Fractals and BaTiO3-Ceramic Microstructure Analysis

Abstract

The complex grainy structure of BaTiO₃ is difficult to describe by using traditional analytical or geometrical methods. Here, an attempt is made to establish new mathematical models based on both Euclidean and fractal geometrical methods. The first uses ellipsoidal approximations for barium-titanate grains describing the contact area as surface patches with an ellipsoidal boundary. The fractal method offers a better approach in describing the irregular and wavy surface of such contact zones and therefore, it defines aspects that are complementary to those defined by Euclidean methods. Electric, ferroelectric and opto-electric properties of BaTi03 are influenced strongly by the fractal dimension of the intergranular contact surfaces. This parameter is measured in a laboratory environment using SEM micrographs with different magnifications. The BaTiO₃ samples examined have been sintered using different sintering pressures and temperatures. Then, the fractal dimension is calculated from a log-log diagram, and the grain contours are constructed using Iterated Function Systems connected with fractal interpolation.