Quantum mechanics

Convection–diffusion equation

Perturbation theory (quantum mechanics)

Materials science

Density functional theory

Thermal conductivity

Scattering

Phonon

Statistical physics

Thermodynamics

Physics

Transport theory

Boltzmann equation

Condensed matter physics

Lattice Boltzmann methods

Journal of Applied Physics

A computational framework for predicting phonon frequencies, group velocities, scattering rates, and the resulting lattice thermal conductivity is described. The underlying theory and implementation suggestions are also provided. By using input from first principles calculations and taking advantage of advances in computational power, this framework has enabled thermal conductivity predictions that agree with experimental measurements for diverse crystalline materials over a wide range of temperatures. Density functional theory and density functional perturbation theory calculations are first used to obtain the harmonic and cubic force constants. The harmonic force constants are the input to harmonic lattice dynamics calculations, which provide the phonon frequencies and eigenvectors. The harmonic properties and the cubic force constants are then used with perturbation theory and/or phenomenological models to determine intrinsic and extrinsic scattering rates. The full set of phonon properties is then used to solve the Boltzmann transport equation for the mode populations and thermal conductivity. The extension of the framework to include higher-order processes, capture finite temperature effects, and model alloys is described. A case study on silicon is presented that provides benchmarking and convergence data. Available packages that implement the framework are compared.

Phonon properties and thermal conductivity from first principles, lattice dynamics, and the Boltzmann transport equation