Solid Mixture Permittivities

Abstract

A macroscopically homogeneous aggregate contains two materials A, B, with dielectric constants ε_A, ε_B, in volume ratio p: (1—p); what is the dielectric constant of the aggregate? By a method used by Yvon and others in molecular theory, this very old problem is formulated rigorously and solved in series form. One form of the solution is ε/ε′ = 1+⅓p(1—p)(δ′/ε′)²+..., where ε′ = pε_A+(1—p)ε_B, δ′ = ε_A — ε_B. The cubic and higher terms depend on statistical properties of particle geometry: namely, on such functions as p⁽³⁾₁₂₃, the probability that three specified points 1, 2, 3 are all in material A. The relation to earlier calculations is discussed.