Intergranular fractal impedance analysis of microstructure and electrical properties of rare-earth doped BaTiO3

Abstract

Microstructure properties of barium-titanate based materials, expressed in grain boundary contacts, are of basic importance for electric properties of these material. In this study, the model of intergranular impedance applied on two-grain contact is considered. Globally, BaTiO3-ceramics sample is consisted of a huge number of mutually contacted grains which form clusters. Such clusters can be presented as a specific fractal formations. For each of them, it is possible to establish the equivalent electrical model and, for defined set of input parameters, using symbolic analysis, obtain the frequency diagram. The influence of fractal structure is especially stressed. Realizing the totality of relations between clusters grains groups, their microelectrical schemes and corresponding frequency characteristics, from one side, and global equivalent electrical scheme and corresponding acquired frequency characteristics of BaTiO3-ceramics samples, on the other side, we set a goal of coinciding experimental results with the summing effect of microelectric equivalent schemes. The model is successfully tested on doped barium- titanate ceramics.