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Application of the pattern‐fitting structure‐refinement method of X‐ray powder diffractometer patterns
Author(s) -
Young R. A.,
Mackie P. E.,
Von Dreele R. B.
Publication year - 1977
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/s0021889877013466
Subject(s) - diffractometer , powder diffractometer , materials science , rietveld refinement , cauchy distribution , crystal structure , powder diffraction , tetragonal crystal system , crystallography , mathematics , diffraction , analytical chemistry (journal) , optics , chemistry , mathematical analysis , physics , chromatography
The whole‐pattern least‐squares fitting method (herein called the pattern‐fitting structure‐refinement, PFSR, method) developed by Rietveld and used by many with neutron powder data has been extended for use with X‐ray powder diffractometer data. Examples of PFSR for specimens in five different space groups are given. Structural parameters generally agree, within 2σ, with those from single‐crystal results where available. Atom positions and site occupancies were determined for LaPO 4 Ca 5 PO 4 ) 3 F, and quartz. R (pattern) values generally ranged from 9 to 20% while R (Bragg) values were a few percent lower. Reflection profiles were represented by either Gaussian or Cauchy functions: better representations are shown to be needed with an expected result of improved sensitivity accompanying lower R values. Possibilities for improved pattern‐stripping for minor phase study via PFSR of the major phase are exhibited. Remarkably precise lattice parameters, e.g. 1 part in 35000 from data all below 2θ < 77° in the fluorapatite case, and parametric characterization of the diffraction broadening of the Bragg profiles are obtained as additional benefits.