XRD Measurement of Mean Thickness, Thickness Distribution and Strain for Illite and Illite-Smectite Crystallites by the Bertaut-Warren-Averbach Technique

Abstract

A modified version of the Bertaut-Warren-Averbach (BWA) technique (Bertaut 1949(Bertaut , 1950Warren 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-,~ periodic structures. BWA analysis yields the thickness distribution of mixed-layer crystals (coherently diffracting stacks of fundamental illite particles). For most I-S sampies, 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.

Thickness and Surface Characteristics of Colloidal 2:1 Aluminosilicates Using an Indirect Fourier Transform of Small-Angle X-Ray Scattering Data

“…The CEC of this illite sample (<0.1 txm) is 18 cmolc kg -1 as estimated by cationic surfactant adsorption. The thickness of illites measured by XRD peak broadening, TEM and fixed cation content may vary from a few to 100 nm depending on the percentage of smectite in the sample (Nadeau et al, 1984;Srodofi et al, 1990Srodofi et al, , 1992Drits et al, 1997Drits et al, , 1998. Based on the percent smectite of the studied illite, the thickness (6-7 nm) determined by SAXS falls closely within the thickness range reported in those studies.…”

“…Based on the percent smectite of the studied illite, the thickness (6-7 nm) determined by SAXS falls closely within the thickness range reported in those studies. Beckett et al (1997) used sedimentation field-flow fractionation to determine the thickness of kaolinite and illite clays, and the plate thickness of one illite clay they determined was 5 to 10 times greater than that reported for the same sample by Drits et al (1998). Note that the PDDF is curvilinear (Figure 3a), deviating from the shape expected for an ideal thin layer particle (Figure la).…”

“…This interstratification makes it difficult to determine the thickness of the fundamental illite particle by conventional analysis of X-ray data. Various attempts have been made in recent years using TEM, fixed cation content, and X-ray peak broadening (Nadeau et al, 1984;Srodofi et al, 1990Srodofi et al, , 1992Drits et al, 1997Drits et al, , 1998. Each of these methods suffers from its own uncertainties.…”

“…Each of these methods suffers from its own uncertainties. As noted by Drits et al (1997Drits et al ( , 1998, the thickness of most illite samples present in nature can be measured by SAXS, and this method offers two advantages over other methods: illite particles in dilute suspensions are independent and free of swelling problems, and at least one million particles are scanned and averaged. By comparison, TEM only 'sees' hundreds of particles.…”

Introduction to Advanced X-ray Diffraction Techniques for Polymeric Thin Films

“…The combination of the first two terms form the total paracrystallinity in the absence of intra-plane disorders and can be assessed by XRD via Warren-Averbach (peak-shape) analysis. This involves analyzing the peak shape of multiple harmonics of XRD peaks, which may also give an estimate for mean crystallite size [21,29,30].…”