A Qualitative Account for Anisotropic Broadening in Whole-Powder-Diffraction-Pattern Fitting by Second-Rank Tensors

Abstract

Anisotropic line broadening in cell-constrained wholepowder-pattern fitting (including the Rietveld method) is proposed to be modelled qualitatively. The object is primarily to improve the fit, with the expectation of an increase in the feasibility of an ab initio structure determination in difficult cases. In a first simple approach, distances from an origin to ellipsoid surface are considered to represent the directionally dependent widths and shapes. Improvements in the profile refinements with a decrease of up to about 50% in the R factors may be obtained in cases unaffected by faulting. Experimental cases support the method and show the application limits.

Phenomenological model of anisotropic peak broadening in powder diffraction

“…While the details differ among these treatments, they share the common feature that the width of the diffraction peak is expressed in terms of the six components of a symmetric tensor of the Miller indices. For example, this expansion has been applied to the parameters U, V and W of Caglioti et al (1958) by Le Bail & Jouanneaux (1997), such that…”

Synthesis, crystal structure and magnetism of Eu3Sc2O5Fe2As2

“…Spherical harmonics functions were used to describe the preferred orientation of the crystallites. Shape anisotropy effects were described by the approach of Le Bail and Jouanneaux [27].…”

Profile Analysis

“…Currently, most popular approaches are second-rank tensors (Le Bail and Jouanneaux, 1997), symmetrized spherical harmonics (Popa, 1998) or multidimensional distribution of lattice metrics (Stephens, 1999). All these approaches can easily be used in the context of convolution-based profile fitting.…”