We present a morphological analysis of atom probe data of nanoscale microstructural features, using methods developed by the astrophysics community to describe the shape of superclusters of galaxies. We describe second-phase regions using Minkowski functionals, representing the regions' volume, surface area, mean curvature and Euler characteristic. The alloy data in this work show microstructures that can be described as sponge-like, filament-like, plate-like, and sphere-like at different concentration levels, and we find quantitative measurements of these features. To reduce user decision-making in constructing isosurfaces and to enhance the accuracy of the analysis a maximum likelihood based denoising filter was developed. We show that this filter performs significantly better than a simple Gaussian smoothing filter. We also interpolate the data using natural cubic splines, to refine voxel sizes and to refine the surface. We demonstrate that it is possible to find a mathematically well-defined, quantitative description of microstructure from atomistic datasets, to sub-voxel resolution, without user-tuneable parameters.

中文翻译：

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使用 Minkowski 泛函对 3d 原子探针数据进行形态学分析

我们使用天体物理学界开发的方法来描述星系超星系团的形状，对纳米级微观结构特征的原子探针数据进行形态学分析。我们使用 Minkowski 泛函描述第二阶段区域，代表区域的体积、表面积、平均曲率和欧拉特征。这项工作中的合金数据显示了在不同浓度水平下可以描述为海绵状、细丝状、板状和球状的微观结构，我们发现这些特征的定量测量。为了减少用户在构建等值面时的决策并提高分析的准确性，开发了基于最大似然的去噪滤波器。我们表明该滤波器的性能明显优于简单的高斯平滑滤波器。我们还使用自然三次样条对数据进行插值，以细化体素大小并细化表面。我们证明，可以在没有用户可调参数的情况下，从原子数据集到亚体素分辨率，找到数学上定义明确的微观结构的定量描述。