The determination of crystallite dimensions using synchrotron-radiation X-ray diffraction photographs

Synchrotron-radiation Laue patterns give valuable information on the sizes and shapes of grains in a polycrystalline material even if these are too small for synchrotron topography. A calculation, based on kinematic theory, is presented for the radial and lateral broadening of the diffraction spots obtained with white radiation. The most conspicuous broadening is to be expected when the dimensions of the reflecting planes are small and not their number; this is at variance with the conditions leading to broadening with conventional monochromatic methods. Quantitative assessment of the crystal dimensions is possible if auxiliary spectral information is obtained by using selectively absorbing filters. The theory was applied to the analysis of Laue photographs of xenon and krypton crystallites condensed on a cooled beryllium substrate. Crystal dimension down to a few nanometers could be determined. The method is, in principle, applicable to the determination of the grain size and shape distribution of fine-grained polycrystalline samples of any material. Changes during crystallization and recrystallization can be easily followed by virtue of the simple experimental set-up and short exposure times involved.