconia 
grinding pellets. The weight ratio among the raw material, zirconia grinding pellet and 
mixing liquid media was 1: 2: 3, respectively. The mixing liquid media used in the 
experiments was either deionized (D.I) water or ethanol. After ball milling, the powder 
was sieved by using an 80 mesh copper sieve and then dried at 100 
o
C in an oven for 8 
hours. The dry powder was calcined at 1075 ?C or 900 
o
C in Al
2
O
3
 crucible for different 
times using a 48000 Barnstead Thermolyne furnace, as shown in Figure 2-1. The 
calcination results in a dark gray colored solid, which was ground to pass an 200 mesh 
54 
 
copper sieve to get fine powder. The final powder mixed with a binder was uniaxially 
pressed into pellets that have a diameter of 13 mm, a thickness of about 1.5 mm, and 
were sintered at 1075 ?C for different times.  The final ceramic pellet is shown in Figure 
2-2. Those ceramic processing conditions are shown in Table 2-1.  
 
 
 
 
 
Figure 2-1 Image of 48000 Barnstead Thermolyne furnace. 
 
 
 
 
55 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2-2 Image of Al
2
O
3
 crucible and sintered ceramic pellet. 
 
 
Table 2-1 The CaCu
3
Ti
4
O
12
 processing conditions. 
[1]
 Ball mill for 48,72 and 96 hrs respectively. 
[2]
 Sintering for 24, 48 and 72 hrs respectively. 
 
 
 
Procedure 
No. 
1
st
 powder milling Calcinaiton 2
nd
 powder milling Sintering 
1 D.I water ball mill
[1]
 1075 
o
C/12 hr N/A 1075 
o
C
[2]
 
2 D.I water ball mill
[1]
 900 
o
C/12 hr N/A 1075 
o
C
[2]
 
3 Ethanol ball mill
[1]
 900 
o
C/12 hr N/A 1075 
o
C
[2]
 
4 Ethanol ball mill
[1]
 900 
o
C/12 hr Ethanol ball mill 1075 
o
C
[2]
 
Sintered Ceramic Pellets 
Al
2
O
3
 Crucible 
56 
 
2.2 Ceramic-Polymer 0-3 Composite Fabrication 
2.2.1 Ceramic-Polymer 0-3 Composite Casting Procedure 
   The CaCu
3
Ti
4
O
12
-P(VDF-TrFE) 0-3 composite was prepared by traditional 
casting method and hot pressing technique. P(VDF-TrFE) 55/45 mol% copolymer was 
dissolved in dimethyl formamide (DMF) under magnetic stirring for 5 hours. The image 
of milled CaCu
3
Ti
4
O
12
 powder is shown in Figure 2-3 and its particle size distribution of 
milled CaCu
3
Ti
4
O
12
 powder is given in Figure 2-4, with D
50
?10.5 ?m (weight percentage) 
from microtrac S3500 particle size analysis system. After the CaCu
3
Ti
4
O
12
 powder had 
been added into the solution, it was stirred for 8 hours and then sonicated for about 20 
minutes. The final CaCu
3
Ti
4
O
12
- P(VDF-TrFE) solution was casted on  a glass plate at 70 
?C for 8 hours. The final film was released from glass plate by immersing it into D.I 
water. The final product is a flexible film, as shown in Figure 2-5.  In order to improve 
the wettability, hot pressing technique was used. The overall process flowchart for 
CaCu
3
Ti
4
O
12
- P(VDF-TrFE) 0-3 composite fabrication is shown in Figure 2-6. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2-3 SEM image of milled CaCu
3
Ti
4
O
12
 powder. 
 
 
57 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2-4  Particle size distribution of milled CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
Figure 2-5 Image of flexible CaCu
3
Ti
4
O
12
- P(VDF-TrFE) 0-3 composite. 
 
 
 
 
 
110
0
20
40
60
80
100
 
 
% P
assi
n
g
Size (micros)
58 
 
CuO
TiO
2
CaCO
3
Calcination at 900 ?C
Sintering at 1075 ?C
Ball Milling Polymer Matrix
Film Casting
Annealing
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2-6 Process flowchart for CaCu
3
Ti
4
O
12
-P(VDF-TrFE) 0-3 composite fabrication. 
 
 
2.2.2 Optimization of Ceramic-Polymer 0-3 Composite 
           The CaCu
3
Ti
4
O
12
- P(VDF-TrFE) composites with different CaCu
3
Ti
4
O
12
 volume 
concentrations (10, 20, 30, 40, 50 vol%)  were prepared. A volumetric ratio table for  
CaCu
3
Ti
4
O
12
- P(VDF-TrFE)  samples over a 10 cm ? 15 cm solution casting glass plate 
is given in Table 2-2. As shown in Table 2-2, a fixed amount of solvent (25 ml) was used 
in all the experiments.  
 
2.2.2.1 Hot Pressing Process 
  In order to achieve further improvement in the uniformity of ceramic polymer 0-3 
composite, the composite samples were pressed with high force (7.5 tons) and high 
temperature (200 
o
C). In this work, it was found the solution cast film consisted of two 
layers: polymer rich layer and ceramic rich layer
3
. Then, two different hot pressing 
patterns were studied, as shown in Figure 2-7: 1.) PC hot pressing: Polymer rich layer in 
59 
 
one film stacking with the ceramic rich layer in another film; 2.) CC hot pressing: 
Ceramic rich layer in one film stacking with the ceramic rich layer in another film.  
 
Table 2-2 Volumetric ratio table for CaCu
3
Ti
4
O
12
- P(VDF-TrFE) composite samples. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2-7 The schematic of (a) PC hot pressing and (b) CC hot pressing. 
 
 
 
 
 
 
Polymer ceramic 
volumetric ratios 
55/45  P(VDF-TrFE) 
(g) 
CaCu
3
Ti
4
O
12 
(g) 
Dimethyl formamide 
(ml) 
100/0 3.2 0 10 
90/10 6.09 1.98 25
80/20 4.66 3.41 25 
70/30 3.55 4.45 25
60/40 2.74 5.35 25 
55/50 2.04 5.97 25
40/60 1.49 6.54 25 
(a) PC hot pressing (b) CC hot pressing
P
o
l
y
m
er ri
ch
 l
a
yer
C
e
r
a
m
i
c ri
ch
 l
a
yer
60 
 
2.2.2.2 Silane Coupling Process 
   Besides the optimization method using hot pressing technology, the effect by 
using silane coupling agent was studied. In this work, CaCu
3
Ti
4
O
12
-P(VDF-TrFE) 
composites modified with 0.3, 0.5, 0.75, 1, 5, 10 wt% silane were prepared. The silane 
coupling agent is manufactured by Alfa Aeasr (A Johnson Matthey Company) and its 
physical and chemical properties are listed in Table 2-3.  It is believed that the bridge-
linked action of silane coupling agent can improve the uniformity and then optimize the 
dielectric response of the composite. The schematic of silane coupling agent reaction 
process is shown in Figure 2-8. 
 
Table 2-3 Physical and chemical properties of silane coupling agent. 
 
P(VDF-TrFE) CaCu
3
Ti
4
O
12
Reaction with P(VDF-TrFE)  Reaction with CaCu
3
Ti
4
O
12
C
F
F
F
C
C
C
C
C
C
C
F
F
F
F
F
F
F
F
F
F
H
H
H
H
Si
Cl
Cl
Cl
1 H, 1H, 2H, 2H-Perfluorooctyltrichlorosilane
 
Figure 2-8 The schematic of silane coupling agent reaction process with P(VDF-TrFE) 
and CaCu
3
Ti
4
O
12
. 
 
 Physical and chemical data 
Product name 1 H, 1H, 2H, 2H-Perfluorooctyltrichlorosilane 
Synonyms Trichloro- 1 H, 1H, 2H, 2H-Perfluorooctylsilane 
CAS# 78560-45-9 
% Weight 97 
Flash Point 54
o
C 
Boiling Point 84-85
o
C 
Melting Point No data 
Solubility in water Reacts 
Density (g/ml) 1.638 
Molecular Formula C
8
H
4
Cl
3
F
13
Si 
Molecular Weight (g/mol) 481.55 
61 
 
2.2.2.3 Annealing Process 
  The removal of DMF solvent and the improvement in crystallinity of P(VDF-
TrFE) played an important role on the overall electric properties of the CaCu
3
Ti
4
O
12
- 
P(VDF-TrFE) composites. Therefore, an additional process was carried out to study the 
dielectric response of the composite. As-casted composite films were securely 
sandwiched between two glass plates in an oven and the annealing process was kept at 
125  
o
C for 8 hours.   
 
2.3 Materials Characterization Methods 
2.3.1 Crystalline Structure Determination Using Wide Angle X-ray Diffraction 
  X-ray diffraction (XRD) method has been widely used to characterize different 
materials such as ceramics and polymers. XRD can provide unique information about 
materials, such as phases, crystallinity, orientation, etc. The samples were placed on a 
home-made holder and then were inserted into a Rigaku DMAX-B vertical diffractometer.  
The X-ray diffraction was scanned at 40 kV and 30 mA with Ni-filtered, CuK? radiation 
(wavelength?1.54 ?) and the intensity of diffracted X-ray was measured between 15 to 
90 
o
 for CaCu
3
Ti
4
O
12
 powder, or CaCu
3
Ti
4
O
12
-P(VDF-TrFE) composite, respectively. A 
scanning speed of 5 
o
/min and a sampling interval of 0.05 
o
 were used in this work. The 
obtained diffraction pattern was compared with standard JCPDF data library to confirm 
the presence of the phase in the materials by matching their unique peaks. The d-spacing 
can be calculated by Bragg?s law as following
4
: 
?? sin2dn =                                                                                 (2-1)       
Where n is the layer index number, ? is the wavelength of X-rays, d is the spacing 
between the planes in the atomic lattice, ? is angle between the incident ray and the 
scattering planes. 
 
2.3.2 Microstructure Analysis Using SEM 
  Scanning Electron Microscopy (SEM) is a type of electron microscope that 
images the sample surface with high-energy beam of electrons.  By interacting with the 
atoms, those electrons can produce signals that contain information such as the surface 
morphology and composition distribution.  The types of signals produced by the SEM 
62 
 
include: secondary electrons, back scattered electrons, characteristic X-ray, 
cathodoluminescence, and transmitted electrons. Among those signals, secondary 
electron imaging can produce very high-resolution images of sample surface, which is as 
high as 1 to 5 nm in size. 
  Samples obtained from the synthesis or fabrication process were stuck on 
conductive tape and then gold coating using a Pelco SC-6 sputter coater, as shown in 
Figure 2-9.  JEOL JSM 7000F FE-SEM was operated at 20 kV to take the secondary 
electron images at high magnifications, and compositional analysis was completed using 
the Oxford Instruments Electron Dispersive X-ray Spectroscopy (EDS) system, as shown 
in Figure 2-10. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
63 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2-9 Image of Pelco SC-6 sputter coater. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2-10 Measurement setup of Scanning Electron Microscopy (SEM). 
 
 
SEM Control PC 
SEM Sample Chamber 
Electron Gun 
Sample Chamber 
64 
 
2.3.3 Dielectric Analysis Using Impedane Analyzer 
  In order to characterize the electric properties of the material, there must be a 
conductive layer used as an electrode on the top. It can be done by either brushing pastes 
or sputtering metallic materials, such as gold and silver, on the surface of the sample. As 
for the ceramic pellets, they were polished with 1000 and 2000 grade 3M polishing paper 
separately in order to obtain a smooth surface prior to the sputtering process. Those 
ceramic samples were then sputtered with gold on top and bottom surfaces using a Pelco 
SC-6 sputter coater, as shown in Figure 2-9. However, special masks with diameter of 1.7 
and 3.2 mm were designed for a composite purpose, as shown in Figure 2-11. A gold 
layer about 40 nm thickness was deposited. In the work, Agilent 4294A impedance 
analyzer (100 Hz to 1,000 kHz) was employed to characterize the dielectric property of 
the samples and the measured frequency range was 100 to 1,000 kHz, as shown in Figure 
2-12. This experiment was calibrated each time to eliminate any background noise. In 
order to characterize the temperature dependence of the dielectric response, samples were 
held with a home-made measurement probe, as shown in Figure 2-13, and were then 
heated using a Fisher Isotemp 800 Series Programmable oven.  When two parallel metal 
plates of area A are separated by a distance d with dielectric materials in between and 
then attached to the electric circuit, the capacitance can be expressed as
2, 5-7
:  
                                 
d
A
C
r 0
' ??
=                                                                                    (2-2) 
where: C is capacitance, '?
r
 is the relative permittivity, 
0
? is the permittivity in vacuum, A 
is area of electrodes of the capacitor, d is distance between two conductive plates. 
 
 
 
 
 
 
 
 
 
65 
 
 
 
 
 
Figure 2-11 Image of mask with diameter of 1.7 millimeter. 
 
 
Figure 2-12 Image of Agilent 4294A impedance analyzer. 
 
 
 
66 
 
 
 
 
Figure 2-13 Setup of home-made probe for temperature dependence measurement. 
 
 
 
References 
1. Homes, C. C.; Vogt, T.; Shapiro, S. M.; Wakimoto, S.; Ramirez, A. P. Science  
            2001, 293, (27), 673-676. 
2. Arbatti, M. Development of High-Dielectric-Constant Polymer-Ceramic  
            Composites Based on Calcium Copper Titanate. Auburn University,  
             Alabama, 2004. 
3. Arbatti, M.; Shan, X. B.; Cheng, Z.-Y. Adv. Mater 2007, 19, 1369-1372. 
4. Cullity, B. D.; Stock, S. R., Elements of X-Ray Diffraction. Prentice Hall:  
             New Jersey, 2001. 
5. Barsoum, M. W., Fundamentals of Ceramics. Institute of Physics Publishing:  
            Bristol and Philadephia, 1997. 
6. Kao, K. C., Dielectric Phenomena in Solids. Elsevier Academic Press: San Diego,  
            CA, 2004. 
7. Rao, Y.; Ogitani, S.; Kohl, P.; Wong, C. P. J. Appl. Poly. Sci 2002, 83, 1084-1090. 
 
Measurement Probe 
Teflon Platform 
67 
 
 
 
 
 
CHAPTER 3 
 
PROCESSING AND CHARACTERIZATION OF CaCu
3
Ti
4
O
12
 
CERAMIC 
 
 
3.1 Introduction 
 In this chapter, the research on the processing and characterization of 
CaCu
3
Ti
4
O
12
 has been carried out and it is well known that the dielectric properties and 
microstructure of CaCu
3
Ti
4
O
12
 varied with different processing conditions, such as 
calcination temperature, sintering time and post-annealing atmosphere, etc.  
  During the processing study on the CaCu
3
Ti
4
O
12
 ceramic, it was observed that 
with suitable tuned processing parameters, better dielectric performance in CaCu
3
Ti
4
O
12
 
can be obtained, and this high performance CaCu
3
Ti
4
O
12
 could directly benefit the 
following work in high dielectric constant CaCu
3
Ti
4
O
12
-composites study, which is going 
to be addressed in Chapter 4 and 5. Therefore in this work, the final goal is to pursue a 
rectified experimental route in order to produce high performance ceramic. In this chapter, 
we study the dielectric response of the CaCu
3
Ti
4
O
12
 ceramic under different processing 
conditions, such as sintering temperature, sintering time and annealing condition, etc.  
3.2 Experimental 
High purity metal oxide powders of calcium carbonate (CaCO
3
, 99.5 %, Alfa 
Aesar), copper oxide (CuO, 99.7 %, Alfa Aesar) and titanium dioxide (TiO
2
, 99.8 %, 
Alfa Aesar) were used to prepare the polycrystalline samples of CaCu
3
Ti
4
O
12
 by solid-
state synthesis as described in Chapter 2
1
.  
  Crystalline structure determination: X-ray diffraction (XRD) method has been 
utilized to characterize the phases of CaCu
3
Ti
4
O
12
 ceramic and the measurement angle 
ranges from 20 to 75 
o
. 
68 
 
  Dielectric properties: Those samples were polished and gold was coated on the 
surface of the pellets as electrodes. Agilent 4294A impedance analyzer was employed to 
characterize the dielectric property of the samples. The measured frequency range was 
from 100 Hz to 1 MHz and measured temperature ranged from 25 to 125 
o
C. 
  Microstructure analysis: The grain size and uniformity of the ceramic were 
determined by a scanning electron microscope with EDS (SEM JSM-7000F, JEOL). 
Compositional analysis was completed using the Oxford Instruments Electron Dispersive 
X-ray Spectroscopy (EDS) system. 
 
3.3 Results and Discussion 
3.3.1 Solid State Synthesis 
The material CaCu
3
Ti
4
O
12
 was first prepared using solid state synthesis. The 
ceramic processing conditions are described in Table 3-1. The phases involved in the 
formation of the CaCu
3
Ti
4
O
12
 were examined using XRD. XRD patterns of calcined 
CaCu
3
Ti
4
O
12
 obtained from the solid state reaction are shown in Figure 3-1. 
Figure 3-1 shows XRD peaks from oxide mixtures which were calcined at 
different temperatures (1075 
o
C and 900 
o
C) for a period of 12 hours after 48, 72 and 96 
hours ball milling process. After confirmation by the XRD of the references (JCPDS), 
XRD patterns of ceramics show the presence of CaCu
3
Ti
4
O
12
 as a single phase and the 
lattice parameters are close to 7.393(4) ?, which is in agreement with the literature
2, 3
 and 
reference card (75-2188) obtained from the Joint Committee on Powder Diffraction 
Standards (JCPDS)
4
. Those results suggest that almost all the raw materials have 
completely reacted and formed the expected main phases. However, it was found that 
there were two unexpected weak peaks at 2??33 and 58 degrees for calcining at 1075 
o
C, 
and three weak peaks at 2??27, 33 and 54 degrees for calcining at 900 
o
C. Moreover, all 
the samples calcining at 900
 o
C behaved with relatively high intensity compared to those 
at 1075 
o
C. It indicated that in comparison with calcining at 1075
 o
C, calcining at 900 
o
C 
is prone to result in higher percentage of main CaCu
3
Ti
4
O
12
 phases, however due to its 
low calcination temperature, it also introduces more second phase as shown in Figure 3-1.   
 
 
69 
 
 
 
 
 
 
 
 
Table 3-1 The CaCu
3
Ti
4
O
12
 processing conditions. 
[1]
 Ball mill for 24, 48, 72 and 96 hrs respectively. 
[2]
 Sintering for 24, 48 and 72 hrs respectively. 
 
 
 
 
 
 
 
 
 
 
Procedure 
No. 
1
st
 powder milling Calcinaiton 2
nd
 powder milling Sintering 
1 D.I water ball mill 
[1]
 1075 
o
C/12hrs N/A 1075 
o
C 
[2]
 
2 D.I water ball mill 
[1]
 900 
o
C/12hrs N/A 1075 
o
C 
[2]
 
3 Ethanol ball mill 
[1]
 900 
o
C/12hrs N/A 1075 
o
C 
[2]
 
4 Ethanol ball mill 
[1]
 900 
o
C/12hrs Ethanol ball mill 1075 
o
C 
[2]
 
70 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-1 XRD patterns on the CaCu
3
Ti
4
O
12
: (a) calcination at 1075
o
C after 48, 72 and 
96 hrs milling; (b) calcination at 900
o
C after 48, 72 and 96 hrs milling according to the 
procedure #1 and 2 in table 3-1. 
 
 
 
 
20 25 30 35 40 45 50 55 60 65 70 75
 
 
2?
Int
e
ns
it
y
 
 
(a)
 
 
96hrs
72hrs
(
440
)
(
440
)
(
422
)
(
422
)
(
411
)
(
411
)
(
400
)
(
40
0
)
(
32
1
)
(
321
)
(
22
2
)
(
222
)
(
310
)
(
310
)
(
220
)
(2
20)
(
211)
(2
11)
(
440
)
(
42
2
)
(
411
)
(
400
)
(
321
)
(
222
)
(
310
)
(2
20
)
(2
11)
48hrs
Calcination:1075
o
C
20 25 30 35 40 45 50 55 60 65 70 75
 
 
2?
48hrs
72hrs
96hrs
Calcination: 900
o
C
Inte
nsity
 
 
(b)
 
(
211)
(
422
)
(
440
)
(
440
)
(
42
2
)
(
411
)
(
40
0
)
(
400
)
(
321
)
(
321
)
(
222
)
(
22
2
)
(
310
)
(
310
)
(
220)
(22
0
)
(
211)
(
440
)
(
422
)
(
411
)
(
400
)
(
32
1
)
(
222
)
(
310
)
(
220)
(211
)
71 
 
3.3.2 Effect of Processing On Dielectric Properties 
  The CaCu
3
Ti
4
O
12 
exhibited an extraordinarily high dielectric constant, and current 
experiments have detected no presence of superstructure or crystal structure change. 
Based on those studies, it appears that the mechanism for the high permittivity is not 
intrinsic, so the processing may play an important role on the dielectric properties of 
CaCu
3
Ti
4
O
12
.  In the following study, the effect of processing on CaCu
3
Ti
4
O
12 
is carried 
out. Several experimental routes were designed, such as different pellet molding 
pressures (2500 PSI and 3000 PSI), different ceramic milling time (48 hours, 72 hours 
and 96 hours), different sintering temperatures (24 hours, 48 hours and 72 hours), and 
different annealing atmospheres (vacuum and argon gas).  
 
3.3.2.1 Effect of Molding Pressure 
  In this part, the effect of pellet molding pressure on the dielectric properties was 
studied under the same processing conditions, such as milling time, calcining and 
sintering temperature. The milling time for those ceramic samples were fixed at 24 hours 
and the calcining temperature and sintering temperature were set at 1075 
o
C, respectively. 
Their dielectric spectrums using different molding pressures are shown in Figure 3-2, and 
their corresponding SEM images of those fractured samples are listed in Figure 3-3 and 
3-4.    
  In the ceramic processing, it is well known that in the preparation stage, the 
quality of molded ceramic pellet was critical for the final dielectric performance 
enhancement. Especially, with high molding pressure, it was prone to generate cracks 
inside the ceramic during the calcination process, which would then prevent the grain size 
growth and hinder final dielectric property improvement. Based on the results in Figure 
3-2, those dielectric spectrums obtained in samples using two molding pressures behave 
very similarly. The dielectric constant varied from 17,000 to 23,000, and corresponding 
dielectric loss was stabilized below 0.25 at 1 kHz, as sintering time varied from 24 to 72 
hours. It was also found that it tends to result in high loss at high frequency using 2500 
PSI. Their SEM images in Figure 3-3 and 3-4 showed that they tend to give small 
morphology difference. The average grain size using 2500 PSI is: 6.8 ?m, 7.5 ?m, 11.1 
?m and 16.5 ?m for 1 hour, 24 hours, 48 hours and 72 hours sintering, while for 3000 
72 
 
PSI, 6.8 ?m, 12.3 ?m, 13.8 ?m and 14.3 ?m for 1 hour, 24 hours, 48 hours and 72 hours 
sintering, respectively. Based on experimental results, it indicated that ceramic sample 
using 2500 PSI exhibited lagged grain size growth. Especially for sintering 24 hours, the 
SEM image indicated that it was in the early calcination stage with average grain size of 
7.5 ?m for 2500 PSI, while the grain was about 12.3 ?m with 3000 PSI molding pressure. 
Moreover, it was found that those samples under 3000 PSI exhibited more porosity, and 
this porosity phenomenon may be associated with its lower loss at high frequency. Later 
on, more studies on porosity will be carried out. This suggested that molding pressure 
could be used as an optimization method in following studies, and longer sintering time 
such as 24 to 72 hours was necessary in order to enhance the dielectric response.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
73 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-2 Dielectric response vs. frequency for CaCu
3
Ti
4
O
12
 samples with 24 hrs D.I 
water ball milling, calcinated at 1075 
o
C, and then sintered at 1075 
o
C for 1 hr, 24 hrs, 48 
hrs and 72 hrs using  (a) 2500 PSI, and (b) 3000 PSI  pellet molding pressure.  
 
 
 
 
 
100 1k 10k 100k 1M
0
5
10
15
20
25
30
0.0
0.5
1.0
1.5
2.0
2.5
 
?
'
r 
(x1000)
Freq(Hz)
 1 hr
 24 hrs
 48 hrs
 72 hrs
2500 PSI
 
 1 hr
 24 hrs
 48 hrs
 72 hrs
(a)
tan
?
100 1k 10k 100k 1M
0
5
10
15
20
25
30
0.0
0.5
1.0
1.5
2.0
2.5
 1 hr
 24 hrs
 48 hrs
 72 hrs
 
 
?
'
r 
(x1000)
Freq(Hz)
3000 PSI
 1 hr
 24 hrs
 48 hrs
 72 hrs
(b)
ta
n
?
 
74 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-3  SEM fractographs of CaCu
3
Ti
4
O
12
 after 24 hrs D.I water ball milling, 
calcinated at 1075 
o
C, sintered at 1075 
o
C for (a) 1 hrs, (b) 24 hrs, (c) 48 hrs (d) 72 hr 
using 2500 PSI pellet molding pressure.  
 
 
 
 
 
 
(a) 
(b) 
(c) (d)
75 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-4  SEM fractographs of CaCu
3
Ti
4
O
12
 after 24 hrs D.I water ball milling, 
calcinated at 1075 
o
C, sintered at 1075 
o
C for (a) 1 hr, (b 24 hrs, (c) 48 hrs (d) 72 hrs by 
3000 PSI pellet molding pressure.  
 
 
 
 
 
(a) 
(b) 
(c) (d)
76 
 
3.3.2.2 Effect of Ball Milling Time and Sintering time 
  To further investigate the effect of processing on the dielectric properties of 
CaCu
3
Ti
4
O
12
 ceramics, ceramic samples were prepared after 48, 72 and 96 hours ball 
milling and then sintering for 24, 48, and 72 hours respectively, according the procedure 
#1 in Table 3-1. The effects of milling time and sintering time have been studied. Their 
dielectric spectrums and SEM images are shown in Figure 3-5, 3-6, 3-7 and 3-8, 
respectively. 
  After the initial milling of raw powder for 48, 72, and 96 hours and then 
following calcination at 1075 
o
C, the average grain sizes were 2.242?0.3, 2.266?0.4 and 
2.372?0.4 ?m, respectively. However, it was found that their dielectric response and the 
corresponding microstructure changed dramatically after sintering processing.  As seen in 
Figure 3-5 (a), the dielectric constant at 1 kHz was about 24,000 to 42,000 for 48 hours 
milling, however, the dielectric constant increased abruptly from 70,000 to 85,000 at 1 
kHz as for 96 hours milling in Figure 3-5 (c). This difference among different milling 
times was closely related with particle size reduction and the substantial reduction of the 
amount in the minor phases via longer milling time. Among those results, a relative better 
processing condition was observed with 96 hours milling and 72 hours sintering, at which 
a dielectric constant of 82,300 and loss of 0.12 were achieved. Since it is possible that 
longer milling time creates a more defect-laden particle which enhances the conductivity 
properties of the grain, this increase in the conductivity of the grain?s core region could 
act to increase the permittivity of the materials
5
. After considering the results in Figure 3-
5, longer milling time, such as 96 hours and sintering time such as 72 hours was prone to 
give better dielectric properties, and thus it can best illustrate the milling effect and 
sintering effect, respectively. SEM observations in Figure 3-6 indicated that the typical 
particle size was about 10 to 50?m for 48 hours milling. The grain size for 48 hours 
milling indicated an increasing trend as sintering time varying from 24 to 48 hours. 
However, there were substantial differences in the microstructure of the longer milling 
time, such as 72 and 96 hours, as seen in Figure 3-7 and 3-8. Especially for 96 hours 
milling, due to the way the material fractured it was difficult to distinguish the grain size, 
so no precise grain size was given, but it can be clearly seen that there was substantial 
grain growth, which would collaborate the fact of dielectric enhancements with extended 
77 
 
milling time. The improvement of the high frequency dielectric constant usually involves 
a variation of enhancement factors, such as no oxygen deficiency in the vicinity of grain 
boundaries, etc. They are closely related with the size of the CaCu
3
Ti
4
O
12
 grain divided 
by the grain boundary thickness
5, 6
. In short, the processing parameters, such as milling 
time and sintering time, were closely associated with the presence of large 
semiconducting grains which are seen in Figure 3-8, and could directly influence the final 
dielectric properties.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
78 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-5 Dielectric response vs. frequency for samples: (a), (b) and (c) after 48, 72 and 
96 hrs milling respectively,  calcining at 1075
 o
C for 12 hrs,  then sintering at 1075 
o
C for 
24, 48, and 72 hrs according to procedure #1 in table 3-1. 
 
100 1k 10k 100k 1M
0
10
20
30
40
50
60
0.0
0.5
1.0
1.5
2.0
 24 hrs
 48 hrs
 72 hrs
 
?
'
r 
(x1000)
Freq(Hz)
tan
?
 
 24 hrs
 48 hrs
 72 hrs
(a) 48 hrs milling
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
400
450
0
2
4
6
8
10
12
 
  24 hrs
  48 hrs
  72 hrs
 
 
tan
?
?
'
r 
(x1000)
Freq(Hz)
 
  24 hrs
  48 hrs
  72 hrs
(b) 72 hrs milling
100 1k 10k 100k 1M
0
20
40
60
80
100
120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
 
 
tan
?
?
'
r 
(x1000)
Freq(Hz)
  24 hrs
  48 hrs
  72 hrs
 
 
(c) 96 hrs milling
  24 hrs
  48 hrs
  72 hrs
79 
 
 
 
 
 
 
Figure 3-6 SEM fractographs of CaCu
3
Ti
4
O
12
 for 48 hrs D.I water ball milling, calcining 
at 1075
 o
C for 12 hrs, then sintering at 1075
o
C for (a) 24 hrs, (b) 48 hrs, (c) 72 hrs. 
 
(a) 
(b) 
(c) 
80 
 
 
 
 
 
Figure 3-7 SEM fractographs of CaCu
3
Ti
4
O
12
 for 72 hrs D.I water ball milling, calcining 
at 1075
 o
C for 12 hrs, then sintering at 1075
o
C for (a) 24 hrs, (b) 48 hrs, (c) 72 hrs. 
 
(b) 
(c) 
(a) 
81 
 
 
 
 
 
 
Figure 3-8 SEM fractographs of CaCu
3
Ti
4
O
12
 for 96 hrs D.I water ball milling, calcining 
at 1075
 o
C for 12 hrs, then sintering at 1075 
o
C for (a) 24 hrs, (b) 48 hrs, (c) 72 hrs. 
 
(a) 
(b) 
(c) 
82 
 
3.3.2.3 Effect of Calcination Temperature and Milling Solvent 
  Besides the milling effect and sintering effect to the CaCu
3
Ti
4
O
12
, the calcination 
temperature of the material is crucial. Since the calcination temperature might change the 
densification and grain growth process, elaborate calcination characterization of the 
material is important to the dielectric enhancement.  
  The results in Figure 3-9 exhibit dielectric spectrum measured from CaCu
3
Ti
4
O
12
 
calcining at 900 
o
C. After the initial raw powder milling for 48, 72, and 96 hours and 
following calcination at 900
o
C, corresponding average grain sizes were 5.23?1.1, 
5.45?1.2 and 5.89?1.3 ?m respectively, which was relatively larger than the results 
calcining at 1075
 o
C. In comparison with those sintered samples under two different 
calcination processes, it was interesting to note that both shared similar trend that all the 
experimental results after 48 and 72 hours milling exhibited unsatisfactory dielectric 
response. Only when the milling time exceeds 96 hours which may reach its critical grain 
size that their dielectric response can be enhanced. Especially, it was found that the 
dielectric constant increased from 83,000 and 160,000, and dielectric loss remained as 
small as 0.15 at 1 kHz, as shown in Figure 3-5 and 3-9. With both calcination 
temperatures, it was clear that the dielectric response was not satisfactory, due to either 
the dielectric constant being relatively low, or the dielectric loss was high if milling time 
is bellow 72 hours, as shown in Figure 3-5 and Figure 3-9.  The dielectric enhancement is 
obviously correlated with differences in ceramic microstructure and especially, with the 
average grain size. According to IBLC model, the enhancement of the dielectric constant 
was related to the ratio between grain and grain boundary thickness, and the dielectric 
constant of ceramic can be expressed as
7
: 
                               
gb
gbg
gbeff
d
dd +
=??                                                                            (3-1) 
Where ?
eff
 is the effective dielectric constant of a given material, ?
gb
 is the dielectric 
constant of intrinsic bulk, d
g
 and d
gb
 are the thickness of the grains and grain boundary 
layers. Corresponding SEM images are shown in Figure 3-10. It can be clearly observed 
that the structure tends to be more homogeneous and substantial grain growth occured 
with dimensions above 60 ?m for CaCu
3
Ti
4
O
12
 calcining at 900 ?C, in comparison to 10 
to 50 ?m at 1075 ?C in Figure 3-6. Based on the SEM images shown in Figure 3-10 and 
83 
 
dielectric results in Figure 3-9, the highest of dielectric constant at 1 kHz was up to 
160,000 and accordingly, larger grain size was obtained in the same sample. In order to 
better understand what is occurring during sintering, the shrinkage rate and density 
change were been measured (see Table 3-2 and 3-3). The shrinkage rate of calcining at 
900 ?C was almost double that at 1075 ?C, which strongly proved the better densification 
and grain growth. All the results together with the results in Tables 3-2 and 3-3 support 
the argument that lower calcination temperature such as at 900 ?C is beneficial for density 
improvement and grain size growth, which then contributed the increasing of dielectric 
constant with extended milling time and sintering time.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
84 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-9 Dielectric response vs. frequency for samples: (a), (b) and (c) after 48, 72 and 
96 hrs milling respectively, then sintering for 24, 48, and 72 hrs according to procedure 
#2 in Table 3-1. 
 
 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
400
450
0
2
4
6
8
10
 
ta
n
?
Freq(Hz)
 24 hrs
 48 hrs
 72 hrs
?
'
r 
(x1000)
 
 24 hrs
 48 hrs
 72 hrs
(a) 48 hrs milling
100 1k 10k 100k 1M
0
70
140
210
280
350
420
490
560
630
0
2
4
6
8
10
 
 24 hrs
 48 hrs
 72 hrs
tan
?
Freq(Hz)
?
'
r 
(x1000)
(b) 72 hrs milling
 
 24 hrs
 48 hrs
 72 hrs
100 1k 10k 100k 1M
0
30
60
90
120
150
180
210
240
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
tan
?
 24 hrs
 48 hrs
 72 hrs
?
'
r 
(x1000)
Freq(Hz)
(c) 96 hrs milling
 
 24 hrs
 48 hrs
 72 hrs
85 
 
 
 
 
 
 
Figure 3-10 SEM fractographs of CaCu
3
Ti
4
O
12
 for 48 hrs D.I water ball milling, 
calcinated at 900
 o
C, then sintering at 1075
 o
C for (a) 24 hrs, (b) 48 hrs, (c) 72 hrs. 
 
(a) 
(b) 
(c) 
86 
 
 
 
Table 3-2  Shrinking rate of the pellet. 
 
[1] [2] 
 
Ball mill 48 hrs 
Sintering 24 hrs 7.6% 14.1% 
Sintering 48 hrs 8.4% 14.2% 
Sintering 72 hrs 7.5% 14.2% 
 
Ball mill 72 hrs 
Sintering 24 hrs 9.1% 14.8% 
Sintering 48 hrs 9.5% 13.5% 
Sintering 72 hrs 9.5% 14.4% 
 
Ball mill 96 hrs 
Sintering 24 hrs 7.5% 15.1% 
Sintering 48 hrs 8.1% 14.0% 
Sintering 72 hrs 8.0% 14.0% 
[1]
 Method one: Calcinations at 1075 ?C for 12 hrs, then sintering at 1075 ?C. 
[2]
 Method two: Calcinations at 900 ?C for 12 hrs, then sintering at 1075 ?C. 
* Sample diameter shrinking rate. 
 
Table 3-3  Density of the pellet: g/cm
3
. 
 
[1] [2] 
 
Ball mill 48 hrs 
Sintering 24 hrs 4.4 4.7 
Sintering 48 hrs 4.5 4.7 
Sintering 72 hrs 4.4 4.7 
 
Ball mill 72 hrs 
Sintering 24 hrs 4.6 4.8 
Sintering 48 hrs 4.7 4.8 
Sintering 72 hrs 4.5 4.9 
 
Ball mill 96 hrs 
Sintering 24 hrs 4.6 4.7 
Sintering 48 hrs 4.6 4.8 
Sintering 72 hrs 4.6 4.8 
[1]
 Method one: Calcinations at 1075 ?C for 12 hrs, then sintering at 1075 ?C. 
[2]
 Method two: Calcinations at 900 ?C for 12 hrs, then sintering at 1075 ?C. 
 
87 
 
  Figure 3-11 (a) and (b) show the dielectric spectrums of the CaCu
3
Ti
4
O
12
 with 72 
hours ethanol milling, whose experimental route was based on the procedure #3 and #4 in 
Table 3-1. Compared with the D.I water milling results, due to the fact that ethanol can 
lower the surface energy of powder and thereby efficiently avoid agglomeration between 
particles, a better milling effect was achieved, and dielectric results were shown in Figure 
3-11 (a). In addition, the dielectric properties were further enhanced by introducing a 2
nd
 
ethanol ball milling. For instance, with the same processing in Figure 3-11 (a) followed 
by a 2
nd
 24 hours ethanol ball milling after calcinations, the dielectric constant has been 
improved to 190,000, while loss remained as small as 0.152 at 1 kHz, as shown in Figure 
3-11 (b) which was even better than the results with 96 hours D.I water milling as shown 
in Figure 3-9 (c). Those results have experimentally elucidated the fact that besides the 
influence of the thermal treatment, milling solvent also played important role in the 
dielectric response. Upon verification, the technique could prove useful in enhancing the 
dielectric properties of CaCu
3
Ti
4
O
12
. 
 
 
 
 
 
 
 
 
 
 
 
 
 
88 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-11 Dielectric response vs. frequency for samples: (a) after 72 hrs milling 
according to procedure #3 in Table 3-1; (b) after 72 hrs milling according to procedure #4 
in Table 3-1. 
 
 
100 1k 10k 100k 1M
0
40
80
120
160
200
240
280
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
 
 24 hrs
 48 hrs
 72 hrs
 
tan
?
Freq(Hz)
?
'
r 
(x1000)
 
(b) 72 hrs milling
 24 hrs
 48 hrs
 72 hrs
100 1k 10k 100k 1M
0
20
40
60
80
100
120
0
2
4
6
8
10
 
 
?
'
r 
(x1000)
Freq(Hz)
 24 hrs
 48 hrs
 72 hrs
(a) 72 hrs milling
tan
?
 24 hrs
 48 hrs
 72 hrs
89 
 
3.3.2.4 Effect of Thickness on Dielectric Properties 
  Based on those SEM fractographs which were shown in Figure 3-6 to 3-8 and 
Figure 3-10, it was clear that there were pores on those ceramic samples. By extending 
the sintering time, those pores generally tended to diminish, while their dielectric 
properties also showed indication of enhancement. Therefore, those pores were obviously 
related to their corresponding dielectric properties. In order to better understand the role 
of those pores on dielectric properties, further experiments on the effect of thickness have 
been carried out. Ceramic samples after 96 hours milling according to procedure #2 in 
Table 3-1 were chosen in this study and their corresponding results were already shown 
in Figure 3-9 (c). For each sample, it was polished on both surfaces (top and bottom) to 
three different sample thicknesses, such as 0.79 mm, 0.60 mm and 0.38 mm, and their 
individual experimental results are shown in Figure 3-12 to 3-14. Due to the limitation of 
polishing techniques, thickness errors were allowed and corresponding )( ?ErSD  were 
0.015, 0 and 0.015 mm.  
  In Figures 3-12 to 3-14, it was curious to find that the corresponding dielectric 
constant was increasing with decreasing sample thickness. More specially, for example, 
for 24 hours sintering, it increased from 41,100 to 56,100, for 48 hours sintering, it 
increased from 186,000 to 289,000 and for 72 hours sintering, it changed from 199,000 to 
238,000. Compared with the results in Figure 3-9 (c), those results were significantly 
improved, except the sample with 24 hours sintering. This difference originated from the 
fact that the dielectric property was not only influenced by sintering time, but also 
associated with their thickness. As the sintering time was short, such as 24 hours in this 
study, grain growth was between its initial stage and intermediate stage, which were 
characterized with neck growth and enclosing pore channels at grain edges. Thus, 
especially at the edge area in those sintered samples, their dielectric properties were 
easily prone to fluctuate. SEM fractographs of those samples before polishing processing 
are shown in Figures 3-16 to 3-18. For each sintered sample, three different locations, 
such as edge, middle and core areas were studied as shown in Figure 3-15. In Figures 3-
16 to 3-18, they presented a slight increase on the pores? surface density as moving from 
edge to core area, for example, 51 to 60 pores for 24 hours sintering, 57 to 75 pores for 
48 hours sintering and 55 to 100 pores for 72 hours sintering. Each individual pore 
90 
 
resembled one individual dipole in dielectrics, which can bound equal charge in 
magnitude but opposite in polarity. Therefore, it was found that with diminishing 
thickness, the increasing pore surface density lead to increasing quantities of dipole 
moments, which was associated with dielectric constant increase. SEM fractographs have 
collaborated with results in Figure 3-12 to 3-14. With further studies with Cole-Cole 
equations, analyzed results were shown in Figure 3-18 to 3-20. The empirical Cole-Cole 
relation is shown as following: 
    
?
?
r
??
*
=
?
??
??
???
?
?
?
+
?
=??
1
0
)(1
'''
j
j
rrs
rrr
                                        (3-2) 
Based on the results in Figure 3-19 to 3-21, the relaxation time ?
0
 for 24, 48 and 72 hours 
sintering increased from 0.215 ?s to 0.318 ?s, 0.937 ?s to 1.707 ?s and 0.959 ?s to 1.667 
?s, respectively. Figure 3-22 shows the relationship of ?? (?
s
-?
?
) vs. sample thickness 
and it was found that the ?? was increasing with decreasing thickness. As there are more 
dipoles inside, it corresponds to longer relaxation time, which has been well confirmed 
with Cole-Cole equations. All the experimental results have indicated that those pores in 
those ceramic samples played an important role in the dielectric properties.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
91 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-12 Dielectric response vs. frequency for samples with different sample thickness 
(1.60 mm, 0.78 mm, 0.60 mm and 0.36 mm, respectively) after 96 hrs milling and then 
24 hrs sintering according to procedure #2 in Table 3-1. 
 
 
 
 
 
 
 
 
 
Figure 3-13 Dielectric response vs. frequency for samples with different sample thickness 
(1.25 mm, 0.79 mm, 0.60 mm and 0.39 mm, respectively) after 96 hrs milling and then 
48 hrs sintering according to procedure #2 in Table 3-1. 
 
 
100 1k 10k 100k 1M
0
20
40
60
80
100
120
140
0
2
4
6
8
10
24 hrs
ta
n
?
Freq(Hz)
 
?
'
r 
(x1000)
 1.60 mm
 0.78 mm
 0.60 mm
 0.36 mm
 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
0
2
4
6
8
10
 
 
tan
?
?
'
r 
(x1000)
Freq(Hz)
 1.25 mm
 0.79 mm
 0.60 mm
 0.39 mm
48 hrs
 
92 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-14 Dielectric response vs. frequency for samples with different sample thickness 
(1.13 mm, 0.81 mm, 0.60 mm and 0.38 mm, respectively) after 96 hrs milling and then 
72 hrs sintering according to procedure #2 in Table 3-1. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-15 Illustration of edge, middle, core areas in CaCu
3
Ti
4
O
12
 ceramic pellet for 
SEM fractographs. 
 
 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
0
2
4
6
8
10
72 hrs
ta
n
?
Freq(Hz)
?
'
r 
(x1000)
 
 
 1.13 mm
 0.81 mm
 0.60 mm
 0.38 mm
 
Core 
Edge
Middle 
Middle 
Edge 
Top surface 
Bottom surface 
93 
 
 
 
 
 
 
 
Figure 3-16 SEM fractographs of CaCu
3
Ti
4
O
12
 after 96 hrs milling and then 24 hrs 
sintering according to procedure #2 in Table 3-1: (a) edge area, (b) middle area, (c) core 
area. 
 
(a) 
(b) 
(c) 
Edge 
Middle
Core 
Pore 
94 
 
 
 
 
 
 
 
Figure 3-17 SEM fractographs of CaCu
3
Ti
4
O
12
 after 96 hrs milling and then 48 hrs 
sintering according to procedure #2 in Table 3-1: (a) edge area, (b) middle area, (c) core 
area. 
 
(a) 
(b) 
(c) 
Edge 
Middle
Core 
95 
 
 
 
 
 
 
 
Figure 3-18 SEM fractographs of CaCu
3
Ti
4
O
12
 after 96 hrs milling and then 72 hrs 
sintering according to procedure #2 in Table 3-1: (a) edge area, (b) middle area, (c) core 
area. 
 
(a) 
(b) 
(c) 
Edge 
Middle
Core 
96 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-19  Cole-cole plot of the dielectric data of samples with different sample 
thickness (0.78 mm, 0.60 mm and 0.36 mm, respectively) after 96 hrs milling and then 24 
hrs sintering according to procedure #2 in Table 3-1. 
 
 
 
 
 
 
 
 
 
Figure 3-20 Cole-cole plot of the dielectric data of samples with different sample 
thickness (0.79 mm, 0.60 mm and 0.39 mm, respectively) after 96 hrs milling and then 48 
hrs sintering according to procedure #2 in Table 3-1. 
 
0 1020304050607080
5
10
15
20
25
30
0.318?s
0.230?s
0.215?s
?
"
r
 (x1000)
?'
r
 (x1000)
 0.78 mm
 0.60 mm
 0.36 mm
24 hrs
0 50 100 150 200 250 300 350
0
50
100
150
1.707?s
0.937?s
1.630?s
48 hrs
?
"
r
 (x1000)
?'
r
 (x1000)
 
 0.79 mm
 0.60 mm
 0.39 mm
97 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-21 Cole-cole plot of the dielectric data of samples with different sample 
thickness (0.81 mm, 0.60 mm and 0.38 mm, respectively) after 96 hrs milling and then 72 
hrs sintering according to procedure #2 in Table 3-1. 
 
 
 
 
 
 
 
 
 
Figure 3-22 The relationship of ?? (?
rs
-?
r?
) vs. sample thickness after 96 hrs milling and 
then 24, 48 and 72 hrs sintering according to procedure #2 in Table 3-1. 
 
 
0 50 100 150 200 250 300
0
20
40
60
80
100
1.667?s
0.959?s
1.01?s
72 hrs
?
"
r
 (x1000)
?'
r
 (x1000)
 
0.81 mm
0.60 mm
0.38 mm
0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
50
100
150
200
250
300
??
 (x1000)
 
Thickness (mm)
 Sintering 24 hrs
 Sintering 48 hrs
 Sintering 72 hrs
98 
 
3.3.2.4 Effect of CuO Doping on Dielectric Properties 
  In order to study the dielectric behavior in CaCu
3
Ti
4
O
12
, the effect of CuO doping 
was quantitatively evaluated in this study. CaCu
3
Ti
4
O
12
 with 5% and 10% CuO doping 
were prepared according to procedure #1 after 72 hours D.I water milling in Table 3-1.  
  Many efforts have been devoted recently to understand the role of CuO on the 
enhancement of dielectric constant. It was generally thought when large abnormal grains 
are developed, the dielectric constant become improved
8
. For polycrystalline sample, the 
main defects are at grain boundary, however in single crystal, they are the dislocation and 
the planar defects, which could be caused by cation disorder
9
. It has been reported that 
those defects would form internal barrier layer capacitor (IBLC) and they would lead to 
unusual dielectric properties. In recent work, the discontinuous grain growth has been 
found in the place where there is the Cu-deficiency. The important role of CuO has been 
reported 
2, 10
. Those  Cu ions are segregated at grain boundary and a second phase of CuO 
located at the triple-point site
8
. Experimental results show the formation of oxygen 
deficiency that happen in the grain is sufficient to establish conductivity within the 
grains
6
. With the CuO dopant, it enhances the oxygen deficiency and then improves the 
conductivity. It means that it is the high conductivity resulting in the high dielectric 
constant. Figure 3-23 shows the frequency spectra of dielectric constant and dielectric 
loss obtained on a representative sample as-sintered. It was found that the maximum 
dielectric constant was 15,900 at 1 kHz after 48 hours sintering with 5% CuO doping, 
while it increased to 28,200 at 1 kHz after 72 hours sintering with 10% CuO doping. At 
the same time, the dielectric loss remained as low as 0.06 to 0.13 at 1 kHz. It indicated 
that increasing of CuO doping altered the conductivity at the grain boundary and 
attributed the formation of IBLC under extended sintering time such as 72 hours, which 
would explain the improvement. This process is associated with the formation of a liquid 
CuO-TiO
2
 phase during the sintering process, where the densification of the ceramic can 
be improved by liquid phase
11
. In order to understand it, the EDS were carried out at two 
different sites: one was at grain and the other was at grain boundary. Figures 3-24 to 3-35 
show the SEM and EDS results with 5% and 10% CuO doping after sintering for 24, 48 
and 72 hours. Based on the EDS experiments, a strong Cu signal was detected along the 
grain boundaries, which reveals the segregations of Cu ions to the grain boundaries. 
99 
 
Especially for the 10% CuO, the signal of CuO increased from 50 to 69 wt%, which was 
correspondent to the enhancement of dielectric response. Combined with all the results, it 
was believed that CuO doping played an important role in attributing to the formation of 
the barrier layer capacitors.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-23 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
 after 72 hrs D.I water 
ball milling according to procedure #1 in table 3-1 with (a) 5 % CuO doping; (b) 10 % 
CuO doping 
 
 
 
100 1k 10k 100k 1M
0
5
10
15
20
0.0
0.2
0.4
0.6
0.8
1.0
 
 24 hrs
 48 hrs
 72 hrs
 
tan
?
Freq(Hz)
?
'
r 
(x1000)
(a)
 
 24 hrs
 48 hrs
 72 hrs
5% CuO
100 1k 10k 100k 1M
0
5
10
15
20
25
30
35
40
0.0
0.2
0.4
0.6
0.8
1.0
ta
n
?
 
?
'
r 
(x1000)
Freq(Hz)
 24 hrs
 48 hrs
 72 hrs
 
(b)10% CuO
 24 hrs
 48 hrs
 72 hrs
100 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-24 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 24 hrs at site #1. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 19.86 0.4900 41.89 0.73 70.35  
Ca K 6.02 1.1127 5.59 0.15 3.75  
Ti K 23.15 0.8922 26.82 0.41 15.04  
Cu K 21.21 0.8530 25.70 0.50 10.87  
      
Totals   100.00    
Site #1 
101 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-25 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 24 hrs at site #2. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 2.22 0.4425 16.09 1.84 39.75  
Ca K 1.85 1.1428 5.20 0.38 5.13  
Ti K 8.86 0.9402 30.30 1.07 25.00  
Cu K 13.75 0.9125 48.41 1.51 30.12  
      
Totals   100.00    
Site #2 
102 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-26 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 48 hrs at site #1. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 15.27 0.4936 39.34 0.81 68.32  
Ca K 4.69 1.1140 5.36 0.16 3.72
Ti K 18.70 0.8978 26.51 0.45 15.38  
Cu K 19.44 0.8597 28.79 0.57 12.59  
     
Totals   100.00    
Site #1 
103 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
Figure 3-27 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 48 hrs at site #2. 
 
 
 
Element App Intensity Weight% Weight% Atomic%  
  Conc. Corrn. Sigma  
O K 9.51 0.5116 34.55 0.99 64.19  
Ca K 2.93 1.1143 4.89 0.18 3.63
Ti K 12.29 0.9083 25.16 0.51 15.61  
Cu K 16.62 0.8730 35.40 0.74 16.56  
     
Totals   100.00    
Site #2 
104 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-28 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 72 hrs at site #1. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 12.47 0.4496 34.04 0.85 63.06  
Ca K 5.63 1.1258 6.13 0.17 4.53
Ti K 21.79 0.9039 29.58 0.48 18.30  
Cu K 21.38 0.8677 30.24 0.57 14.11  
     
Totals   100.00    
Site #1 
105 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-29 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 5% CuO 
dopant sintering for 72 hrs at site #2. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 0.59 0.5159 3.74 0.61 12.27  
Ca K 1.35 1.1397 3.87 0.21 5.07  
Ti K 6.94 0.9693 23.32 0.52 25.57  
Cu K 20.25 0.9550 69.07 0.72 57.09  
      
Totals   100.00    
Site #2 
106 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-30 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 24 hrs at site #1. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 25.24 0.4929 41.91 0.46 70.39  
Ca K 7.53 1.1122 5.54 0.09 3.72  
Ti K 29.04 0.8924 26.63 0.25 14.94  
Cu K 27.03 0.8532 25.92 0.31 10.96  
      
Totals   100.00    
Site #1 
107 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-31 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 24 hrs at site #2. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 2.05 0.4026 9.84 0.55 27.16  
Ca K 3.66 1.1572 6.11 0.14 6.73  
Ti K 16.71 0.9479 33.99 0.37 31.33  
Cu K 23.96 0.9231 50.06 0.47 34.78  
      
Totals   100.00    
Site #2 
108 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-32 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 48 hrs at site #1. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 17.75 0.4584 36.45 0.50 65.42  
Ca K 7.11 1.1225 5.97 0.10 4.27  
Ti K 27.70 0.9003 28.98 0.28 17.38  
Cu K 26.20 0.8630 28.60 0.34 12.93  
      
Totals   100.00    
Site #1 
109 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-33 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 48 hrs at site #2. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 1.01 0.4980 5.72 0.49 17.81  
Ca K 1.62 1.1413 3.99 0.13 4.97  
Ti K 8.61 0.9650 25.03 0.36 26.04  
Cu K 22.03 0.9476 65.26 0.51 51.19  
      
Totals   100.00    
Site #2 
110 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-34 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 72 hrs at site #1. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 9.29 0.4042 25.84 0.55 53.50  
Ca K 7.07 1.1422 6.96 0.12 5.75  
Ti K 27.34 0.9151 33.57 0.33 23.22  
Cu K 26.39 0.8819 33.63 0.38 17.53  
      
Totals   100.00    
Site #1 
111 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-35 SEM fractographs and EDS analysis results of CaCu
3
Ti
4
O
12
 with 10% CuO 
dopant sintering for 72 hrs at site #2. 
 
 
Element App Intensity Weight% Weight% Atomic%  
    Conc. Corrn.   Sigma    
O K 14.65 0.8022 18.56 0.38 46.21  
Ca K 2.34 1.0952 2.17 0.07 2.16  
Ti K 8.84 0.9506 9.45 0.14 7.86  
Cu K 64.09 0.9335 69.82 0.37 43.77  
      
Totals   100.00    
Site #2 
112 
 
3.3.2.5 Effect of the Annealing Time on Dielectric Properties 
  Ceramic samples prepared according to procedure #1 in Table 3-1 with sintering 
24 hours were treated with post-annealing such as vacuum or argon. Figure 3-36 (a), (b) 
and (c) show their dielectric spectrum of the CaCu
3
Ti
4
O
12
 subjected to post-annealing. As 
annealed in vacuum or argon at 1000 
o
C, an increase in dielectric constant at 1 kHz from 
1,210 to 62,900 in vacuum for 1 to 5 hours and 425,000 to 4,010,000 in argon for 1 to 24 
hours were observed as shown in Figure 3-36 (a) and (b). XRD results confirmed that 
there were no phase changes, and SEM images reveal no differences with its as-sintered 
ceramics, except a heavy oxidation layer on the sample surfaces in Figure 3-37. Wang 
and Zhang
12 
have reported that the dielectric peak can be eliminated by annealing in 
oxidizing (O
2
) atmosphere and created by annealing in reducing (N
2
) atmosphere. This 
demonstrated that the colossal dielectric constant was closely related with oxygen 
vacancies which enabled the grains of the CaCu
3
Ti
4
O
12
 ceramic to be more conductive. 
The increase in conductivity of the grains would lead to enhanced dielectric constant
5
. 
Later on, in the following annealing study, it exhibits the similar trend that the dielectric 
constant at 1 kHz increased with annealing time, which may be associated with oxygen 
vacancy accumulation. Moreover, it was interesting to observe that with longer annealing 
time, for example in argon as shown in Figure 3-36 (b), the dielectric constant at 1 kHz 
initially kept increasing to 4,010,000 and then slowly decreased to 425,000 while 
annealing up to 24 hours. Similarly, the trend was also observed as the annealing 
temperature varied from 800 to 1100 
o
C, and the optimized temperature was found at 
1020 
o
C, as shown in Figure 3-36 (c). Upon annealing, the grain boundaries reoxidized 
faster than the bulk of the grain, which enhanced the conductivity of the bulk of the 
grains. Thus, based on the results, it was believed that the dielectric response subjected to 
post-annealing was related to a dynamic oxidation/reduction process. 
 
 
 
 
 
 
113 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-36 Dielectric response vs. frequency for CaCu
3
Ti
4
O
12
 samples with initial 48 hrs 
milling according to procedure #1 in table 3-1: (a) post annealing in vacuum for different 
time at 1000 
o
C; (b) post annealing in flowing argon for different time at 1000 
o
C; (c) 
post annealing in flowing argon at different temperature for 1 hr. 
 
100 1k 10k 100k 1M
0
10
20
30
40
50
60
70
80
90
100
110
0
20
40
60
80
100
(a)
tan
?
 
?
'
r 
(x1000)
Freq(Hz)
 1 hr
 2 hrs
 3 hrs
 4 hrs
 5 hrs
Annealing in Vacuum        
 
100 1k 10k 100k 1M
0
1500
3000
4500
6000
7500
9000
10500
12000
0
10
20
30
40
50
60
ta
n
?
 
?
'
r 
(x1000)
Freq(Hz)
 1 hr
 2 hrs
 3 hrs
 4 hrs
 5 hrs
 6 hrs
 10 hrs
 24 hrs
 
(b)
Annealing in Argon
100 1k 10k 100k 1M
0
500
1000
1500
2000
2500
3000
3500
4000
0
10
20
30
40
50
60
 800
o
C/1 hr
 950
o
C/1 hr
 980
o
C/1 hr
 1000
o
C/1 hr
 1020
o
C/1 hr
 1050
o
C/1 hr
 1070
o
C/1 hr
 1100
o
C/1 hr
ta
n
?
 
?
'
r 
(x1000)
Freq(Hz)
 
(c)Annealing in Argon
114 
 
 
Figure 3-37 SEM fractographs of CaCu
3
Ti
4
O
12
 with post annealing in flowing argon at 
1000 
o
C for 10 hrs with magnification of : (a)-1 X150, (a)-2 X450, (a)-3 X450; for 24 hrs: 
(b)-1 X150, (b)-2 X450, (b)-3 X450. 
 
(a)-1 
(a)-2 
(a)-3 
(b)-1 
(b)-2 
(b)-3 
115 
 
3.3.2.6 Impedance Analysis 
  Corresponding to the results in Figure 3-5 and 3-9, the complex permittivity plots 
??
r
 vs. ???
r
 are shown in Figure 3-38 and 3-39. Debye equation was applied for dynamic 
polarization, which only behaved one relaxation time. For the polycrystalline 
CaCu
3
Ti
4
O
12
 ceramic, it required for multiple relaxation times, so Debye equations 
cannot be treated as an effective tool, and it can be fitted by Cole-Cole equations 
(Equation 3-2) to understand its mechanisms. 
  In the those figures, there are two obvious half circles, which demonstrate there 
are two mechanisms dominating the high permittivity in CaCu
3
Ti
4
O
12
. As known, the 
first circle in high frequency is due to the grain relaxation, and the second half circle is 
due to the grain boundary relaxation. The fitting data in Figure 3-38 and 3-39 fit well 
with the first half circle into the semicircular arc with the center underneath the abscissa. 
With the increasing ball milling time, such as 48 to 96 hours,  and calcining at 1075 
o
C, 
the ? decreased slowly from 0.055 to 0.028, while the relaxation time ? varied from 0.18 
to 0.45 ?s. As for calcining at 900
 o
C, the ? changed from 0.02 to 0.01, and the relaxation 
time ? increased from 0.3 to 0.7 ?s. It is interesting to note that the relaxation time 
increased with milling time and decreased with calcining temperature. The relaxation 
time tends to become longer, indicating it needs more time for dipole orientation. With 
increasing milling time and decreased calcining temperature, the energy barrier between 
the grain and grain boundary becomes smaller, which leads to more grain growth than 
usual. Comparing the results milling for 48, 72 hours, the complex permittivity plots ??
r
 
vs. ???
r
 for milling 96 hours become more complicated. It is found that besides the 
obvious two half circles, there is one more small circle between the two half circles, 
which demonstrates there exists the third mechanism (III), other than the grain relaxation 
(I) and grain boundary relaxation (II)
13
.  
 
 
 
 
 
 
116 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-38 Impedance plot of CaCu
3
Ti
4
O
12
 calcinating at 1075 ?C and then sintering at 
1075 ?C for 24, 48 and 72 hrs after (a) 48 hrs D.I water ball milling; (b) 72 hrs D.I water 
ball milling; (c) 96 hrs D.I water ball milling. 
 
0 102030405060708090100
0
10
20
30
40
50
60
70
 Sintering for 24 hrs
 Sintering for 48 hrs
 Sintering for 72 hrs
 Fitting for 24 hrs
 Fitting for 48 hrs
 Fitting for 72 hrs
III
 
 
?'
r
 (x1000)
?
"
r
 (x1000)
(c)
 
 
III
0 102030405060708090100
0
10
20
30
40
50
60
70
 Sintering for 24 hrs
 Sintering for 48 hrs
 Sintering for 72 hrs
 Fitting for 24 hrs
 Fitting for 48 hrs
 Fitting for 72 hrs
 
 
?
"
r
 (x1000)
?'
r
 (x1000)
(b)
 
 
0 1020304050
0
5
10
15
20
25
30
 
 
 
 Sintering for 24 hrs
 Sintering for 48 hrs
 Sintering for 72 hrs
 Fitting for 24 hrs
 Fitting for 48 hrs
 Fitting for 72 hrs
?
"
r
 (x1000)
(a)
?'
r
 (x1000)
117 
 
0 1020304050607080
0
10
20
30
40
50
60
 Sintering for 24 hrs
 Sintering for 48 hrs
 Sintering for 72 hrs
 Fitting for 24 hrs
 Fitting for 48 hrs
 Fitting for 72 hrs
 
 
?'
r
 (x1000)
?
"
r
 (
x1000)
(b)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3-39 Impedance plot of CaCu
3
Ti
4
O
12
 calcinating at 900 ?C and then sintering at 
1075 ?C for 24, 48 and 72 hrs after (a) 48 hrs D.I water ball milling; (b) 72 hrs D.I water 
ball milling; (c) 96 hrs D.I water ball milling. 
 
0 20 40 60 80 100 120 140 160 180
0
10
20
30
40
50
60
70
80
90
100
 Sintering for 24 hrs
 Sintering for 48 hrs
 Sintering for 72 hrs
 Fitting for 24 hrs
 Fitting for 48 hrs
 Fitting for 72 hrs
IIIIII
 
 
?
"
r
 (x1000)
?'
r
 (x1000)
(c)
 
 
0 102030405060
0
5
10
15
20
25
30
35
40
45
 Sintering for 24 hrs
 Sintering for 48 hrs
 Sintering for 72 hrs
 Fitting for 24 hrs
 Fitting for 48 hrs
 Fitting for 72 hrs
 
 
?
"
r
 (x1000)
?'
r
 (x1000)
(a)
 
118 
 
3.4 Summary 
  The influence of process parameters such as molding pressure, milling condition, 
milling media, calcination temperature and sintering time on the dielectric properties of 
the CaCu
3
Ti
4
O
12
 ceramic was studied. Ceramic samples with a dielectric constant of 
160,000 and loss of 0.15 at 1 kHz were obtained after calcination at 900 
o
C and sintering 
at 1075 
o
C for 72 hours, which is then adopted for the 0-3 composite study described in 
Chapter 4 and 5. The structure and morphology of the ceramics were studied using XRD 
and SEM. Their dielectric responses were studied over a frequency range from 100 to 1 
MHz.  It was found that the dielectric response of the ceramic is determined by three 
different processes. The pores structure observed in ceramic may be responsible for the 
observed high dielectric constant. When the ceramic disks were polished down to 
different thicknesses, it was found that although the dielectric response at low frequency 
is strongly dependent on the thickness, the high frequency relaxation process is weakly 
dependent on the thickness, and this thickness dependence cannot be explained using 
surface relaxation model. It was interesting to note that the relaxation time was increasing 
with decreasing thickness, which may be associated with the fact that the more dipoles, 
the longer relaxation time. 
 
 
 
 
 
 
 
 
 
 
 
 
 
119 
 
References 
(1) Arbatti, M. Development of High-Dielectric-Constant Polymer-Ceramic  
            Composites Based on Calcium Copper Titanate. Auburn University,  
            Alabama, 2004. 
(2) Subramanian, M. A.; Li, D.; Duan, N.; B. A. Reisner; Sleight, A. W. J  Solid State  
            Chem 2000, 151, 323-325. 
(3) Almeida, A. F. L.; Fechine, P. B. A.; Graca, M. P. F.; Valente, M. A.; Sombra, A.  
            S. B. J Mater Sci: Mater Electron 2008, 8, 9675. 
(4) Joint committee on Powder Diffraction Standard (JCPDS). In International Centre  
            for Diffraction Data, (JCPDS File 75-2188): 1979. 
(5) Raevskia, I. P.; Prosandeev, S. A.; Bogatin, A. S.; Malitskaya, M. A.; Jastrabik, L.  
            J.Appl. Phys 2003, 93, (7), 4130-4136. 
(6) Cohen, M. H.; Neaton, J. B.; Lixin He; Vanderbilt, D. J.Appl.Phys 2003, 94,  
            3299-3306. 
(7) Liu, J.; Duan, C.-G.; Yin, W.-G.; Mei, W. N.; Smith, R. W.; Hardy, J. R.  
            Phys.Rev.B 2004, 70, 144106. 
(8) Fang, T.-T.; Shiau, H.-K. J. Am. Ceram. Soc 2004, 87, (11), 2072-2079. 
(9) Wu, L.; Y. Zhu; S. Park; S. Shapiro; Shirane, G. Phys.Rev.B 2005, 71, 014118. 
(10) Capsoni, D.; Bini, M.; V.Massarotti; G.Chiodelli; M.C.Mozzatic; Azzoni, C. B. J   
            Solid State Chem 2004, 177, 4494-4500. 
(11) Marchin, L.; Guillemet-Fritsch, S.; Durand, B.; Levchenko, A. A.; Navrotsky, A.;  
            Lebey, T. J. Am. Ceram. Soc 2008, 91, 485 - 489. 
(12) Wang, C. C.; Zhang, L. W. Phys.Rev.B 2006, 74, 024106. 
(13) Cheng, Z. Y.; Bharti, V.; Xu, H. S.; Wang, S.; Zhang, Q. M. J.Appl. Phys 1999,  
            86, (4), 2208-2214. 
 
 
 
 
 
 
120 
 
 
 
 
 
CHAPTER 4 
 
PROCESS INFLUENCE ON THE DIELECTRIC PROPERTIES OF 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) COMPOSITES 
 
 
4.1 Introduction 
In this chapter, a 0-3 composite based on CaCu
3
Ti
4
O
12
 ceramic was studied
1, 2
. 
Processing influence on the dielectric properties in the CaCu
3
Ti
4
O
12
 /P(VDF-TrFE) 
composites was studied. To improve the uniformity of the composite, the processing 
effects, such as hot pressing pattern, number of pressing layers, and hot pressing time, 
were investigated. The dielectric constant exhibited a complicated law with 
CaCu
3
Ti
4
O
12
 powder concentration, number of layers and time. Based on SEM images, 
the experimental results can be better understood with different effective dielectric 
constant fitting models. Moreover, The effect of polymer matrix is compared between 
two different polymer matrices systems: P(VDF-TrFE) and P(VDF-CTFE) 88/12 
(VC88). Due to its relative high dielectric constant and less temperature dependence in 
CaCu
3
Ti
4
O
12
/VC88 composite, this composite is very suitable for future smart material 
application. 
4.2 Experimental 
  According to the procedure in Chapter 3, CaCu
3
Ti
4
O
12
 ceramic with high 
dielectric constant was successfully fabricated after 96 hours milling, calcining at 900 
o
C 
and then sintering at 1075 
o
C for 72 hours. These ceramics exhibited a high dielectric 
constant (?160,000) with weak temperature dependence below 1 MHz. The ceramic 
pellets were milled to particles with D
50
?10.5 ?m (particle size percentage). Due to 
P(VDF-TrFE) exhibiting high dielectric strength and relative high dielectric constant 
(?14 at RT), it was selected as the polymer matrix in this work. 
121 
 
  The CaCu
3
Ti
4
O
12
- P(VDF-TrFE) 0-3 composite was prepared by solution casting 
method at 70 
o
C/8 hours. In order to achieve high uniformity in 0-3 composite, hot 
pressing technique and annealing processing were adopted. The composite samples were 
hot pressed at a force of 7.5 tons and temperature of 200 
o
C. The final as-casted film 
consisted of two layers: polymer rich layer and ceramic rich layer. Then two different hot 
pressing patterns were studied
3
: 1) PC hot pressing: Polymer rich layer in one film 
stacking with the ceramic rich layer in another film; 2) CC hot pressing: Ceramic rich 
layer in one film stacking with the ceramic rich layer in another film. In order to study the 
polymer matrix effect, P(VDF-CTFE) 88/12 mol% (VC88) copolymer was selected as 
alternative polymer matrix in comparison to its counterpart P(VDF-TrFE) 55/45 mol%. 
  Dielectric properties: Gold was coated on the surface of the pellets as electrodes 
using a Pelco SC-6 sputter coater. Agilent 4294A impedance analyzer was employed to 
characterize the dielectric property of the samples. The measured frequency range was 
from 100 Hz to 1 MHz.  
  Microstructure analysis: The grain size and uniformity of the ceramic were 
determined by scanning electron microscope with EDS (SEM JSM-7000F, JEOL). 
4.3 Results and Discussion 
4.3.1 Dielectric Behavior and Annealing Effect 
 The annealing effect study was performed on CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites after they were casted at 70 
o
C for 8 hours. The annealing temperature was 
fixed at 125 
o
C and the CaCu
3
Ti
4
O
12
 volume concentration in 0-3 composites varied from 
10 to 50. The dielectric results from the pure P(VDF-TrFE) film are shown in Figure 4-1. 
As comparing with those one layer pure polymer films and as-casted composite samples, 
their annealing results are shown in Figure 4-2 to 4-6.  
  Figure 4-1 plots the dielectric responses versus the frequency after casting and 
annealing respectively. It is well known that the thermal annealing processing will result 
in a high crystallinity, which corresponds to higher dielectric response
4, 5, 6
. Figures 4-2 to 
4-6 plot the data between non-annealing samples and annealing samples with different 
CaCu
3
Ti
4
O
12
  concentrations, 10, 20, 30, 40, and 50 vol% respectively to present this 
general trend for the annealing effect. As we can observe from Figure 4-2 to 4-6, almost 
all the annealing samples possessed relative high dielectric constant in comparison with 
122 
 
un-annealed samples. More specifically: 18 to 25 for 10 vol% CaCu
3
Ti
4
O
12
 composite, 
23 to 34 for 20 vol% CaCu
3
Ti
4
O
12
 composite, 32 to 43 for 30 vol% CaCu
3
Ti
4
O
12
 
composite, 65 to 105 for 40 vol% CaCu
3
Ti
4
O
12
 composite, and 67 to 69 for 50 vol% 
CaCu
3
Ti
4
O
12
 composite. Those results are shown in Table 4-1 and Figure 4-7.  Based on 
the results in Figure 4-7, the dielectric constant of non-annealing increased from 18 to 67. 
While it is interesting to find that the dielectric constant of annealing sample exhibited 
similar trend at low CaCu
3
Ti
4
O
12
 concentration, it reached a maximum value of 105 at 40 
vol% and was followed by a decrease to 69 at 50 vol%. By assuming that the annealing 
process does not change the morphology of the composite, this behavior may stem from 
the fact that annealing can improve the crystallinity of the polymer and also the overall 
density of the composite by evaporating the remaining solvent. However, another 
possible explanation for the increase in dielectric constant may stem from the knowledge 
that the annealing process enhances the interlinking between ceramic and polymer matrix 
and caused the crystallinity improvement, which also consequently enhanced the 
interfacial layer effect.    
  The major relaxation process of the composites was analyzed and it was found 
that the dielectric results in Figure 4-1 to 4-7 can be fitted well using the Cole-Cole 
equation: 
   
?
??
??
??
?
?
?
+
?
+=
1
0
)(1
*
j
rrs
r
                                                               (4-1) 
Where 
rs
? is the static permittivity at low frequency limit, 
?r
? is the permittivity at high 
frequency limit, 
0
?  is the characteristic relaxation time, ? varies from 0<?<1.  The detail 
fitting results are shown in Figure 4-8. From the view of relaxation time, annealed 
samples tend to have longer relaxation time than their counterparts without annealing. As 
the concentration varied from 10 to 50 vol%, the relaxation time ? started from 0.159?s 
and then reached to a maximum value of 0.230?s at 40 vol% in non-annealed samples. 
Correspondingly, in the annealed sample, the maximum value changed to 0.373?s at 40 
vol% as shown in Figure 4-9.  As it is known that for one layer composite, the structure 
was not so uniform, which generally presented separating layers between ceramic and 
polymer. Thus, it indicated that for a heterogeneous structure with series layers separation, 
better dielectric response occurs while longer relaxation time dominates.  
123 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-1 Dielectric response vs. frequency of pure P(VDF-TrFE) film: (a) casting at  
70 
o
C/8 hrs; (b) casting at 70 
o
C/8 hrs and annealing at 125 
o
C/8 hrs. 
 
 
 
 
 
 
 
 
 
Figure 4-2 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (10 vol% CCTO) without annealing,  with annealing in comparison with 
P(VDF-TrFE). 
 
 
100 1k 10k 100k 1M
0
5
10
15
20
25
30
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
 
 
Freq(Hz)
ta
n
?
?
'
r
 Casting 70 
o
C
 Casting 70 
o
C and annealing 125 
o
C
P(VDF-TrFE)
 
100 1k 10k 100k 1M
0
5
10
15
20
25
30
35
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
 
Freq(Hz)
?
'
r
 P(VDF-TrFE)
 1 layer 
 1 layer annealing
10vol% 
ta
n
?
 
124 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-3 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (20 vol% CCTO) without annealing,  with annealing in comparison with 
P(VDF-TrFE). 
 
 
 
 
 
 
 
 
 
 
Figure 4-4 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (30 vol% CCTO) without annealing,  with annealing in comparison with 
P(VDF-TrFE). 
 
 
100 1k 10k 100k 1M
0
5
10
15
20
25
30
35
40
45
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Freq(Hz)
 
?
'
r
 P(VDF-TrFE)
 1 layer 
 1 layer annealing
20vol% 
tan
?
 
100 1k 10k 100k 1M
0
10
20
30
40
50
60
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
 P(VDF-TrFE)
 1 layer 
 1 layer annealing
 
Freq(Hz)
?
'
r
30vol% 
tan
?
 
125 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-5 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (40 vol% CaCu
3
Ti
4
O
12
) without annealing,  with annealing in comparison with 
P(VDF-TrFE). 
 
 
 
 
 
 
 
 
 
Figure 4-6 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% CaCu
3
Ti
4
O
12
) without annealing,  with annealing in comparison with 
P(VDF-TrFE). 
 
 
100 1k 10k 100k 1M
0
20
40
60
80
100
120
140
160
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
 P(VDF-TrFE)
 1 layer 
 1 layer annealing
 
 
Freq(Hz)
?
'
r
40vol% 
ta
n
?
 
100 1k 10k 100k 1M
0
20
40
60
80
100
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
 P(VDF-TrFE)
 1 layer 
 1 layer annealing
 
Freq(Hz)
?
'
r
50vol% 
tan
?
 
126 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-7 Dependence of dielectric response (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite at room temperature without annealing 
and with annealing respectively. 
 
 
Table 4-1 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(?-size CaCu
3
Ti
4
O
12
) (1 kHz). 
 
CaCu
3
Ti
4
O
12
 Concentration (vol%) 
10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
1 layer
[1]
 18/0.04 23/0.04 32/0.06 65/0.1 67/0.09 
1 layer annealing
[2]
 25/0.05 34/0.08 43/0.09 105/0.2 69/0.1 
[1]
: Casting at 70 
o
C/8 hrs. 
[2]
: Casting at 70 
o
C/8 hrs and annealing at 125 
o
C/8 hrs. 
 
 
 
 
 
 
 
 
10 20 30 40 50
0
25
50
75
100
125
0.0
0.2
0.4
0.6
0.8
 
 
 
 1 layer
 1 layer annealing
?
'
r
CaCu
3
Ti
4
O
12
 Volume (%) 
 
 
tan
?
127 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-8 Cole-cole plot of the dielectric data of (a) 1 layer and (b) 1 annealed layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 10 to 50 vol% CaCu
3
Ti
4
O
12
 powder at RT. 
 
 
 
 
 
 
 
0 10203040506070
0
2
4
6
8
10
12
14
0.191?s
0.230?s
0.159?s
0.159?s
0.159?s
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
?'
r
?"
r  
(a)
0 20 40 60 80 100
0
5
10
15
20
25
30
0.318?s
0.373?s
0.332?s
0.325?s
0.318?s
(b)
 
 
?"
r
?'
r
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
 
 
128 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-9 The relationship of relaxation time and   CaCu
3
Ti
4
O
12
 volume concentration 
between 1 layer and 1 annealed layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite samples 
with 10 to 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
10 20 30 40 50
0.0
0.1
0.2
0.3
0.4
0.5
0.6
CaCu
3
Ti
4
O
12
 Volume (%) 
 
 
 
Relaxation time 
?
 
(
?
s
)
 No annealing
 Annealing
129 
 
4.3.2 Hot Pressing Effect  
  The hot pressing processing (HP) was carried out with 7.5 tons force and a 
temperature at 200 
o
C for different times, such as 10s in this study. Figure 4-10 to 4-15 
show the dielectric results with hot pressing (HP), and the CaCu
3
Ti
4
O
12
 volume 
concentration in 0-3 composites varies from10 to 60. Table 4-2 summarizes all results 
regarding annealing and HP processing.  
  The dielectric properties of the composites were significantly influenced by HP 
process, as illustrated in Figure 4-10 to 4-15. It was found that no matter whether 
composites were annealed or not, the dielectric results generally exhibited an increasing 
trend after HP. When the CaCu
3
Ti
4
O
12
 volume concentration varied from 10 to 50, the 
dielectric constant revealed similar tendencies as those in the non-treatment sample; 
however, it exhibited even higher dielectric constant and experienced a maximum value 
of 78 at 40 vol%. While for the samples treated with annealing, the dielectric results were 
even promising with HP. A dielectric constant of 148 and dielectric loss of 0.2 at 1 kHz 
were achieved. That is, HP results in a higher dielectric constant, as summarized in Table 
4-2. Moreover, it was also interestingly noted that they tended to exhibit small dielectric 
loss at low frequency range with HP as for 10, 20 and 30 vol% composite. As stated 
before, the increasing of dielectric constant with annealing process is due to the 
crystallinity improvement, however this did not optimize their microstructure and the as-
casted composite still consisted of polymer-rich layer and ceramic-rich layer. With HP 
processing, it enables the diffusion of ceramic particle into polymer and leads to more 
uniform structure. Thus, an improved dielectric response originated from a more 
homogenous structure between ceramic particle and polymer matrix.  
  Their dielectric responses were further analyzed with Cole-Cole equation, as 
shown in Figure 4-16. Based on the results in Figure 4-18, the relaxation time ? first 
decreased from 0.332?s to 0.283?s, and then increased to 0.310?s. It is evident that the 
relaxation time ? experienced a minimum value of 0.283?s at 40 vol%, which 
corresponds to the maximum dielectric constant in Figure 4-16. HP process is prone to 
alter the morphology of composite, which tries to minimize the series polymer and 
ceramic separation and can result in a more homogenous structure. In this case, different 
130 
 
from those none-HP-treated results, as shown in Figure 4-8 to 4-9, improved dielectric 
response occurs while there is fast relaxation time in HP process.  
Figure 4-17 to 4-18 present a comparison between the model prediction and 
experimental data for the effective dielectric constant of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite after HP processing. Also shown are the predictions based on: logarithmic 
mixing (LM) law, modified logarithmic mixing (MLM) law, Maxwell-Wagner (MW) 
model, Yamada (YA) model, series model and Bruggeman (BM) model. Based on the 
previous experimental results in Figures 4-1, the values of 
polymercr?
'?  were predetermined 
as 20 and 14 respectively prior to the fitting, depending on whether the composite 
annealed or not. The summary of fitted dielectric data from prediction models is shown in 
Table 4-3. Based on the fitting results in Figure 4-17, 4-18 and Table 4-3, it was found 
that the LM, MLM, YA and BM models achieved better matches to experimental data 
than MW and series models from 0 to 50 vol%, even though MW model exhibited very 
good fitting results in low volume concentration range. This is believed to be related with 
the limitation of the model equation itself, because they are only good for composite with 
small effective dielectric constants; for example, 59 at 50 vol% for MW model and 39 at 
50 vol% for series model. These fitted experimental results in Table 4-3 also proven the 
annealing effect since all annealed results are larger than these without annealing.   
 
 
 
 
 
 
 
 
 
 
 
 
 
131 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-10 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 10 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing. 
 
 
 
 
100 1k 10k 100k 1M
0
5
10
15
20
25
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
 
tan
?
10vol% (a)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
 
100 1k 10k 100k 1M
0
5
10
15
20
25
30
35
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
 
10vol% Annealing 
tan
?
(b)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
 
132 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-11 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 20 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing. 
 
 
 
 
100 1k 10k 100k 1M
0
5
10
15
20
25
30
35
40
45
50
55
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
 
20vol% Annealing 
tan
?
(b)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
 
100 1k 10k 100k 1M
0
5
10
15
20
25
30
35
40
45
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
 
tan
?
20vol% (a)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
 
133 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-12 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 30 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing. 
 
 
 
 
100 1k 10k 100k 1M
0
5
10
15
20
25
30
35
40
45
50
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
 
ta
n
?
30vol% (a)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
 
100 1k 10k 100k 1M
0
5
10
15
20
25
30
35
40
45
50
55
60
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
 
30vol% Annealing 
ta
n
?
(b)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
 
134 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-13 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 40 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing. 
 
 
 
 
100 1k 10k 100k 1M
0
25
50
75
100
125
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
 
ta
n
?
40vol% (a)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
100 1k 10k 100k 1M
0
25
50
75
100
125
150
175
200
225
250
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
40vol% Annealing 
ta
n
?
(b)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
 
 
135 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-14 Dielectric response vs. frequency of  1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing. 
 
 
 
 
100 1k 10k 100k 1M
0
25
50
75
100
125
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
 
ta
n
?
50vol% (a)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
 
100 1k 10k 100k 1M
0
25
50
75
100
125
150
175
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 
50vol% Annealing 
tan
?
(b)
Freq(Hz)
?
'
r
 
 1 layer 
 1 layer HP
 
136 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-15 Dependence of dielectric constant (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
using 1 layers hot pressing (HP) at room temperature: (a) without annealing; (b) with 
annealing. 
 
 
 
10 20 30 40 50
0
20
40
60
80
100
120
140
160
CaCu
3
Ti
4
O
12
 Volume (%) 
 
 
 
?
'
r
 1 layer
 1 layer HP
(a)
10 20 30 40 50
0
20
40
60
80
100
120
140
160
180
CaCu
3
Ti
4
O
12
 Volume (%)  
 
(b)
 1 layer
 1 layer HP
?
'
r
 
 
Annealing
137 
 
 
 
 
 
 
Table 4-2 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(?-size CaCu
3
Ti
4
O
12
) with hot pressing (1 kHz). 
 
CaCu
3
Ti
4
O
12
 Concentration (vol%) 
10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
As casted 1 layer
[1]
 18/0.04 23/0.04 32/0.06 65/0.1 67/0.1 
Annealed 1 layer
[2]
 25/0.05 34/0.08 43/0.09 105/0.2 69/0.1 
1 layer HP
[3]
 17/0.04 35/0.05 37/0.05 78/0.1 73/0.1 
Annealed 1 layer HP
[4]
 26/0.05 40/0.07 47/0.07 148/0.2 110/0.2 
[1]
: Casting at 70 
o
C/8 hrs. 
[2]
: Casting at 70 
o
C/8 hrs and annealing at 125 
o
C/8 hrs. 
[3]
: Casting at 70 
o
C/8 hrs and hot pressing at 200 
o
C.  
[4]
: Casting at 70 
o
C/8 hrs, hot pressing at 200 
o
C and then annealing at 125 
o
C/8 hrs. 
HP: Hot pressing. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-16 Cole-cole plot of the dielectric data of 1 layer HP annealed 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 10 to 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
0 20 40 60 80 100 120 140 160
0
10
20
30
40
10 20 30 40 50
0.250
0.275
0.300
0.325
0.350
 
 
 CCTO Volume (%) 
Re
l
a
xat
io
n t
i
me 
? 
(
?
s
)
 1 layer HP annealing 
 
?'
r
?"
r
0.310?s
0.283?s
0.297?s
0.310?s
0.332?s
 
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
138 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-17  Comparison of the present model predictions with experimental data for 1 
HP layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-18 Comparison of the present model predictions with experimental data for 1 
layer HP annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. 
 
 
0 1020304050
0
25
50
75
100
CaCu
3
Ti
4
O
12
 Volume (%) 
 Experimental data
 Logarithmic mixing law
 Modified logarithmic mixing law
 Maxwell-Wagner model
 Yamada model
 Series model
 Bruggeman model
?
'
r
 
0 1020304050
0
25
50
75
100
125
150
175
200
CaCu
3
Ti
4
O
12
 Volume (%) 
 Experimental data
 Logarithmic mixing law
 Modified logarithmic mixing law
 Maxwell-Wagner model
 Yamada model
 Series model
 Bruggeman model
?
'
r
 
139 
 
 
 
 
 
 
 
 
Table 4-3 Summary of fitted dielectric data for CaCu
3
Ti
4
O
12 
in1 layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (?-size CaCu
3
Ti
4
O
12
) with hot pressing (1 kHz). 
[1]
: Casting at 70 
o
C/8 hrs and hot pressing at 200 
o
C.  
[2]
: Casting at 70 
o
C/8 hrs, hot pressing at 200 
o
C and then annealing at 125 
o
C/8 hrs. 
HP: Hot pressing. 
Modified logarithmic mixing law: k=0.5. 
Yamada model: N=25. 
 
 
 
 
 
 
 
 
 
 1 layer HP
[1]
 Annealed 1 layer HP
[2]
 
Logarithmic mixing law 502 580 
Modified logarithmic mixing law 17,980 18,000 
Maxwell-Wagner model ? ? 
Yamada  model 167 200 
Series  model ? ? 
Bruggeman  model 240 300 
140 
 
4.3.3 Multiple-Layer Configuration 
4.3.3.1 Dielectric Response using PC Hot Pressing  
  In order to further study its processing influence on the dielectric response, 
multilayer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) as-cast composites were used for hot pressing. 
Dielectric responses of these samples before and after annealing are shown in Figure 4-19 
to 4-23. Those multilayer composite samples were hot pressed using PC hot pressing 
method, as described in Chapter 2, and multilayer composites varied from two layers to 
six layers.  
  Figure 4-19 to 4-23 show the dielectric response of multilayer composite using 
PC hot pressing for 10s. The maximum dielectric constant increased from 34 to 179 at 1 
kHz at RT for none-annealing samples, and 34 to 234 at 1 kHz at RT for annealing 
samples, as the CaCu
3
Ti
4
O
12
 concentration increased. However, for each concentration, 
the maximum dielectric constant was obtained on the HP samples with different number 
of layers. For example, the maximum value for 10 vol% samples appeared in two layers 
HP, as well as four layers in 20 vol%, five layers in 30 vol%, three layers in 40 vol% and 
three layers in 50 vol% samples. In order to understand the changes in dielectric constant, 
the microstructure of the multiple layers composite was examined using SEM. These 
results for 50 vol% samples are shown in Figure 4-24. Compared to other multiple layers 
composite by PC hot pressing, only three layers display good ceramic distribution into 
polymer matrix, which tend to minimize the thin apparent interfacial layer between 
CaCu
3
Ti
4
O
12
 and P(VDF-TrFE), and corresponding dielectric constant can reach as high 
as 147 at 1 kHz. As seen in Figure 4-24, the dispersions of ceramic to polymer in the two 
layer, four layer, five layer and six layer composites are poor, and they exhibit more 
pores and apparent polymer aggregation which influences its dielectric performance. 
Confirmed by their dielectric results in Figures 4-19 to 4-23 and the morphologies in 
Figure 4-24, it is believed that the abrupt increase in the dielectric constant using PC hot 
pressing may originate from the improvement of the uniform structure.   
 
 
 
141 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-19 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10 vol% CaCu
3
Ti
4
O
12
 powder: (a) without annealing; (b) with annealing. 
 
 
 
100 1k 10k 100k 1M
10
15
20
25
30
35
40
45
(a) 10vol% 
 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
 
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
100 1k 10k 100k 1M
10
15
20
25
30
35
40
45
(b) 10vol% Annealing 
 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
 
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
142 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-20 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 20 vol% CaCu
3
Ti
4
O
12 
powder: (a) without annealing; (b) with annealing. 
 
 
 
100 1k 10k 100k 1M
10
15
20
25
30
35
40
45
50
55
60
(a) 20vol% 
 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
 
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
100 1k 10k 100k 1M
10
15
20
25
30
35
40
45
50
55
60
65
70
(b) 20vol% Annealing 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
 
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
143 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-21 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 30 vol% CaCu
3
Ti
4
O
12 
powder: (a) without annealing; (b) with annealing. 
 
 
 
 
100 1k 10k 100k 1M
10
20
30
40
50
60
70
80
90
100
(a) 30vol% 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
100 1k 10k 100k 1M
10
20
30
40
50
60
70
80
90
100
110
(b) 30vol% Annealing 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
144 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-22 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12 
powder: (a) without annealing; (b) with annealing. 
 
 
 
100 1k 10k 100k 1M
0
25
50
75
100
125
150
175
200
(a) 40vol% 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
400
(b) 40vol% Annealing 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
145 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-23 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12 
powder: (a) without annealing; (b) with annealing. 
 
 
 
100 1k 10k 100k 1M
0
25
50
75
100
125
150
175
200
225
250
275
(a) 50vol% 
 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
 
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
100 1k 10k 100k 1M
0
25
50
75
100
125
150
175
200
225
250
(b) 50vol% Annealing 
 
 
?
'
r
tan
?
100 1k 10k 100k 1M
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
 
  
 
 1 layer No HP
 1 layr HP
 2 layer HP
 3 layer HP
 4 layer HP
 5 layer HP
 6 layer HP
Freq(Hz)
146 
 
 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
  
  
 
 
 
Figure 4-24 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% 
CaCu
3
Ti
4
O
12
 powder using hot pressing for 10 seconds, (a) 1 layer without hot pressing, 
(b) 2 layer PC pressing,  (c) 3 layer PC pressing, (d) 4 layer PC pressing, (e) 5 layer PC 
pressing, (f) 6 layer PC pressing respectively. 
(a) (b) 
(c) 
(d) 
(e) (f) 
147 
 
4.3.3.2 Dielectric Response using CC Hot Pressing  
  Multilayer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites, such as two, four, and six 
layer, were prepared using CC hot pressing as described in Chapter 2. Figure 4-25 shows 
the dielectric responses of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with CC hot pressing 
for 10s. Table 4-4 summarizes their corresponding dielectric constant at 1 kHz.  
  Clearly, the dielectric constant is higher, for example, as the concentration 
increased from 10 to 50 vol%: the dielectric response steadily increased from 28 to 333 
and then decreased to 165 at 1 kHz, as shown in Figure 4-25 (a) and Table 4-4. However, 
as for more layers such as four and six layer, the dielectric constant exhibited less 
tendency of increasing. This phenomenon can be associated with their thickness: relative 
fast diffusions between ceramic particle and polymer matrix usually take place at samples 
with relative small thickness. Thus, in order to achieve enhancement in four and six 
layers composites, extended hot pressing time is necessary. Figure 4-26 to 4-27 plot the 
results of the composites after CC hot pressing for 20s and 30s, respectively. Tables 4-5 
to 4-6 summarize their corresponding dielectric constants and loss at 1 kHz. As the hot 
pressing time changed to 20s, both two layer and four layer composites displayed the 
similar trend that they experienced maximum value.  However, for six layer composites, 
there was no maximum peak, and they steadily increased to 328 at 50 vol% CaCu
3
Ti
4
O
12
. 
Those experimental results have confirmed the conclusion that a relatively longer hot 
pressing time is necessary for multiple layer composites in order to achieve optimization. 
As increasing to 30s, a dielectric constant of 510 and dielectric loss of 0.25 were realized 
at 50 vol% CaCu
3
Ti
4
O
12
 powder.  
  Besides the effect of multiple layers versus CaCu
3
Ti
4
O
12
 volume concentration, 
the influence of hot pressing time on the dielectric response has been observed. The 
dependence of dielectric constant on CaCu
3
Ti
4
O
12
 concentration under two, four and six 
layer CC hot pressing for different time is carefully studied in Figure 4-28 to 4-30.  
  The plot in Figure 4-28 elucidated that when the CaCu
3
Ti
4
O
12
 concentration 
ranged from 10 to 60 vol%, the dielectric constant presented an increasing relationship 
with ceramic volume concentration, except at 40 vol%, where a dielectric constant of 368 
was achieved. Furthermore, it was interestingly found that as pressing time increased 
from 20 to 30 seconds, a dielectric peak shifting from 40 vol% to a higher CaCu
3
Ti
4
O
12
 
148 
 
concentration (50 vol%) appeared in the spectrum with two layer CC hot pressing. This 
peak stabilized at 50 vol%, as can be found in Figure 4-29 and 4-30. It indicated that hot 
pressing is a dynamic process which can alter the relative concentration gradient between 
ceramic and polymer. Especially for six layers CC pressing for 10 to 30s, an abrupt 
increase in dielectric constant at 1 kHz from 239 to 510 appeared. It is believed that this 
is rooted in theinsulation-conduction transition.  
  Figure 4-31 to 4-33 elucidate the comparison between model prediction and 
experimental data for the effective constant of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite. 
The same models, such as logarithmic mixing (LM) law, modified logarithmic mixing 
(MLM) law, Maxwell-Wagner (MW) model, Yamada (YA) model, series model and 
Bruggeman (BM) model, were used for CC hot pressing model prediction. Similarly to 
the previous model fitting, the values of 
polymercr?
'? were predetermined as 20 and 14. The 
values of 
ceramicr?
'? have been calculated and listed in Table 4-7. According to Figure 4-31 
to 4-33, LM, MLM, and BM showed better fitting results in two layer composite samples, 
as well as in four layer and six layer samples. Furthermore, a maximum dielectric 
constant in each concentration, varying from 10 to 50 vol%, had been selected and was 
plotted in comparison with model fitting, as shown in Figure 4-34. Clearly, ML, MLM 
and BM models fitted very well at from 10 to 50 vol%, and especially, it was found that 
the BM model resulted in best match to experimental data. At the same time, it was 
known that the BM model was related to percolation, thus the fitting results indicated that 
high dielectric constant may originate from the percolation. In the overall fitting process, 
it was also noted that the MW and series models can only give close fitting results up to 
40 vol%. Based on fitted experimental results in Table 4-7, the fitted dielectric constant 
generally presented an increasing trend with number of HP layers, and inversely, they 
have corroborated the important role of HP on the dielectric constant improvement.  
  Figure 4-35 to 4-37 show the SEM images of 50 vol% CC hot pressed 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites. Compared with microstructures of PC HP 
samples, as shown in Figure 4-24, a more homogenous composite, without obvious 
polymer and ceramic segregation, and correspondingly, a higher dielectric constant were 
observed in CC HP. For instance with 10 second hot pressing, compared with 50 vol%, 
six layer PC hot pressed composite, the cross-section in 50 vol% six layer CC hot pressed 
149 
 
composite shows no signs of obvious segregation, and its dielectric constant increased 
from 147 to 182 in Figure 4-23 (b), and 4-25 (c). This is strongly corroborated by their 
SEM images as shown in Figure 4-24 (f) and 4-37 (a). In short, corroborated with the 
microstructure studies, their corresponding dielectric responses were relatively enhanced 
with CC hot pressing process, and this enhancement processing was even more 
experimentally controllable than its counterpart using PC hot pressing. However, based 
on the results, it was also found that the maximum dielectric constant was observed in 
samples with different number of layers, such as two layers in 10 vol% composite and six 
layers in 50 vol% composite with HP 10s, respectively. Moreover, the order of the 
number of layers corresponding to the maximum dielectric constant was changing as the 
HP time increasing from 10s to 30s, except for 50 vol%, where the maximum value was 
stabilized at six layers.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
150 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-25 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10~50 vol% CaCu
3
Ti
4
O
12 
powder: (a) 2 layer; (b) 4 layer; (c) 6 layer 
after 10s CC HP. 
 
100 1k 10k 100k 1M
0
100
200
300
400
500
(a) 2 layer HP 10s 
?
'
r
 
 
100 1k 10k 100k 1M
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Freq(Hz)
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
tan
?
 
  
100 1k 10k 100k 1M
0
25
50
75
100
125
150
(b) 4 layer HP 10s 
?
'
r
 
 
100 1k 10k 100k 1M
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Freq(Hz)
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
tan
?
 
  
100 1k 10k 100k 1M
0
50
100
150
200
250
300
(c) 6 layer HP 10s 
?
'
r
 
 
 
100 1k 10k 100k 1M
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Freq(Hz)
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
tan
?
 
 
 
 
151 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-26 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10~50 vol% CaCu
3
Ti
4
O
12 
powder: (a) 2 layer; (b) 4 layer; (c) 6 layer 
after 20s CC HP. 
 
100 1k 10k 100k 1M
0
100
200
300
400
500
(a) 2 layer HP 20s 
?
'
r
 
 
100 1k 10k 100k 1M
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Freq(Hz)
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
tan
?
 
  
100 1k 10k 100k 1M
0
100
200
300
400
500
(b) 4 layer HP 20s 
?
'
r
 
 
100 1k 10k 100k 1M
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Freq(Hz)
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
tan
?
 
  
100 1k 10k 100k 1M
0
100
200
300
400
500
600
(c) 6 layer HP 20s 
?
'
r
 
 
100 1k 10k 100k 1M
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Freq(Hz)
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
tan
?
 
  
152 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-27 Dielectric response vs. frequency of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10~50 vol% CaCu
3
Ti
4
O
12 
powder: (a) 2 layer; (b) 4 layer; (c) 6 layer 
after 30s CC HP. 
 
100 1k 10k 100k 1M
0
100
200
300
400
500
600
700
800
(a) 2 layer HP 30s 
?
'
r
 
 
100 1k 10k 100k 1M
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Freq(Hz)
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
tan
?
 
  
100 1k 10k 100k 1M
0
100
200
300
400
500
(b) 4 layer HP 30s 
?
'
r
 
 
100 1k 10k 100k 1M
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Freq(Hz)
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
tan
?
 
  
100 1k 10k 100k 1M
0
100
200
300
400
500
600
700
800
900
(c) 6 layer HP 30s 
?
'
r
 
100 1k 10k 100k 1M
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Freq(Hz)
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
tan
?
 
  
153 
 
 
 
 
 
 
Table 4-4  Summary of dielectric data for multiple layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 10s (1 kHz). 
 CaCu
3
Ti
4
O
12
 Concentration (vol%) 
 10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
2 layer 28/0.05 45/0.06 50/0.10 333/0.19 165/0.25 
4 layer 27/0.05 37/0.07 54/0.10 64/0.22 94/0.15 
6 layer 27/0.05 43/0.08 82/0.15 106/0.11 182/0.20 
 
Table 4-5 Summary of dielectric data for multiple layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 20s (1 kHz). 
 CaCu
3
Ti
4
O
12
 Concentration (vol%) 
 10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
2 layer 25/0.05 35/0.06 46/0.09 338/0.17 146/0.28 
4 layer 26/0.06 39/0.08 59/0.09 249/0.24 156/0.25 
6 layer 26/0.05 55/0.10 57/0.11 84/0.13 328/0.20 
 
Table 4-6 Summary of dielectric data for multiple layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 30s (1 kHz). 
 CaCu
3
Ti
4
O
12
 Concentration (vol%) 
 10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
2 layer 24/0.05 28/0.06 54/0.10 368/0.43 150/0.33 
4 layer 26/0.05 39/0.08 61/0.11 101/0.17 246/0.30 
6 layer 27/0.05 44/0.08 46/0.08 85/0.15 510/0.25 
 
 
 
 
154 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-28 Dependence of dielectric response (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
using 2 layer CC hot pressing (HP) for 10, 20, and 30s at room temperature. 
 
 
 
 
 
 
 
 
 
Figure 4-29 Dependence of dielectric response (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
using 4 layer CC hot pressing (HP) for 10, 20, and 30s at room temperature. 
 
 
10 20 30 40 50 60
0
50
100
150
200
250
300
350
400
?
'
r
 
 10s
 20s
 30s
2 layer
10 20 30 40 50 60
0.0
0.1
0.2
0.3
0.4
0.5
CaCu
3
Ti
4
O
12
 Volume (%) 
 
  
 10s
 20s
 30s
tan
?
10 20 30 40 50 60
0
50
100
150
200
250
300
 
 
 10s
 20s
 30s
10 20 30 40 50 60
0.0
0.1
0.2
0.3
0.4
0.5
CaCu
3
Ti
4
O
12
 Volume (%) 
tan
??
'
r
  
4 layer
 10s
 20s
 30s
155 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-30 Dependence of dielectric response (1 kHz) on the CaCu
3
Ti
4
O
12
 concentration 
using 4 layer CC hot pressing (HP) for 10, 20, and 30s at room temperature. 
 
 
 
 
 
 
 
10 20 30 40 50 60
0
100
200
300
400
500
600
6 layer
 10s
 20s
 30s
 
 
10 20 30 40 50 60
0.0
0.1
0.2
0.3
0.4
0.5
CaCu
3
Ti
4
O
12
 Volume (%) 
tan
?
 
 10s
 20s
 30s
?
'
r
 
 
156 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-31 Comparison of the present model predictions with experimental data for 2 
layer 30s CC-HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. 
 
 
 
 
 
 
 
 
 
 
Figure 4-32 Comparison of the present model predictions with experimental data for 4 
layer 30s CC-HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. 
 
 
0 1020304050
0
100
200
300
400
CaCu
3
Ti
4
O
12
 Volume (%) 
 Experimental data
 Logarithmic mixing law
 Modified logarithmic mixing law
 Maxwell-Wagner model
 Yamada model
 Series model
 Bruggeman model
?
'
r
 
 
0 1020304050
0
100
200
300
400
CaCu
3
Ti
4
O
12
 Volume (%) 
 Experimental data
 Logarithmic mixing law
 Modified logarithmic mixing law
 Maxwell-Wagner model
 Yamada model
 Series model
 Bruggeman model
?
'
r
 
157 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-33 Comparison of the present model predictions with experimental data for 6 
layer 30s CC-HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-34 Comparison of the present model predictions with highest experimental data 
for 10, 20, 30, 40 and 50 vol% CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample in this work. 
 
 
 
0 1020304050
0
100
200
300
400
500
600
CaCu
3
Ti
4
O
12
 Volume (%) 
 Experimental data
 Logarithmic mixing law
 Modified logarithmic mixing law
 Maxwell-Wagner model
 Yamada model
 Series model
 Bruggeman model
?
'
r
 
0 1020304050
0
100
200
300
400
500
600
CaCu
3
Ti
4
O
12
 Volume (%) 
 Experimental data
 Logarithmic mixing law
 Modified logarithmic mixing law
 Maxwell-Wagner model
 Yamada model
 Series model
 Bruggeman model
?
'
r
 
 
158 
 
 
 
 
 
 
 
 
 
Table 4-7 Summary of fitted dielectric data for CaCu
3
Ti
4
O
12 
multiple layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 
30s (1 kHz). 
Modified logarithmic mixing law: k=0.5. 
Yamada model: N=25. 
 
 
 
 
 
 
 
 
 
 2 layer 4 layer 6 layer Highest results 
Logarithmic mixing law 1,040 1,040 650 15,000 
Modified logarithmic mixing law 55,000 50,000 20,000 10,000,000 
Maxwell-Wagner model ? ? ? ? 
Yamada  model 290 230 200 9550 
Series  model ? ? ? ? 
Bruggeman model 450 460 300 2,020 
159 
 
 
 
 
 
 
 
Figure 4-35 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% 
CCTO powder using 2 layer CC hot pressing for: (a) 10s; (b) 20s; and (c) 30s 
respectively. 
(a) 
(b) 
(c) 
160 
 
 
 
 
 
 
 
 
Figure 4-36 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% 
CCTO powder using 4 layer CC hot pressing for: (a) 10s; (b) 20s; and (c) 30s 
respectively. 
(a) 
(b) 
(c) 
161 
 
 
 
 
 
 
 
Figure 4-37 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% 
CCTO powder using 6 layer CC hot pressing for: (a) 10s; (b) 20s; and (c) 30s 
respectively. 
(a) 
(b) 
(c) 
162 
 
4.3.3.3 Uniformity of 0-3 Composite under CC Hot Pressing  
  In the previous experiments, the studies between PC hot pressing and CC hot 
pressing technologies were carried out, and it is found that CC hot pressing is more prone 
to achieve a homogenous structure with less porosity, which results in high dielectric 
constant. In this work, the repeatability on the dielectric constant was studied. For each 
sample with the same composition and processing conditions, three individual samples 
were prepared and corresponding measurements were carried out. Their corresponding 
experimental results are shown in Figure 4-38 to 4-43 and Table 4-8 to 4-9. 40 vol% and 
50 vol% composites after four layer CC hot pressing for 10, 20, and 30s were chosen in 
this study.  
In Figure 4-38 to 4-40, the variation of dielectric constant was observed to change 
with hot pressing time. Except hot pressing for 10s, extended hot pressing exhibited 
considerably small standard deviation. For example, 40 vol% after hot pressing for 10s, 
the SD was: ?17 at 100 Hz, ? 24 at 1 kHz, ?26 at 10 kHz, ? 24 at 100 kHz and ? 21at 1 
MHz, respectively, However for 20s HP, it changed to: ? 39 at 100 Hz, 14 at 1 kHz,  5.1 
at 10 kHz, 3.5 kHz at 100 kHz and 2.3 Hz at 1 MHz respectively; and for 30s HP, ?14 at 
100 Hz, ?8.1 at 1 kHz, ?7.5 at 10 kHz, 5.6 at 100 kHz, and ?5.9 at 1 MHz, respectively. 
Moreover, the reliability results on 50 vol% composites exhibited similar trends, as 
illustrated in Figure 4-41 to 4-43. There is no large apparent variation as the hot pressing 
increased to 30s. As stated earlier, the interface between ceramic and polymer layers was 
presented in a uniform fashion. Based on the experimental results, we can draw a 
conclusion that longer HP time tends to result in a more uniform sample and small 
SD(Er?).  
 
.  
 
 
 
 
 
 
163 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-38 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 10s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). 
 
 
 
 
 
 
100 1k 10k 100k 1M
0
50
100
150
200
(a)40vol% CC HP10s
 ?
'
r
Freq(Hz)
100 1k 10k 100k 1M
0
50
100
150
200
0.0
0.5
1.0
1.5
2.0
 
?
'
r
Freq(Hz)
 Sample 1
 Sample 2
 Sample 3
40vol% CC HP10s
(a)
 
ta
n
?
164 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-39 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 20s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). 
 
 
 
 
 
 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
400
450
0.0
0.5
1.0
1.5
2.0
(a) 40vol% CC HP20s
?
'
r
Freq(Hz)
 Sample 1
 Sample 2
 Sample 3
 
tan
?
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
400
450
(b) 40vol% CC HP20s
?
'
r
Freq(Hz)
 
 
165 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-40 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 30s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). 
 
 
 
 
 
 
100 1k 10k 100k 1M
0
50
100
150
200
0.0
0.5
1.0
1.5
2.0
(a)40vol% CC HP30s
 Sample 1
 Sample 2
 Sample 3
 
?
'
r
Freq(Hz)
 
 
ta
n
?
100 1k 10k 100k 1M
0
50
100
150
200
(b)
 
40vol% CC HP30s
?
'
r
Freq(Hz)
 
166 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-41 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 10s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). 
 
 
 
 
 
 
100 1k 10k 100k 1M
0
50
100
150
200
0.0
0.2
0.4
0.6
0.8
1.0
 
?
'
r
Freq (Hz)
 Sample 1
 Sample 2
 Sample 3
(a)
 
 
50vol% CC HP10s
tan
?
100 1k 10k 100k 1M
0
50
100
150
200
(b)50vol% CC HP10s
?
'
r
Freq(Hz)
 
 
167 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-42 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 20s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). 
 
 
 
 
 
 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
(b) 50vol% CC HP20s
?
'
r
Freq(Hz)
 
 
100 1k 10k 100k 1M
50
100
150
200
250
300
0.0
0.5
1.0
1.5
2.0
(a)
 
50vol% CC HP20s
 
 
?
'
r
Freq (Hz)
 Sample 1
 Sample 2
 Sample 3
 
ta
n
?
168 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-43 Dielectric response vs. frequency of 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12 
powder using CC HP for 30s: (a) Reliability 
measurements; (b) Reliability results (Error bars indicate standard deviation). 
 
 
 
 
 
 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
400
450
(b)50vol% CC HP30s
?
'
r
Freq(Hz)
 
 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
400
450
0.0
0.5
1.0
1.5
2.0
(a)
 
50vol% CC HP30s
?
'
r
Freq(Hz)
 Sample 1
 Sample 2
 Sample 3
 
ta
n
?
169 
 
 
 
 
 
 
 
 
 
Table 4-8 Summary of reliability measurements of 4 layer CC HP CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite with 40 vol% ?-size CaCu
3
Ti
4
O
12
 powder (1 kHz). 
 Sample 
Dielectric property (?'
r
/Tan?) 
100 1k 10k 100k 1M 
HP 
10s 
#1 95/0.37 64/0.22 52/0.13 44/0.13 34/0.19 
#2 107/0.03 101/0.03 96/0.05 87/0.09 73/0.14 
#3 128/0.13 110/0.1 97/0.09 85/0.11 70/0.14 
AVE 110/0.18 92/0.12 82/0.09 72/0.11 59/0.16 
SD ? 17/0.17 24/0.10 26/0.04 24/0.02 21/0.02 
?'
r
 110(1?0.15) 92(1?0.26) 82(1?0.31) 72(1?0.33) 59(1?0.35) 
Tan? 0.18(1?0.94) 0.12(1?0.83) 0.09(1?0.44) 0.11(1?0.18) 0.16(1?0.13)
 
HP 
20s 
#1 370/0.37 249/0.24 193/0.16 158/0.16 115/0.25 
#2 366/0.40 250/0.24 190/0.16 155/0.15 119/0.19 
#3 300/0.28 226/0.19 183/0.14 151/0.15 115/0.21 
AVE 345/0.35 242/0.22 188/0.15 155/0.15 116/0.22 
SD ? 39/0.06 14/0.03 5/0.01 3/0.005 2/0.03 
?'
r
 345(1?0.11) 242(1?0.05) 188(1?0.03) 155(1?0.02) 116(1?0.18) 
Tan? 0.35(1?0.17) 0.22(1?0.14) 0.15(1?0.07) 0.15(1?0.03) 0.22(1?0.14)
 
HP 
30s 
#1 133/0.21 101/0.17 82/0.13 68/0.16 49/0.25 
#2 156/0.27 117/0.17 97/0.13 79/0.16 60/0.19 
#3 130/0.13 107/0.12 91/0.12 75/0.15 58/0.18 
AVE 140/0.20 108/0.15 90/0.13 74/0.16 56/0.20 
SD ? 14/0.07 8/0.03 7/0.005 6/0.006 6/0.04 
?'
r
 140(1?0.10) 108(1?0.07) 90(1?0.08) 74(1?0.08) 56(1?0.11) 
Tan? 0.20(1?0.35) 0.15(1?0.20) 0.13(1?0.04) 0.16(1?0.04) 0.20(1?0.2) 
 
 
 
 
 
 
 
 
 
 
170 
 
 
 
 
 
 
 
 
 
Table 4-9 Summary of reliability measurements of 4 layer CC HP CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder (1 kHz). 
 Sample 
?'
r
/Tan? 
100 1k 10k 100k 1M 
HP 
10s 
#1 117/0.16 94/0.15 77/0.13 63/0.17 45/0.25 
#2 164/0.30 122/0.20 97/0.14 81/0.14 63/0.18 
#3 155/0.18 125/0.15 105/0.12 88/0.13 69/0.17 
AVE 145/0.21 114/0.17 93/0.13 77/0.15 59/0.20 
SD ? 25/0.075 17/0.03 14/0.01 13/0.02 12/0.04 
?'
r
 145(1?0.17) 114(1?0.15) 93(1?0.15) 77(1?0.17) 59(1?0.20) 
Tan? 0.21(1?0.36) 0.17(1?0.18) 0.13(1?0.08) 0.15(1?0.13) 0.20(1?0.2) 
 
HP 
20s 
#1 236/0.35 156/0.25 120/0.16 98/0.17 71/0.21 
#2 240/0.20 178/0.17 144/0.14 120/0.14 95/0.17 
#3 174/0.22 138/0.17 113/0.13 93/0.15 71/0.19 
AVE 216/0.26 157/0.20 126/0.14 103/0.15 79/0.21 
SD ? 37/0.08 20/0.05 16/0.015 14/0.015 14/0.02 
?'
r
 216(1?0.17) 157(1?0.13) 126(1?0.13) 103(1?0.14) 79(1?0.18) 
Tan? 0.26(1?0.31) 0.20(1?0.25) 0.14(1?0.11) 0.15(1?0.10) 0.21(1?0.10)
 
HP 
30s 
#1 381/0.39 246/0.29 178/0.20 141/0.18 103/0.25 
#2 342/0.38 239/0.25 181/0.18 145/0.17 110/0.21 
#3 347/0.28 237/0.22 186/0.16 151/0.16 116/0.19 
AVE 358/0.35 240/0.26 182/0.18 146/0.17 110/0.21 
SD ? 25/0.06 5/0.04 4/0.02 5/0.01 7/0.03
?'
r
 358(1?0.07) 240(1?0.02) 182(1?0.02) 146(1?0.03) 110(1?0.06) 
Tan? 0.35(1?0.17) 0.26(1?0.15) 0.18(1?0.11) 0.17(1?0.06) 0.21(1?0.14)
?
 
 
 
 
171 
 
4.3.3.4 Temperature Dependent of Dielectric Response 
Figure 4-44 shows the temperature dependence of the dielectric constant and the 
loss factor for CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% CaCu
3
Ti
4
O
12
 
concentration, where two, four and six CC layer samples were hot pressed for 10, 20 and 
30s, respectively.  
It was seen that the temperature dependence of the dielectric constant is strongly 
affected by hot pressing, increasing from 10 to 30s, and multiple layers, increasing from 
two to six. Additionally, they all experienced a maximum value and then leveled off, as 
clearly illustrated in Figure 4-45, which suggests a relaxation process. For example, for 
those multiple layers hot pressing for 10s, their corresponding maximum values were: 
491, 381 and 514 for two, four and six layer, respectively. However, for HP 20s, those 
values were: 417, 467 and 859 for two, four and six layers respectively; and for HP 30s, 
the peak values increased to: 402, 648 and 1,240 for two, four and six layer respectively. 
The results obtained in the Figure 4-44 to 4-45 reflect the structure and dielectric 
behavior of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite were closely correlated with each 
other. As mentioned before, when the time is below its critical time such as 10s, those 
interfaces between ceramic and polymer layers still dominated, so the structure is 
relatively hard to control using CC HP. This explanation could be one possible reason 
why the dielectric constant is relatively small in comparison to extended time such as 20 
and 30s. There is no indication of any phase transition: the CaCu
3
Ti
4
O
12
 structure 
remains cubic and centric down to 35 K
7, 8
, and the CaCu
3
Ti
4
O
12
 is in marked contrast to 
known ferroelectrics, which exhibit a dipole moment in the absence of an electric field. 
Therefore, the apparent relaxation process, as shown in Figure 4-45 is closely related 
with the polymer matrix P(VDF-TrFE) which exhibited relaxation process
9
. More study 
on the temperature dependence of the dielectric constant will be studied.  
Moreover, it is known that complex permittivity is a complex function of both the 
frequency and the temperature, apart from the dependence of other parameters, such as 
pressure, etc. Based on those temperature dependent experiments, as shown in Figure 4-
44 to 4-45, the dielectric response vs. frequency, such as 
r
'?  vs. frequency, ?tan vs. 
frequency and 
r
"?  vs. frequency in CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% 
CaCu
3
Ti
4
O
12
 powder is listed in Figure 4-46 to 4-54. Those six layer composite samples 
172 
 
were hot pressed for 10, 20 and 30s, respectively, and the temperature range chosen in 
this study was between 25 to 85 
o
C, which was just before its observed curie temperature 
about 90 
o
C. As mentioned before, the temperature dependence results indicated that it 
may be related with a relaxation-like phenomenon, however there posed a question: did 
the high dielectric loss observed in the composite truly originate from relaxation, or in 
fact was it associated with conductivity?  More temperature dependence studies were 
carried out in order to understand this process. Results in Figure 4-46 to 4-54 indicated 
that no matter CC HP time in two, four and six layer composite, all the dielectric constant 
increased with temperature from 25 to 85 
o
C, while the dielectric loss tended to give the 
similar tendency from 25 to 75 
o
C and showed some variations at 80 and 85 
o
C for most 
of the samples. All the 
r
"?  results increased with temperature, which shared identical 
trend with the dielectric constant. Those behaviors in 
r
'? and 
r
"? are very similar to the 
typical relaxation phenomena, which shift to high frequency with increasing temperature. 
Moreover, those
r
"?  of six layer composites are further analyzed using Cole-Cole 
equation at low frequency (100 to 250 Hz), and long relaxation time (
0
?? >>1) as 
following: 
                  
)1(2
0
1
0
1
0
)(
2
sin)(21
2
cos)(
)()("
??
?
???
?
??
?
?
??
????
??
?
?
++
?=
rsrr
                  (4-2) 
Because 
0
?? >>1, thus Equation (4-2) becomes: 
                             
??
?
??
?
?
??
??
?
?
??
????
???
?
?
?=??
1
0
)1(2
0
1
0
)(
2
cos
)(
)(
2
cos)(
)()("
rsrrsrr
          (4-3) 
Then by taking the nature logarithm of both sides of the Equation (4-3), we can get: 
                              )ln()1(]
2
cos)ln[()]("ln[
0
????
?
???? ???=
?rsrr
 
                                 )ln()1()ln()1(]
2
cos)ln[(
0
?????
?
?? ?????=
?rsr
                (4-4) 
Equation (4-4) is equivalent to: 
   )ln()1()2ln()1()ln()1(]
2
cos)ln[()]("ln[
0
ff
rsrr
??????
?
??? ???????=
?
  (4-5) 
173 
 
Then Equation (4-5) is simplified as: 
                              )ln()]("ln[ fKAf
r
?=?                                                                  (4-6) 
where A is )2ln()1()ln()1(]
2
cos)ln[(
0
?????
?
?? ?????
?rsr
, and K is )1( ?? . The 
relationships between )"(
r
Ln ? and )( fLn for six layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite have been plotted in Figure 4-55 to 4-57.  Incorporated with 10, 20 and 30s 
CC HP, temperatures varying from 25 to 85 
o
C were selected in the study. The fitting 
results are shown in Table 4-10 to 4-12. As found in Figure 4-55 to 4-57, they presented a 
linear trend between )"(
r
Ln ? and )( fLn , whose slope was slightly increasing from 0.292 
to 0.389 for 10s CC HP, 0.408 to 0.443 for 20s CC HP and 0.438 to 0.512 for 30s CC HP, 
as temperature increased from 25 to 85 
o
C.   
If this behavior is related with conductivity, those
r
"? of six layers composites are 
written as below: 
                              
??
?
??
0
)(" =
r
                                                                                   (4-7) 
Then by taking the nature logarithm of both sides of the Equation (4-7), we can get: 
                  )ln(')]("ln[ fAf
r
?=?                                                                      (4-8) 
where 'A
 
is )2ln()ln(ln
0
??? ?? . Based on the equation (4-8), the slope should equal to 
1 for conductivity. However, comparing with the results in Figure 4-55 to 4-57, the real 
slope is much smaller than 1. All the results demonstrate that the high dielectric loss 
originates from relaxation process. 
            The relaxation time ? can be expressed by Arrhenius equation: 
                              )exp(
0
TK
E
B
a
?=??                                                                            (4-9) 
            Combined with Equation (4-4): 
                              
T
KAf
r
1
"")]("ln[ +=?                                                                    (4-10) 
Where "A is 
0
)1()2ln()1(]
2
cos)ln[( ?????
?
?? ?????
?
f
rsr
, "K is 
B
a
K
E
)1( ?? , E
a
 is the 
activation energy for the process, K
B
 is the Boltzmann constant and T is the temperature 
in K. The values of ? are selected from the Table 4-10 to 4-12, such as 0.31 for 10s, 0.43 
174 
 
for 20s and 0.47 for 30s. Figure 4-58 to 4-60 shows the plots for 6 layer composite. The 
summary of the results is listed in Table 4-13. The measurement result clearly shows that 
the temperature dependent process consisted of two temperature regions, which 
corresponded to two mechanisms. At low temperatures (25 to 45 
o
C), the calculated 
activation energy E
a
 increased from 0.06 to 0.21 eV at 100 Hz, while at high 
temperatures, the activation energy ranged from 0.29 to 0.38 eV at 100 Hz. Unlike the 
linear behavior of ? vs. 1/T, experimental results further confirmed that this temperature 
dependent process originated from the relaxation process.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
175 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-44 Temperature dependence of the 2, 4, 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder for: (a) 10s CC HP, (b) 20s CC HP, and 
(c) 30s CC HP, repectivley. 
30 40 50 60 70 80 90 100110120
0
100
200
300
400
500
600
700
800
900
1000
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 2 layer at 1kHz
 4 layer at 1kHz
 6 layer at 1kHz
tan
?
 
?
'
r
Temperature (? C)
(a)HP 10s
 
30 40 50 60 70 80 90 100110120
0
100
200
300
400
500
600
700
800
900
1000
0.0
0.2
0.4
0.6
0.8
1.0
1.2
HP 20s(b)
tan
?
 2 layer at 1kHz
 4 layer at 1kHz
 6 layer at 1kHz
 
?
'
r
Temperature (? C)
 
30 40 50 60 70 80 90 100110120
0
200
400
600
800
1000
1200
1400
1600
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
ta
n
?
 2 layer at 1kHz
 4 layer at 1kHz
 6 layer at 1kHz
?
'
r
Temperature (? C)
HP 30s
 
 
(c)
176 
 
 
 
 
Figure 4-45  Temperature dependence of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites 
with 50 vol% CaCu
3
Ti
4
O
12
 powder using: (a) 2 layer CC HP, (b) 4 layer CC HP, and (c) 
6 layer CC HP for 10, 20, and 30s, respectively. 
 
 
 
40 60 80 100 120
0
100
200
300
400
500
600
700
40 60 80 100 120 40 60 80 100 120
0
100
200
300
400
500
600
700
 
2 Layers
HP 10s
 
 
?
'
r
HP 20s
 100
 1K
 10K
 100K
 1M
 
Temperature (? C)
HP 30s
  
 
 
(a)
40 60 80 100 120
0
100
200
300
400
500
600
700
800
900
1000
40 60 80 100 120 40 60 80 100 120
0
100
200
300
400
500
600
700
800
900
1000
 
 
 
?
'
r
HP 10s
 
 100
 1K
 10K
 100K
 1M
HP 20s
(b)
 
4 Layers
 
 
Temperature (? C)
HP 30s
40 60 80 100 120
0
200
400
600
800
1000
1200
1400
1600
1800
40 60 80 100 120 40 60 80 100 120
0
200
400
600
800
1000
1200
1400
1600
1800
 
HP 10s
 
 ?
'
r
 
6 Layers
 
HP 20s
 100
 1K
 10K
 100K
 1M
(c)
 
 
Temperature (? C)
HP 30s
177 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-46 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 2 layer 10s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
100 1k 10k 100k 1M
0
100
200
300
400
500
600
(a)
?
'
r
 
 
Freq(Hz)
85 
o
C (5 
o
C interval) 
25 
o
C 
2 layer CC HP 10s
100 1k 10k 100k 1M
0.08
0.12
0.16
0.20
0.24
0.28
0.32
(b)
85 
o
C 
25 
o
C to 80 
o
C 
2 layer CC HP 10s
tan
?
Freq(Hz)
 
(5 
o
C interval) 
100 1k 10k 100k 1M
0
20
40
60
80
100
120
140
160
(c)
2 layer CC HP 10s
25 
o
C 
85 
o
C (5 
o
C interval) 
Freq(Hz)
 
?
"
r
178 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-47 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 2 layer 20s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
100 1k 10k 100k 1M
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
(b)
85 
o
C 
25 
o
C to 80 
o
C 
2 layer CC HP 20s
ta
n
?
Freq(Hz)
 
( 5 
o
C interval)  
100 1k 10k 100k 1M
0
20
40
60
80
100
120
140
160
(c)
85 
o
C ( 5 
o
C interval)  
25 
o
C 
2 layer CC HP 20s
?
"
r
Freq(Hz)
 
100 1k 10k 100k 1M
50
100
150
200
250
300
350
400
450
(a)
?
'
r
 
 
 
 
Freq(Hz)
85 
o
C ( 5 
o
C interval)  
25 
o
C 
2 layer CC HP 20s
179 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-48 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 2 layer 30s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
100 1k 10k 100k 1M
0
100
200
300
400
500
(a)
?
'
r
 
 
 
Freq(Hz)
85 
o
C (5 
o
C interval) 
25 
o
C 
2 layer CC HP 30s
100 1k 10k 100k 1M
0
25
50
75
100
125
150
175
200
(c)
2 layer CC HP 30s
Freq(Hz)
85 
o
C (5 
o
C interval) 
25 
o
C 
?
"
r
 
100 1k 10k 100k 1M
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
0.40
0.44
85 
o
C 
25 
o
C to 80 
o
C 
2 layer CC HP 30s
tan
?
Freq(Hz)
 
(5 
o
C interval) 
180 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-49 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 4 layer 10s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
100 1k 10k 100k 1M
50
75
100
125
150
175
200
225
250
(a)
?
'
r
 
 
 
Freq(Hz)
85 
o
C (5 
o
C interval) 
25 
o
C 
4 layer CC HP 10s
100 1k 10k 100k 1M
0.08
0.12
0.16
0.20
0.24
(b)
4 layer CC HP 10s
25 
o
C 
85 
o
C
ta
n
?
Freq(Hz)
 (5 
o
C interval) 
100 1k 10k 100k 1M
0
10
20
30
40
50
(c)
4 layer CC HP 10s
25 
o
C 
85 
o
C (5 
o
C interval) 
?
"
r
 
Freq(Hz)
 
181 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-50 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 4 layer 20s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
100 1k 10k 100k 1M
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
0.40
(b)
85 
o
C 
(5 
o
C interval) 
25 
o
C to 80 
o
C 
 
4 layer CC HP 20s
ta
n
?
Freq(Hz)
 
100 1k 10k 100k 1M
0
25
50
75
100
125
150
175
200
(c)
4 layer CC HP 20s
85 
o
C (5 
o
C interval) 
25 
o
C 
?
"
r
 
Freq(Hz)
 
100 1k 10k 100k 1M
50
100
150
200
250
300
350
400
450
500
(a)
?
'
r
 
 
 
 
Freq(Hz)
85 
o
C ( 5 
o
C interval)  
25 
o
C 
4 layer CC HP 20s
182 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-51 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 4 layer 30s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
100 1k 10k 100k 1M
100
200
300
400
500
600
700
(a)
?
'
r
 
 
 
Freq(Hz)
85 
o
C (5 
o
C interval) 
25 
o
C 
4 layer CC HP 30s
100 1k 10k 100k 1M
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
0.40
(b)
80 
o
C 
85 
o
C 
(5 
o
C interval) 
25 
o
C to 75 
o
C 
 
4 layer CC HP 30s
tan
?
Freq(Hz)
 
100 1k 10k 100k 1M
0
40
80
120
160
200
240
280
(c)
4 layer CC HP 30s
85 
o
C (5 
o
C interval) 
25 
o
C 
?
"
r
Freq(Hz)
 
183 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-52 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 6 layer 10s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
100 1k 10k 100k 1M
0
30
60
90
120
150
180
210
(c)
85 
o
C (5 
o
C interval) 
25 
o
C 
6 layer CC HP 10s
?
"
r
 
Freq(Hz)
 
100 1k 10k 100k 1M
0.08
0.12
0.16
0.20
0.24
0.28
0.32
(5 
o
C interval) 
ta
n
?
85 
o
C 
25 
o
C to 80 
o
C 
6 layer CC HP 10s
Freq(Hz)
100 1k 10k 100k 1M
100
200
300
400
500
600
700
(a)
  ?
'
r
Freq(Hz)
85 
o
C (5 
o
C interval) 
25 
o
C 
6 layer CC HP 10s
184 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-53 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 6 layer 20s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
(c)
6 layer CC HP 20s
85 
o
C (5 
o
C interval) 
25 
o
C 
  
 
Freq(Hz)
?
"
r
 
100 1k 10k 100k 1M
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
0.40
(b)
85 
o
C 
(5 
o
C interval) 
25 
o
C to 80 
o
C 
6 layer CC HP 20s
 
 
tan
?
 
Freq(Hz)
100 1k 10k 100k 1M
100
200
300
400
500
600
700
800
900
(a)
?
'
r
25 
o
C 
  
Freq(Hz)
85 
o
C (5 
o
C interval) 
6 layer CC HP 20s
185 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-54 Dielectric response vs. frequency: (a) 
r
'?  vs. frequency, (b) ?tan vs. 
frequency, (c) 
r
"?  vs. frequency of 6 layer 30s CC HP CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
100 1k 10k 100k 1M
0
150
300
450
600
750
(c)
6 layer CC HP 30s
85 
o
C (5 
o
C interval) 
25 
o
C 
?
"
r
Freq(Hz)
 
100 1k 10k 100k 1M
200
400
600
800
1000
1200
1400
1600
(a)
?
'
r
25 
o
C 
 
 
 
Freq(Hz)
85 
o
C (5 
o
C interval) 
6 layer CC HP 30s
100 1k 10k 100k 1M
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
0.40
0.44
0.48
0.52
(b)
85 
o
C 
(5 
o
C interval) 
25 
o
C to 80 
o
C 
6 layer CC HP 30s
 
 
tan
?
 
Freq(Hz)
186 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-55 The relationship of )"(
r
Ln ?  vs. )( fLn of 6 layer 10s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-56 The relationship of )"(
r
Ln ?  vs. )( fLn of 6 layer 20s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
4.6 4.8 5.0 5.2 5.4 5.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
25 
o
C 
85 
o
C (5 
o
C interval) 
6 layer CC HP 10s
Ln(f) 
Ln
(
?
"
r
)
 
 
 
4.6 4.8 5.0 5.2 5.4 5.6
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
25 
o
C 
85 
o
C (5 
o
C interval) 
6 layer CC HP 20s
Ln(f) 
Ln
(
?
"
r
)
 
 
 
187 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-57 The relationship of )"(
r
Ln ?  vs. )( fLn of 6 layer 30s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
Table 4-10 Summary of fitting results for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder after 10s CC HP. 
 
 
 
 
 A K ? SD? P 
25 
o
C 5.656 0.292 0.708 0.01108 <0.0001 
30 
o
C 5.611 0.285 0.715 0.00831 <0.0001 
35 
o
C 5.645 0.293 0.707 0.00405 <0.0001 
40 
o
C 5.729 0.303 0.697 0.00515 <0.0001 
45 
o
C 5.804 0.308 0.692 0.00482 <0.0001 
50 
o
C 5.740 0.283 0.717 0.00555 <0.0001 
55 
o
C 5.813 0.281 0.719 0.00572 <0.0001 
60 
o
C 6.048 0.310 0.690 0.00628 <0.0001 
65 
o
C 6.080 0.304 0.696 0.00343 <0.0001 
70 
o
C 6.222 0.316 0.684 0.00507 <0.0001 
75 
o
C 6.331 0.322 0.678 0.00417 <0.0001 
80 
o
C 6.518 0.339 0.661 0.00525 <0.0001 
85 
o
C 7.092 0.389 0.611 0.00447 <0.0001 
AVE 6.022 0.310 0.690 0.00564 <0.0001 
4.6 4.8 5.0 5.2 5.4 5.6
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
25 
o
C 
85 
o
C (5 
o
C interval) 
6 layer CC HP 30s
Ln(f) 
Ln
(
?
"
r
)
 
 
 
188 
 
 
 
 
 
Table 4-11 Summary of fitting results for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder after 20s CC HP. 
 A K ? SD? P 
25 
o
C 6.883 0.408 0.592 0.00446 <0.0001 
30 
o
C 6.914 0.413 0.587 0.00475 <0.0001 
35 
o
C 6.928 0.411 0.589 0.00480 <0.0001 
40 
o
C 6.984 0.413 0.587 0.00406 <0.0001 
45 
o
C 7.094 0.422 0.578 0.00565 <0.0001 
50 
o
C 7.141 0.417 0.583 0.00448 <0.0001 
55 
o
C 7.261 0.424 0.576 0.00500 <0.0001 
60 
o
C 7.395 0.431 0.569 0.00392 <0.0001 
65 
o
C 7.517 0.441 0.559 0.00385 <0.0001 
70 
o
C 7.591 0.441 0.559 0.00582 <0.0001 
75 
o
C 7.725 0.453 0.547 0.00342 <0.0001 
80 
o
C 7.799 0.455 0.545 0.00321 <0.0001 
85 
o
C 7.811 0.443 0.557 0.00290 <0.0001 
AVE 7.311 0.429 0.571 0.00433 <0.0001 
 
 
Table 4-12 Summary of fitting results for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder after 30s CC HP. 
 
 
 
 A K ? SD? P 
25 
o
C 7.604 0.438 0.562 0.00357 <0.0001 
30 
o
C 7.614 0.437 0.563 0.00339 <0.0001 
35 
o
C 7.753 0.437 0.563 0.00340 <0.0001 
40 
o
C 7.848 0.453 0.547 0.00442 <0.0001 
45 
o
C 7.959 0.460 0.540 0.00377 <0.0001 
50 
o
C 8.032 0.458 0.542 0.00356 <0.0001 
55 
o
C 8.241 0.472 0.528 0.00251 <0.0001 
60 
o
C 8.385 0.478 0.522 0.00304 <0.0001 
65 
o
C 8.499 0.486 0.514 0.00271 <0.0001 
70 
o
C 8.664 0.495 0.505 0.00230 <0.0001 
75 
o
C 8.762 0.503 0.497 0.00185 <0.0001 
80 
o
C 8.898 0.512 0.488 0.00245 <0.0001 
85 
o
C 8.985 0.512 0.488 0.00334 <0.0001 
AVE 8.249 0.472 0.527 0.00310 <0.0001 
189 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-58 The relationship of )"(
r
Ln ?  vs. temperature of 6 layer 10s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-59 The relationship of )"(
r
Ln ?  vs. temperature of 6 layer 20s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
2.70 2.85 3.00 3.15 3.30 3.45
3.6
4.0
4.4
4.8
5.2
5.6
H=0.06 eV
H=0.29 eV
Ln
(
?
"
r
)
 
1000/T (K
-1
)
6 layer HP 10s
 
 100 Hz
2.70 2.85 3.00 3.15 3.30 3.45
4.4
4.8
5.2
5.6
6.0
6.4
H=0.11 eV
H=0.28 eV
Ln
(
?
"
r
)
 
1000/T (K
-1
)
6 layer HP 20s
 
 100 Hz
190 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-60 The relationship of )"(
r
Ln ?  vs. temperature of 6 layer 30s CC HP 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
Table 4-13 Summary of activation energy for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder after 10s, 20s, and 30s CC HP. 
 
 
 
 
 
 
 
 Activation energy (eV)
 6 layer  HP 10s 6 layer HP 20s 6 layer HP 30s 
25 ~45 
o
C (at 100 Hz) 0.06 0.11 0.21 
45 ~85 
o
C (at 100 Hz) 0.29 0.28 0.38 
2.70 2.85 3.00 3.15 3.30 3.45
4.8
5.2
5.6
6.0
6.4
6.8
7.2
H=0.21 eV
H=0.38 eV
Ln
(
?
"
r
)
 
1000/T (K
-1
)
6 layer HP 30s
 
 100 Hz
191 
 
4.3.3.5 Impedance Analysis 
  The relationship between the dielectric constant and loss of the CC hot pressed 
composite samples has been already discussed under different processings, such as hot 
pressing pattern and hot pressing time. Correspondingly, their complex permittivity plots 
??
r
 vs. ???
r
 are shown in Figure 4-61 and 4-63. It is interesting to note besides the main 
relaxation process, a low frequency relaxation process is observed with up-right tail. This 
low-frequency process can be due to a heterogeneous relaxation process from the 
interface between the polymer matrix and CaCu
3
Ti
4
O
12
 particle.  The major relaxation 
process of the composites has been analyzed, and it was found that ??
r
 vs. ???
r
 plot can be 
well fitted using the Cole-Cole equation (4-1).  The detail fitting summary is listed in 
Table 4-14 to 4-19.  
  Figure 4-61 shows the permittivity results of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder, which were hot pressed for two, four and 
six layers, respectively, with constant time such as 10, 20s and 30s. As the hot pressing 
time was set at 10s, the relaxation time ? decreased from 0.310 to 0.205?s with 
increasing layers. When increasing from 20s and 30s, it exhibited a similar trend that 
relaxation time ? decreased from 0.325 to 0.159?s and from 0.650 to 0.159?s, 
respectively. Figure 4-62 illustrated the results of CC HP two, four and six layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% CaCu
3
Ti
4
O
12
 powder, which were 
hot pressed for different time such as 10s, 20s and 30s, respectively.  Corresponding to 10, 
20 and 30s hot pressing, the relaxation time ?  for two layer was 0.310, 0.325 and 
0.650?s respectively, and for four layer, it became 0.252, 0.179 and 0.504?s. In both two 
and four layer hot pressing, they behaved in an increasing trend. However, it was found 
that the relaxation time ?  for six layer was slightly decreasing from 0.20 to 0.16?s. As it 
is known that less relaxation time ?  means less polarization time, it could result in 
relative high dielectric constant at high frequency. Those fitting results indicated that 
multiple layers can uniformly distribute charge along the interface between ceramic and 
polymer layers and thus sample tends to give less polarization time. At the same time, it 
was found that only for six layers, hot pressing time can take effect.  In Table 4-14 to 4-
19, by considering the results in multiple layer HP samples at low CaCu
3
Ti
4
O
12
 volume 
concentration such as 10 to 30 vol%, it was noted that one layer annealed samples 
192 
 
exhibited longer relaxation time ? , which varied from 0.2 to 0.3?s. At higher 
CaCu
3
Ti
4
O
12
 volume concentration such as 40 and 50 vol%, less relaxation time ? can 
only take place with longer hot pressing time and extended multiple layers, which is very 
obviously for 50 vol%. In Figure 4-63, the relationship of the relaxation time vs. 
concentration for six layer HP 10s, 20s and 30s represented the similar trend that they 
have experienced a maximum value. This phenomenon is believed to be associated with a 
critical point which can reach structure optimization between ceramic and polymer 
matrix. All the results demonstrate that from the view of polarization time, hot pressing 
layer and its hot pressing time can arrange the charge distribution and then lead to fast 
response time and high dielectric constant at higher frequency.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
193 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-61 Cole-cole plot of the dielectric data of 2, 4 and 6 layer CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder and HP for (a) 10s, (b) 20s and (c) 
30s, respectively. 
0 50 100 150 200
0
10
20
30
40
50
?
"
r
 
0.205?s
0.252?s
0.310?s
50vol%
?'
r
 2 layer for 10s
 4 layer for 10s
 6 layer for 10s
 
 
(a)
0 50 100 150 200 250 300 350
0
25
50
75
?
"
r
 
?'
r
0.325?s
0.179?s
0.159?s
(b)
50vol%
 2 layer for 20s
 4 layer for 20s
 6 layer for 20s
 
0 100 200 300 400 500
0
25
50
75
100
?'
r
?
"
r
 
0.650?s
0.504?s
(c)
50vol%
 2 layer for 30s
 4 layer for 30s
 6 layer for 30s
 
0.159?s
194 
 
0 50 100 150 200
0
10
20
30
40
50
?
"
r
 
?'
r
0.650?s
0.325?s
0.310?s
 2 layer for 10s
 2 layer for 20s
 2 layer for 30s
50vol%
 
(a)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-62 Cole-cole plot of the dielectric data of (a) 2 layer, (b) 4 layer and (c) 6 layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50vol% CaCu
3
Ti
4
O
12
 powder and HP for 10s, 
20s and 30s, respectively. 
 
0 100 200 300 400 500
0
25
50
75
?
"
r
 
?'
r
0.159?s
0.159?s
0.205?s
(c)
50vol%
 6 layer for 10s
 6 layer for 20s
 6 layer for 30s
 
 
0 50 100 150 200 250
0
10
20
30
40
50
?'
r
?
"
r
 
0.504?s
0.179?s
0.252?s
(b)
 4 layer for 10s
 4 layer for 20s
 4 layer for 30s
50vol%
 
 
195 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-63 Cole-cole plot of the dielectric data of 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 10 to 50vol% CaCu
3
Ti
4
O
12
 powder and HP for (a) 10s, (b) 20s and (c) 
30s, respectively. 
 
0 100 200 300 400
0
10
20
30
40
50
?
"
r
 
?'
r
(a)
0.205?s
0.277?s
0.428?s
0.205?s
0.159?s
6 layer 10s
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
 
0 100 200 300 400
0
10
20
30
40
50
?
"
r
 
?'
r
(b)
0.159?s
0.283?s
0.264?s
0.163?s
0.159?s
6 layer 20s
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
 
0 100 200 300 400 500
0
25
50
75
100
?
"
r
 
?'
r
0.159?s
0.332?s
0.290?s
0.159?s
0.159?s
6 layer 30s
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
 
(c)
196 
 
 
 
 
 
Table 4-14 Fitting results for 1 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
with 10 to 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder. 
 
 
Table 4-15 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 10 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. 
 
 
 
 
 ?
rs
 ?
r?
 ?? (?
rs
-?
r?
) ? f (Hz) ? (?s) 
1 layer 10 vol% 26 5 31 0.54 501000 0.318 
1 layer 20 vol% 35 5 30 0.58 490000 0.325 
1 layer 30 vol% 45 5 40 0.61 479000 0.332 
1 layer 40 vol% 102 7 95 0.65 427000 0.373 
1 layer 50 vol% 68 5 63 0.63 501000 0.318 
 ?
rs
 ?
r?
 ?? (?
rs
-?
r?
) ? f (Hz) ? (?s) 
2 layer HP 10s 28 5 23 0.57 832000 0.193 
2 layer HP 20s 26 4 22 0.57 977000 0.163 
2 layer HP 30s 24 4 20 0.59 977000 0.163 
 
4 layer HP 10s 28 4 24 0.59 1000000 0.159 
4 layer HP 20s 27 4 23 0.59 1000000 0.159 
4 layer HP 30s 27 4 23 0.58 1000000 0.159 
 
6 layer HP 10s 27 4 23 0.57 1000000 0.159 
6 layer HP 20s 27 2 25 0.63 1000000 0.159 
6 layer HP 30s 28 4 26 0.59 1000000 0.159 
197 
 
 
 
Table 4-16 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 20 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. 
 
Table 4-17 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 30 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. 
 
 ?
rs
 ?
r?
 ?? (?
rs
-?
r?
) ? f (Hz) ? (?s) 
2 layer HP 10s 47 7 40 0.59 447000 0.356 
2 layer HP 20s 37 1 36 0.65 912000 0.175 
2 layer HP 30s 29 1 28 0.64 1000000 0.159 
 
4 layer HP 10s 38 3 35 0.63 1000000 0.159 
4 layer HP 20s 39 5 34 0.62 933000 0.171 
4 layer HP 30s 40 2 38 0.65 1000000 0.159 
 
6 layer HP 10s 44 5 39 0.62 776000 0.205 
6 layer HP 20s 56 4 52 0.65 977000 0.163 
6 layer HP 30s 45 4 41 0.63 1000000 0.159 
 ?
rs
 ?
r?
 ?? (?
rs
-?
r?
) ? f (Hz) ? (?s) 
2 layer HP 10s 50 8 42 0.62 513000 0.310 
2 layer HP 20s 47 5 42 0.63 575000 0.277 
2 layer HP 30s 54 6 48 0.64 575000 0.277 
 
4 layer HP 10s 54 8 46 0.60 427000 0.373 
4 layer HP 20s 60 6 54 0.632 724000 0.220 
4 layer HP 30s 61 6 55 0.639 741000 0.215 
 
6 layer HP 10s 80 12 68 0.613 372000 0.428 
6 layer HP 20s 58 6 52 0.636 603000 0.264 
6 layer HP 30s 49 2 47 0.65 537000 0.290 
198 
 
 
 
Table 4-18 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 40 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. 
 
Table 4-19 Fitting results for 2, 4 and 6 layer annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite with 50 vol% ?-size CaCu
3
Ti
4
O
12
 powder CC HP for 10, 20 and 30s. 
 
 ?
rs
 ?
r?
 ?? (?
rs
-?
r?
) ? f (Hz) ? (?s) 
2 layer HP 10s 320 20 300 0.66 1000000 0.159 
2 layer HP 20s 320 20 300 0.64 >1000000 0.159 
2 layer HP 30s 320 20 300 0.69 513000 0.310 
 
4 layer HP 10s 60 8 52 0.68 1000000 0.159 
4 layer HP 20s 230 8 222 0.675 832000 0.191 
4 layer HP 30s 102 1 101 0.69 794000 0.201 
 
6 layer HP 10s 108 13 95 0.619 575000 0.277 
6 layer HP 20s 81 14 67 0.602 562000 0.283 
6 layer HP 30s 79 16 63 0.58 479000 0.332 
 ?
rs
 ?
r?
 ?? (?
rs
-?
r?
) ? f (Hz) ? (?s) 
2 layer HP 10s 140 20 120 0.63 513000 0.310 
2 layer HP 20s 120 20 100 0.62 490000 0.325 
2 layer HP 30s 140 10 130 0.70 245000 0.650 
 
4 layer HP 10s 90 8 82 0.64 631000 0.252 
4 layer HP 20s 130 8 122 0.61 891000 0.179 
4 layer HP 30s 231 15 216 0.70 316000 0.504 
 
6 layer HP 10s 180 8 172 0.69 776000 0.205 
6 layer HP 20s 300 20 280 0.64 1000000 0.159 
6 layer HP 30s 450 30 420 0.64 1000000 0.159 
199 
 
4.3.4 P-E Hysteresis Loop 
  For dielectric materials, the polarization electric (P-E) hysteresis loop is a very 
useful material property since the loop is related to its energy storage ability. The 
polarization electric hysteresis loop can be expressed in terms of three parameters: 
coercive field (Ec), remnant polarization (Pr), and the saturated polarization l (Ps) under 
external electric field. The P-E hysteresis loops of pure P(VDF-TrFE) copolymer are 
given in Figure 4-64 for reference. The decrease of polarization level and coercive field 
in the irradiated copolymer may be due to the introduction of defects into the polymer 
chains using high-energy radiation. The P-E loops of one layer CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite with 10 to 50 vol% CaCu
3
Ti
4
O
12
 are shown in Figure 4-65 to 4-69, and 
those results for multiple layers, such as two, four and six layers after CC HP 10s, are 
shown in Figure 4-70 to 4-72.  
  In Figure 4-65 to 4-69, the CaCu
3
Ti
4
O
12
 concentration played an important role 
on the break-down electric field for CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite. With the 
increasing of ceramic concentration from 10 to 50 vol%, the break-down electric field 
generally decreased from 47 MV/m to 1.1 MV/m. Besides the CaCu
3
Ti
4
O
12
 concentration, 
it is clear that the remnant polarization (Pr) has been significantly influenced by the 
multiple layers, such as two to six layer. The remnant polarization (Pr) value of 0.04 
C/m
2
 decreased to 0.02 C/m
2
 and the break-down electric field increased from 1.1 to 5.5 
MV/m, as illustrated in Figure 4-69 and 4-70. In the four and six layer composites, as 
shown in Figure 4-71 and 4-72, the remnant polarization (Pr) exhibited the similar value 
of 0.04 C/cm
2
, while the break-down field decreased from 0.9 to 0.7 MV/m. Therefore, 
the significant effect of HP multiple layers on remnant polarization and break-down field 
was observed. A possible reason for this behavior may come from the polymer matrix, 
which contributes to the relaxor-ferroelectric behavior. Another possible reason, with 
high volume percentage of ceramic powder such as 50 vol%, the diminishing of the 
interface between polymer and ceramic can uniformly disperse the electric charge and 
avoid their accumulation on the interface to improve the break-down field. Thus, it is 
believed to be responsible for the decreasing of the remnant polarization (Pr) and 
improving of maximum electric field. Based on the polarization electric hysteresis, they 
have corroborated the statement that hot pressing layer plays an important role on the 
200 
 
dielectric response, which is consistent with the previous results such as annealing effect 
and hot pressing effect.  
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-64 Polarization electric hysteresis loop for pure P(VDF-TrFE). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-65 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
-450 -300 -150 0 150 300 450
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
E(MV/cm)
P
(
C/m
2
)
Pure P(VDF-TrFE)
 300 MV/cm
 325 MV/cm
 350 MV/cm
 
 
-75 -50 -25 0 25 50 75
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
E(MV/m)
P
(
C/m
2
)
10vol%-1 layer
 41 MV/m
 44 MV/m
 47 MV/m
 
201 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-66 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 20 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-67 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 30 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
-75 -50 -25 0 25 50 75
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
E(MV/m)
P
(
C/
m
2
)
20vol%-1 layer
 29 MV/m
 31 MV/m
 33 MV/m
 
-75 -50 -25 0 25 50 75
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
E(MV/m)
P
(
C/m
2
)
30vol%-1 layer
 27 MV/m
 28 MV/m
 29 MV/m
 
202 
 
-75 -50 -25 0 25 50 75
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
E(MV/m)
P
(
C/m
2
)
40vol%-1 layer
 2.0 MV/m
 2.1 MV/m
 2.2 MV/m
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-68 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-69 Polarization electric hysteresis loop for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-0.005
-0.004
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0.004
0.005
E(MV/m)
P
(
C/m
2
)
50vol%-1 layer
 0.9 MV/m
 1.0 MV/m
 1.1 MV/m
 
203 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-70  Polarization electric hysteresis loop for 2 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder using CC HP for 10s. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-71 Polarization electric hysteresis loop for 4 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder using CC HP for 10s. 
 
 
 
 
-8-6-4-202468
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
 4.5 MV/m
 5.0 MV/m
 5.5 Mv/m
2 layer HP 10s
P
(
C/m
2
)
E(MV/m)
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
 0.7 MV/m
 0.8 MV/m
 0.9 MV/m
4 layer HP 10s
 
P
(
C/m
2
)
E(MV/m)
204 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-72 Polarization electric hysteresis loop for 6 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder using CC HP for 10s 
 
 
 
 
 
 
 
 
 
 
 
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
 0.5 MV/m
 0.6 MV/m
 0.7 MV/m
6 layer HP 10s
 
P 
(
C/m
2
)
E (MV/cm)
205 
 
4.3.5 Polymer Matrix Effect on Dielectric Behavior 
  The dielectric properties of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite have already 
been discussed previously. It is known that its dielectric properties vary with different 
processing, such as annealing, hot pressing, etc. However, none of the experiments 
involved the study of the influence of polymer matrix. In this work, polymer matrix, such 
as P(VDF-CTFE) 88/12 mol% (VC88), was introduced and its influence of polymer 
matrix will be witnessed.  
 
4.3.5.1 Dielectric Behavior  
  As mentioned above, the dielectric properties of CaCu
3
Ti
4
O
12
/VC88 composite 
will be studied in this work. The annealing effect on CaCu
3
Ti
4
O
12
/VC88 composite was 
carried out with casting at 70 
o
C/8 hours and then annealing at 125 
o
C/8 hours. The 
volume concentration of CaCu
3
Ti
4
O
12
 varies from 10 to 50. The dielectric results of one 
layer as-casted composite samples are shown in Figure 4-73 to 4-77. The summary of 
dielectric constant at 1 kHz is shown in Table 4-20.  
  Based on the results in Figure 4-73 to 4-77, it presented an increasing trend from 
19 to 45 at 1 kHz for one layer as-casted sample. However, it was found that as for the 
as-annealed samples, there was a maximum peak of 35 at 30 vol%, which resemble the 
dielectric properties of one layer as-annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample, and is 
associated with crystallinity improvement. With careful observation, it was found that the 
overall dielectric property of an as-casted sample was generally better than as-annealed 
ones, as shown in Figure 4-78. It indicated that annealed treatment could only have 
limited effect on the CaCu
3
Ti
4
O
12
/VC88 composite.  
 
 
 
 
 
 
 
 
206 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-73 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(10 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-74 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(20 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. 
 
 
 
100 1k 10k 100k 1M
10
15
20
25
30
0.0
0.1
0.2
0.3
0.4
0.5
 1 Layer 
 1 Layer Annealing
tan
?
 
 
?
'
r
Freq(Hz)
 
10 vol% 
100 1k 10k 100k 1M
10
15
20
25
30
0.0
0.1
0.2
0.3
0.4
0.5
tan
?
 1 Layer 
 1 Layer Annealing
 
?
'
r
Freq(Hz)
20 vol% 
207 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-75 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(30 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-76 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(40 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. 
 
 
 
100 1k 10k 100k 1M
10
15
20
25
30
35
40
45
0.0
0.1
0.2
0.3
0.4
0.5
ta
n
?
 1 Layer 
 1 Layer Annealing
 
?
'
r
Freq(Hz)
30 vol% 
100 1k 10k 100k 1M
10
15
20
25
30
35
40
45
0.0
0.1
0.2
0.3
0.4
0.5
tan
?
 1 Layer 
 1 Layer Annealing
 
 
?
'
r
Freq(Hz)
40 vol% 
208 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-77 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) without annealing and with annealing. 
 
 
Table 4-20 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/VC88 composite (?-size 
CaCu
3
Ti
4
O
12
) (1 kHz). 
 CaCu
3
Ti
4
O
12
 Concentration (vol%) 
 10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
1 layer
[1]
 19/0.03 25/0.03 29/0.03 35/0.05 45/0.05 
 1 layer
[2]
 19/0.02 21/0.03 35/0.04 30/0.04 30/0.04 
[1]
: Casting at 70
o
C/8 hrs. 
[2]
: Casting at 70
o
C/8 hrs and annealing at 125 
o
C/8 hrs. 
 
 
 
 
 
 
100 1k 10k 100k 1M
10
15
20
25
30
35
40
45
50
55
0.0
0.1
0.2
0.3
0.4
0.5
tan
?
 1 Layer 
 1 Layer Annealing
 
 
?
'
r
Freq(Hz)
50 vol% 
209 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-78 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration (?-size 
CaCu
3
Ti
4
O
12
) for 1 layer CaCu
3
Ti
4
O
12
/VC88 composite at room temperature. 
 
 
 
 
 
 
 
 
 
 
 
10 20 30 40 50
10
20
30
40
50
0.0
0.2
0.4
0.6
0.8
CaCu
3
Ti
4
O
12
 Volume (%) 
?
'
r
 
 1 layer 
 1 layer Annealing
tan
?
210 
 
4.3.5.2 Hot Pressing Effect 
  Figure 4-79 to 4-83 illustrate the dielectric response of CaCu
3
Ti
4
O
12
/VC88 
composite with CC HP. Since it is well discussed in Chapter 4 that CC HP process is 
more promising than PC HP, more studies about CC HP will be discussed in this work. 
CaCu
3
Ti
4
O
12
/VC88 composite samples were hot pressed for two, four and six layers, and 
Table 4-21 lists their corresponding summary at 1 kHz.  
  Based on the those results in Figure 4-79 to 4-83, it shared the same trend in 
polymer matrix VC88 as well as in P(VDF-TrFE), when the volume concentration of 
CaCu
3
Ti
4
O
12
 was as low as 10 and 20. Their differences in dielectric constant within 
different HP layers are very small. The reason is very straightforward: the polymer matrix 
with a relatively large proportion already has enough capability to accommodate the 
ceramic particle, and it can neutralize the influence of multiple layer to the microstructure, 
which is closely associated with the dielectric response. At the same time, it is observed 
that when the volume concentration of CaCu
3
Ti
4
O
12
 exceeded 20, we find that the 
influence of multiple layers dominated, since there existed large portions of ceramic 
particle. For all the concentration from 30 to 50 vol%, maximum value happened with 
four layers CC HP. With CC HP, the best value is 151 for four layers CC HP, while the 
dielectric loss remained at 0.14, as shown in Figure 4-84. The dielectric results are very 
close with the results in CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite, as seen in Table 4-2.  
  Figure 4-85 shows the SEM image of one layer CaCu
3
Ti
4
O
12
/VC88 composite. 
According to the SEM image, its microstructure was very similar with the one in 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites. It consisted of one ceramic layer and one thin 
polymer layers. However, with the CC HP, this obvious interface between ceramic and 
polymer layer disappeared when they were hot pressed for 10s with two, four and six 
layers, as seen in Figure 4-85. In comparison with Figure 4-85 and 4-86, it has 
corroborated their corresponding dielectric results.  
 
 
 
 
 
211 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-79 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (10 vol% ?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C. 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-80 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (20 vol% ?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C. 
 
 
 
100 1k 10k 100k 1M
10
12
14
16
18
20
22
24
26
0.0
0.1
0.2
0.3
0.4
0.5
tan
?
10 vol% 
 
?
'
r
Freq(Hz)
 2 Layer HP
 4 Layer HP
 6 Layer HP 
 
100 1k 10k 100k 1M
10
15
20
25
30
35
40
45
0.0
0.1
0.2
0.3
0.4
0.5
20 vol%
 
 
?
'
r
Freq(Hz)
 2 Layer HP
 4 Layer HP
 6 Layer HP 
ta
n
?
 
212 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-81 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (30 vol%?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C. 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-82 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (40 vol% ?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C. 
 
 
 
100 1k 10k 100k 1M
20
30
40
50
60
70
80
90
100
0.0
0.1
0.2
0.3
0.4
0.5
30 vol% 
 
?
'
r
Freq(Hz)
 2 Layer HP
 4 Layer HP
 6 Layer HP 
 
tan
?
100 1k 10k 100k 1M
30
40
50
60
70
80
90
100
110
120
0.0
0.1
0.2
0.3
0.4
0.5
tan
?
40 vol% 
 
?
'
r
Freq(Hz)
 2 Layer HP
 4 Layer HP
 6 Layer HP 
 
213 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-83 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (50 vol% ?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s and annealing at 125 
o
C. 
 
 
Table 4-21 Summary of dielectric data for multiple layers CaCu
3
Ti
4
O
12
/VC88 composite  
in contrast to CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (?-size CaCu
3
Ti
4
O
12
) with CC hot 
pressing for 10s (1 kHz). 
 [1]
: CaCu
3
Ti
4
O
12
/VC88 composite (?-size CaCu
3
Ti
4
O
12
). 
[2]
: CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (?-size CaCu
3
Ti
4
O
12
). 
 
 
 CaCu
3
Ti
4
O
12
 Concentration (vol%) 
 10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
2 layer
[1]
 17/0.03 28/0.04 64/0.14 76/0.18 130/0.17 
4 layer
[1]
 22/0.03 30/0.04 74/0.14 86/0.13 151/0.14 
6 layer
[1]
 21/0.03 34/0.05 59/0.10 61/0.12 126/0.14 
    
2 layer
[2]
 28/0.05 45/0.06 50/0.1 333/0.19 165/0.25 
4 layer
[2]
 27/0.05 37/0.07 54/0.10 64/0.22 94/0.15 
6 layer
[2]
 27/0.05 43/0.08 82/0.15 106/0.11 182/0.20 
100 1k 10k 100k 1M
80
100
120
140
160
180
200
0.0
0.1
0.2
0.3
0.4
0.5
tan
?
50 vol% 
 
 
?
'
r
Freq(Hz)
 2 Layer HP
 4 Layer HP
 6 Layer HP 
 
214 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-84 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration for 
CaCu
3
Ti
4
O
12
/VC88 composite (?-size CaCu
3
Ti
4
O
12
) using 10s CC HP for 2, 4, and 6 
layer respectively at room temperature. 
 
 
Figure 4-85 SEM fractographs of 1 layer annealed CaCu
3
Ti
4
O
12
/VC88 composite (50 
vol % ?-size CaCu
3
Ti
4
O
12
). 
 
10 20 30 40 50
0
25
50
75
100
125
150
175
200
0.0
0.2
0.4
0.6
0.8
1.0
CaCu
3
Ti
4
O
12
 Volume (%) 
 
 
 
 ?
'
r
 2 Layer CC HP 10s
 4 Layer CC HP 10s
 6 Layer CC HP 10s
tan
?
 
215 
 
 
 
 
 
 
Figure 4-86 SEM fractographs of CaCu
3
Ti
4
O
12
/VC88 composites (50 vol% ?-size 
CaCu
3
Ti
4
O
12
)  using 10s CC HP for (a) 2 layer, (b) 4 layer and (c) 6 layers, respectively. 
 
(a) 
(b) 
(c) 
216 
 
4.3.5.3 Temperature Dependent of Dielectric Response 
  The temperature dependent studies on the CaCu
3
Ti
4
O
12
/VC88 composites have 
been performed and their corresponding results are shown in Figure 4-87 to 4-92. Among 
them, Figure 4-87 lists the temperature dependence of pure VC88. The volume 
concentration of CaCu
3
Ti
4
O
12
 varies from 10 to 50 vol% and multiple layers samples, 
such as two, four and six layer, were hot pressed for 10s.  
  In Figure 4-87, the temperature dependent of pure VC88 indicated that it posed 
less temperature influence and exhibited no relaxation-like peak. Moreover, according 
to the further experimental results in Figure 4-88 to 4-92, regardless of CaCu
3
Ti
4
O
12
 
concentration and multiple layers, it was found that they all share similar temperature 
dependent tendencies: the variation of dielectric constant shows less dependence with 
temperatures, except at low frequency such as 100 Hz. For example as temperatures 
increased from 25 to 125 
o
C at 1 kHz, dielectric constant varied from 127 to 111 for 50 
vol% two layer sample, 147 to 143 for 50 vol% four layer sample, and 126 to 143 for 50 
vol% six layer sample, which were summarized in Table 4-22. On the contrary, in 
comparison with the temperature dependent results in nano-size/micro-szie 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites, it was noticeable that they all experienced a 
maximum dielectric peak and then leveled off.  This phenomenon is in sharp contrast 
with the results in CaCu
3
Ti
4
O
12
/VC88 composites. Since it was well known that 
CaCu
3
Ti
4
O
12
 shows marked contrast to known ferroelectrics and exhibits none of 
relaxation process, the experimental results on the polymer matrix between P(VDF-
TrFE) and VC88 have strongly proved that the relaxation process in 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites originated from the polymer matrix  P(VDF-
TrFE), which is widely known as ferroelectric polymers. Due to their relative high 
dielectric constant and less temperature dependency, it make this composite very 
suitable for future smart material application. 
 
 
 
 
 
217 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-87 Temperature dependence of pure VC88. 
 
 
 
 
 
 
 
 
 
 
 
30 40 50 60 70 80 90 100110120
0
5
10
15
20
0.0
0.2
0.4
0.6
0.8
1.0
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
tan
?
Pure VC88 
218 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-88 Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (10 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. 
30 40 50 60 70 80 90 100110120
0
5
10
15
20
25
30
35
40
45
50
0
1
2
3
4
5
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
ta
n
?
10 vol% 2 layer 
(a)
30 40 50 60 70 80 90 100110120
0
5
10
15
20
25
30
35
40
45
50
0
1
2
3
4
5
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(b)
 
tan
?
10 vol% 4 layer 
30 40 50 60 70 80 90 100110120
0
5
10
15
20
25
30
35
40
45
50
0
1
2
3
4
5
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(c)
 
ta
n
?
10 vol% 6 layer 
219 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-89 Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (20 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. 
30 40 50 60 70 80 90 100110120
10
15
20
25
30
35
40
45
50
55
60
0
1
2
3
4
5
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(a)
 
ta
n
?
20 vol% 2 layer 
30 40 50 60 70 80 90 100110120
10
15
20
25
30
35
40
45
50
55
60
0
1
2
3
4
5
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(b)
 
tan
?
20 vol% 4 layer 
30 40 50 60 70 80 90 100110120
10
15
20
25
30
35
40
45
50
55
60
0
1
2
3
4
5
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
(c)
tan
?
20 vol% 6 layer 
220 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-90 Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (30 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. 
 
30 40 50 60 70 80 90 100110120
10
20
30
40
50
60
70
80
90
100
110
120
0
1
2
3
4
5
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(a)
 
tan
?
30 vol% 2 layer 
30 40 50 60 70 80 90 100110120
20
30
40
50
60
70
80
90
100
110
120
0
1
2
3
4
5
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(b)
 
tan
?
30 vol% 4 layer 
30 40 50 60 70 80 90 100110120
10
20
30
40
50
60
70
80
90
100
110
120
0
1
2
3
4
5
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(c)
 
ta
n
?
30 vol% 6 layer 
221 
 
30 40 50 60 70 80 90 100110120
0
100
200
300
400
500
0
1
2
3
4
5
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(b)
 
40 vol% 4 layer 
tan
?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-91Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (40 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. 
 
30 40 50 60 70 80 90 100110120
0
20
40
60
80
100
120
140
160
0
1
2
3
4
5
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(a)
 
tan
?
40 vol% 2 layer 
30 40 50 60 70 80 90 100110120
0
20
40
60
80
100
120
0
1
2
3
4
5
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
(c)
40 vol% 6 layer 
tan
?
222 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4-92 Temperature dependence of CaCu
3
Ti
4
O
12
/VC88 composite (50 vol% ?-size 
CaCu
3
Ti
4
O
12
) with: (a) 2 layer, (b) 4 layer, and (c) 6 layer 10s CC HP. 
 
30 40 50 60 70 80 90 100110120
0
50
100
150
200
250
300
0
1
2
3
4
5
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
(a)
50 vol% 2 layer 
tan
?
30 40 50 60 70 80 90 100110120
0
50
100
150
200
250
300
0
1
2
3
4
5
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
(b)
 
50 vol% 4 layer 
tan
?
30 40 50 60 70 80 90 100110120
0
50
100
150
200
250
300
0
1
2
3
4
5
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
(c)
50 vol% 6 layer 
tan
?
223 
 
 
 
 
 
Table 4-22 Summary of dielectric constant for multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite (?-size CaCu
3
Ti
4
O
12
) with CC HP for 10s at different temperature (1 kHz). 
 
Temperature (
o
C) 
25 50 75 100 125 
10vol% 
2 layer 19 19 19 19 20 
4 layer 25 25 24 25 27 
6 layer 23 23 23 23 24 
 
20vol% 
2 layer 29 29 29 28 28 
4 layer 32 32 31 31 31 
6 layer 32 34 34 32 33 
       
30vol% 
2 layer 61 60 57 55 57 
4 layer 71 70 65 63 63 
6 layer 54 54 52 51 51 
       
40vol% 
2 layer 71 71 64 60 59 
4 layer 83 81 77 80 115 
6 layer 60 59 55 52 51 
       
50vol% 
2 layer 127 125 114 109 111 
4 layer 147 145 135 133 143 
6 layer 126 122 114 117 143 
 
 
 
 
224 
 
4.4 Summary 
   0-3 composites based on micro-size CaCu
3
Ti
4
O
12
 were prepared and their 
dielectric, electric properties and the microstructures of the composites were studied.  
   For the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite, the composite was prepared using 
solution casting method and then was thermally and mechanically treated. The 
morphology of the ceramics was studied using SEM. Their dielectric responses were 
studied over a frequency range from 100 to 1 MHz. For the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite, the as-cast film was treated using annealing and HP in order to modify the 
distribution of the CaCu
3
Ti
4
O
12
 particles in polymer matrix and the morphology of semi-
crystal polymer matrix. The annealing process resulted in a higher dielectric constant due 
to the increase of crystallinity with polymer matrix. For the HP treatment, it was found 
that the configuration of the initial stack has a strong influence on the properties of the 
composites. In general, the HP process is prone to result in a high dielectric response in 
the composite at room temperature. For example, composite with a dielectric constant of 
510 and loss of 0.25 at 1 kHz was obtained at room temperature and when it reached 95 
o
C, a dielectric constant of 1,240 was obtained. The dielectric response of the composite 
was studied at different temperatures. Based on the results, it was found that the observed 
loss at low frequency in the composite is due to a relaxation process, and may be related 
to the interfacial layer between the CaCu
3
Ti
4
O
12
 particle and polymer matrix. The 
dielectric response was analyzed using Cole-Cole plot. It was found that the relaxation 
time of the major relaxation process obtained in the composite changes with processing 
condition, such as annealing, HP and concentration. It indicates that the interfacial layers 
between ceramic particles and polymer matrix play an important role on the dielectric 
response of the composite. As for the HP samples, it was interestingly observed that as 
HP time changes, there is a critical HP time at which the composite exhibits a much 
higher dielectric constant. The experimental results were analyzed using different 
prediction models. It was found that Logarithmic mixing law, Modified logarithmic 
mixing law, Yamada model and Bruggeman model can fit the experimental results, and 
especially, the BM model can result in best match to experimental results. All the fitting 
results demonstrated that the effective dielectric constant of CaCu
3
Ti
4
O
12
 actually is 
much smaller than the dielectric constant for CaCu
3
Ti
4
O
12
 ceramic. 
225 
 
   For CaCu
3
Ti
4
O
12
/P(VDF-CTFE) 88/12 mol% (VC88) composite, similar 
research was carried out. Composites with a dielectric constant of 151 and loss of 0.14 at 
1 kHz were obtained. Most importantly, it was found that the dielectric responses in the 
composites using P(VDF-CTFE) 88/12 mol% (VC88) as matrix are almost independent 
of temperature, which is good for dielectric applications. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
226 
 
References 
(1) Arbatti, M. Development of High-Dielectric-Constant Polymer-Ceramic  
            Composites Based on Calcium Copper Titanate. Auburn University,  
            Alabama, 2004. 
(2) Shan, X. B.; Yang, X.; Zhang, K. W.; Cheng, Z.-Y. Mater. Res. Soc. Symp. Proc.  
            2007, 949, 0949-C05-07. 
(3) Arbatti, M.; Shan, X. B.; Cheng, Z.-Y. Adv. Mater 2007, 19, 1369-1372. 
(4) Zhang, Q. M.; Xu, H.; Fang, F.; Cheng, Z.-Y.; Xia, F. J.Appl. Phys 2001, 89, (5),  
            2613-2616. 
(5) Kimura, K.; Ohigashi, H. J.Appl. Phys 1983, 43, (9), 834-836. 
(6) Choi, J.; Borca, C. N.; Dowben, P. A.; Bune, A.; Poulsen, M.; Pebley, S.;  
            Adenwalla, S.; Ducharme, S.; Robertson, L.; Fridkin, V. M.; Palto, S. P.;  
            Petukhova, N. N.; Yudin, S. G. Phys.Rev.B 2000, 61, (8), 5760-5770. 
(7) Subramanian, M. A.; Li, D.; Duan, N.; B. A. Reisner; Sleight, A. W. J  Solid State  
            Chem 2000, 151, 323-325. 
(8) Homes, C. C.; Vogt, T.; Shapiro, S. M.; Wakimoto, S.; Ramirez, A. P. Science  
            2001, 293, (27), 673-676. 
(9) Nalwa, H. S., Ferroelectric Polymers:chemistry, physics,and applications. Marcel  
            Dekker, Inc.: New York.Basel.Hong Kong, 1995. 
 
 
 
 
 
 
 
 
 
 
 
 
227 
 
 
 
 
 
CHAPTER 5 
 
STUDY OF DIELECTRIC BEHAVIOR ON THE CaCu
3
Ti
4
O
12
-BASED 
COMPOSITES 
 
 
5.1 Introduction 
 There has been a great deal of research work directed towards exploring the 
dielectric properties in CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites as discussed in Chapter 4. 
The study on CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites revealed that  process conditions 
such as annealing, hot pressing patter, number of hot pressing layers and hot pressing 
time as well as their morphology, posed a strong impact on the dielectric properties such 
as its dielectric constant and break-down electric field
1-3
. According to the experimental 
results, it was found that with better tuning of those processing parameters, it would give 
increased dielectric response.  
  In this chapter, based on a previous fundamental study on CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composites in Chapter 4, a more systematic study on CaCu
3
Ti
4
O
12
-based 
composites will be introduced. In order to optimize the dielectric response in 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites, effects such as the ceramic particle size, and 
silane coupling are going to be studied in detail. The size effect will be studied between 
two different particle size categories: micro-size and nano-size. Similarly, the effect of 
polymer matrix will be observed within two different polymer matrices systems: P(VDF-
TrFE) and P(VDF-CTFE). According to the initial purpose of improving the uniformity 
between the ceramic particle and polymer matrix, the silane coupling agent was 
incorporated and corresponding dielectric studies were carried out. Finally, it was 
observed that the optimum value of CaCu
3
Ti
4
O
12
 volume concentration or silane 
concentration was decisive on its dielectric performance
3, 4
.  
 
228 
 
5.2 Experimental 
  CaCu
3
Ti
4
O
12 
was prepared using a conventional powder processing method and 
the ceramic pellets were then milled to two different particles size categories: D
50
?10.5 
?m and 500 nm, respectively. The CaCu
3
Ti
4
O
12
- P(VDF-TrFE) 0-3 composite was 
prepared by solution casting method and hot pressing technique. The composite samples 
were pressed at a force of 7.5 tons and temperature of 200 
o
C. The loaded CCTO 
concentration varied within 0, 10, 20, 30, 40, and 50 vol%, respectively, and P(VDF-
CTFE) 88/12 mol% (VC88) copolymer was selected as alternative polymer matrix in 
comparison to its counterpart P(VDF-TrFE) 55/45 mol%, which was already discussed in 
Chapter 4. The silane coupling agent used in this work was Trichloro- 1 H, 1H, 2H, 2H-
Perfluorooctylsilane. The detailed experimental procedures were already described in 
Chapter 2.   
  Dielectric properties: Gold was coated on the surface of the pellets as electrodes 
using a Pelco SC-6 sputter coater. Agilent 4294A impedance analyzer was employed to 
characterize the dielectric property of the samples. The measured frequency range was 
from 100 Hz to 1 MHz. 
  Microstructure analysis: The grain size and uniformity of the ceramic were 
determined by scanning electron microscope with EDS (SEM JSM-7000F, JEOL). 
5.3 Results and Discussion 
5.3.1 Size Effect on Dielectric Behavior 
  In Chapter 4, the dielectric response of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
based on micro-size CaCu
3
Ti
4
O
12
 ceramic powder was discussed. It has been 
demonstrated in some research work that as a particle shrinks to nano-size range, its 
properties will be increasingly dominated by its interfacial interactions with its 
environment
5, 6
. The expected Maxwell-Wagner interfacial polarization associated with 
such composite materials is significantly changed as the particle size is reduced. 
Therefore, the study of the dielectric behavior on nano-size CaCu
3
Ti
4
O
12
 ceramic powder 
was designed and carried out, and then the size effect on dielectric behavior was observed.  
 
229 
 
5.3.1.1 Dielectric Behavior  
  In Chapter 4, the annealing effect on the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
was studied in detail and it was found that it had profound influence on the dielectric 
properties of the composite sample. Thus, regardless of un-annealed sample, this work 
only focused on annealed sample. CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites were prepared 
with different volume concentrations (0, 10, 20, 30, 40 and 50 vol% CaCu
3
Ti
4
O
12
), and 
then were followed by annealing at 125 
o
C for 8 hours.  
 Figure 5-1 illustrates the dielectric response of one layer annealed 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite. After comparing with pure P(VDF-TrFE), the 
dielectric constant of the as-annealed composite improved from 15.5 to 37.1 as the 
CaCu
3
Ti
4
O
12
 volume concentration increased from 10 to 50 vol%. All the experimental 
results indicated that it exhibited a linear relationship with CaCu
3
Ti
4
O
12
 volume 
concentration. The comparison between nano-size and micro-size CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite is listed in Table 5-1. This trend is very similar with the results based on 
the micro-size CaCu
3
Ti
4
O
12
 powder, when the CaCu
3
Ti
4
O
12
 volume concentration is 
below 30 vol% for both nano-size and micro-size ceramic particles, as shown in Figure 5-
2. However, as for micro-size CaCu
3
Ti
4
O
12
 powder, it reached a dielectric peak at 
40vol% and then leveled off, as seen in Chapter 4. More specifically: when switching 
from nano-size to micro-size CaCu
3
Ti
4
O
12
 powder, 14 to 25 for 10 vol% CaCu
3
Ti
4
O
12
 
composite, 23 to 34 for 20 vol% CaCu
3
Ti
4
O
12
 composite, 29 to 43 for 30 vol% 
CaCu
3
Ti
4
O
12
 composite, 33 to 105 for 40 vol% CaCu
3
Ti
4
O
12
 composite, 35 to 67 for 50 
vol% CaCu
3
Ti
4
O
12
 composite. A reasonable explanation may come from considering 
their corresponding microstructure in Figure 5-3. The cross-section of nano-size 
composite presented two apparent interfacial layers, however, in micro-size composite, 
due to its relative large particle size, it can accommodate more polymer matrix in 
between, and thus separation of polymer layer and ceramic layer becomes less obvious. 
The microstructure difference may account for their difference in dielectric properties.  
 
 
 
 
230 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-1  Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (10, 20, 30, 40, and 50 vol% nano-size CaCu
3
Ti
4
O
12
)  with annealing in 
comparison with P(VDF-TrFE): (a) Dielectric constant vs. frequency; (b) Dielectric loss 
vs. frequency.  
 
 
 
 
100 1k 10k 100k 1M
0
10
20
30
40
50
1 layer annealing 
 
?
'
r
Freq(Hz)
 0 vol%
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
(a)
100 1k 10k 100k 1M
0.00
0.05
0.10
0.15
0.20
0.25
0.30
1 layer annealing 
(b)
 0 vol%
 10 vol%
 20 vol%
 30 vol%
 40 vol%
 50 vol%
 
 
ta
n
?
Freq(Hz)
231 
 
 
 
 
 
 
Table 5-1  Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(nano-size /?-size CaCu
3
Ti
4
O
12
) annealed at 125 
o
C (1 kHz). 
 CaCu
3
Ti
4
O
12
 Concentration (vol%) 
 10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
Nano-1 layer
[1]
 14/0.05 23/0.05 29/0.05 33/0.05 35/0.05 
Micro-1 layer
[2]
 25/0.25 34/0.08 43/0.09 105/0.2 67/0.1 
[1]
:  Nano-size CaCu
3
Ti
4
O
12
. 
[2]
: ?-size CaCu
3
Ti
4
O
12
. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-2  Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration for 1 layer  
CaCu
3
Ti
4
O
12
/ P(VDF-TrFE) composite (nano-size /?-size CaCu
3
Ti
4
O
12
) at room 
temperature with annealing at 125 
o
C for 8 hrs.  
 
 
 
 
 
10 20 30 40 50
0
20
40
60
80
100
120
0.0
0.2
0.4
0.6
0.8
1.0
CaCu
3
Ti
4
O
12
 Volume (%) 
?
'
r
 
 1 layer Annealing (Nano-size) 
 1 layer Annealing (Micro-size)
tan
?
232 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-3 SEM fractographs of annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 
50 vol%: (a) nano-size; (b) ?-size CaCu
3
Ti
4
O
12
 ceramic powder. 
 
 
 
(a) 
(b) 
233 
 
5.3.1.2 Hot Pressing Effect 
  As known in Chapter 4, with hot pressing processing, a homogeneous structure 
can be achieved and its corresponding dielectric response could be enhanced. As for the 
nano-size composite, 10 to 50 vol% CaCu
3
Ti
4
O
12
 composites were prepared and then 
they were hot pressed using CC HP for 10s in this work. Their corresponding 
experimental results are shown in Figure 5-4 to 5-8 and the summary of their dielectric 
constant at 1 kHz is listed in Table 5-2.  
  In Figure 5-4 to 5-8 and Table 5-2, the variation of dielectric constant was 
observed to change with CaCu
3
Ti
4
O
12
 concentration. When the CaCu
3
Ti
4
O
12
 
concentration is small such as 10 vol%, the difference in dielectric constant between 
multiple layers CC HP is relatively small, which arises from the fact that there is large 
portion of polymer matrix, and the dispersion of ceramic into polymer matrix is not so 
significant as the one with higher CaCu
3
Ti
4
O
12
 concentration. With a higher volume 
concentration such as 20 and 30 vol%, it was clear that both experienced a maximum 
value of 28 and 48, respectively, at four layers. With volume concentration such as 40 
and 50 vol%, they exhibit an increasing trend up to 50 and 53, respectively, as the HP 
layer increases from two to six layer. Based on Figure 5-9, it was interesting to find that 
the dielectric peak first appeared at four layer for 20 and 30 vol% CaCu
3
Ti
4
O
12
 composite, 
while it switched to six layer for 40 and 50 vol% CaCu
3
Ti
4
O
12
 composite. At the same 
time, all the experimental results with different ceramic concentrations tended to give 
small dielectric constant loss around 0.05, which is very close to the results in 10 and 20 
vol% micro-size CaCu
3
Ti
4
O
12
 composites as shown in Chapter 4. However, comparing 
with the maximum dielectric constant achieved in micro-size composite, the maximum 
dielectric constant in nano-size composite is around 53, which was smaller than 
corresponding value of 182 in micro-size composite, as shown in Table 5-2. In order to 
study the CC hot pressing, their microstructures were studied using SEM. Figure 5-10 
shows the SEM images of 50 vol% CC hot pressed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites. Based on SEM images, a very clear ceramic-rich layer can be observed in the 
internal core area, which is marked in red. This clear interfacial layer should be 
responsible for the poor response in nano-size CaCu
3
Ti
4
O
12
 composite.  
 
234 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-4  Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (10 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C. 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-5 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (20 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C. 
 
 
 
100 1k 10k 100k 1M
10
12
14
16
18
20
22
24
26
0.0
0.2
0.4
0.6
0.8
1.0
tan
?
 2 layers
 4 layers
 6 layers
10% Annealing HP 10s
Freq(Hz)
?
'
r
 
 
 
100 1k 10k 100k 1M
10
15
20
25
30
35
0.0
0.2
0.4
0.6
0.8
1.0
tan
?
 2 layers
 4 layers
 6 layers
20% Annealing HP 10s
Freq(Hz)
?
'
r
 
 
 
 
235 
 
100 1k 10k 100k 1M
10
20
30
40
50
60
70
0.0
0.2
0.4
0.6
0.8
1.0
ta
n
?
 2 layers
 4 layers
 6 layers
40% Annealing HP 10s
Freq(Hz)
?
'
r
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-6  Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (30 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C. 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-7 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (40 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C. 
 
 
 
 
100 1k 10k 100k 1M
10
20
30
40
50
60
0.0
0.2
0.4
0.6
0.8
1.0
ta
n
?
 2 layers
 4 layers
 6 layers
30% Annealing HP 10s
Freq(Hz)
?
'
r
 
 
 
 
236 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-8 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (20 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 10s and annealing at 
125 
o
C. 
 
Table 5-2 Summary of dielectric data for multiple layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (nano-size/?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 10s (1 kHz). 
[1]
: Nano-size CaCu
3
Ti
4
O
12
. 
[2]
: ?-size CaCu
3
Ti
4
O
12
. 
 
 
 CaCu
3
Ti
4
O
12
 Concentration (vol%) 
 10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
2 layer
[1]
 20/0.04 26/0.05 35/0.05 40/0.05 37/0.05 
4 layer
[1]
 19/0.04 28/0.05 48/0.06 43/0.05 40/0.05 
6 layer
[1]
 21/0.04 25/0.05 41/0.05 50/0.05 53/0.05 
     
2 layer
[2]
 28/0.05 45/0.06 50/0.1 333/0.19 165/0.25 
4 layer
[2]
 27/0.05 37/0.07 54/0.10 64/0.22 94/0.15 
6 layer
[2]
 27/0.05 43/0.08 82/0.15 106/0.11 182/0.20 
100 1k 10k 100k 1M
10
20
30
40
50
60
70
0.0
0.2
0.4
0.6
0.8
1.0
tan
?
 2 layers
 4 layers
 6 layers
50% Annealing HP 10s
Freq(Hz)
?
'
r
 
 
 
 
237 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-9 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration (nano-size 
CaCu
3
Ti
4
O
12
) using 10s CC HP for 2, 4, and 6 layers respectively at room temperature. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
10 20 30 40 50
10
20
30
40
50
60
0.00
0.05
0.10
0.15
0.20
0.25
0.30
CaCu
3
Ti
4
O
12
 Volume (%) 
 
 
 
 
?
'
r
 2 Layer CC HP 10s
 4 Layer CC HP 10s
 6 Layer CC HP 10s
tan
?
 
238 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-10 SEM fractographs of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites  (50vol% nano-
size CaCu
3
Ti
4
O
12
) using 10s CC HP for (a) 2 layer, (b) 4 layer and (c) 6 layers, 
respectively. 
(a) 
(b) 
(c) 
239 
 
5.3.1.3 Hot Pressing Time on Dielectric Properties 
 The effect of hot pressing time on the dielectric properties in nano-size 
CaCu
3
Ti
4
O
12
 composite has been studied. In this work, 10 to 50 vol% CaCu
3
Ti
4
O
12
 
composites were prepared and then they were hot pressed using CC HP for 30s. 
Correspondingly, their experimental results are shown in Figure 5-11 to 5- 15. Table 5-3 
summarizes the dielectric constant at 1 kHz for two, four and six layer CC HP composite 
samples.  
  After comparing the dielectric results with 10s CC HP, the dielectric constant 
shared the same trend as that at low concentrations, such as 10 and 20vol% CaCu
3
Ti
4
O
12
. 
The dielectric results were very similar within two, four and six layer, while for 30 to 50 
vol%, four layer CC HP dominated significantly, which results in a high dielectric 
constant, as shown in Figure 5-16. Both the experimental results exhibited low dielectric 
constants, which is associated with their corresponding microstructure and was already 
demonstrated using SEM images in 10s CC HP. The dielectric results are relatively 
smaller than the one in micro-size CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites, especially at 
40 and 50 vol% in Table 5-3.  
  Based on results in Figure 5-16, Figure 5-17 to 5-19 presented a comparison 
between the model prediction and experimental data for the effective dielectric constant 
of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite after CC HP processing. Together shown were 
the predictions based on logarithmic mixing (LM) law, modified logarithmic mixing 
(MLM) law, Maxwell-Wagner (MW) model, Yamada (YA) model, series model and 
Bruggeman (BM) model. The determination procedures of the 
polymercr?
'? and 
ceramicr?
'?  
have been well described in Chapter 4. The values of 
polymercr?
'? were predetermined as 20 
and 14 for annealing and non-annealing samples respectively. These calculated values of 
ceramicr?
'? have been listed in Table 5-4. Unlike the model prediction for micro-size 
multiple layers composite, most models including LM, MLM, MW, YA and BM, gave 
desired fitting results. Moreover, among these models, LM, MLM, YA and BM models 
showed best match to experimental data. The series model can only have good fitted 
results in low volume concentrations from 0 to 10 vol%. Especially, comparing with the 
CC HP fitted results in Chapter 4 and Table 5-4, it was found that their dielectric constant 
240 
 
tended to decrease dramatically as the CaCu
3
Ti
4
O
12
 size changed from micro-size to 
nano-size. The dramatic change indicated that the size of CaCu
3
Ti
4
O
12
 particle may play 
an important role in its corresponding dielectric response.  
  Moreover, much more detailed experiments about hot pressing time on the 
composite were carried out on 50 vol% nano-size CaCu
3
Ti
4
O
12
 composite. Different hot 
pressing times, such as 10, 20, 30 and 40s were selected in the experiments. As shown in 
Figure 5-20 and Table 5-5, with increasing vol% of CaCu
3
Ti
4
O
12
, the dielectric constant 
increased from 35 to 51 and then decreased to 43 for two layer CC HP. Meanwhile, it 
was found that for both four and six layer CC HP, the dielectric constant reached a 
maximum value and then degraded, as shown in Figure 5-21. The results indicated that 
by incorporating with the hot pressing process, the so-called interfacial layer is a dynamic 
process, and excessive hot time would undermine the established uniformed structure. In 
the experiments, the optimum time to achieve the best dielectric constant was found at 
30s CC HP.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
241 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-11 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (10 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C. 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-12 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (20 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C. 
 
 
 
100 1k 10k 100k 1M
10
12
14
16
18
20
22
24
26
28
30
0.0
0.2
0.4
0.6
0.8
1.0
tan
?
 2 layers
 4 layers
 6 layers
10% Annealing HP 30s
Freq(Hz)
?
'
r
 
 
 
 
100 1k 10k 100k 1M
10
15
20
25
30
35
40
45
0.0
0.2
0.4
0.6
0.8
1.0
tan
?
 2 layers
 4 layers
 6 layers
20% Annealing HP 30s
Freq(Hz)
?
'
r
 
 
 
 
242 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-13 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (30 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C. 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-14 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (40 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C. 
 
 
 
100 1k 10k 100k 1M
10
20
30
40
50
0.0
0.2
0.4
0.6
0.8
1.0
tan
?
 2 layers
 4 layers
 6 layers
30% Annealing HP 30s
Freq(Hz)
?
'
r
 
 
100 1k 10k 100k 1M
10
20
30
40
50
60
70
0.0
0.2
0.4
0.6
0.8
1.0
tan
?
 2 layers
 4 layers
 6 layers
40% Annealing HP 30s
Freq(Hz)
?
'
r
 
 
243 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-15 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (50 vol% nano-size CaCu
3
Ti
4
O
12
)  with CC HP for 30s and annealing at 
125 
o
C. 
 
 
Table 5-3  Summary of dielectric data for multiple layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (nano-size/?-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 30s (1 kHz). 
 [1]
:  Nano-size CaCu
3
Ti
4
O
12.
 
[2]
: ?-size CaCu
3
Ti
4
O
12.
 
 
 
 CaCu
3
Ti
4
O
12
 Concentration (vol%) 
 10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
2 layer
[1]
 25/0.04 28/0.04 33/0.05 43/0.04 55/0.05 
4 layer
[1]
 23/0.04 34/0.05 40/0.04 56/0.04 62/0.05 
6 layer
[1]
 23/0.04 35/0.05 37/0.04 51/0.04 60/0.06 
     
2 layer
[2]
 24/0.05 28/0.06 54/0.10 368/0.43 150/0.33 
4 layer
[2]
 26/0.05 39/0.08 61/0.11 101/0.17 246/0.30 
6 layer
[2]
 27/0.05 44/0.08 46/0.08 85/0.15 510/0.25 
100 1k 10k 100k 1M
10
20
30
40
50
60
70
80
0.0
0.2
0.4
0.6
0.8
1.0
tan
?
 2 layers
 4 layers
 6 layers
50% Annealing HP 30s
Freq(Hz)
?
'
r
 
 
 
244 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-16 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration (nano-size 
CaCu
3
Ti
4
O
12
) using 30s CC HP for 2, 4, and 6 layers respectively at room temperature. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-17 Comparison of the present model predictions with experimental data for 2 
layer CC HP 30s annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. 
 
 
 
10 20 30 40 50
10
20
30
40
50
60
70
80
0.00
0.05
0.10
0.15
0.20
0.25
0.30
CaCu
3
Ti
4
O
12
 Volume (%) 
 
 
  ?
'
r
 2 Layer CC HP 30s
 4 Layer CC HP 30s
 6 Layer CC HP 30s
tan
?  
0 1020304050
15
30
45
60
CaCu
3
Ti
4
O
12
 Volume (%) 
 Experimental data
 Logarithmic mixing law
 Modified logarithmic mixing law
 Maxwell-Wagner model
 Yamada model
 Series model
 Bruggeman model
?
'
r
 
245 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-18 Comparison of the present model predictions with experimental data for 4 
layer CC HP 30s annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-19 Comparison of the present model predictions with experimental data for 6 
layer CC HP 30s annealed CaCu
3
Ti
4
O
12
/P(VDF-TrFE) sample. 
 
 
 
0 1020304050
15
30
45
60
75
CaCu
3
Ti
4
O
12
 Volume (%) 
 Experimental data
 Logarithmic mixing law
 Modified logarithmic mixing law
 Maxwell-Wagner model
 Yamada model
 Series model
 Bruggeman model
?
'
r
 
 
0 1020304050
15
30
45
60
75
CaCu
3
Ti
4
O
12
 Volume (%) 
 Experimental data
 Logarithmic mixing law
 Modified logarithmic mixing law
 Maxwell-Wagner model
 Yamada model
 Series model
 Bruggeman model
?
'
r
 
246 
 
 
 
 
 
 
 
 
 
 
 
 
Table 5-4 Summary of fitted dielectric data for CaCu
3
Ti
4
O
12 
multiple layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (nano-size CaCu
3
Ti
4
O
12
) with CC hot pressing for 
30s (1 kHz). 
Modified logarithmic mixing law: k=0.5. 
Yamada model: N=25. 
 
 
 
 
 
 
 
 
 
 
 
 
 2 layer 4 layer 6 layer 
Logarithmic mixing law 141 211 186 
Modified logarithmic mixing law 994 2,225 1,748 
Maxwell-Wagner model 165 373 278 
Yamada  model 85 110 102 
Series  model ? ? ? 
Bruggeman  model 110 150 140 
247 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-20 Dielectric response vs. frequency of multiple layers CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite (50 vol% nano-size CaCu
3
Ti
4
O
12
): (a) 2 layer CC HP, (b) 4 layer CC 
HP, (c) 6 layer CC HP for 10, 20, 30 and 40s. 
100 1k 10k 100k 1M
0
10
20
30
40
50
60
70
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Freq(Hz)
ta
n
?
?
'
r
 10s
 20s
 30s
 40s
 
 
 
50 vol%2layer CC HP(a)
100 1k 10k 100k 1M
0
10
20
30
40
50
60
70
80
0.0
0.2
0.4
0.6
0.8
1.0
1.2
(b)
Freq(Hz)
ta
n
?
?
'
r
 10s
 20s
 30s
 40s
 
 
 
 
50 vol%4layer CC HP
100 1k 10k 100k 1M
0
10
20
30
40
50
60
70
80
0.0
0.2
0.4
0.6
0.8
1.0
1.2
(c)
Freq(Hz)
ta
n
?
?
'
r
 10s
 20s
 30s
 40s
 
 
 
50 vol%6layer CC HP
248 
 
 
 
 
 
 
Table 5-5 Summary of dielectric data for multiple layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (50vol% nano-size CaCu
3
Ti
4
O
12
)  with CC hot pressing for 10, 20, 30 and 40s 
(1 kHz). 
 
CC HP Time (seconds) 
10s 20s 30s 40s 
2 layer HP 35/0.07 38/0.06 51/0.06 43/0.07 
4 layer HP 40/0.05 42/0.04 62/0.05 39/0.05 
6 layer HP 53/0.05 56/0.05 60/0.05 39/0.04 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-21 Dependence of dielectric response on CaCu
3
Ti
4
O
12
 concentration (50 vol% 
nano-size CaCu
3
Ti
4
O
12
) of 2, 4 and 6 layers CC HP for 10, 20, 30 and 40s at room 
temperature, respectively. 
 
 
 
 
10 20 30 40
20
30
40
50
60
70
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
tan
?
?
'
r
 
CC HP Time (s)
 2 layer
 4 layer
 6 layer
 
50 vol%
249 
 
5.3.1.4 Temperature Dependent of Dielectric Response 
  Earlier in this chapter, we reported that the effect of hot pressing on the dielectric 
properties and how their corresponding microstructure is associated with the morphology 
changes. In order to understand how temperature would influence the dielectric behavior, 
temperature dependent measurements were carried out. Figure 5-22 to 5-24 illustrate the 
temperature dependence of the dielectric constant and loss factor for 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites with 50 vol% CaCu
3
Ti
4
O
12
 powder.  
  Based on the results shown in Figure 5-22 to 5-24, it was found that the 
temperature dependence of the dielectric constant was influenced by hot pressing time, 
varying between 10 and 30s, and multiple layers, changing from two to six layers. 
Clearly, it was observed that they experienced a dielectric peak, which resembles a 
relaxation phenomenon. In Chapter 4, for the micro-size composite, it was well known 
that this relaxation phenomenon is clearly associated with its polymer matrix P(VDF-
TrFE). As for the peak value, more specifically as hot pressing time increased from 10 to 
30s, the maximum dielectric constant at 1 kHz was changing from 96 to 146 for two layer, 
88 to 117 for four layer, and 148 to 143 for six layer. The curie-temperature 
corresponding to this maximum value ranged between 95 and 100 
o
C. However, in 
contrast with the results of micro-size composite, those maximum values at its curie 
temperature were very small. With regards to micro-size composites as shown in Chapter 
4, the peak value was 514 for 10s six layer CC HP, and 1,240 for 30s six layer CC HP. 
The possible explanation for the differences may lie in their microstructure. As we 
already discussed previously, the cross-section of the composite sample presented a very 
obvious separation between ceramic particle and polymer matrix, which was even more 
significant than the one observed in micro-size sample. In return, this microstructure 
could deteriorate the dielectric response, as well as the temperature dependence 
properties.  
 
 
 
 
 
250 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-22 Temperature dependence of the 2 layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (50 vol% nano-size CaCu
3
Ti
4
O
12
) for: (a) 10s, and (b) 30s CC HP. 
 
 
 
 
30 40 50 60 70 80 90 100110120
0
25
50
75
100
125
150
175
200
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
tan
?
 2 layer HP10s(a)
30 40 50 60 70 80 90 100110120
0
25
50
75
100
125
150
175
200
0.0
0.5
1.0
1.5
2.0
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
ta
n
?
 2 layer HP 30s
(b)
251 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-23 Temperature dependence of the 4 layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite  (50 vol% nano-size CaCu
3
Ti
4
O
12
) for: (a) 10s, and (b) 30s CC HP. 
 
 
 
 
30 40 50 60 70 80 90 100110120
0
25
50
75
100
125
150
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
(a)
ta
n
?
 4 layer HP 10s
30 40 50 60 70 80 90 100110120
0
25
50
75
100
125
150
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
(b)
tan
?
 4 layer HP 30s
252 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-24 Temperature dependence of the 6 layers CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% nano-size CaCu
3
Ti
4
O
12
) for: (a) 10s, and (b) 30s CC HP. 
 
 
 
 
30 40 50 60 70 80 90 100110120
0
25
50
75
100
125
150
175
200
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
(a)
tan
?
 6 layer HP 10s
30 40 50 60 70 80 90 100110120
0
25
50
75
100
125
150
175
200
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
(b)
ta
n
?
 6 layer HP 30s
253 
 
5.3.1.5 P-E Hysteresis Loop 
  Since the properties of P-E loops for micro-size CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite have been addressed in Chapter 4, in order to better understand the size effect 
on the P-E properties, P-E studies on nano-size CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
were carried out in this Chapter. Figure 5-25 to 5-29 list the P-E loops of one layer 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 10 to 50 vol% CaCu
3
Ti
4
O
12
 powder. 
Corresponding P-E loops of multiple layers, such as two, four, six layers after CC HP 10s, 
are shown in Figure 5-30 to 5-32.  
  In Figure 5-25 to 5-29, it presented a similar trend that was also presented in 
micro-size CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite: as increasing ceramic concentration 
from 10 to 50 vol%, the break-down field decreased from 133 MV/m to 48 MV/m, while 
47 MV/m to 1.1 MV/m in micro-size CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite. 
Correspondingly, the remnant polarization (Pr) decreased from 0.046 to 0.044 C/m
2
. As 
for multiple layers, the break-down filed changed from 14 MV/m to 8 MV/m. After 
comparing with micro-size CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites, it was found that 
those P-E results were enormously improved. Different from the micro-size ceramic 
particle, the nano-size ceramic particle can improve the affinity between ceramic and 
polymer matrix, and then it enables the elimination of porosity due to the introduction of 
ceramic particle, which is essential for the break-down field improvement.  
  Moreover, in order to understand whether it is a simple dielectric or a ferroelectric, 
studies about the effects of temperature to the P-E properties were carried out. Based on 
their temperature dependent results, the temperature was set at its curie temperature at 95 
o
C and their results are shown in Figure 5-33 to 5-37. Table 5-6 shows the summary of P-
E results for one layer 10 to 50 vol% CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite at 95 
o
C. 
The break-down field decreased from 100 MV/m to 45 MV/m, as the ceramic 
concentration increased from 10 to 50 vol%. In contrast to P-E loops at room temperature, 
the polarization hysteresis loop gradually disappeared with increasing temperature for 
each ceramic concentration. That is, the remnant polarization (Pr) and coercive field (Ec) 
slowly decreased with increasing temperature, a feature reminiscent of relaxor 
ferroelectrics.  
 
254 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-25 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-26 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 20 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
-150 -100 -50 0 50 100 150
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
E(MV/m)
P
(
C/m
2
)
10vol%-1 layer
 117 MV/m
 125 MV/m
 133 MV/m
 
-150 -100 -50 0 50 100 150
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
E(MV/m)
P
(
C/m
2
)
20vol%-1 layer
 97 MV/m
 110 MV/m
 122 MV/m
 
 
255 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-27  Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 30 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-28 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
-100-80 -60 -40 -20 0 20 40 60 80 100
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
E (MV/m)
P
(
C/m
2
)
30vol%-1 layer
 62 MV/m
 70 MV/m
 78 MV/m
 
-75 -50 -25 0 25 50 75
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
E(MV/m)
P
(
C/m
2
)
40vol%-1 layer
 46 MV/m
 54 MV/m
 62 MV/m
 
256 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-29 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-30 Polarization electric hysteresis loop for two layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
-75 -50 -25 0 25 50 75
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
E(MV/m)
P
(
C/m
2
)
50vol%-1 layer
 37 MV/m
 44 MV/m
 48 MV/m
 
-15 -10 -5 0 5 10 15
-0.0012
-0.0008
-0.0004
0.0000
0.0004
0.0008
0.0012
E(MV/m)
P
(
C/m
2
)
2 layer HP 10s
 10 MV/m
 12 MV/m
 14 MV/m
 
257 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-31 Polarization electric hysteresis loop for two layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-32 Polarization electric hysteresis loop for two layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder. 
 
 
 
-15 -10 -5 0 5 10 15
-0.0012
-0.0008
-0.0004
0.0000
0.0004
0.0008
0.0012
E(MV/m)
P
(
C/m
2
)
4 layer HP 10s
 10 MV/m
 11 MV/m
 13 MV/m
 
-10 -5 0 5 10
-0.0012
-0.0008
-0.0004
0.0000
0.0004
0.0008
0.0012
E(MV/m)
P
(
C/m
2
)
6 layer HP 10s
 6 MV/m
 7 MV/m
 8 MV/m
 
258 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-33 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 10 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-34 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 20 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. 
 
 
 
-150 -100 -50 0 50 100 150
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
95 
o
C
E(MV/m)
P
(
C/m
2
)
10vol%-1 layer
 100 MV/m
 
 
 
-150 -100 -50 0 50 100 150
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
95 
o
C
E(MV/m)
P
(
C/m
2
)
20vol%-1 layer
 73 MV/m
 
 
259 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-35 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 30 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-36 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 40 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. 
 
 
 
-150 -100 -50 0 50 100 150
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
E(MV/m)
P
(
C/m
2
)
30vol%-1 layer
 66 MV/m
 
 
95 
o
C
-150 -100 -50 0 50 100 150
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
95 
o
C
E(MV/m)
P
(
C/m
2
)
40vol%-1 layer
 56 MV/m
 
 
260 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-37 Polarization electric hysteresis loop for one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites with 50 vol% CaCu
3
Ti
4
O
12
 powder at 95 
o
C. 
 
 
 
 
 
 
 
 
 
 
 
 
-150 -100 -50 0 50 100 150
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
95 
o
C
E(MV/m)
P
(
C/m
2
)
50vol%-1 layer
 45 MV/m
 
 
 
261 
 
 
 
 
 
Table 5-6 Summary of P-E results for one layer 10 to 50 vol% CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite at 95 
o
C. 
Composites Sample Thickness (?m) V
Max
 (V) E
B 
(MV/m) P
Max 
(?C/cm
2
) 
 
 
 
10% 
A 66 6200 93.9 4.44 
B 67 6500 97.0 4.65
C 66 6300 95.5 4.61 
D 65 6000 92.3 4.53
E 65 6500 100.0 4.81 
Average 65.8 6300 95.7 4.61
 
 
 
20% 
A 46 3100 67.4 3.98 
B 46 3400 73.9 4.36
C 48 3200 66.7 3.07 
D 47 3500 74.5 5.62
E 48 3000 62.5 4.54 
Average 47.0 3240 69.0 4.31
 
 
 
30% 
A 63 4000 63.5 5.58 
B 62 3700 59.7 4.39
C 63 4000 63.5 5.09 
D 60 4000 66.7 4.44
E 64 3900 60.9 4.47 
Average 62.4 3920 62.9 4.79
 
 
 
40% 
A 66 3200 48.5 5.76 
B 69 4000 57.9 5.35
C 63 3200 50.7 6.80 
D 64 3800 59.3 5.91
E 63 3000 47.6 5.13 
Average 65 3440 52.8 5.79
 
 
 
50% 
A 100 4500 45.0 4.55 
B 100 4100 41.0 4.84
C 94 4000 42.5 4.95 
D 102 4000 39.2 4.09
E 95 3500 36.8 4.75 
Average 98.2 4020 40.9 4.64
 
 
 
 
262 
 
5.3.1.6 Polymer Matrix Effect on Dielectric Behavior 
  The size effect on dielectric properties of CaCu
3
Ti
4
O
12
/VC88 composite was 
performed. CaCu
3
Ti
4
O
12
/VC88 composite with 50 vol% nano-size CaCu
3
Ti
4
O
12
 has been 
prepared and then those as-casted composite samples were annealed at 125 
o
C/8 hours.  
Figure 5-38 lists their corresponding dielectric response.  
  In contrast with the micro-size CaCu
3
Ti
4
O
12
/VC88 composite, the value of 
dielectric constant in nano-size composite tended to be smaller and with annealing, it 
increased from 28.7 to 29.2, which is shown in Figure 5-38. With two, four and six layer 
CC HP, the effect of multiple layers dominated, as the dielectric constant increased from 
54 to 79 at 1 kHz, while the dielectric loss remained at 0.03. It was also observed that this 
value is about half of that in micro-size composite, as can be found in Table 5-7. Figure 
5-39 to 5-40 list SEM images of one layer and multiple layers CaCu
3
Ti
4
O
12
/VC88 
composite. A very clear interface between ceramic and polymer layers can also be 
observed in one layer composite. Under CC HP, their microstructure has been optimized, 
however due to its nano-size particles, there still remained clear interfaces as there were 
two, four and six layers CC HP. Similarly, as in P(VDF-TrFE) polymer matrix, it 
answered why the dielectric property was poorer than that in micro-size composite. 
Figure 5-41 to 5-44 illustrate temperature dependence of dielectric properties. The entire 
CaCu
3
Ti
4
O
12
/VC88 composite sample with nano-size CaCu
3
Ti
4
O
12
 exhibited a relatively 
flat curve as temperature increased. The temperature dependence properties are very 
similar with the results of micro-size CaCu
3
Ti
4
O
12
/VC88 composite.  
 
 
 
 
 
 
 
 
 
 
263 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-38 Dielectric response vs. frequency of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(10 vol% nano-size CaCu
3
Ti
4
O
12
) : (a) as-casted 1 layer vs. as annealed 1 layer, (b) 2, 4, 
and 6 layers CC HP for 10s. 
 
 
 
 
100 1k 10k 100k 1M
20
22
24
26
28
30
32
34
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 1 Layer 
 1 Layer Annealing
 
 
?
'
r
Freq(Hz)
ta
n
?
 
 
50 vol%(a)
100 1k 10k 100k 1M
20
30
40
50
60
70
80
90
100
0.0
0.2
0.4
0.6
0.8
1.0
1.2
tan
?
 
 
?
'
r
Freq(Hz)
 2 Layer HP
 4 Layer HP
 6 Layer HP
(b)50 vol%
 
264 
 
 
 
 
Table 5-7  Summary of dielectric data for multiple layers CaCu
3
Ti
4
O
12
/VC88 composite 
(nano-size /?-size CaCu
3
Ti
4
O
12
) annealed at 125 
o
C (1 kHz). 
 CC HP layers
 2 layer 4 layer 6 layer 
Nano-sample
[1]
 54/0.04 74/0.04 79/0.04 
Micro-sample
[2]
130/0.17 151/0.14 126/0.14 
[1]
: Nano-size CaCu
3
Ti
4
O
12 
ceramic powder. 
[2]
: Micro-size CaCu
3
Ti
4
O
12 
ceramic powder. 
 
 
 
 
Figure 5-39 SEM fractographs of 1 layer annealed CaCu
3
Ti
4
O
12
/VC88 composite (50 
vol% nano-size CaCu
3
Ti
4
O
12
). 
 
 
 
265 
 
 
 
 
 
 
Figure 5-40 SEM fractographs of CaCu
3
Ti
4
O
12
/VC88 composites (50 vol% nano-size 
CaCu
3
Ti
4
O
12
)  using 10s CC HP for (a) 2 layer, (b) 4 layer and (c) 6 layers, respectively. 
 
(a) 
(b) 
(c) 
266 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-41 Temperature dependence of 1 layer CaCu
3
Ti
4
O
12
/VC88 composite (50 vol% 
nano-size CaCu
3
Ti
4
O
12
). 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-42 Temperature dependence of 2 layer CaCu
3
Ti
4
O
12
/VC88 composite for 10s 
CC HP (50 vol% nano-size CaCu
3
Ti
4
O
12
). 
 
 
 
30 40 50 60 70 80 90 100110120
10
20
30
40
50
60
0
1
2
3
4
5
50 vol% 1 layer 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
tan
?
30 40 50 60 70 80 90 100110120
20
40
60
80
100
120
140
0
1
2
3
4
5
50 vol% 2 layer 
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
 
tan
?
267 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-43 Temperature dependence of 4 layer CaCu
3
Ti
4
O
12
/VC88 composite for 10s 
CC HP (50 vol% nano-size CaCu
3
Ti
4
O
12
). 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-44 Temperature dependence of 6 layer CaCu
3
Ti
4
O
12
/VC88 composite for 10s 
CC HP (50 vol% nano-size CaCu
3
Ti
4
O
12
). 
 
 
 
30 40 50 60 70 80 90 100110120
20
40
60
80
100
120
140
0
1
2
3
4
5
50 vol% 4 layer 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
tan
?
30 40 50 60 70 80 90 100110120
20
40
60
80
100
120
140
0
1
2
3
4
5
50 vol% 6 layer 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
tan
?
268 
 
5.3.2 Silane Coupling Effect on Dielectric Behavior 
  In previous experiments, it was found that the microstructure played an important 
role on the dielectric constant. In order to optimize the microstructure, different 
processing, such as annealing and hot pressing, have been adopted. Especially with CC 
hot pressing, the apparent interfaces between polymer layer and ceramic layer were 
minimized, and corresponding dielectric responses were enhanced. Besides hot pressing 
method, another optimizing method with silane coupling agent is introduced in this work. 
It is known that coupling is maximized when silanes react with ceramic particles and 
present the maximum number of sites with reactivity specific and accessible to the 
polymer matrix. The interphase would then promote a dielectric response in 
CaCu
3
Ti
4
O
12
-based composite.  
 
 
5.3.2.1 Theoretical Calculation for Silane Coupling Agent  
  In order to achieve the expected coupling effect, a theoretical calculation about 
the minimum amount of silane was carried out. The physical properties of silane and 
ceramic are shown in Table 5-8. The molecule structure of the silane coupling agent is 
shown in Figure 5-42. 
 
Table 5-8 Physical properties of silane coupling agent (C
8
H
4
Cl
3
F
13
Si) and ceramic 
(CaCu
3
Ti
4
O
12
). 
 M
mol
(g/mol) ?(g/cm
3
) 
Silane coupling agent (C
8
H
4
Cl
3
F
13
Si): 481.55 1.638 
Ceramic (CaCu
3
Ti
4
O
12
) 614 5.267 
 
 
269 
 
C
F
F
F
C
C
C
C
C
C
C
F
F
F
F
F
F
F
F
F
F
H
H
H
H
Si
Cl
Cl
Cl
 
Figure 5-45  The molecule structure of the silane coupling agent (C
8
H
4
Cl
3
F
13
Si). 
 
Silane coupling agent (C
8
H
4
Cl
3
F
13
Si): 
  As the silane coupling agent (C
8
H
4
Cl
3
F
13
Si) is concerned, based on the data in 
Table 5-1, then one molecule weight of C
8
H
4
Cl
3
F
13
Si is given as following: 
                             )(109952.7
10023.6
1055.481
25
23
3
kgm
s
?
?
?=
?
?
=                                        (5-1) 
  The single molecule volume (C
8
H
4
Cl
3
F
13
Si) is: 
                              )(108811.4
10638.1
109952.7
328
3
25
mV
s
?
?
?=
?
?
=                                        (5-2) 
  Assuming the molecule structure (C
8
H
4
Cl
3
F
13
Si) resembles cylinder structure 
with a radius of r and length of 10r, then the radius can be given as below: 
                              )(104957.2
10
1010
10
3
32
m
V
rrrrV
s
s
?
?==?==
?
??                  (5-3) 
  The surface area of top or bottom (C
8
H
4
Cl
3
F
13
Si), which will attach the 
CaCu
3
Ti
4
O
12
 particle, is given as: 
                              )(109558.1
2192
mrA
s
?
?==?                                                         (5-4) 
 
Ceramic (CaCu
3
Ti
4
O
12
): 
  Assuming the CaCu
3
Ti
4
O
12
 weight is about 1 g and its average particle size is 
about 10 ?m, then one particle weight is about: 
                             )(1075.210267.5)
2
101
(
3
4
)
2
(
3
4
1233
6
3
kg
D
m
c
?
?
?=?
?
== ???     (5-5) 
 
 
 
270 
 
  The total number of ceramic particle is: 
                            
9
15
3
103636.0
1075.2
101
?=
?
?
=
?
?
c
n                                                       (5-6) 
  The surface area of one ceramic particle is: 
                             )(1014.3)
2
(4
2102
m
D
s
c
?
?== ?                                                      (5-7) 
  The total surface area will be: 
                             )(114.0
2
mnsS
ccc
==                                                                      (5-8) 
  If the average ceramic particle size is about 500 nm, then with the same 
calculation procedure, the total surface area is about: 
                              )(278.2
2
mnsS
ccc
==                                                                      (5-9) 
 
Theoretical Calculation  
  In order to cover all the CaCu
3
Ti
4
O
12
 ?-size particle, the total number of silane 
molecule is given as: 
                             
18
19
105837.0
109558.1
1417.1
?=
?
=
?
N                                                   (5-10) 
  The corresponding total weight of silane molecule is: 
                            )(0004695.055.481
10023.6
105837.0
23
19
gM =?
?
?
=                                    (5-11) 
  Therefore in comparison with 1 g 10 ?m CaCu
3
Ti
4
O
12
 ceramic, the minimum 
silane concentration is about 0.05 wt%. 
  With the same calculation, in comparison with 1 g 500 nm CaCu
3
Ti
4
O
12
, the 
minimum silane concentration is about 0.93 wt%?1 wt%. 
 
 
 
 
 
 
271 
 
5.3.3.1 Dielectric Behavior  
  The dielectric properties with silane have been studied under a series of 
conditions, such as annealing and various silane concentrations. The annealing effect 
study was performed on the CaCu
3
Ti
4
O
12
-based composite (micro-size CaCu
3
Ti
4
O
12
). 
The annealing temperature was fixed at 125 
o
C for 8 hours and CaCu
3
Ti
4
O
12
 volume 
concentration varied from 10 to 50 vol%. In order to study the effect of silane 
concentration, silane concentrations, such as 1, 5 and 10 wt%, were selected in the 
experiment. Figure 5-46 to 5-50 list the dielectric results of one layer as-casted composite 
sample. Table 5-9 summarizes the dielectric results at 1 kHz.  
  Their frequency dependent results were observed in Figure 46 to 5-50. When the 
CaCu
3
Ti
4
O
12
 volume concentration increased from 10 to 50 and silane concentration 
varied from 1 to 5 wt%, it presented a general trend that annealed sample always 
exhibited higher dielectric results, which is consistent with previous results without silane. 
For example, for 50 vol% CaCu
3
Ti
4
O
12
, the dielectric constant changed from 47 to 73 
with 1 wt% silane, 145 to 154 with 5 wt% silane and 15 to 23 with 19 wt%, as shown in 
Table 5-9. This phenomenon is closely associated with crystallinity improvement in the 
composite with annealing, which has been discussed in Chapter 4. The effect of silane 
was observed in different CaCu
3
Ti
4
O
12
 volume concentrations, 10 to 50 vol%. 
Corresponding to each individual silane concentration, a dielectric peak appeared at 40 
vol% and its dielectric value differed in each silane concentration. As the CaCu
3
Ti
4
O
12
 
volume concentration was small, such as 10 and 20, the dielectric constant was indeed 
improved, but not that much. The maximum value of 81 appeared at 20 vol% with 1 
wt % silane. As the CaCu
3
Ti
4
O
12
 volume concentration was higher, such as 40 vol%, a 
maximum value of 836 was achieved, however its dielectric loss is very high. After 
considering its dielectric loss, an optimized value was found within 30 and 50 vol%. For 
both the concentration after annealing, as the silane concentration varying from 1 to 10 
wt%, they exhibited maximum peaks of 118 and 154 with 5 wt% silane for 30 and 50 
vol% CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite. Those experiment results indicated that the 
silane concentration is also decisive for the improvement of dielectric response. More 
studies on the silane concentration will be performed.  
 
272 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-46 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (10 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. 
 
100 1k 10k 100k 1M
0
10
20
30
40
50
60
70
0.0
0.2
0.4
0.6
0.8
1.0
1.2
 1 Layer 
 1 Layer Annealing
ta
n
?
 
 
?
'
r
Freq(Hz)
(a)1wt% Silane
10 vol%
100 1k 10k 100k 1M
0
10
20
30
40
50
60
70
0.0
0.2
0.4
0.6
0.8
1.0
1.2
10 vol%
tan
?
 1 Layer 
 1 Layer Annealing
 
?
'
r
Freq(Hz)
 
(b) 5 wt% Silane
100 1k 10k 100k 1M
0
10
20
30
40
50
60
70
0.0
0.2
0.4
0.6
0.8
1.0
1.2
10 vol%
 1 Layer 
 1 Layer Annealing
tan
?
 
?
'
r
Freq(Hz)
(c) 10 wt% Silane
273 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-47 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (20 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. 
 
100 1k 10k 100k 1M
0
20
40
60
80
100
120
140
0.0
0.2
0.4
0.6
0.8
1.0
1.2
20 vol%
 1 Layer 
 1 Layer Annealing
tan
?
 
?
'
r
Freq(Hz)
(a) 1 wt% Silane
100 1k 10k 100k 1M
0
20
40
60
80
100
120
140
0.0
0.2
0.4
0.6
0.8
1.0
1.2
20 vol%
ta
n
?
 1 Layer 
 1 Layer Annealing
 
?
'
r
Freq(Hz)
(b) 5 wt% Silane
100 1k 10k 100k 1M
0
20
40
60
80
0.0
0.2
0.4
0.6
0.8
1.0
1.2
20 vol%
 1 Layer No Annealing
 1 Layer Annealing
 
 
?
'
r
Freq(Hz)
ta
n
?
(c) 10 wt% Silane
274 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-48 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (30 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. 
 
100 1k 10k 100k 1M
0
25
50
75
100
125
0
1
2
3
4
5
30 vol%
tan
?
 1 Layer No Annealing
 1 Layer Annealing
 
 
?
'
r
Freq(Hz)
(a) 1 wt% Silane
100 1k 10k 100k 1M
0
50
100
150
200
250
0
2
4
6
8
10
30 vol%
ta
n
?
 1 Layer No Annealing
 1 Layer Annealing
 ?
'
r
Freq(Hz)
(b) 5 wt% Silane
100 1k 10k 100k 1M
0
50
100
150
200
250
0
2
4
6
8
10
30 vol%
tan
?
 1 Layer No Annealing
 1 Layer Annealing
 
?
'
r
Freq(Hz)
(c) 10 wt% Silane
275 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-49 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (40 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. 
 
100 1k 10k 100k 1M
0
50
100
150
200
250
0.0
0.2
0.4
0.6
0.8
1.0
1.2
40 vol%
ta
n
?
 
?
'
r
 1 Layer 
 1 Layer Annealing
Freq(Hz)
 
(a) 1 wt% Silane
100 1k 10k 100k 1M
0
50
100
150
200
250
300
0
2
4
6
8
10
40 vol%
tan
?
 1 Layer 
 1 Layer Annealing
 
?
'
r
Freq(Hz)
(b) 5 wt% Silane
100 1k 10k 100k 1M
0
2000
4000
6000
8000
10000
0
10
20
30
40
50
40 vol%
 
ta
n
?
(c) 10 wt% Silane
?
'
r
Freq(Hz)
 1 Layer 
 1 Layer Annealing
 
276 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-50 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5, and (c) 10 wt% silane. 
 
100 1k 10k 100k 1M
0
20
40
60
80
100
120
0.0
0.2
0.4
0.6
0.8
1.0
1.2
50 vol%
tan
?
?
'
r
Freq(Hz)
 1 Layer 
 1 Layer Annealing
(a) 1 wt% Silane
100 1k 10k 100k 1M
0
50
100
150
200
250
300
350
0.0
0.2
0.4
0.6
0.8
1.0
1.2
50 vol%
 1 Layer 
 1 Layer Annealing
 
?
'
r
Freq(Hz)
(b) 5 wt% Silane
tan
?
100 1k 10k 100k 1M
0
10
20
30
40
50
60
0
1
2
3
4
5
50 vol%
 1 Layer 
 1 Layer Annealing
tan
?
 ?
'
r
Freq(Hz)
(c) 10 wt% Silane
277 
 
 
 
 
 
 
 
 
Table 5-9 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(?-size CaCu
3
Ti
4
O
12
) with 0, 1, 5 and 10 wt% silane with annealed at 125 
o
C (1 kHz). 
 
CaCu
3
Ti
4
O
12
 Concentration (vol%) 
10 vol% 20 vol% 30 vol% 40 vol% 50 vol% 
1 layer
[1]
 0 wt% 18/0.04 23/0.04 32/0.06 65/0.1 69/0.1 
1 layer
[2]
 0 wt% 25/0.05 34/0.08 43/0.09 105/0.2 67/0.1 
       
1 layer
[1]
 
1 wt% 22/0.08 70/0.13 46/0.40 113/0.28 47/0.17 
5 wt% 35/0.17 43/0.13 88/0.14 102/1.00 145/0.41 
10 wt% 38/0.17 26/0.11 45/1.78 505/9.99 15/0.57 
 
1 layer
[2]
 
1 wt% 39/0.07 81/0.14 65/0.40 127/0.31 73/0.17 
5 wt% 47/0.08 55/0.14 118/0.27 154/1.05 154/0.31 
10 wt% 47/0.08 46/0.09 73/0.98 836/9.55 23/0.61 
[1]
: Casting at 70 
o
C/8 hrs. 
[2]
: Casting at 70 
o
C/8 hr and annealing at 125 
o
C/8 hrs. 
 
 
 
 
 
 
 
 
278 
 
5.3.3.3 Silane Concentration Effect on Dielectric Behavior  
  As stated earlier, different silane concentrations, such as 1, 5 and 10 wt%, were 
used in the experiments. It was found in the experiment that the silane concentration 
played an important role in the dielectric properties of the CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite. However, what about the dielectric response with low silane concentration 
such as below 1 wt%? Thus in the following experiments, the dielectric properties with 
0.3, 0.5 and 0.75 wt% silane were observed, and the composite with 50 vol% 
CaCu
3
Ti
4
O
12
 was chosen. Figure 5-51 illustrates the dielectric results for one layer 50 
vol% composites with 0.3, 0.5 and 0.75 wt% silane. The corresponding dielectric results 
with 0.3, 0.5, 0.75, 1, 5 and 10 wt% silane at 1 kHz are summarized in Table 5-10.  
  Based on the results, the first impression was that the dielectric properties after 
annealing were better than non-annealed samples, which was consistent with previous 
results in CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite. In previous experiment results, as the 
silane varied from 1 to 10 wt%, a one layer flexible composite sample at 5 wt% silane 
with better dielectric response was fabricated, whose maximum dielectric constant can be 
as high as 154 and loss is around 0.31.  However, as silane concentration went below 1 
wt%, an even better dielectric response was achieved at 0.5 wt% silane, whose dielectric 
constant is about 170 and loss about 0.20, as seen in Figure 5-52. The possible 
explanation responsible for this phenomenon is the percolation, which generated at low 
concentration, such as with 0.5 wt% silane, and can lead to better microstructure as seen 
in Figure 5-53, which corresponded to a better dielectric response. Also, with too much 
silane inside, it would form thick layer between ceramic and polymer matrix, which leads 
to high conductivity and high loss, and then results in a porous structure as shown in 5-53 
(f).  
 
 
 
 
 
 
 
279 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-51 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% ?-size CaCu
3
Ti
4
O
12
) with (a) 0.3, (b) 0. 5 and (c) 0.75 wt% silane. 
 
100 1k 10k 100k 1M
0
25
50
75
100
0.0
0.2
0.4
0.6
0.8
1.0
1.2
50 vol%
(a) 0.3 wt% Silane
 1 layer 
 1 layer Annealing
 
?
'
r
Freq(Hz)
tan
?
100 1k 10k 100k 1M
0
50
100
150
200
250
300
0.0
0.2
0.4
0.6
0.8
1.0
1.2
50 vol%
ta
n
?
(c) 0.75wt% Silane
 1 Layer 
 1 Layer Annealing
 
?
'
r
Freq(Hz)
 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
0.0
0.2
0.4
0.6
0.8
1.0
1.2
50 vol%
(b) 0.5wt% Silane
 1 Layer 
 1 Layer Annealing
 
?
'
r
Freq(Hz)
 
ta
n
?
280 
 
 
 
 
 
 
Table 5-10 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(?-size CaCu
3
Ti
4
O
12
) with 0.3, 0.5, 0.75, 1, 5 and 10 wt% silane with annealed at 125
o
C 
(1 kHz). 
 Silane Concentration (wt%) 
0.3 wt% 0.5 wt% 0.75 wt% 1 wt% 5 wt% 10 wt% 
1 layer
[1]
 55/0.06 74/0.07 94/0.26 47/0.17 145/0.41 15/0.57 
1 layer
[2]
 64/0.07 170/0.20 114/0.21 73/0.17 154/0.31 23/0.61 
[1]
: Casting at 70 
o
C/8 hrs. 
[2]
: Casting at 70 
o
C/8 hr and annealing at 125 
o
C/8 hrs. 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-52 Dependence of dielectric response vs. silane coupling concentration in 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite (?-size CaCu
3
Ti
4
O
12
): (a) 1 layer vs. 1 annealed 
layer, (b) multiple layers using 10s CC HP at room temperature. 
 
 
 
 
 
110
0
50
100
150
200
50 vol%
?
'
r
 
 
Silane concentration (wt%)
 1 layer
 1 layer Annealing
281 
 
 
 
 
 
Figure 5-53 SEM fractographs of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites  
(50vol% ?-size CaCu
3
Ti
4
O
12
) with:  (a) 0.3 wt%, (b) 0.5 wt%, (c) 0.75 wt%, (d) 1 wt%, 
(e) 5 wt% and (f) 10 wt% silane,  respectively. 
(a) (b) 
(c) (d) 
(e) (f) 
282 
 
5.3.3.4 Temperature Dependent of Dielectric Response 
  Besides of the dielectric response, the temperature dependence properties of one 
layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 0.5, 0.75 and 1 wt% silane were 
studied. Their experimental results are shown in Figure 5-54 to 5-56. 
CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite with 50 vol% CaCu
3
Ti
4
O
12
 powder was chosen 
in the work.  
  No matter the silane volume concentration, their temperature dependent properties 
with silane exhibited the similar tendency as previous results in CaCu
3
Ti
4
O
12
/P(VDF-
TrFE) composite: those curves resemble a relaxation process, which is believed to be 
associated with ferroelectrics: P(VDF-TrFE) polymer matrix. As for the one layer 
composite with 0.5 wt%, 0.75 wt% and 1 wt% silane, all the temperature dependent 
curves reached their dielectric peaks and then leveled off, as shown in Figure 5-54 to 5-
56. It is noted that with higher silane concentration, the results at 100 Hz exhibited 
tailing up at high temperature and this phenomenon may be associated with increasing 
conductivity. Moreover, it is found that the curie-temperature exhibited an increasing 
trend from 95 to 105 
o
C as the silane concentration increased from 0.5 to 1 wt%.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
283 
 
30 40 50 60 70 80 90 100110120
0
100
200
300
400
500
600
700
0
2
4
6
8
10
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
0.75 wt% silane 1 layer
 
tan
?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-54 Temperature dependence of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) with 0.75 wt% silane. 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-55 Temperature dependence of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) with 0.75 wt% silane. 
 
 
 
30 40 50 60 70 80 90 100110120
0
100
200
300
400
500
0
1
2
3
4
5
0.5 wt% silane 1 layer
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
tan
?
284 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-56 Temperature dependence of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) with 1 wt% silane. 
 
 
 
 
 
 
 
 
 
 
30 40 50 60 70 80 90 100110120
0
50
100
150
200
250
300
350
400
0
2
4
6
8
10
1 wt% silane 1 layer
 
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
tan
?
285 
 
5.3.3.5 Size Effect on Dielectric Behavior 
  The dielectric behaviors based on 50 vol% nano-size CaCu
3
Ti
4
O
12
 ceramic 
particle with different silane concentrations are shown in Figure 5-54. Table 5-11 
summarizes their corresponding dielectric constant at 1 kHz. As described previously in 
the nano-size CaCu
3
Ti
4
O
12
 ceramic particle, the theoretical minimum silane 
concentration is about 1 wt%. In this work, the silane concentration varied among 1, 5 
and 10 wt%. As shown in the Figure 5-57, with nano-size ceramic particle, it was found 
that the dielectric responses improved with 1, 5 and 10 wt% silane. In Table 5-11, the 
dielectric constant in a one layer annealed sample varied from 73 to 67 at 1 wt% silane, 
154 to 159 at 5 wt% and 23 to 84 at 10 wt%, while the dielectric loss was stabilized 
below 0.31.  
 Figure 5-58 lists SEM images of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composites. It should be noted that the interface?s problem, which used to persist in nano-
size composites disappeared, and the microstructure becomes even more uniform than the 
previous hot pressed sample. However, with higher silane concentration, the 
microstructure tends to give porous structure, which is similar to the results in micro-size 
composites, and indicates the necessity to optimize the silane concentration. Those SEM 
images have corroborated with the dielectric results. The temperature dependent results in 
Figure 5-59 showed the same behavior as the one in the micro-size composite. Based on 
the dielectric results and microstructure analysis, the bridge-linked action between 
CaCu
3
Ti
4
O
12
 ceramic particle and polymer matrix can be better fulfilled with nano-size 
CaCu
3
Ti
4
O
12
 ceramic particle, which own higher surface-volume ratio and relative mass. 
In short, a more flexible composite based on coupling effect with good dielectric 
performance has been fabricated.  
 
 
 
 
 
 
 
286 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-57 Dielectric response vs. frequency of 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) 
composite (50 vol% nano-size CaCu
3
Ti
4
O
12
) with (a) 1, (b) 5 and (c) 10 wt% silane. 
100 1k 10k 100k 1M
25
50
75
100
125
0.0
0.2
0.4
0.6
0.8
1.0
1.2
50vol%
 1 Layer No Annealing
 1 Layer Annealing
(a) 1 wt% Silane
 
?
'
r
Freq(Hz)
ta
n
?
100 1k 10k 100k 1M
0
50
100
150
200
250
300
0.0
0.2
0.4
0.6
0.8
1.0
1.2
50vol%
ta
n
?
 1 Layer 
 1 Layer Annealing
(b) 5 wt% Silane
 
?
'
r
Freq(Hz)
 
100 1k 10k 100k 1M
0
50
100
150
200
250
300
0.0
0.2
0.4
0.6
0.8
1.0
1.2
tan
?
 1 layer 
 1 layer Annealing
(c) 10 wt% Silane
 
 
?
'
r
Freq(Hz)
50vol%
 
287 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 5-11 Summary of dielectric data for 1 layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(nano-size and ?-size CaCu
3
Ti
4
O
12
) with 1, 5 and 10 wt% silane with annealed at 125 
o
C 
(1 kHz). 
 [1]
: Casting at 70 
o
C/8 hrs. 
[2]
: Casting at 70 
o
C/8 hr and annealing at 125 
o
C/8 hrs. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Silane concentration (wt%) 
1 wt% 5 wt% 10 wt% 
Nano-size 
[1]
 47/0.1 151/0.2 65/0.2 
[2]
 67/0.2 159/0.2 84/0.3
        
?-size 
[1]
 47/0.2 145/0.4 15/0.6
[2]
 73/0.2 154/0.3 23/0.6 
288 
 
 
 
 
 
 
Figure 5-58 SEM fractographs of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites  
(50vol% nano-size CaCu
3
Ti
4
O
12
) with: (a) 1, (b) 5 and (c) 10 wt% silane, respectively. 
 
(a) 
(b) 
(c) 
289 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5-59 Temperature dependence of one layer CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composite 
(50 vol% ?-size CaCu
3
Ti
4
O
12
) with 1 wt% silane. 
 
 
 
 
 
 
 
 
 
 
30 40 50 60 70 80 90 100110120
0
25
50
75
100
125
150
175
200
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 wt% silane 1 layer
?
'
r
Temperature (? C)
 100
 1K
 10K
 100K
 1M
 
tan
?
290 
 
5.4 Summary 
  Composites based on nano-size CaCu
3
Ti
4
O
12 
ceramic particles were studied. The 
morphology of the ceramics was studied using SEM. Their dielectric responses were 
studied over a frequency range from 100 to 1 MHz. It was found that the dielectric 
constant in a nano-size composite is smaller than that in a micro-size composite. Based 
on the fitting results using different models, it was found that the effective dielectric 
constant of the nano-size CaCu
3
Ti
4
O
12 
particles is much smaller than that of micro-size 
CaCu
3
Ti
4
O
12 
particles. This may be caused by the interfacial layers. That is, the dielectric 
constant from the fitting is actually the effective dielectric constant of CaCu
3
Ti
4
O
12
 
particles and the interfacial layers. However, CaCu
3
Ti
4
O
12
/P(VDF-CTFE) 88/12 mol% 
(VC88) composites exhibit a smaller difference in dielectric constant between nano-size 
and micro-size particles than that in P(VDF-TrFE) 55/45 mol% copolymer. Moreover, in 
order to improve the wettability between ceramic and polymer, silane has been used as a 
coupling agent and the silane coupling effect on the CaCu
3
Ti
4
O
12
-based composites was 
studied. Flexible composites with a dielectric constant of 159 and loss of 0.2 were 
obtained.  
 
 
 
 
 
 
 
 
 
 
 
 
 
291 
 
References 
(1) Arbatti, M.; Shan, X. B.; Cheng, Z.-Y. Adv. Mater 2007, 19, 1369-1372. 
(2) Arbatti, M. Development of High-Dielectric-Constant Polymer-Ceramic   
            Composites Based on Calcium Copper Titanate. Auburn University, Alabama,   
            2004. 
(3) Shan, X. B.; Yang, X.; Zhang, K. W.; Cheng, Z.-Y. Mater. Res. Soc. Symp. Proc.  
            2007, 949, 0949-C05-07. 
(4) Shan, X. B.; Zhang, L.; Wu, P. X.; Xu, C. R.; Cheng, Z.-Y. Mater. Res. Soc. Symp.  
            Proc., 2009, In Processing. 
(5) Lewis, T. J. J. Phys. D: Appl. Phys. 2005, 38, 202-212. 
(6) Nelson, J. K.; Hu, Y. J. Phys. D: Appl. Phys. 2005, 38, 213-222. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
292 
 
 
 
 
 
CHAPTER 6 
 
CONCLUSION AND FUTURE WORKS 
 
 
6.1 Summary of Results and Conclusions 
(1) CaCu
3
Ti
4
O
12
 ceramics were prepared using a conventional solid-state reaction under 
different conditions, such as molding pressure, milling media and time, and calcination 
temperature and time. Ceramic samples with a dielectric constant of 160,000 and loss of 
0.15 at 1 kHz were obtained after calcination at 900 
o
C and sintering at 1075 
o
C for 72 
hours. 
 
(2) Regarding the polarization mechanism in CaCu
3
Ti
4
O
12
 ceramic, three different 
processes were founded. Although the dielectric response at low frequency increases with 
decreasing thickness, the dielectric behavior for the high frequency relaxation process is 
weakly dependent on thickness. 
 
(3) Composites based on micro-size CaCu
3
Ti
4
O
12
 ceramic and P(VDF-TrFE) 55/45 
mol% copolymer were prepared and studied. The influence of processing parameters 
such as annealing and HP on the properties of the composites has been studied. Flexible 
composite with dielectric constant of 510 and loss of 0.25 at 1 kHz was obtained at room 
temperature.  
 
(4) The dielectric response of the composites was analyzed. It was found that the 
relaxation time of the major relaxation process obtained in the composite changes with 
concentration, as well as on process conditions. This indicates the existence of the 
interfacial layer in the composite. It was also found that the observed loss at low 
frequency in the composite is due to a relaxation process, instead of conductivity. 
293 
 
(5) The dielectric response of CaCu
3
Ti
4
O
12
/P(VDF-TrFE) composites based on nano-size 
ceramic particles was studied. Compared with micro-size composites, both the dielectric 
constant and loss in nano-size composites are found to be smaller than that in micro-size 
composites.  
 
(6) The dielectric properties of CaCu
3
Ti
4
O
12
/P(VDF-CTFE) 88/12 mol% (VC88) 
composites were studied. These composites exhibited a high dielectric constant and small 
loss almost independent of the temperature, which is good for some applications. It was 
also found that the difference of dielectric constant between nano-size and micro-size 
particles is much smaller than that in P(VDF-TrFE) 55/45 mol% copolymer. 
 
6.2 Future Works 
(1) High dielectric constant has been demonstrated within CaCu
3
Ti
4
O
12
/ P(VDF-TrFE) 
55/45 mol% composites. It would be interesting to prepare the CaCu
3
Ti
4
O
12
-based 
composite using a different polymer matrix in order to develop different composites for 
various applications.  
 
(2) It should be noted that the high dielectric constant was observed in the composite 
using HP. Certainly, HP is not desirable for industrial processes. Therefore, a new 
process to produce high dielectric constant should be exploited, such as solution casting 
using silane agent and extrusion process.   
 
(3) Three processes were founded in the CaCu
3
Ti
4
O
12
 ceramics. Continuous study on the 
three processes and corresponding microstructure of the ceramics would deepen the 
understanding of the polarization mechanism of the ceramics.