Modeling of Field Distribution and Energy Storage in Diphasic Dielectrics

Modeling of electrostatic field distribution and energy storage in diphasic dielectrics containing high-permittivity BaTiO₃ in a glass host has been carried out using analytical modeling based on the Maxwell Garnett (MG) mixing rule, and numerical simulations accomplished using boundary element method (BEM) method software. The field distribution was studied as a function of the dielectric contrasts and volume fractions of the phases. For the geometry with a high-permittivity sphere enclosed in a low-permittivity glass cube it was found that a dielectric contrast of 75 and volume fraction of 46.8% led to higher energy storage densities than other geometries. For composites with lower volume fractions of high-permittivity inclusions, field enhancement factors of 2.6 were observed, whereas for higher volume fraction composites, field enhancements of 10 were noted. Higher field enhancement factors are expected to lead to dielectric breakdown at lower applied fields, limiting energy density. The upper limit of applicability of the MG formulation in terms of the inclusion volume fraction was also established and is a function of dielectric contrast. The host material permittivity causes a substantial variation in the applicability limit of the MG mixing rule, while the permittivity of inclusion phase does not affect the limit.