Structure and dynamics of a lattice of tetragonal germanates $R_{2}$Ge$_{2}$O$_{7}$ ($R$ = Tb–Lu, Y): ab initio calculation

Within the framework of density functional theory, an ab initio calculation was carried out to study the crystal structure, phonon spectrum and elastic constants of a series of rare-earth germanates, including yttrium germanate $R_{2}$Ge$_{2}$O$_{7}$ ($R$ = Tb–Lu, Y) with tetragonal structure. The frequencies and types of fundamental vibrations as well as the intensities of the IR and Raman modes were determined. The degree of participation of ions in each mode was determined from the analysis of the displacement vectors obtained from the ab initio calculation. The calculations were performed for the first time. The corresponding experimental data for the entire series, with the exception of the IR and Raman spectra of yttrium germanate, are absent. The calculations made it possible to interpret and supplement available in the scientific articles results of measurements of the IR and Raman spectra of yttrium germanate Y$_{2}$Ge$_{2}$O$_{7}$.