Vibrational spectra and force constants of rare earth and scandium thiospinels

Infrared and Raman spectra were measured for AB₂S ₄ spinels ( A = Cd, Mg, or Zn; B = Sc, Yb, or Tm). The four T_{1 u} ir bands and four of the five ( A_{1 g} + E_g + 3 T_{2 g}) Raman bands were generally observed. Symmetry coordinates were calculated for the spinel structure and normal coordinates were calculated using a model containing four force constants. Good fits of the eight observed vibrational frequencies were obtained from four force constants. The tetrahedral stretching constants have values between 1.41 and 0.49 mdyn/Å, while the octahedral stretching constants have values between 0.61 and 0.38 mdyn/Å. The tetrahedral stretching constant was always larger for Cd compounds than for compounds containing the smaller Mg ion in tetrahedral sites, suggesting a measure of the additional stabilization of Cd through covalent bonding. Calculated absorbances for the ir transverse mode frequencies were in reasonable agreement with experiment and support the four-force-constant model.