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In this investigation, the ability of Rietveld refinement method was used to simultaneously refine the structure and microstructure and evaluate the linear defects of cubic crystals. To do this, the basis of Stephans theory, about the anisotropic strain broadening, was developed and the values of dislocation density as well as the fraction of dislocation types were estimated. The reliability of this procedure was checked by selecting four different nanocrystaslline samples and evaluating the microstructure of these materials. Finally, the results were compared with those extracted from the whole powder pattern modeling method. Good agreement was achieved between the results of two methods.

The microstructural characteristics of mechanically milled (MM) iron (Fe) and copper (Cu) powders are investigated by means of various X-ray crystallography analysis methods. The conventional Williamson–Hall and Warren–Averbach methods are used besides the modified Williamson–Hall, the modified Warren–Averbach, and the Variance approaches, in proper cases. Afterward, the obtained crystallite size and dislocation density are used to calculate the stored energy in the nanostructured powders. For this aim, a new geometrical approach is developed which can consider three-dimensional crystallites and the thickness of boundaries between them. Moreover, the released energy during annealing of MM Cu and Fe powders is measured using differential scanning calorimetry. The results of line broadening analysis and geometrical modelling are combined to the calorimetry of a room temperature aged Cu powder. In this way, the thickness of grain boundary in the nanostructured Cu is calculated to be 1.6 nm.

Received 5 October 2007; accepted 9 January 2008A comparison of different methods of X-ray diffraction analysis for the determination of crystallitesize and microstrain; namely, line profile analysis, Rietveld refinement, and three approaches basedon the variance method, is presented. The analyses have been applied to data collected on a ceriasample prepared by the IUCr Commission on Powder Diffraction. In the variance method, splitPearson VII, the Voigt function, and its approximation pseudo-Voigt function were fitted to X-raydiffraction line profiles. Based on the fitting results, the variances of line profiles were calculatedand then the crystallite size and root mean square strain were obtained from variance coefficients.A SS plot of Langford as well as a Fourier analysis and Rietveld refinement have been carried out.The average crystallite size and microstrain were determined. The values of area-weighted domainsize determined from the variance method are in agreement with those obtained from line profileanalysis within a single largest standard uncertainty, and the volume-weighted domain sizesderived from the SS plot, Fourier size distribution, and Rietveld refinement agree within a singlestandard uncertainty. The results of rms strain calculated from variance and Pearson VII shapefunction and those from Rietveld refinements fall within a single esd. However, the variance methodin conjunction with pseudo-Voigt and Voigt functions produce rms strains substantially larger thanthose determined from line profile analysis and Rietveld refinements. ©