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We derive a compact matrix expression for the linear thermal expansioncoefficients (TECs) for a general orthorhombic system which relates the elasticproperties and the integrated quantities based on deformation and modedependent Gruneisen parameters and mode dependent heat capacities. The densityof Gruneisen parameters $\Gamma(\nu)$ as a function of frequency $\nu$,weighted by the number of phonon modes, is introduced and found to beinsightful in interpreting the TEC results. Using density-functionalperturbation theory and Gruneisen formalism for thermal expansion, weillustrate the general usefulness of this method by calculating the linear andvolumetric TECs of a low-symmetry orthorhombic compound antimony sulfide(Sb2S3), a compound belonging to a large class of technologically andfundamentally important materials. Even though negative Gruneisen parametersare found for deformations in all three crystal directions, the $\Gamma(\nu)$data rule out the occurrences of negative TECs at all temperatures. Sb2S3exhibits 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-principlesapproach to calculate the thermal properties of other complicated low-symmetrysystems.

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