Statistical Modeling of soft magnetic composite's permeability

Derivation of the demagnetizing coefficients of non ellipsoidal solids or composite media is one of the most difficult problems in electromagnetism. For a single solid object, exact solutions may be derived for various simple shapes involving quite complicated mathematics but never without ambiguity since the coefficient depends on the susceptibility of the material. For composite medium, usually called soft magnetic composites (SMC) or powder cores, essentially two approaches are used both based on spatial periodicity hypothesis: the non magnetic grain boundary model and the effective medium theory. Actually, the first one works only for dense materials and the second works at low concentration. Both need fitting of two parameters, the inner demagnetizing factor and the particle’s susceptibility, just because the periodicity hypothesis is never verified for magnetic filling factors larger than 20%. A breakaway model is proposed based on the computation of mathematical esperance of the statistical distribution of magnetic chains and the subsequent determination of demagnetizing coefficient of an ellipsoid of equivalent aspect ratio. The model is collated with permeability data from the literature for spherical or non-spherical particles based SMCs and shows a excellent agreement with only one or even without fitting parameter in the whole concentration range.