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An Evaluation of Some Profile Models and the Optimization Procedures Used in Profile Fitting

Published online by Cambridge University Press:  06 March 2019

Scott A. Howard  and
Robert L. Snyder
Scott A. Howard
Affiliation:
N.Y.S. College of Ceramics at Alfred-University, Alfred, N.Y. 14802
Robert L. Snyder
Affiliation:
N.Y.S. College of Ceramics at Alfred-University, Alfred, N.Y. 14802
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Abstract

This paper examines some of the concerns regarding the development of an algorithm for the refinement of X-ray diffraction profiles. The object of the algorithm is to provide a time efficient method of refinement through the choice of a suitable profile function and optimization technique.

Seven profile models were tested using a least-squares error criterion for refinement. Profile parameters were refined using non-linear Gauss-Newton, Marquardt and Simplex algorithms. The profiles were refined on a pattern digitally collected from an NBS 640A silicon sample.

The results of this study indicate the repetitive function evaluations are not necessarily the time consuming step in the profile fitting process. As the number of parameters needed to evaluate the profile and the number of points in the profile increases, the time required to perform the mathematics in the Gauss-Newton and Marquardt algorithms increases. Although the Simplex was most memory and time efficient, our Gauss-Newton optimization algorithm provided a more consistent set of refined values which were not as dependent on the initial estimates of the parameters.

The most favorable results were obtained by using the split Pearson VII profile with the alpha 2 reflection fixed in position and intensity with respect to the alpha 1 reflsction. This method generated the lowest residual error and was found to avoid some problems resulting from the alpha 1, alpha 2 line overlap.

Type
II. Search/Match Procedures, Powder Diffraction File
Information
Advances in X-Ray Analysis , Volume 26: Thirty-First Annual Conference on Applications of X-ray Analysis, August 1-6, 1982 , 1982 , pp. 73 - 80
Copyright
Copyright © International Centre for Diffraction Data 1982

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References

1. Marquardt, D. W., An algorithm for least-squares estimation of nonlinear parameters, J. Soc. Indust. Appl. Math., 11:431 (1963).Google Scholar
2. Nelder, J. A. and Mead, R., A simplex method for function minimization, Comput. J., 308 (1965).Google Scholar
3. Rietveld, H. M., A profile refinement method for nuclear and magnetic structures, J. Appl. Cryst, 2:65 (1969).Google Scholar
4. Huang, T. C. and Parrish, W., Accurate and rapid reduction of experimentail X-ray data, App, Phys. Letters, 27:123 (1975).Google Scholar
5. de Keijser, Th. H., Langford, J. I., Mlttemeijer, E. J., and Vogels, A. B. P., Use of the Voigt function in a singleline method for the analysis of X-ray diffraction line broadening, J. Appl. Cryst., 15:308 (1982).Google Scholar
6. Hall, M. M., Jr. and Henslee, W. W., The approximation of symmetric X-ray peaks by Pearson type VXI distributions, J. Appl. Cryst., 10:66 (1977).Google Scholar
7. Brown, A. and Edmonds, J. W., The fitting of powder diffraction profiles to an analytical expression and the influence of line broadening factors, Adv. in X-ray Anal., 23:361 (1970).Google Scholar