Ceramic materials and energy—Extended Coble’s model and fractal nature

Abstract

The new frontiers open different directions within the higher and deeper knowledge structure using unemployed nano sizes domains. The BaTiO3 and other ceramic materials have fractal configuration nature based on three phenomena. First, ceramic grains have fractal shape looking as a contour in cross section or as a surface. Second, there is the so-called “negative space” made of pores and intergranular space. Third, there is fractal Brownian motion (fBm) within the material, during and after sintering, in the form of microparticle flow: ions, atoms, and electrons. Here, we took upon ourselves the task of extending Coble’s model, with already generalized Euclidean geometries, by fractal nature correction. These triple factors make the very peculiar microelectronic environment electro-static/dynamic combination. The stress is here set on inter-granular micro-capacity in function of higher energy harvesting and storage. Constructive fractal theory allows identifying micro-capacitors with fractal electrodes. The method is based on the iterative process of interpolation which is compatible with the grain model itself. Inter-granular permeability is taken as the fundamental thermodynamic parameter function of temperature and enthalpy (Gibbs free energy), which are very important for a structure-energy relation.