Structure and Lattice Dynamics of R _2 Sn _2 O _7 and R _2 Zr _2 O _7 (R = La–Lu) Crystals: Ab Initio Calculation

Crystal structure and phonon spectrum of rare-earth stannates R _2 Sn _2 O _7 and zirconates R _2 Zr _2 O _7 (R = La–Lu) with the pyrochlore structure were studied within the framework of DFT and MO LCAO approach. The calculations were performed by using hybrid functional PBE0 that take into account nonlocal exchange at the Hartree-Fock formalism. The calculation of the phonon spectrum at the Γ -point made it possible to supplement the available experimental data on the IR and Raman spectra of stannates and zirconates. In the framework of the ab initio approach, the change of the elastic properties of zirconium oxide t-ZrO _2 by doping the yttrium was studied. Calculations were performed in the CRYSTAL17 program designed to simulate periodic structures.