Large anharmonic effect and thermal expansion anisotropy of metal chalcogenides: The case of antimony sulfide

We derive a compact matrix expression for the linear thermal expansion coefficients (TECs) for a general orthorhombic system which relates the elastic properties and the integrated quantities based on deformation and mode dependent Gruneisen parameters and mode dependent heat capacities. The density of Gruneisen parameters $\Gamma(\nu)$ as a function of frequency $\nu$, weighted by the number of phonon modes, is introduced and found to be insightful in interpreting the TEC results. Using density-functional perturbation theory and Gruneisen formalism for thermal expansion, we illustrate the general usefulness of this method by calculating the linear and volumetric TECs of a low-symmetry orthorhombic compound antimony sulfide (Sb2S3), a compound belonging to a large class of technologically and fundamentally important materials. Even though negative Gruneisen parameters are found for deformations in all three crystal directions, the $\Gamma(\nu)$ data rule out the occurrences of negative TECs at all temperatures. Sb2S3 exhibits a large thermal expansion anisotropy where the TEC in the $b$ direction can reach as high as $13\times 10^{-6}$~(1/K) at high temperatures, about two and seven times larger than the TECs in the $c$ and $a$ direction, respectively. Our work suggests a general and practical first-principles approach to calculate the thermal properties of other complicated low-symmetry systems.