Relationship between microstructures and magnetic properties of ferrites containing closed pores

A model for the effect of demagnetizing field caused by closed pores and grain boundaries in ferrites was developed. This paper presents the expressions to transform the magnetic properties free from the demagnetizing field into the apparent magnetic properties. The expression for the apparent permeability isμₐₚₚ = {(1 - P)μ₁}{(1 + P/2)(1 + 0.75 t/D{μ₁}{μb}}, where p is porosity, D is average grain size, t is effective thickness of the grain boundary region, μb is the permeability of the grain boundary region and μl corresponds to the permeability free from the demagnetizing field, it was found that the demagnetizing field caused by the pores is proportional to the magnetic field, whereas that caused by the grain boundaries is proportional to the flux density, and that the grain boundary region is important for the control of the magnetic properties of ferrites.