Lattice dynamics and vibrational properties of scheelite-type alkali-metal perrhenates

The present work provides insight into the structural, vibrational, and elastic properties of scheelite-type alkali-metal perrhenates AReO₄(<i>A</i>= Na, K, Rb, and Cs) via first-principles calculations. Sodium, potassium, and rubidium perrhenates are isostructural and crystallize in a tetragonal structure, whereas cesium perrhenate crystallizes in an orthorhombic structure. All the phonon frequencies and their corresponding mode assignments were estimated through the linear response method within density-functional-perturbation theory. The phonon density of states highlights the participation of the oxygen anions and both the A-type and rhenium (Re) cations in the low-frequency range. In contrast, the oxygen and Re atoms make relatively high and moderate contributions to the remaining phonon frequency spectrum. Considerable splitting of the longitudinal and traverse optic modes was observed. Elastic constants and phonon dispersion calculations confirmed the mechanical and dynamic stability of the studied AReO₄compounds. A redshift was observed with the frequency of the phonons following the sequence Na→Cs. The low value calculated for the bulk modulus (ranging from 28.36 GPa to 14.15 GPa) and shear modulus indicates the perrhenates have a low resistance to deformation. The values of these moduli decrease in the order of Na→Cs, which correlates with an increase in an ionic radius of the cation. The response to pressure was found to be anisotropic. This characteristic and the ductile nature of the alkali-metal perrhenates were confirmed through elastic analysis.