A size-consistent Gr\"uneisen-quasiharmonic approach for lattice thermal conductivity

We propose a size-consistent Gr\"uneisen-quasiharmonic approach (GQA) to calculate the lattice thermal conductivity $\kappa_l$ where the Gr\"uneisen parameters that measure the degree of phonon anharmonicity are calculated directly using first-principles calculations. This is achieved by identifying and modifying two existing equations related to the Slack formulae for $\kappa_l$ that suffer from the size-inconsistency problem when dealing with non-monoatomic primitive cells (where the number of atoms in the primitive cell $n$ is greater than one). In conjunction with other thermal parameters such as the acoustic Debye temperature $\theta_a$ that can also be obtained within the GQA, we predict $\kappa_l$ for a range of materials taken from the diamond, zincblende, rocksalt, and wurtzite compounds. The results are compared with that from the experiment and the quasiharmonic Debye model (QDM). We find that in general the prediction of $\theta_a$ is rather consistent among the GQA, experiment, and QDM. However, while the QDM somewhat overestimates the Gr\"uneisen parameters and hence underestimates $\kappa_l$ for most materials, the GQA predicts the experimental trends of Gr\"uneisen parameters and $\kappa_l$ more closely. We expect the GQA with the modified Slack formulae could be used as an effective and practical predictor for $\kappa_l$, especially for crystals with large $n$.