X-ray diffraction profiles described by refined analytical functions

Abstract
The line profiles from a sample containing small spherical particles, non-uniform strain and instrumental broadening can be described exactly by using error functions with complex arguments. Consequently, the development by Houska & Smith [J. Appl. Phys. (1981). 52, 748-754] has been revised in terms of these functions. This calculation has been extended, by the use of error functions with complex arguments, to include a more general distribution of particle size or column heights than that obtained from a single sphere. The latter extension is applied to profiles obtained from a partially stabilized zirconia wear debris. It is found, in this example, that a column-height variation coefficient that is greater than that from a single sphere gives a somewhat better fit of the experimental line profiles. We find that if the single-sphere model is used to fit the profiles the particle size and root-mean-square strain differ by about 12 and 5% respectively.

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