A modified application of the variance method, using the pseudo‐Voigt function as a good approximation to the X‐ray diffraction profiles, is proposed in order to obtain microstructural quantities such as the mean crystallite size and root‐mean‐square (r.m.s.) strain. Whereas the variance method in its original form is applicable only to well separated reflections, this technique can be employed in the cases where there is line‐profile overlap. Determination of the mean crystallite size and r.m.s. strain for several crystallographic directions in a nanocrystalline cubic sample of 9‐YSZ (yttria‐stabilized zirconia) has been performed by means of this procedure.

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Accurate quantitative X-ray diffraction analysis of SiC-based ceramics is difficult because of the significant overlap of the Bragg reflections from the different SiC polytypes. In this regard, the Rietveld method is a powerful tool for the accurate and precise analysis of the phase/polytype compositions in these materials. In this study, we have used two different types of Rietveld codes for the quantitative phase/polytype analysis of a liquid-phase-sintered SiC specimen: FULLPROF, which is based on the classical Rietveld approach, and BGMN, which is based on the new fundamental parameter approach. In both cases, the effect of texture corrections on the precision of the analysis also was studied. The accuracy of the analysis, in terms of the weight percentage of SiC (all polytypes) and yttrium aluminum garnet liquid phase, as determined from the starting powder composition, is within the standard deviation of the analysis in both cases (FULLPROF and BGMN), with and without the texture corrections. In addition, in the case of the classical code (FULLPROF), inclusion of the texture corrections has been shown to improve the precision. In contrast, the precision of the analysis using the BGMN code without the texture corrections is better. However, inclusion of the texture corrections is expected to improve the accuracy of the analysis.

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An alternative formulation of the variance method for the line-broadening analysis of polycrystalline materials is presented. It maintains the theoretical basis of the earlier formulations of the variance method, but differs in the manner of calculating the variance coefficients of the line profiles. In the proposed formulation, these are evaluated analytically in terms of the shape parameters of Voigt functions fitted to the X-ray diffraction data. Explicit expressions are thus derived for calculating the (surface-weighted) crystal sizes and (root-mean-square) lattice microstrains from the integral breadths of the Gauss and Lorentz components of the Voigt functions that model the experimental and instrumental line profiles.

A worked example of polytypism is presented, aimed at assisting undergraduates in the learning and instructors in the teaching of this topic. In particular, this crystallography concept, not necessarily obvious for beginners, is illustrated pedagogically using to that end the model case of the prolific polytypism of silicon carbide (SiC). On the basis of concepts that are easily assimilated by students (i.e. simple topological constraints) this article first presents a unified description of the polytypism phenomenon in SiC that allows one to understand without difficulty the existence of its numerous polytypic variants and how they develop. Then the various notations used to designate these different polytypes are described, and finally the crystal structures of the most common are discussed. This worked example is thus expected to contribute to motivating undergraduates in the study of a crystallography topic that often is not treated in sufficient depth in class.