A Mixing Formula Accounting for Inversion of Matrix Structure

Known mixing models are analyzed with the aim to retrieve permeability of metal inclusions from the measured constitutive parameters of a binary composite. The application-oriented models are interpreted in terms of inclusion shape-factor and percolation threshold, which are two measurement-fitted parameters. A model that accounts for the inversion of the Maxwell Garnett matrix structure is proposed. The structure inversion point is close to the percolation threshold, and the inversion takes place within a transition filling range that is a third fitting parameter. The proposed model is compared with the effective medium model in terms of the complex susceptibility calculated as the function of filling and of frequency and in terms of Bergman-Milton shape-factor distribution charts. The model validity is illustrated by treatment of the measured microwave constitutive parameters of a composite filled with carbonyl nickel.