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Abstract
In this study, in order to establish grain shapes of sintered ceramics, new approach on correlation between microstructure and doped BaTiO3 -ceramics properties based, on Voronoi model and mathematical statistics calculations on fractal geometry, has been developed. BaTiO3-ceramics doped with Yb2O3 (from 0.1 to 1.0wt% of Yb) were prepared by using conventional solid state procedure and were sintered from 1320?C to 1380?C for four hours. The microstructure of sintered specimens was investigated by Scanning electron microscope JEOL-SEM-5300. For better and deeper characterization and understanding of the ceramics material microstructure, the methods which include the fractal nature structure, and also Voronoi model and mathematical statistics calculations, are applied. In our research the Voronoi is one specific interface between fractal structure nature and different stochastically contact surfaces, defined by statistical mathematical methods. Also, the Voronoi model practically provided possibility to control the ceramics microstructure fractal nature. Mathematical statistic methods enabled establishing the real model for the prognosis based on correlation: synthesis-structures-properties.
Highlights
Barium-titanate ceramics are one of the most important ferroelectric materials, used for obtaining different electro ceramic components
We showed some results for intergranular contact surfaces based on statistical methods and calculations
The Voronoi model represents a specific interface between fractal structure nature and different stochastically contact surfaces, practically provided possibility to control the ceramics microstructure fractal nature
Summary
Barium-titanate ceramics are one of the most important ferroelectric materials, used for obtaining different electro ceramic components. Diffusion process, it is essential to have an equivalent circuit model that provides a more realistic representation of the electrical properties It has been established modeling of random microstructures like aggregates of grains in polycrystals, patterns of intergranular cracks, and composites, theory of Iterated Function Systems (IFS) and the concept of Voronoi tessellation, can be used [3, 4]. A Voronoi tessellation represents a cell structure, constructed from a Poisson point process by introducing planar cell walls perpendicular to lines connecting neighboring points These results, in a set of convex polygons/polyhedra (Fig. 1.), embed the points and their domains of attraction, which partitioned the underlying space [8, 9]. We showed some results for intergranular contact surfaces based on statistical methods and calculations
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