Understanding Powder X‑ray Diffraction Profiles from Layered Minerals: The Case of Kaolinite Nanocrystals

Powder X-ray diffraction (PXRD) techniques are widely used to characterize the nature of stacking of submicrometer-wide nanometer-thick layers that form layered mineral nanocrystals, but application of these methods to infer the in-plane configuration of the layers is difficult. Line-profile-analysis algorithms based on the Bragg equation cannot describe the broken periodicity in the stacking direction. The Debye scattering equation is an alternative approach, but it is limited by the large-scale atomistic models required to capture the multiscale nature of the layered systems. Here, we solve the Debye scattering equation for kaolinite nanocrystals to understand the contribution of different layer-stacking defects to PXRD profiles. We chose kaolinite as a case study because its approximately constant composition and lack of interlayer expansion ensure that interstitial cations and/or molecules and substitutional ions can be ignored. We investigated the structure factor change as a function of crystal structural and microstructural features such as layer structure in-plane misorientation and shift (in or out of the 2D plane) and the diameter, number, and lateral indentation of the layers. Perfect and turbostratic stacking configurations bounded the range of intensity variation for hkl and 00l reflections, as well as for any scattering angle. A unique degree of disorder was computed by the average deviation from such limiting cases, and multivariate analysis was used to interpret the observed diffraction profiles. Analysis of the data for KGa-1, KGa-2, and API-9 standard kaolinites demonstrated that the estimated densities of different stacking defects are highly correlated. In addition, analysis of API-9 particle-size fractions revealed a dispersion of four or more components in the standard sample. The results illustrate that the use of a distribution of sizes, defects, and even individual kaolinite components is necessary to accurately characterize any sample of natural kaolinite.