Raman Spectra of Bismuth Germanium Oxide and Bismuth Silicon Oxide

Raman spectra of single crystals of bismuth germanium oxide (${\mathrm{Bi}}_{12}$Ge${\mathrm{O}}_{20}$) and bismuth silicon oxide (${\mathrm{Bi}}_{12}$Si${\mathrm{O}}_{20}$) are studied at 300, 77, and 15 °K. These crystals are isomorphous, exhibit optical activity, and belong to the cubic space group $T^3\mathrm{}\left(I23\mathrm{}\right)\mathrm{}$. On the basis of one formula unit per primitive cell, a group-theoretical analysis predicts $8A$ (totally symmetric), $8E$ (doubly degenerate), and $24F$ (triply degenerate) zone-center optical phonons, without taking into account the LO-TO splitting of the polar $F$ modes. Phonons belonging to all three symmetries are Raman active. The most detailed spectra with well-resolved lines are observed in both crystals at 15 °K. The spectrum of ${\mathrm{Bi}}_{12}$Ge${\mathrm{O}}_{20}$ at 15 °K consists of a total of 36 lines which lie in the region 40-720 ${\mathrm{cm}}^{-1\mathrm{}}$. A total of 43 lines in the region 40-850 ${\mathrm{cm}}^{-1\mathrm{}}$ are observed in ${\mathrm{Bi}}_{12}$Si${\mathrm{O}}_{20}$ at 15 °K. The polarization of the Raman lines in both crystals is studied at 15 °K for the following two crystalline orientations: one with {100} faces and the other with (100), (011), and ($0\overline{1}1$) faces. Both right-angle and back-scattering geometries were used in polarization studies, and all the observed lines have been classified according to the irreducible representations of the point group $T$. Some of the $F$ modes in each crystal show LO-TO splitting. With plane-polarized radiation incident along [100] and scattered along [010] or [011], the intensity oscillations of prominent lines of ${\mathrm{Bi}}_{12}$Ge${\mathrm{O}}_{20}$ are studied as a function of the angle between the electric vector of the incident radiation and the scattering plane. The observed intensity oscillations for the lines studied in this manner lead to symmetry assignments which are in agreement with those determined from polarization studies. In view of the fact that there exist tightly bound groups of $M{\mathrm{O}}_4$ units in these crystals, where $M\equiv \mathrm{Ge}\mathrm{or}\mathrm{Si}$, a possible approach towards correlating some of the observed lines as originating from the normal modes of the $M{\mathrm{O}}_4$ unit is suggested.