Leonardi Alberto, Bish David L
Department of Earth and Atmospheric Sciences, Indiana University, Bloomington, Indiana 47405, United States.
Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States.
Inorg Chem. 2020 Apr 20;59(8):5357-5367. doi: 10.1021/acs.inorgchem.9b03464. Epub 2020 Apr 1.
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 and 00 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.
粉末X射线衍射（PXRD）技术被广泛用于表征形成层状矿物纳米晶体的亚微米宽、纳米厚层的堆积性质，但将这些方法应用于推断层的面内构型却很困难。基于布拉格方程的线形轮廓分析算法无法描述堆积方向上的周期性破坏。德拜散射方程是一种替代方法，但它受到捕获层状系统多尺度性质所需的大规模原子模型的限制。在这里，我们求解高岭石纳米晶体的德拜散射方程，以了解不同层堆积缺陷对PXRD图谱的贡献。我们选择高岭石作为案例研究，因为其组成近似恒定且缺乏层间膨胀，确保了间隙阳离子和/或分子以及替代离子可以被忽略。我们研究了结构因子随晶体结构和微观结构特征的变化，如层结构的面内取向错误和位移（在二维平面内或外）以及层的直径、数量和横向凹陷。完美和准晶堆积构型界定了hkl和00l反射以及任何散射角的强度变化范围。通过与这些极限情况的平均偏差计算出独特的无序度，并使用多变量分析来解释观察到的衍射图谱。对KGa - 1、KGa - 2和API - 9标准高岭石的数据分析表明，不同堆积缺陷的估计密度高度相关。此外，对API - 9粒度级分的分析揭示了标准样品中四种或更多组分的分散情况。结果表明，使用尺寸、缺陷甚至单个高岭石组分的分布对于准确表征任何天然高岭石样品是必要的。
