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The effect of profile step width on the determination of crystal structure parameters and estimated standard deviations by X‐ray Rietveld analysis
Author(s) -
Hill R. J.,
Madsen I. C.
Publication year - 1986
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889886090076
Subject(s) - standard deviation , rietveld refinement , diffractometer , mathematics , r value (soils) , analytical chemistry (journal) , diffraction , chemistry , crystallography , crystal structure , statistics , physics , optics , chromatography , structural engineering , subgrade , engineering
Crystal‐structure parameters and their associated estimated standard deviations (e.s.d.'s) have been determined for α‐Al 2 O 3 by Rietveld analysis of Cu K α X‐ray powder diffraction data collected on a standard diffractometer with profile step widths ranging from 0.01 to 0.32° 2 θ . Estimates of the true precision of the parameters have been obtained by replication of the experiment five times. The degree of serial correlation between adjacent points in the profiles has been quantitatively determined by the use of the Durbin–Watson d statistic. Values of the conventional profile agreement indices, R p , R wp and goodness of fit, are not influenced by the scan‐point density, but the Bragg R ‐factor decreases to a limiting value as the step width is decreased. The structural parameters obtained at all step widths are statistically indistinguishable at the 1 σ level, although there is some loss of accuracy relative to single‐crystal values at widths larger than 0.16°. The least‐squares e.s.d.'s decrease linearly with the reciprocal square root of the number of steps in the pattern, as expected, but the e.s.d.'s of the unit‐cell dimensions are the only ones that are significantly smaller than estimates of their true precision obtained from repetitions of the experiment. In the case of α‐Al 2 O 3 , and possibly in general, the optimum step width for Rietveld analysis corresponds approximately to the minimum value of the full‐width at half‐maximum for well resolved peaks.