Leonardi Alberto
Institute for Multiscale Simulation, IZNF, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse, 3, Erlangen, Bavaria 91052, Germany.
IUCrJ. 2021 Feb 10;8(Pt 2):257-269. doi: 10.1107/S2052252521000324. eCollection 2021 Mar 1.
Microstructure-based design of materials requires an atomic level understanding of the mechanisms underlying structure-dependent properties. Methods for analyzing either the traditional diffraction profile or the pair distribution function (PDF) differ in how the information is accessed and in the approximations usually applied. Any variation of structural and microstructural features over the whole sample affects the Bragg peaks as well as any diffuse scattering. Accuracy of characterization relies, therefore, on the reliability of the analysis methods. Methods based on Bragg's law investigate the diffraction peaks in the intensity plot as distinct pieces of information. This approach reaches a limitation when dealing with disorder scenarios that do not conform to such a peak-by-peak basis. Methods based on the Debye scattering equation (DSE) are, otherwise, well suited to evaluate the scattering from a disordered phase but the structure information is averaged over short-range distances usually accessed by experiments. Moreover, statistical reliability is usually sacrificed to recover some of the computing-efficiency loss compared with traditional line-profile-analysis methods. Here, models based on Bragg's law are used to facilitate the computation of a whole PDF and then model powder-scattering data the DSE. Models based on Bragg's law allow the efficient solution of the dispersion of a crystal's properties in a powder sample with statistical reliability, and the PDF provides the flexibility of the DSE. The whole PDF is decomposed into the independent directional components, and the number of atom pairs separated by a given distance is statistically estimated using the common-volume functions. This approach overcomes the need for an atomistic model of the material sample and the computation of billions of pair distances. The results of this combined method are in agreement with the explicit solution of the DSE although the computing efficiency is comparable with that of methods based on Bragg's law. Most importantly, the method exploits the strengths and different sensitivities of the Bragg and Debye theories.
基于微观结构的材料设计需要对与结构相关的性能背后的机制有原子层面的理解。分析传统衍射图谱或对分布函数（PDF）的方法在信息获取方式以及通常采用的近似方法上存在差异。整个样品上结构和微观结构特征的任何变化都会影响布拉格峰以及任何漫散射。因此，表征的准确性依赖于分析方法的可靠性。基于布拉格定律的方法将强度图中的衍射峰作为不同的信息片段进行研究。当处理不符合逐个峰基础的无序情况时，这种方法会达到极限。另一方面，基于德拜散射方程（DSE）的方法非常适合评估来自无序相的散射，但结构信息是在通常由实验获取的短程距离上进行平均的。此外，与传统的线形轮廓分析方法相比，通常会牺牲统计可靠性以弥补一些计算效率的损失。在这里，基于布拉格定律的模型被用于促进整个PDF的计算，然后对粉末散射数据进行DSE建模。基于布拉格定律的模型允许在具有统计可靠性的情况下有效解决晶体性质在粉末样品中的色散问题，并提供了DSE的灵活性。整个PDF被分解为独立的方向分量，并使用公共体积函数对由给定距离分隔的原子对数量进行统计估计。这种方法克服了对材料样品原子模型的需求以及数十亿对距离计算的需求。尽管计算效率与基于布拉格定律的方法相当，但这种组合方法的结果与DSE的显式解一致。最重要的是，该方法利用了布拉格理论和德拜理论的优势以及不同的灵敏度。
