Geometrical parameterization of the crystal chemistry of P63/m apatite. II. Precision, accuracy and numerical stability of the crystal-chemical Rietveld refinement

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DOIResolve DOI: http://doi.org/10.1107/S0021889806009903
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TypeArticle
Journal titleJournal of Applied Crystallography
Volume39
Issue3
Pages369375; # of pages: 7
Subjectapatites; Rietveld analysis; crystal-chemical constraints; singular value decomposition; least-squares matrices; numerical stability
AbstractA script developed for crystal-chemical Rietveld refinement of P63/m apatite with TOPAS is implemented in parallel with standard structure refinement. Least-squares standard uncertainty (s.u.) values for directly extracted crystalchemical parameters are nearly an order of magnitude lower than those obtained indirectly by analysis of atom coordinates derived by standard Rietveld refinement. This amazing finding originates partly in the reduction of the number of refinement parameters from 21 to 17 and partly in the fact that cell data now derive from crystal-chemical parameters instead of vice versa. Great precision and accuracy otherwise funneled into unit-cell parameters is then more distributed among mostly crystal-chemical distance parameters. The least-squares s.u. values are supported by analysis of numerous refinements of the same experimental data with added artificial intensity noise. Structural parameters from single-crystal results agree better with those extracted by crystal-chemical refinement. On the basis of singular value decomposition analyses performed using the program SVDdiagnostic [Mercier et al. (2006). J. Appl. Cryst. 39, 458舑465], crystal-chemical and standard Rietveld refinements are shown to have similar numerical stability. Crystal-chemical parameters extracted by direct Rietveld refinement, therefore, are more precise than, more accurate than and numerically as reliable as those derived from analysis of regular crystallographic refinement of the same data.
Publication date
LanguageEnglish
AffiliationNational Research Council Canada; NRC Institute for Chemical Process and Environmental Technology; NRC Institute for Research in Construction
Peer reviewedNo
NRC number47878
NPARC number8925932
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Record identifier6bb4e0f9-2282-4d3f-95e3-2724556aab34
Record created2009-04-23
Record modified2016-05-09
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