Temperature-dependent X-ray dynamical diffraction: Darwin theory simulations

Thermal vibrations destroy the perfect crystalline periodicity generally as sumed by dynamical diffraction theories. This can lead to some difficulty i n deriving the temperature dependence of X-ray reflectivity from otherwise perfect crystals. This difficulty is overcome here in numerical simulations based on the extended Darwin theory, which does not require periodicity. U sing Si and Ge as model materials, it is shown how to map the lattice vibra tions derived from measured phonon dispersion curves onto a suitable Darwin model. Good agreement is observed with the usual Debye-Waller behavior pre dicted by standard theories, except at high temperatures for high-order ref lections. These deviations are discussed in terms of a possible breakdown o f the ergodic hypothesis for X-ray diffraction.