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

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