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

Abstract

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 CaF₂, InP, ZnS, hexagonal ZnS, BeO and tetragonal BaTiO₃ 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.