Application of matrix decomposition algorithms for singular matrices to the Pawley method in Z-Rietveld

R. Oishi-Tomiyasu, M. Yonemura, T. Morishima

Research output: Contribution to journalArticle

76 Citations (Scopus)

Abstract

Z-Rietveld is a program suite for Rietveld analysis and the Pawley method; it was developed for analyses of powder diffraction data in the Materials and Life Science Facility of the Japan Proton Accelerator Research Complex. Improvements have been made to the nonlinear least-squares algorithms of Z-Rietveld so that it can deal with singular matrices and intensity non-negativity constraints. Owing to these improvements, Z-Rietveld successfully executes the Pawley method without requiring any constraints on the integrated intensities, even in the case of severely or exactly overlapping peaks. In this paper, details of these improvements are presented and their advantages discussed. A new approach to estimate the number of independent reflections contained in a powder pattern is introduced, and the concept of good reflections proposed by Sivia [J. Appl. Cryst. (2000), 33, 1295-1301] is shown to be explained by the presence of intensity non-negativity constraints, not the intensity linear constraints.

Original languageEnglish
Pages (from-to)299-308
Number of pages10
JournalJournal of Applied Crystallography
Volume45
Issue number2
DOIs
Publication statusPublished - Feb 9 2012

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Decomposition
Powder Diffraction
Rietveld analysis
Biological Science Disciplines
Least-Squares Analysis
Powders
Particle accelerators
Protons
Japan
Research

All Science Journal Classification (ASJC) codes

  • Biochemistry, Genetics and Molecular Biology(all)

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Application of matrix decomposition algorithms for singular matrices to the Pawley method in Z-Rietveld. / Oishi-Tomiyasu, R.; Yonemura, M.; Morishima, T.

In: Journal of Applied Crystallography, Vol. 45, No. 2, 09.02.2012, p. 299-308.

Research output: Contribution to journalArticle

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