Lattice Vibration Spectra. LX. Lattice Dynamical Calculations on Spinel Type MCr2S4 (M = Mn, Fe, Cd)

Lattice dynamical calculations of the spinel type MCr2S4 (M = Mn, Fe, Cd) have been done using various potential models (short-range, rigid-ion, polarizable-ion). The main results are that (i) the vibrational modes (eigenvectors) and potential energy distributions of the Raman and IR allowed phonon modes of the three chromium sulfides are very similar, (ii) the A-X and B-X short-range force constants (referring to AB2X4) strongly depend on the structural parameter u, i.e., the tetrahedral A-X force constants are smaller than the respective octahedral B-X ones opposite to previous calculations on the basis of an ideal spinel structure with u = 0.25, (iii) bending force constants (X-A-X and X-B-X), but not X-X and B-B repulsive forces, are negligible, (iv) in the case of the breathing mode of the tetrahedral AX4 unit (species A1g) the demand on B-X and X-X (stretching and repulsion) forces is larger than that on the A-X force, and (v) the effective dynamic charges of the bivalent metal ions are nearly zero.