Accurate structure factor determination and electron charge distributions of binary cubic solid solutions

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Abstract
By combining the accurate low-angle X-ray structure factors of binary cubic solid solutions determined by high-energy electron diffraction (HEED) with higher-angle values obtained by interpolation between best pure-element form factors, a complete set of accurate X-ray structure factors for these alloys can be produced. This approach is an improvement over previous analyses of this sort, where the pure-element form factors were considered unchanged by alloying (except for lattice parameter changes). This new method has been applied to the alloy systems CuAu, CuAl and FeCr, where sufficient electron diffraction information is available for a full analysis. The results show that the average low-angle form factors are significantly modified by alloying. These electron charge distribution changes can be explained in terms of the known Fermi surface behaviour of these alloys. In addition to these electron charge distribution studies, the effects of short-range order (s.r.o.) were also investigated. Changes in s.r.o. affect the structure factors of solid solution alloys predominantly through the Debye–Waller factors, and both theoretical and experimental investigations showed that for FeCr and CuAl which have small atomic radius differences. the effects of s.r.o. on the structure factors are negligible. In the case of CuAu, the differences in s.r.o. due to differing heat treatments have been detected by electron diffraction measurements. Such changes, however, were found to be fairly small, and if the effects of s.r.o. are ignored, only very small increases are introduced into the errors in the measured values of the low-angle structure factors. Cubic elements for which accurate form factors are known are indicated, and alloy combinations of these should provide the basis for useful further work.