FRACTALS AND BATIO3-CERAMIC MICROSTRUCTURE ANALYSIS

The complex grainy structure of BaTiO3 is difficult to describe by usi ng 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 pat ches 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 thos e defined by Euclidean methods. Electric, ferroelectric and optoelectr ic properties of BaTiO3 are influenced strongly by the fractal dimensi on of the intergranular contact surfaces. This parameter is measured i n a laboratory environment using SEM micrographs with different magnif ications. The BaTiO3 samples examined have been sintered using differe nt sintering pressures and temperatures. Then, the fractal dimension i s calculated from a log-log diagram, and the grain contours are constr ucted using Iterated Function Systems connected with fractal interpola tion.