Magnetic and Electronic Properties of BaTiO₃–(Ni,Cu,Zn)Fe₂O₄ Ceramic Composite: Reflection of Kepler Conjecture

Abstract

Ceramic composites [xNi_0.15Cu_0.30Zn_0.55Fe₂O₄–(1−x)BaTiO₃] were successfully prepared by a direct solid-state reaction of raw materials (BaCO₃, CuO, α-Fe₂O₃, NiO, TiO₂, and ZnO). The composites are so homogeneous that the ferrite and BaTiO₃ grains do not react with each other. The x-dependent permeability and permittivity are found to obey Maxwell–Garnett effective medium theory, which suggests that the composites consist of ferrite particles with barium titanate medium. This model, however, starts to deviate from the experimental data at x=0.75, and the roles of medium and inclusions seem to be exchanged. It can be qualitatively explained by the fact that geometrical close-packing of spheres is limited up to about 74 vol % (Kepler conjecture).