Statistical modeling of soft magnetic composites’ permeability

Soft magnetic composites (SMC) also known as powder cores are widely used in many applications because of their linearity, controllable permeability and isotropy. Because of the distributed air gap, the permeability is governed by the inner demagnetizing fields. To model the permeability dependence on the filling fraction, 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 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.