Predicting phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations

Two methods for predicting phonon frequencies and relaxation times are presented. The first is based on quasiharmonic and anharmonic lattice dynamics calculations, and the second is based on a combination of quasiharmonic lattice dynamics calculations and molecular dynamics simulations. These phonon properties are then used with the Boltzmann transport equation under the relaxation-time approximation to predict the lattice thermal conductivity. The validity of the low-temperature assumptions made in the lattice dynamics framework are assessed by comparing to thermal conductivities predicted by the Green-Kubo and direct molecular dynamics methods for a test system of Lennard-Jones argon. The predictions of all four methods are in agreement at low temperature (20 K). At temperatures of 40 K (half the Debye temperature of Lennard-Jones argon) and below, the thermal-conductivity predictions from the two methods that use lattice dynamics calculations are within about 30% of those made using the more accurate Green-Kubo and direct molecular dynamics methods. The thermal-conductivity predictions using the lattice dynamics techniques become inaccurate at high temperature (above 40 K) due to the approximations inherent in the lattice dynamics framework. We apply the results to assess the validity of (i) the isotropic approximation in modeling thermal transport and (ii) the common assertion that low-frequency phonons dominate thermal transport. Lastly, we suggest approximations that can be made within the lattice dynamics framework that allow the thermal conductivity of Lennard-Jones argon to be estimated using two orders of magnitude less computing effort than the Green-Kubo or direct molecular dynamics methods.

Figure 1

$1/k$ versus $1/N_0$ and linear fit for extrapolation from BTE-LD calculations at a temperature of 50 K. The line is fit to the four rightmost (filled) circles only.

Figure 2

(Color online) Frequency shift $\left(\Delta \right)$ and inverse of the lifetime $\left(1/\tau \right)$ at temperatures of 20 and 50 K versus reduced wave vector for the longitudinal and transverse dispersion branches in the [100] direction. The MD data is found using (i) the full LJ potential and (ii) the LJ potential truncated after the fourth-order term in the Taylor-series expansion. While the results from the LD calculations are discrete, we plot the data as lines for clarity.

Figure 3

(Color online) Temperature dependence of the thermal conductivity predicted from the four methods. Using an isotropic approximation (isotropic) rather than all the phonons in the full Brillouin zone (full BZ) in the BTE-MD method causes the thermal conductivity to be underpredicted by a factor of about 1.5.

Figure 4

(Color online) Dependence of the thermal conductivity and phonon density of states (DOS) on ${\omega }_A/{\left({\omega }_A\right)}_{\text{max}}$ at a temperature of 50 K.

Figure 5

Schematic of the simulation cell used in the direct method.