Three-Dimensional Modelling of X-Ray Emission in Electron Probe Microanalysis Based on Deterministic Transport Equations

基于确定性输运方程的电子探针显微分析中 X 射线发射的三维建模

• 批准号: 275207500
• 负责人: Dr. Silvia Richter
• 金额: --
• 依托单位: Gemeinschaftslabor für Elektronenmikroskopie (GFE)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/275207500?language=en
• 关键词: Three; Dimensional; Modelling; Ray; Emission

The investigation of material properties and the development of new materials heavily rely on the characterization of their microstructure. A critical aspect of the characterization is to measure the distribution of the different chemical elements present inside a material. A well-established characterization technique is the electron probe microanalysis (EPMA), in which an electron beam interacts with the material causing the emission of x-rays characteristic to the local composition. This technique has the unique advantage to provide accurate quantitative information about the composition of a sample at the micrometer to nanometer scale, while allowing the investigation of a macroscopic sampling area. Although successful, this method is based on the assumption that the sample is homogeneous within the interaction volume of the electron beam, hence the structures of interest must be bigger than the interaction volume in order to be analyzed.Therefore, to apply the quantification procedures to even smaller scales it is necessary to derive fast and accurate mathematical and numerical models of electron-x-ray-matter interactions in complex geometries. In this project the usual approaches by simple analytical models or expensive Monte-Carlo simulations will be replaced by the description of electron scattering as a continuous process following the Boltzmann transport equation. The high dimensionality of the Boltzmann equation can be reduced by moment approximations and a closure procedure based on the maximum-entropy principle. The reduced model is given by a partial differential equation and will be solved numerically by a finite volume method in order to provide a fast and accurate prediction of the electron energy distribution inside a material. The resulting numerical software will be carefully validated against existing analytical models, standardized samples and Monte-Carlo simulations.

对材料特性和新材料的开发的研究在很大程度上取决于其微观结构的表征。表征的一个关键方面是测量材料中存在的不同化学元件的分布。良好的表征技术是电子探针微分析（EPMA），其中电子束与材料相互作用，从而导致X射线发射到局部组成中。该技术具有独特的优势，可以提供有关样品在微米到纳米尺度的组成的准确定量信息，同时允许研究宏观采样区域。尽管成功，但这种方法是基于以下假设：样品在电子光束的相互作用体积中是均匀的，因此，感兴趣的结构必须大于相互作用的体积才能进行分析。因此，要将量化程序应用于较小的尺度，这对于快速而准确的数学和数字模型是必不可少的。在这个项目中，通过简单的分析模型或昂贵的蒙特卡洛模拟采用通常的方法，将被电子散射作为Boltzmann传输方程后的连续过程所取代。玻尔兹曼方程的高维度可以在矩近似值和基于最大透镜原理的闭合过程中降低。还原模型由部分微分方程给出，将通过有限体积方法来求解，以便对材料内的电子能量分布进行快速准确的预测。将对现有的分析模型，标准化样本和蒙特卡洛模拟进行仔细验证所得的数值软件。