Fractal approach to BaTiO3-ceramics micro-impedances

A new approach, based on fractal geometry and correlation between microstructure–nanostructure and rare-earth properties and other additives doped BaTiO3-ceramics and electronics properties, is applied. The grain contacts geometry based on different stereological models and especially intergranular contact surface fractal morphology was the subject of several papers of these authors. The main conclusion was that intergranular capacities have higher values then expected which is induced by contact surfaces sizes augmentation as a consequence of their fractal nature. Bigger micro-capacities were justified by virtually having bigger dielectric constants which was achieved by introducing fractal correction factor α0>1, as a multiplier to the usual dielectric constant εr to gain a bigger value of α0εr. In further BaTiO3-ceramics micro-electronics fractal theory development, different fractal methods were used to describe complexity of the spatial distribution of BaTiO3-grains, as well as pores. This led to a fractal correction factor revisited model, which considers existence of surfaces fractality, pores fractality and the inner liquid dynamics and solid state sintering phase within ceramics material represented by the Brownian motion model. The new correction factor α is a function of these three ceramics fractality “sources”. Here, the relationship between α and α0 is established for doped BaTiO3-ceramics using the Curie–Weiss law and temperature as an omnipresent sintering parameter. Also, the model of two grains contact impedance is studied for different α and frequency values. Ву the control of shapes and contact surfaces numbers on the entire BaTiO3-ceramic sample level, the control over structural properties of these ceramics can be achieved, with the aim of correlation between material electronic properties and corresponding microstructure. The fractal nature for analysis of the ceramics structure provides a new approach for modeling and prognosis of the grain shape and relations between the BaTiO3-ceramic structure, micro- and nano-, and all other electronic properties in the light of new frontier for higher level electronic circuits integration.