In electron probe microanalysis or scanning electron microscopy, the Monte Carlo method is widely used for modeling electron transport within specimens and calculating X-ray spectra. For an accurate simulation, the calculation of secondary fluorescence (SF) is necessary, especially for samples with complex geometries. In this study, we developed a program, using a hybrid model that combines the Monte Carlo simulation with an analytical model, to perform SF correction for three-dimensional (3D) heterogeneous materials. The Monte Carlo simulation is performed using MC X-ray, a Monte Carlo program, to obtain the 3D primary X-ray distribution, which becomes the input of the analytical model. The voxel-based calculation of MC X-ray enables the model to be applicable to arbitrary samples. We demonstrate the derivation of the analytical model in detail and present the 3D X-ray distributions for both primary and secondary fluorescence to illustrate the capability of our program. Examples for non-diffusion couples and spherical inclusions inside matrices are shown. The results of our program are compared with experimental data from references and with results from other Monte Carlo codes. They are found to be in good agreement.

中文翻译：

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使用混合模型的 3D 异质材料的二次荧光

在电子探针微量分析或扫描电子显微镜中，蒙特卡罗方法广泛用于模拟样品内的电子传输和计算 X 射线光谱。为了进行准确的模拟，二次荧光 (SF) 的计算是必要的，特别是对于具有复杂几何形状的样品。在这项研究中，我们开发了一个程序，使用将蒙特卡罗模拟与分析模型相结合的混合模型，对三维 (3D) 异质材料进行 SF 校正。使用蒙特卡罗程序 MC X 射线进行蒙特卡罗模拟，以获得 3D 初级 X 射线分布，该分布成为分析模型的输入。基于体素的 MC X 射线计算使模型适用于任意样本。我们详细演示了分析模型的推导，并展示了初级和次级荧光的 3D X 射线分布，以说明我们程序的能力。显示了矩阵内的非扩散偶和球形夹杂物的示例。我们程序的结果与参考文献中的实验数据和其他蒙特卡洛代码的结果进行了比较。他们被发现非常一致。