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The effects of profile‐function truncation in X‐ray powder‐pattern fitting
Author(s) -
Toraya H.
Publication year - 1985
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/s0021889885010445
Subject(s) - truncation (statistics) , intensity (physics) , function (biology) , truncation error , reflection (computer programming) , symmetry (geometry) , simple (philosophy) , range (aeronautics) , x ray , singlet state , computational physics , chemistry , optics , physics , materials science , mathematical analysis , mathematics , geometry , atomic physics , statistics , computer science , excited state , philosophy , epistemology , evolutionary biology , biology , programming language , composite material
Computer‐synthesized reflection profiles were used to analyze the effects of truncation of the profile functions in X‐ray whole‐powder‐pattern fitting. The effects of truncation on the deduced integrated intensity and background were first elucidated for singlet, doublet and triplet profiles. It was found that weak reflections suffer large truncation errors in their integrated intensities when they overlap with strong reflections. Truncation also influenced the results for both positional and thermal parameters in whole‐pattern‐fitting structure refinement through its effects on the deduced integrated intensities and background levels in the powder pattern. The intensity variations of individual reflections during structure refinement are, however, constrained by the structure. Truncation errors in positional parameters are larger in structures with lower symmetry and more freedom for variations of the atomic positions in the model being refined because more variation is possible in individual reflections, particularly the weak ones. It is shown that truncation errors in the refined parameters can be substantially suppressed by a simple strategem: extending the definition range of the profile function (DRPF) for the strong reflections to include > 99% of the profile area while leaving the DRPF for the other reflections at the smaller values customarily used.