Two different methods of diffraction profile analysis are presented. In the first, the breadths and the first few Fourier coefficients of diffraction profiles are analysed by modified Williamson–Hall and Warren–Averbach procedures. A simple and pragmatic method is suggested to determine the crystallite size distribution in the presence of strain. In the second, the Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well established ab initio functions of size and strain profiles. In both procedures, strain anisotropy is rationalized by the dislocation model of the mean square strain. The procedures are applied and tested on a nanocrystalline powder of silicon nitride and a severely plastically deformed bulk copper specimen. The X‐ray crystallite size distributions are compared with size distributions obtained from transmission electron microscopy (TEM) micrographs. There is good agreement between X‐ray and TEM data for nanocrystalline loose powders. In bulk materials, a deeper insight into the microstructure is needed to correlate the X‐ray and TEM results.

A computer program has been developed for the determination of microstructural parameters from diffraction pro®les of materials with cubic or hexagonal crystal lattices. The measured pro®les or their Fourier transforms are ®tted by ab initio theoretical functions for size and strain broadening. In the calculation of the theoretical functions, it is assumed that the crystallites have log-normal size distribution and that the strain is caused by dislocations. Strain and size anisotropy are taken into account by the dislocation contrast factors and the ellipticity of the crystallites. The ®tting procedure provides the median and the variance of the size distribution and the ellipticity of the crystallites, and the density and arrangement of the dislocations. The ef®ciency of the program is illustrated by examples of severely deformed copper and ball-milled lead sul®de specimens.

A systematic procedure is developed to evaluate the density of planar defects together with dislocations and crystallite or subgrain size by x-ray line profile analysis in fcc crystals. Powder diffraction patterns are numerically calculated by using the DIFFAX software for intrinsic and extrinsic stacking faults, and twin boundaries for the first 15 Bragg reflections up to 20% fault density. It is found that the Bragg reflections consist of five subreflection types categorized by specific selection rules for the hkl indices in accordance with the theory of Warren [Prog. Met. Phys. 8, 147 (1959)]. It is shown that the profiles of the subreflections are Lorentzian-type functions. About 15 000 subreflections are evaluated for their full widths of half maxima and their positions relative to the exact Bragg angle. These values are parametrized as a function of the density and type of planar faults. A whole profile fitting procedure, previously worked out for determining the dislocation structure and crystallite size distributions, is extended for planar fault by including these data into the software. The method is applied to evaluate twin densities in nanocrystalline and submicron grain-size copper specimens. It is found that twinning becomes substantial under a critical crystallite or subgrain size of about 40nm, in accordance with other observations.

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The microstructure of carbon blacks is investigated by X-ray diffraction peak profile analysis. Strain anisotropy is accounted for by the dislocation model of the mean square strain in terms of average dislocation contrast factors. Crystallite shape anisotropy is modeled by ellipsoids incorporated into the size profile function. Different grades of carbon blacks, N990, N774 and N134, untreated, heat-treated and compressed at 2.5 GPa have been investigated. The microstructure is characterized in terms of crystallite size-distribution, dislocation density and crystallite shape anisotropy. Heat treatment results in increased vertical and lateral sizes of graphitic crystallites. Postproduction pressure treatment has little effect on the average sizes of the crystallites, however, it affects the crystallite size distribution function. The average sizes of the crystallites obtained by X-ray diffraction agree with those estimated from Raman spectra. Applied pressure affects the magnitude of strain within the crystallites.