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Analytical formulation of the variance method of line‐broadening analysis for Voigtian X‐ray diffraction peaks
Author(s) -
Ortiz Angel L.,
Cumbrera Francisco L.,
SánchezBajo Florentino
Publication year - 2006
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/s0021889806017122
Subject(s) - voigt profile , diffraction , line (geometry) , mathematics , basis (linear algebra) , gauss , crystallite , variance (accounting) , root mean square , lattice (music) , optics , computational physics , physics , mathematical analysis , statistical physics , spectral line , chemistry , geometry , crystallography , quantum mechanics , accounting , acoustics , business
An alternative formulation of the variance method for the line‐broadening analysis of polycrystalline materials is presented. It maintains the theoretical basis of the earlier formulations of the variance method, but differs in the manner of calculating the variance coefficients of the line profiles. In the proposed formulation, these are evaluated analytically in terms of the shape parameters of Voigt functions fitted to the X‐ray diffraction data. Explicit expressions are thus derived for calculating the (surface‐weighted) crystal sizes and (root‐mean‐square) lattice microstrains from the integral breadths of the Gauss and Lorentz components of the Voigt functions that model the experimental and instrumental line profiles.