Theoretical Study of Thermal Properties and Thermal Conductivities of Crystals

Abstract

Standard first-principles total energy and force calculations were extended to the calculations of harmonic force constant matrices and third order lattice anharmonicity tensors with an efficient super-cell finite-difference algorithm. Phonon spectra calculated within this algorithm are in excellent agreement with other theoretical results calculated with density perturbation functional theory, as well as the available experimental measurements. The newly proposed algorithm for lattice anharmonicity was implemented with both empirical Tersoff potentials and first-principle density functional theory methods. A self testing scheme for the validity of 3rd order lattice anharmonicity was also proposed and sumrule enforcement has been investigated to ensure the numerical accuracy. Statistical ensemble of phonons was then adopted to calculate and simulate the equilibrium thermal properties of solid materials. With the forces calculated from first-principle theory, fundamental thermal properties such as heat capacity, thermal expansion were calculated within the quasi-harmonic approximation. Kinetic theory was implemented to predict the non-equilibrium thermal transport properties such as phonon life time and thermal conductivity. With the newly developed computational method, we have studied the thermal and thermal transport properties of two material systems Si136 and MgO. Our calculation predicted that a negative thermal expansion exist in Si136 at temperature lower than 124K, and was then confirmed by experimental measurement. Green-Kubo calculation yielded 90% reduction of thermal conductivity in Si136 compared with diamond structured Si. Cause of this reduction was then investigated using kinetic transport theory. For MgO, the pressure dependence of lattice anharmonicity was studied. Both intrinsic anharmonicity and extrinsic isotope induced phonon scattering have been considered. The isotope effect on the lattice thermal conductivity was discussed. Preliminary results of lattice thermal conductivity at a wide range of temperature were then presented. At room temperature, our theory calculated lattice thermal conductivity is 51 W/K/m, in a good agreement with experimental measurement 54 W/K/m. In addition, two models were proposed to estimate the pressure dependence of the lattice thermal conductivity.