Fractal nature Heywang model correction and Brownian motions

Abstract

Ceramics grains contacts are essential for understanding complex dielectric properties of electronic ceramics materials. Since the actual contact surface is an irregular object, the theory of fractal sets is applied. Also, the Heywang model of intergranular capacity are introduced as a basic idea for relations with fractal structure. The BaTiO3-ceramics has fractal form in, at least, two levels: shapes and distributions of grains and intergranular contacts. Using fractal modeling approach, reconstruction of microstructure, like shapes of grains or intergranular contacts can be successfully done. Furthermore, the area of grains surface is calculated by using fractal correction that expresses the irregularity of grains surface through fractal dimension. It is known that BaTiO3 and similar ceramics have fractal nature based on three different phenomena. First, there is process of Brownian-fractal motions inside the material during sintering in the form of flowing micro-particles –ions, atoms, electrons which is an essentially fractal phenomena. This motion has fractal structure and can be undergo the process of fractal modification. Second, there are so called “negative space” made of pores and intergranular space. Being extremely complex, the pore space plays an important role in microelectronic, PTC and other phenomena. Third, ceramic grains have fractal shape seeing as a contour in cross section or as grain’s surface. These triple factors, in combination, make the microelectronic environment of very peculiar electro-static and dynamics microelectronic environment. In order to obtain an equivalent circuit model, which provides a more realistic representation of the electronic materials electrical properties, in this article an intergranular contacts model for the BaTiO3 electrical properties characterization were determined and implemented. Considering obtained results, the directions of possible BaTiO3-ceramics materials properties prognosis are determined according to the correlations synthesisstructure- properties.