基于微观结构分形表征的钼-氧化锆材料导电导热性能研究

金属陶瓷物理性能与材料组分和空间组织结构密切相关，其组成相的形态分布具有分形特征。基于渗流理论和分形理论，通过对材料微观结构图像的二值化处理进行导通相分形维数计算，建立分形维数与导通相微观形貌、渗流临界指数之间的定量表征，研究Mo-ZrO2金属陶瓷全组分范围内材料微观结构与电导率和热导率之间的关系。结果表明：导通相面积分形维数随着Mo体积分数的增加而增加，电导率与分形维数遵循渗流转变特征。采用通用有效介质(GEM)方程建立基于导通相分形维数的金属陶瓷电导率和热导率模型，实现材料微观组织定量分析结果与金属陶瓷的渗流模型相结合，有效预测材料宏观物理性质的梯度变化。

Study on electrical and thermal conductivity for Mo-ZrO2 cermet by fractal characterization of microstructure

The physical properties of cermet are closely related to the material composition and spatial structure, and its morphological distribution of composition phase have fractal characteristic. Based on the percolation theory and fractal theory, the fractal dimensions of the conducting phase were calculated through the binarization of the microstructure image analysis. And the quantitative characterizations between the fractal dimension and the microscopic morphology of the conducting phase and the critical exponent of percolation were established. The relationship between the microstructure and its electrical and thermal conductivity in the full composition range of Mo-ZrO2 cermet were studied. The results indicated that the fractal dimension of the conducting phase increases with the increase of the Mo volume fraction, and the relationship between conductivity and fractal dimension is consistent with the percolation theory. Based on the fractal dimension of the conducting phase, the general effective medium (GEM) equation was used to establish the electrical conductivity and the thermal conductivity models of cermet. By combining the quantitative analysis results of the microstructure and the percolation model of cermet, the gradient change of the macroscopic physical properties of the cermet can be effectively predicted.