This research is focused on further developing of application and use of graph theory in order to describe relations between grains and to establish control over layers. We used functionalized BaTiO3nanoparticles coated with Yttrium-based salt. The capacitance change results on super-microstructure levels are the part of the measured values on the bulk samples. The new idea is graph theory application for determination of electronic parameters distribution at the grain boundary and to compare them with the bulk measured values. We present them with vertices in graph, corresponding with grains, connected with edges. Capacitance change with applied voltage was measured on samples sintered in air and nitrogen, up to 100 V. Using graph theory, it has been shown that capacitance change can be successfully calculated on the layers between grains. Within the idea how to get parameters values at microlevel between the grains and pores, mathematical tool can be developed. Besides previously described 1D case, some original calculations for 2D cases were performed in this study, proving successful graph theory use for the calculation of values at nanolevel, leading to a further minituarization in micropackaging.

中文翻译：

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陶瓷、材料、微电子和图论新前沿

本研究的重点是进一步发展图论的应用和使用，以描述晶粒之间的关系并建立对层的控制。我们使用功能化的 BaTiO3涂有钇基盐的纳米颗粒。超微结构水平的电容变化结果是大块样品测量值的一部分。新的想法是将图论应用于确定晶界处的电子参数分布并将它们与体测量值进行比较。我们在图中用顶点表示它们，对应于颗粒，连接边。在最高 100 V 的空气和氮气中烧结的样品上测量了电容随外加电压的变化。使用图论，可以成功地计算出晶粒间层的电容变化。在如何获得颗粒和孔隙之间的微观参数值的想法中，可以开发数学工具。除了之前描述的一维案例，