The vibrational spectra of lithium niobate, barium sodium niobate and barium sodium tantalate

Crystallographic studies of Ba₂ NaNb₅O₁₅ have shown that the possible space groups are D⁶₂, C¹¹_2v and D¹⁹_2h. The coincidences between the infrared and Raman spectra support the conclusion, based on the ferroelectric properties of the crystal, that the space group is C¹¹_2v. The anomalous tantalum compound has a spectrum compatible with a similar structure. The vibrations are classified as internal modes of the Mo₆ octahedron (M=Nb, Ta) and lattice translations involving motion of the cation. Force constants are calculated for internal modes using the Wilson FG matrix method and for lattice modes using the Born-von Karman theory.