A Statistical Approach for Effectively Analyzing the Grain Size Distribution Along the Thickness Direction in Commercial ZnO-Based Varistor Ceramics

Grain size and its spatial distribution are the crucial issues in the study of advanced materials with a grain-grain boundary structure. It not only implies the grain growth mechanism of those materials, but also determines most of their macroscopic properties, such as mechanical strength, current conduction, ageing and so on. Therefore, it is of importance to clarify the grain size distribution (GSD) in ZnO-based varistor ceramics, a key protection element against overvoltage. In the present paper, a new approach based on the log-normal distribution was proposed to analyze the variation of GSD along the thickness direction of two commercial ZnO varistors. It is found that GSD follows log-normal distribution rather than commonly used normal distribution. In addition, with the proposed grain size, i.e., averaged log-normal grain size (dLN) and most probable grain size ($d_{\max}$), the variation of GSD along the thickness direction was clearly revealed, which exhibited quite different behavior depending on the samples. With the probability plot, the microscopic uniformity is carefully analyzed and discussed. It is proposed that probability plots can be divided into three regions, representing large grains, grains whose sizes follow the lognormal rule and small grains, respectively. With the proposed method, it is possible to obtain more quantitative information, which is of significance for the further development of ZnO-based varistor ceramics and other advanced materials.