Thermal expansion tensors, Grüneisen parameters and phonon velocities of bulk MT₂ (M = W and Mo; T = S and Se) from first principles calculations

We calculated the phonon spectra of several 2H-MT₂ structures using the density functional perturbation theory (DFPT). The symmetry properties of phonon modes are analyzed. The mode-Grüneisen parameters and phonon velocities are calculated using phonon spectra. All the investigated structures show very large phase velocities (>10-000 m s^-1) and small group velocities (<600 m s^-1). The macroscopic Grüneisen parameter of the [001] direction is larger than that of the [010] direction for 2H-MT₂ phases. The volumetric and linear thermal expansion coefficients are evaluated using the quasi-harmonic approximation (QHA) between 0 K and 1100 K. The negative thermal expansion coefficients are discovered in the 2H-WS₂ structure. Our results show that the properties in the [001] direction are very different to the [010] direction, because of the significant difference in the chemical bonding in the two crystallographic directions for these layered materials.