Premium
Anisotropic diffraction‐line broadening due to microstrain distribution: parametrization opportunities
Author(s) -
Leineweber Andreas
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/s0021889806019546
Subject(s) - anisotropy , covariance , tensor (intrinsic definition) , isotropy , parametrization (atmospheric modeling) , gaussian , diffraction , rank (graph theory) , physics , mathematical analysis , covariance function , distribution (mathematics) , mathematics , materials science , pure mathematics , quantum mechanics , combinatorics , statistics , radiative transfer
A correlated Gaussian lattice‐parameter distribution of an ensemble of crystals, as leading to line broadening in the course of powder diffraction, can be associated with a correlated Gaussian microstrain distribution. The latter can be described in terms of a fourth‐rank covariance tensor containing as its 81 components E ijpq , the variances and the covariances of the nine components ɛ ij of the symmetric second‐rank strain tensor (formulated with respect to Cartesian coordinates), i.e. E ijpq = 〈ɛ ij ɛ pq 〉. The restrictions for the E ijpq tensor components resulting from assumed crystal class‐symmetry invariance are the same as expected for certain fourth‐rank property tensors, like compliancy. The parametrization of anisotropic microstrain broadening ( e.g. in the course of Rietveld refinement) on the basis of the covariance tensor components E ijpq has, in comparison with earlier approaches, the advantage of straightforward recognizability of the case of isotropic microstrain broadening, independently of the actual crystallographic coordinate system.