Profile fitting of X-ray diffraction lines and Fourier analysis of broadening

Abstract

The extraction of pure-specimen X-ray diffraction-line broadening is described using a convolution of the instrumental profile and an exact Voigt function. Real Fourier coefficients were computed from the Cauchy and Gauss integral breadths and were input for Warren–Averbach analysis. Smooth surface-weighted and volume-weighted column-length distribution functions were obtained and errors in root-mean-square strains as well as effective domain sizes were evaluated. The method was applied to two cubic structures with average volume-weighted domain sizes up to 3600 Å as well as patterns of tetragonal and orthorhombic (La, Sr)₂CuO₄, which exhibit weak line broadenings and highly overlapping reflections. Comparison with the integral-breadth methods is given. Reliability of the method is discussed in the case of a cluster of overlapping peaks.