DIFFaX simulations show that the 3R1 and 3R2 polytypes of hydrotalcites (HT) have distinctly different X-ray powder diffraction (XRPD) patterns. The HT samples obtained by coprecipitation as well as those subjected to a subsequent hydrothermal treatment exhibit non-uniform broadening of lines in their XRPD patterns as well as anomalous variation in the intensities of the basal reflections. The reflections appearing in the mid-2θ region (30–50°; 3–1.8 Å) are excessively broadened and do not correspond to either of the 3R polytypes. This broadening is shown to be due to a stacking of layers randomly rotated about the c crystallographic axis by n × 120° (n = 1,2). The intensities of the basal reflections vary due to the departure of the layer composition from the nominal value, essentially due to an increase in the intercalated water content.

X-ray diffraction patterns of oriented mounts of clay minerals are often used in clay mineralogy for qualitative and quantitative purposes. Fequently occurring stacking defects, in particular, can be characterized by this technique. Modeling of these diffraction profiles has become an important tool in obtaining structural information about the nature of stacking order. Manual matching of calculated and observed patterns is time consuming and user dependent. Automatic refinement procedures are, therefore, desirable. An improved approach for the treatment of disordered layer structures within a Rietveld refinement is presented here. The recursive calculation of structure factors, similar to that of the simulation program DIFFaX, was introduced in the Rietveld code BGMN. Complete implementation is formulated within the interpreter language of the Rietveld code and is transparent as well as flexible. Such a method has opened the application of Rietveld refinement to patterns of oriented mounts where only basal reflections of stacking disordered structures were recorded. The DIFFaX code was used to simulate basal reflections of illite-smectite mixed layers (I-S) with different ratios of illitic and smectitic layers and with different degrees of long-range ordering (Reichweite). Rietveld refinements with these simulated patterns were used to evaluate the application of this new approach. Several I-S with different degrees of ordering were also chosen as tests for the refinement of basal reflections. The samples were prepared as standard airdried and ethylene glycol-solvated, oriented specimens. Realistic structural parameters were obtained for the composition and ordering of the I-S.

Layered metal hydroxides exhibit non-uniform broadening of lines in their X-ray powder diffraction (XRPD) patterns, which cannot always be explained on the basis of crystallite size effects. In the case of hexagonal solids such as nickel hydroxide, DIFFaX simulations of the XRPD patterns show that: (1) stacking faults and turbostratic disorder at low (<30%) incidence selectively broaden the h0l reflections; (2) turbostratic disorder at high (>40%) incidence causes asymmetric broadening of the hk0 reflections and a complete extinction of the hkl reflections while leaving 00l unchanged; (3) interstratification selectively broadens the non-hk0 reflections; and (4) cation vacancies reduce the relative intensity of the 100 reflection. In contrast, a reduction in the thickness of the crystallites along the stacking direction of the layers selectively broadens the 00l reflections while a reduction in the disc diameter causes the progressive broadening and extinction of the hk0 reflections. Comparison with experimental data shows that several kinds of disorders have to be invoked to account for the observed broadening. DIFFaX simulations enable the quantification of the different kinds of disorder.

X-ray diffraction (XRD) of powdered materials is one of the most common methods used for structural characterization as well as for the quantification of mineral contents in mixtures. The application of the Rietveld method for that purpose requires structure models for each phase. The recursive calculation of structure factors was applied here to the Rietveld refinement of XRD powder patterns of illite-smectite (I-S) minerals. This approach allowed implementation of stacking disorder in structural models. Models for disordered stacking of cis-vacant and trans-vacant dioctahedral 2:1 layers as well as rotational disorder were combined with models for mixed layering of illitic and smectitic layers.

The DIFFaX code was used to simulate non-basal (hk) reflections of illites with different degrees of disorder. Rietveld refinements of these simulated patterns were used to evaluate the application of this new approach. A model describing rotational disorder (n·120° and n·60° rotations) and mixed layering of cis-vacant and trans-vacant dioctahedral layers was tested. Different starting parameters led to identical results within the ranges of standard deviations and confirmed the stability of the automatic refinement procedure. The influence on the refinement result of an incorrect choice of fixed parameters was demonstrated.

The hk model was combined with models describing the basal reflections of disordered I-S and tested on measured data. A glauconitic mineral (Urkut, Hungary), an ordered I-S (ISCz-1, a special clay in the Source Clays Repository of The Clay Minerals Society), and a dioctahedral I-S (F4, Füzérradvány, Hungary) were used as test substances. Parameters describing the mixed layering of illitic and smectitic layers were compared with the results from refinements of oriented mounts and showed good agreement. A pattern of a physical mixture of an I-S mineral and a turbostratically disordered smectite was analyzed in order to test the new approach for application in quantitative phase analysis. The quantitative Rietveld phase analysis results were found to be satisfactory.

The program FAULTS has been used to simulate the X-ray powder diffraction (XRD), neutron powder diffraction (NPD), and electron diffraction (ED) patterns of several structural models for LiNi1/3Mn1/3Co1/3O2, including different types of ordering of the transition metal (TM) cations in the TM slabs, different amounts of Li+/NiII+ cation mixing and different amounts of stacking faults. The results demonstrate the relevance of the structural information provided by NPD and ED data as compared with XRD to characterize the microstructure of NMC (LiNi1−y-zMnyCozO2) compounds.