The determination of the content of the conducting phase and the assessment of conductivity by microscopic images are interesting for rapid and non-destructive analysis of the electrophysical properties of two-phase (conductor/dielectric) samples during the atomic force microscopy. In this paper we summarized results of the analysis of the conductivity maps of the shungite surface by the method of discretization by applying a square grid with subsequent binary digital processing. Microstructure and conductivity were evaluated by measuring the average length of continuous conductive circuits isolated on the grid. A model was considered that established a unique correspondence (up to normalizing coefficients) between the length of the conductive circuits on the conductivity maps and the integral conductivity of the sample as a whole. An analytical equation was obtained that described such dependence with an accuracy of units of percent. We proposed a method for measuring the integral conductivity of a shungite samples based on an analysis of its binary conductivity map obtained by spreading resistance microscopy. This method can be used to determine the conductivity by surface conductivity mapping for shungite-like two-phase conductor/dielectric systems, and in general, for any two-phase substances where the phases differ in AFM-determined properties.

中文翻译：

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通过扫描扩散电阻显微镜评估两相材料的微观结构和电导率（以次闪石为例）

通过显微图像确定导电相的含量和评估电导率对于在原子力显微镜期间快速和无损地分析两相（导体/电介质）样品的电物理特性很有趣。在本文中，我们总结了通过应用方形网格并随后进行二进制数字处理的离散化方法对闪石表面电导率图的分析结果。通过测量隔离在网格上的连续导电电路的平均长度来评估微观结构和电导率。一个模型被认为在电导图上的导电电路的长度和整个样品的积分电导率之间建立了唯一的对应关系（直到归一化系数）。获得了一个分析方程，该方程以百分比单位的精度描述了这种相关性。我们基于对扩展电阻显微镜获得的二元电导率图的分析，提出了一种测量闪锌矿样品整体电导率的方法。该方法可用于通过表面电导率映射来确定类似菱镁矿的两相导体/电介质系统的电导率，并且通常用于任何两相物质的电导率，其中相位在 AFM 确定的特性上不同。