X-ray diffraction broadening analysis

Abstract

The microstructural parameters of a crystalline sample can be determined by a proper analysis of XRD line profile broadening. The observed XRD line profile, h(ε), is the convolution of the instrumental profile, g(ε), and pure diffraction profile, f(ε), caused by small crystallite (coherent domain) sizes, by faultings in the sequence of the crystal lattice planes, and by the strains in the crystallites. Similarly, f(ε) is the convolution of the crystallite size/faulting profile, p(ε), and the strain profile, s(ε). The derivation of f(ε) can be performed from h(ε) and g(ε) by the Fourier transform method, which does not require mathe-matical assumptions. The analysis of f(ε) can be done by the Warren-Averbach method applied to the ob-tained Fourier coefficients. Simplified methods based on integral widths may also be used in studies where a good relative accuracy suffices. The relation among integral widths of f(ε), p(ε) and s(ε) can be obtained if one assumes bell-shaped functions for p(ε) and s(ε). Integral width methods overestimate both strain and crystallite size parameters in comparison to the Warren-Averbach method. The crystallite size parameter is more dependent on the accuracy in the diffraction profile measurement, than it is the strain parameter. The precautions necessary for minimization of errors are suggested through examples. The crystallite size and strain parameters obtained by means of integral widths are compared with those which follow from the Warren-Averbach method. Recent approaches in derivation of microstructure are also mentioned in short.