Anharmonic Debye-Waller factors and the study of structural phase transitions

Abstract

Analytical expressions are obtained for the Debye-Waller factors of highly anharmonic double-minimum and flat-bottomed one-particle potential which differ only in the presence or absence of a potential barrier at the mid-point. A lack of sensitivity in the Debye-Waller factors to the presence of the potential barrier is demonstrated for potentials with parameters modelling the hydrogen atom in the KH2PO4-type ferroelectrics at room temperature. The analysis indicates that a series of measurements with decreasing temperature may be necessary for a double minimum in the potential to be resolvable for these systems. The Debye-Waller factors investigated here show an anomalous temperature dependence in certain regions of reciprocal space, where they produce constant or even increasing integrated intensities of Bragg diffraction peaks with increase in temperature. Comparisons are made with the Debye-Waller factors for a disorder model, based on a one-particle probability density constructed from two displaced Gaussian distributions. This model is unable to reproduce the anomalous temperature dependence predicted by the anharmonic potentials.