Phonon spectrum and elastic properties of Y$_{2}$Sn$_{2}$O$_{7}$

The phonon spectrum of yttrium stannate Y$_{2}$Sn$_{2}$O$_{7}$ is calculated within a general ab initio approach and the frequencies and types of IR and Raman modes are determined. The degree of involvement of ions in phonon modes is determined from the analysis of displacement vectors calculated ab initio. The elastic constants and hardness of Y$_{2}$Sn$_{2}$O$_{7}$ are calculated. The impurity ion–ligand distance in Y$_{2}$Sn$_{2}$O$_{7}$ : Yb$^{3+}$, Y$_{2}$Sn$_{2}$O$_{7}$ : Eu$^{3+}$, Lu$_{2}$Sn$_{2}$O$_{7}$ : Yb$^{3+}$, Nd$_{2}$Sn$_{2}$O$_{7}$ : Gd$^{3+}$, Nd$_{2}$Sn$_{2}$O$_{7}$ : Tb$^{3+}$ impurity centers is calculated.