Journal
JOURNAL OF APPLIED CRYSTALLOGRAPHY
Volume 39, Issue -, Pages 509-518Publisher
BLACKWELL PUBLISHING
DOI: 10.1107/S0021889806019546
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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 epsilon(ij) of the symmetric second-rank strain tensor ( formulated with respect to Cartesian coordinates), i.e. E-ijpq = [epsilon(ij)epsilon(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.
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