Anharmonic Debye-Waller factors using quantum statistics

Anharmonic Debye-Waller factors and thermal smearing functions are derived for all temperatures in the one-particle-potential (OPP) model of vibrations by applying a perturbed density-matrix expansion about the harmonic case. Where possible, general results appropriate to sites of arbitrary symmetry are described, while the important case of sites possessing cubic point-group symmetry is investigated in detail. A useful finding is that the OPP model appears capable of describing the temperature dependence of anharmonic Debye-Waller factors at least down to Theta M /4, while the previous classical approaches begin to fail, as expected, at about Theta M , where Theta M is the Debye characteristic temperature.