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Limitations on the additivity of moments in line‐profile analysis
Author(s) -
Wilson A. J. C.
Publication year - 1970
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/s0021889870005678
Subject(s) - additive function , range (aeronautics) , centroid , line (geometry) , inverse , displacement (psychology) , zero (linguistics) , mathematics , variance (accounting) , series (stratigraphy) , statistical physics , mathematical analysis , physics , materials science , geometry , geology , psychology , paleontology , linguistics , philosophy , accounting , business , composite material , psychotherapist
The leading terms in the centroid‐range and the variance‐range curves are additive in the contributions made by the various sources of line displacement and line broadening. The intercept of the variance‐range curve contains non‐additive contributions inherent in the slow approach to zero of the functions convoluted in the line profile. Further terms in the series for these curves contain non‐additive contributions that depend both on the functions convoluted and the range used; these terms approach zero as an inverse power of the range as this is increased.