Vibrational analysis of the two non-equivalent, tetrahedral tungstate (WO 4) units in Ce 2(WO 4) 3 and La 2(WO 4) 3

Abstract

The infrared and Raman spectra of Ce 2(WO 4) 3 and La 2(WO 4) 3, which are complicated by the superposition of bands from two non-equivalent WO 4 units, have been successfully assigned above 300 cm −1 according to T d point group symmetry. Individual assignment of the two types of tungstate units, W IO 4 ( C 2 site symmetry) and W IIO 4 ( C 1 site symmetry), relies on comparison with the spectra of tetrahedral reference tungstates of Na 2WO 4, CaWO 4, and MgWO 4, and on the differences between W IO 4 and W IIO 4 known from the crystal structure. Normal coordinate analysis indicates that the force constants for W IO 4 and W IIO 4 roughly correlate with the amount of deviation from ideal T d point symmetry, W IO 4 being similar to CaWO 4 (both mildly distorted tetrahedrons), while W IIO 4 is closer to MgWO 4 (both highly distorted tetrahedrons). Non-ideality is also indicated by the calculated potential energy distribution (PED), which shows a substantial degree of vibrational interaction between bonds—especially in the less symmetric W IIO 4 unit. Frequency differences between IR and Raman bands that originate from the same T d point group modes are attributed mainly to factor group splitting (i.e. Raman active gerade and IR active ungerade factor group modes). However, the LO-TO polarization mixing and surface modes that generate the observed vibrational frequencies in powders may also contribute to these frequency differences, since the magnitude of these effects may not be the same in Raman as in IR. Finally, it is likely that other rare earth tungstates of stoichiometry Ln 2(WO 4) 3, where Ln=La∼Dy, have similar vibrational spectra due to their similar structures.