X-ray standing waves in garnet crystals

Abstract
Measurement of fluorescent radiation produced by x-ray standing waves is applied to site-occupancy determination in both thin layers and bulk garnet single crystals. The fluorescence yield for atoms in different crystallographic sites has been calculated for the (521) and (444) reflections in the case of gadolinium gallium garnet for both a thin layer and a bulk crystal. Primary extinction is discussed. We find that, although it may play a major role in determining the line shape of the fluorescence yield, the effect is not as dramatic in garnets as it is in silicon or germanium, so that different crystallographic sites give clearly distinctive fluorescence patterns even for bulk crystals. Finally, theoretical and experimental line shapes are compared.