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

Abstract

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.

Thermal expansion in insulating solids from first principles

“…Hence, care must be taken to ensure that the choice of functional and pseudopotential is appropriate for the material under study -for further details, again see the discussion in Ref. 43.…”

“…Though phonons at q points that are not explicitly calculated can be approximated through interpolation, the results become more accurate as more q points are explicitly included, and the supercell size effectively becomes a convergence parameter. Despite the relative simplicity of the finite displacements method, we have encountered problematic behavior related to the convergence of phonon frequencies with respect to the supercell size, namely, phonon frequencies did not converge before the supercell became impracticably large (also see the discussion by McGaughey and co-workers 43 ). In some cases, the phonon dispersion curve developed anomalous features (such as sudden dips in frequency at non-zero q) as the supercell size was increased.…”

Generalization of Fourier’s Law into Viscous Heat Equations

“…These experimental observations have been accompanied by several pioneering efforts aimed at providing a quantitative description of heat hydrodynam-out any fitting parameter, deriving all quantities from first-principles, to accurately describe the thermal properties of many bulk crystals [22,[27][28][29][30][31][32][33][34][35][36], provided phonon branches remain well separated [37,38].…”

First-Principles Study of UO ₂ Lattice Thermal-Conductivity: A Simple Description

“…In this step we determine the appropriate supercell size, magnitude of atomic displacement, and the number of neighboring shells. The appropriate supercell size is intimately connected to the range of forces [34]. We have displaced one atom in a 3 × 3 × 3 supercell with 81 atoms from its equilibrium position by 0.2 Bohr.…”