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

Abstract

We derive a compact matrix expression for the linear thermal expansion coefficients (TECs) for a general orthorhombic system which relates elastic properties and integrated quantities based on deformation and mode dependent Grüneisen parameters and mode dependent heat capacities. The density of Grüneisen parameters Γ(ν) as a function of frequency ν, weighted by the number of phonon modes, is introduced and found to be illuminating in interpreting the TEC results. Using density functional perturbation theory and Grüneisen 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 (Sb[subscript 2]S[subscript 3]), which belongs to a large class of technologically and fundamentally important materials. Even though negative Grüneisen parameters are found for deformations in all three crystal directions, the Γ(ν) data rule out the occurrences of negative TECs at all temperatures. Sb[subscript 2]S[subscript 3] exhibits a large thermal expansion anisotropy where the TEC in the b direction can reach as high as 13×10[superscript −6] K[superscript −1] 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.