Lopresti Mattia, Mangolini Beatrice, Milanesio Marco, Caliandro Rocco, Palin Luca
Università del Piemonte Orientale, Dipartimento di Scienze e Innovazione Tecnologica, Viale T. Michel 11, 15121 Alessandria, Italy.
Institute of Crystallography, CNR, via Amendola 122/o, 70126 Bari, Italy.
J Appl Crystallogr. 2022 Jul 5;55(Pt 4):837-850. doi: 10.1107/S1600576722004708. eCollection 2022 Aug 1.
In materials and earth science, but also in chemistry, pharmaceutics and engineering, the quantification of elements and crystal phases in solid samples is often essential for a full characterization of materials. The most frequently used techniques for this purpose are X-ray fluorescence (XRF) for elemental analysis and X-ray powder diffraction (XRPD) for phase analysis. In both methods, relations between signal and quantity do exist but they are expressed in terms of complex equations including many parameters related to both sample and instruments, and the dependence on the active element or phase amounts to be determined is convoluted among those parameters. Often real-life samples hold relations not suitable for a direct quantification and, therefore, estimations based only on the values of the relative intensities are affected by large errors. Preferred orientation (PO) and microabsorption (MA) in XRPD cannot usually be avoided, and traditional corrections in Rietveld refinement, such as the Brindley MA correction, are not able, in general, to restore the correct phase quantification. In this work, a multivariate approach, where principal component analysis is exploited alone or combined with regression methods, is used on XRPD profiles collected on designed mixtures to face and overcome the typical problems of traditional approaches. Moreover, the partial or no known crystal structure (PONKCS) method was tested on XRPD data, as an example of a hybrid approach between Rietveld and multivariate approaches, to correct for the MA effect. Particular attention is given to the comparison and selection of both method and pre-process, the two key steps for good performance when applying multivariate methods to obtain reliable quantitative estimations from XRPD data, especially when MA and PO are present. A similar approach was tested on XRF data to deal with matrix effects and compared with the more classical fundamental-parameter approach. Finally, useful indications to overcome the difficulties of the general user in managing the parameters for a successful application of multivariate approaches for XRPD and XRF data analysis are given.
在材料科学、地球科学以及化学、制药和工程领域，对固体样品中的元素和晶相进行定量分析，对于全面表征材料往往至关重要。为此目的，最常用的技术是用于元素分析的X射线荧光光谱法（XRF）和用于相分析的X射线粉末衍射法（XRPD）。在这两种方法中，信号与含量之间确实存在关系，但它们是通过包含许多与样品和仪器相关参数的复杂方程来表示的，并且对要测定的活性元素或相含量的依赖性在这些参数中相互交织。实际样品中的关系通常不适合直接定量，因此，仅基于相对强度值的估计会受到较大误差的影响。XRPD中的择优取向（PO）和微吸收（MA）通常无法避免，并且Rietveld精修中的传统校正方法，如布林德利微吸收校正，一般无法恢复正确的相定量。在这项工作中，采用了一种多变量方法，即单独使用主成分分析或与回归方法相结合，对在设计混合物上收集的XRPD图谱进行分析，以应对和克服传统方法的典型问题。此外，还对XRPD数据测试了部分或无已知晶体结构（PONKCS）方法，作为Rietveld方法和多变量方法之间混合方法的一个示例，以校正MA效应。特别关注方法和预处理的比较与选择，这是将多变量方法应用于从XRPD数据获得可靠定量估计时，尤其是存在MA和PO时，实现良好性能的两个关键步骤。对XRF数据也测试了类似的方法以处理基体效应，并与更经典的基本参数方法进行了比较。最后，给出了一些有用的建议，以帮助普通用户克服在管理参数方面的困难，从而成功应用多变量方法进行XRPD和XRF数据分析。
