First-principles study of the lattice dynamics of Sb₂S ₃

We present a lattice dynamics study of orthorhombic antimony sulphide (Sb₂S₃) obtained using density-functional calculations in conjunction with the supercell force-constant method. The effect of Born effective charges is taken into account using a mixed-space approach, resulting in the splitting of longitudinal and transverse optical (LO-TO) phonon branches near the zone center. Zone-center frequencies agree well with Raman scattering experiments. Due to the slow decay of the interatomic force constants (IFC), a minimal 2 × 4 × 2 supercell (Pnma setting) with 320 atoms is crucial for an accurate determination of the dispersion relations. Smaller supercells result in artificial acoustic phonon softening and unphysical lifting of degeneracies along high symmetry directions. We propose a scheme to investigate the convergence of the IFC with respect to the supercell sizes. The phonon softening can be attributed to the periodic images that affect the accuracy of the force constants, and the truncation of long-ranged forces. The commensuration of the q-vectors with the supercell size is crucial to preserve degeneracies in Sb₂S₃ crystals.