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.

TEM characterization of stacking relations in I/S of expanded shale samples from the Gulf Coast and Michigan Basin was carried out to address the issues of the degree of coherency and the nature of layer stacking sequences in smectite, I/S and illite. The two-dimensional lattice fringe images obtained from this study show that cross fringes are commonly observed to be continuous over at least 3–4 layers for smectite, 6–7 layers for ordered I/S and 9–10 layers for illite-rich I/S. This demonstrates that such sequences are coherent, or at least semi-coherent (in smectite) units (MacEwan crystallites). The observations demonstrate that so-called fundamental particles are fragments of MacEwan crystallites formed primarily as a result of disaggregation along weakly-bonded smectite interlayers. However, both 0k1 and h01 reflections may coexist in selected area electron diffraction (SAED) patterns. The frequency of occurrence of the coexistence in SAED patterns decreases in the order smectite, I/S and illite for Gulf Coast samples. This is consistent with the presence of turbostratically-related interfaces in packets of all of these materials. Therefore, any given layer sequence in smectite, ordered I/S and illite may have both turbostratic and coherent interfaces. The proportion of coherently-related layers increases with increasing proportion of illite-like layers. The concept of fundamental or elementary particles is not related to layer sequences in non-disaggregated, original rocks. Indeed, it implies relations that are not valid.

The lattice fringe images, SAED and optical diffraction patterns demonstrate that where layers are coherently-related, 2M1 is the dominant polytypic sequence in all samples. However, this periodic 2M1 stacking is so frequently interrupted by stacking faults in smectite that it gives rise to apparent lMd polytypism. The degree to which the periodic 2M1 sequences are interrupted by stacking faults decreases with increasing proportion of illite-like layers. The SAED patterns of I/S and illite unmodified since its formation are diffuse parallel to c* and have poorly-defined, non-periodic reflections for indices k ≠ 3N as a measure of local ordering superimposed on poorly-ordered coherent sequences with a turbostratic component. X-ray diffraction (XRD) patterns, as integrated over domains with a range of heterogeneous stacking relations, do not represent simple mixtures of discrete IM and 2M1 polytypes.

The observations of this study imply that dissolution-crystallization is a dominant mechanism for the smectite-to-illite transition. The semi-coherent stacking of smectite-like layers in smectite-rich samples implies that either a dissolution-crystallization process took place subsequent to deposition of detrital smectite or that Gulf Coast smectite is an in-situ alteration product of volcanic ash.

Interstratified illite-smectite (I-S) occurring authigenically in diverse earth crust environments reacts toward more illite-rich phases as temperature increases. For that reason, I-S is used for geothermometry when prospecting for hydrocarbons or ore mineral deposits. This study develops the mathematical relations for characterizing the coherent stacking potential of fundamental particles (FP) using the expandability ratio K, where K is defined as (%SMAX –; %SXRD)/%SMAX. The ratio can be applied to differentiating I-S samples from shales, bentonites, and hydrothermal alterations. In particular, patterns on a K vs. T diagram, where T is the average thickness of fundamental particles (FPs), appear to be indicative of the geological conditions related to I-S formation. Shale samples plot in the negative K domain of the diagram, possibly due to the intimate mixing of detrital particles. Both bentonitic and hydrothermal samples display trends of increasing K with T, which suggests the coherent stacking potential progressively decreases as FPs increase in thickness. Hydrothermal samples are more extensively distributed on the diagram than samples from bentonites. This result may reflect differences in particle growth conditions (nutrients and space) between bentonites (short supply) and hydrothermal alterations (good supply).