After pioneering attempts for the introduction of graph theory in the field of ceramics and microstructures, where 1D and 2D graphs were used, in this paper we applied 3D graphs for the breakdown voltage calculation in BaTiO₃ sample with some predefined constraints. We have described the relations between grains in the sample and established a mathematical approach for the calculation of breakdown voltage using experimental results. As a result, we introduced mapping between the property of sample and grain structure, then between the grain structure and mathematical graph, using various crystal structures. The main idea was to apply 3D graph theory for the distribution of electronic parameters between the neighboring grains. With this study, we successfully confirmed the possibilities for applications of graphs as a tool for the determination of properties even at the intergranular level.

中文翻译：

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BaTiO3陶瓷击穿电压计算的3D图形方法

在将图论引入陶瓷和微结构领域的开创性尝试之后，使用 1D 和 2D 图，在本文中，我们将 3D 图应用于 BaTiO _{3的击穿电压计算}带有一些预定义约束的示例。我们已经描述了样品中晶粒之间的关系，并建立了一种使用实验结果计算击穿电压的数学方法。因此，我们使用各种晶体结构引入了样品性质和晶粒结构之间的映射，然后是晶粒结构和数学图之间的映射。主要思想是将 3D 图论应用于相邻晶粒之间的电子参数分布。通过这项研究，我们成功地证实了将图表作为一种工具来应用的可能性，即使是在晶间水平上也能确定特性。