Convolutional whole profile fitting of diffraction patterns using model based physical functions

G. Ribárik and T. Ungár

Department of General Physics,

Eötvös University, Budapest, P.O.Box 32, H-1518, Hungary

Email: ribarik@renyi.hu

X-ray peak profile analysis is a powerful method for determining the microstructural properties of dislocated powders and polycrystalline materials. The Convolutional Multiple Whole Profile (CMWP) fitting method has been developed recently for the extraction of physical parameters for crystallite size distribution and dislocation structure from diffraction patterns of cubic, hexagonal or orthorombic materials. In this procedure the whole measured powder diffraction pattern is fitted by the sum of a background function and profile functions. The background is approximated by a spline function or a sum of Legendre polinomials. The profile functions are calculated as the convolution of the theoretical functions for physical broadening and the measured instrumental profiles. The physical profiles are calculated on the basis of the microstructure assuming that the crystallites have lognormal size distribution and the strain is caused by dislocations. The strain profile is based on the Wilkens dislocation theory. Strain and size anisotropy is taken into account by the dislocation contrast factors and the ellipticity of crystallites, respectively. The fitting procedure is based on a nonlinear least squares method and provides the median and the variance of the size distribution, the ellipticity of crystallites and the density and arrangement of dislocations. Since the CMWP method is a microstructural method, the peak positions and peak intensities are not physically interpreted, they are treated as free parameters. However, in order to get the best results, these peak parameters can be refined and are determined along with the microstructural parameters. The procedure will be illustrated by different specific case studies.