Temperature diffuse scattering of nanocrystals
Abstract:The effects of thermal vibrations on X‐ray powder diffraction patterns are discussed. Special considerations for extremely small crystallites are described, including the occurrence of surface and edge vibrational modes, and a restriction on the maximum phonon wavelength. In doing so, a complete temperature diffuse scattering (TDS) model is presented, which includes the influence of these features on: the Debye–Waller parameter; first‐order TDS; and higher‐order TDS terms. The importance of using an accurate TDS representation is studied as a function of temperature and crystallite size. It is found that a misrepresentation of the TDS for small crystallites can lead to an error in the determined Debye–Waller parameter on the order of 20–40% and a slight overestimation of the peak broadening. While the presented theory is primarily developed considering X‐ray scattering, the same expressions are expected to describe the TDS in faster‐than‐sound neutron powder diffraction measurements.
Document Type: Research Article
Publication date: May 1, 2012