Vibrational amplitudes and Debye-Waller factors from elastic constants and Raman frequencies

Simple formulae, based on the rigid-ion model of lattice dynamical theory, have been obtained for mean square vibrational amplitudes in compound crystals in terms of the elastic constants and infrared or Raman frequencies. Results are obtained for cubic CaF 2 , InP, ZnS, hexagonal ZnS, BeO and tetragonal BaTiO 3 for comparison with experiment and lattice dynamics calculations. The equivalent calculation based on the Debye approximation is found to contain two errors, each of about 25% even at low temperatures.