The thicknesses of fundamental illite particles that compose mixed-layer illite-smectite (I-S) crystals can be measured by X-ray diffraction (XRD) peak broadening techniques (Bertaut-Warren-Averbach [BWA] method and integral peak-width method) if the effects of swelling and XRD background noise are eliminated from XRD patterns of the clays. Swelling is eliminated by intercalating Na-saturated I-S with polyvinylpyrrolidone having a molecular weight of 10,000 (PVP-10). Background is minimized by using polished metallic silicon wafers cut perpendicular to (100) as a substrate for XRD specimens, and by using a single-crystal monochromator. XRD measurements of PVP-intercalated diagenetic, hydrothermal and low-grade metamorphic I-S indicate that there are at least 2 types of crystallite thickness distribution shapes for illite fundamental particles, lognormal and asymptotic; that measurements of mean fundamental illite particle thicknesses made by various techniques (Bertant-Warren-Averbach, integral peak width, fixed cation content, and transmission electron microscopy [TEM]) give comparable results; and that strain (small differences in layer thicknesses) generally has a Gaussian distribution in the log-normal-type illites, but is often absent in the asymptotic-type illites.

The nanostructural features of the gas-phase displacement reaction 2Mg(g)+SiO2→2MgO(s)+{Si}, where SiO2 is in the form of diatom shells were studied via X-ray diffraction and Fourier methods. Diatomaceous powder heated to 700 °C in a sealed graphite cell in the presence of Mg vapor formed MgO via a displacement reaction. Warren-Averbach analysis performed on samples reacted for different times showed an initial sharp MgO grain size distribution which broadened with time. New MgO crystallization was shown to occur until about 60 min, whereafter only MgO grain growth occurred. Median MgO crystallite size increased from 7.5 to 24.9 nm during this period, whereas microstrain decreased dramatically past 60 min annealing time.