A modified version of the Bertaut-Warren-Averbach (BWA) technique (Bertaut 1949, 1950; Warren and Averbach 1950) has been developed to measure coherent scattering domain (CSD) sizes and strains in minerals by analysis of X-ray diffraction (XRD) data. This method is used to measure CSD thickness distributions for calculated and experimental XRD patterns of illites and illite-smectites (I-S). The method almost exactly recovers CSD thickness distributions for calculated illite XRD patterns. Natural I-S samples contain swelling layers that lead to nonperiodic structures in the c* direction and to XRD peaks that are broadened and made asymmetric by mixed layering. Therefore, these peaks cannot be analyzed by the BWA method. These difficulties are overcome by K-saturation and heating prior to X-ray analysis in order to form 10-Å periodic structures. BWA analysis yields the thickness distribution of mixed-layer crystals (coherently diffracting stacks of fundamental illite particles). For most I-S samples, CSD thickness distributions can be approximated by lognormal functions. Mixed-layer crystal mean thickness and expandability then can be used to calculate fundamental illite particle mean thickness. Analyses of the dehydrated, K-saturated samples indicate that basal XRD reflections are broadened by symmetrical strain that may be related to local variations in smectite interlayers caused by dehydration, and that the standard deviation of the strain increases regularly with expandability. The 001 and 002 reflections are affected only slightly by this strain and therefore are suited for CSD thickness analysis. Mean mixed-layer crystal thicknesses for dehydrated I-S measured by the BWA method are very close to those measured by an integral peak width method.
Drits, V. A., Eberl, D. D., & Środon, J. (1998). XRD measurement of mean thickness, thickness distribution and strain for illite and illite-smectite crystallites by the Bertaut-Warren-Averbach technique. Clays and Clay Minerals, 46(1), 38–50. https://doi.org/10.1346/CCMN.1998.0460105