The 3D graph approach for breakdown voltage calculation in BaTiO₃ ceramics

Abstract

After pioneering attempts for the introduction of graph theory in the field of ceramics and microstructures, where 1D and 2D graphs were used, in this paper we applied 3D graphs for the breakdown voltage calculation in BaTiO3 sample with some predefined constraints. We have described the relations between grains in the sample and established a mathematical approach for the calculation of breakdown voltage using experimental results. As a result, we introduced mapping between the property of sample and grain structure, then between the grain structure and mathematical graph, using various crystal structures. The main idea was to apply 3D graph theory for the distribution of electronic parameters between the neighboring grains. With this study, we successfully confirmed the possibilities for applications of graphs as a tool for the determination of properties even at the intergranular level.

Fractal Nature Bridge between Neural Networks and Graph Theory Approach within Material Structure Characterization

“…We assume that a ceramic structure is a coating of multiple thin layers around the grains that are mutually interconnected. The design of such a structure using a graph has already been demonstrated [41,42]. Basic elements of ceramic structures are grains and pores, and they are represented by vertices in graphs and interconnecting lines between them.…”

Artificial neural network applied on sintered BaTiO3-ceramic density

“…Based on the theoretical experiment results presented in Fig. 2-13, we demonstrated successful application of the neural network method on samples' surface density calculation, as an original novelty with many advantages in this field [14][15][16][17][18][19][20][21][22].…”

Síntese e Caracterização do BaTiO3 pelo Método da Coprecipitação e Aplicação em Antenas Patch de Microfita

“…Este parâmetro está associado ao intervalo de frequências a qual a antena opera de forma satisfatória, ou seja, é definido como intervalo de frequências em que o desempenho de uma antena, com relação a alguma característica, atende a um padrão específico BALANIS [9]. O valor absoluto é descrito como: (4) Em termos percentuais, (5) Onde 2 e 1 são as frequências de máxima e mínima de operação, respectivamente, e 0 é a frequência central de operação na faixa de -10 dB.…”

“…Os íons de Ba 2+ estão localizados nos oito vértices do cubo. O íon Ti 4+ localiza-se no centro e cada íon de O 2encontra-se em cada uma das seis faces, como ilustra a Figura 1 [5]. O que difere a fase tetragonal da cúbica é a distância entre as posições de simetria que diferem uma fase da outra.…”