Phonon spectra of eulytite crystals Bi4M3O12 (M = Ge,Si): ab initio study

In this paper we present the results of ab initio DFT calculation of phonon spectra for bismuth ortho-germanate Bi4Ge3O12 and bismuth ortho-silicate Bi4Si3O12 crystals, in the center of the first Brillouin zone. First, the geometry optimization was performed using the analytical energy gradients, with respect to atomic coordinates and unit cell parameters. Vibrational frequencies and normal modes were calculated within the harmonic approximation by diagonalizing the mass-weighted Hessian matrix. The IR and Raman spectra of both crystals were simulated with the periodic ab initio Crystal 09 code and B3LYP hybrid functional and the two sets of Transverse-Optical and Longitudinal-Optical frequencies are generated, together with their intensities. Also, the influence of isotopic substitution for Bi, Ge and O in phonon modes and the picture with values of frequencies shift in each mode by isotopic substitution were calculated. The obtained results are discussed and the comparision between the computed spectra and experimental data is quite satisfactory, which justifies the model and simulation scheme used for the title systems.