Estimation of composites conductivity using a general mixing rule

It is proposed to use a mixing rule for the estimation of conductivity, sigma in 'conductor-insulator' composites (M-A) and composite solid electrolytes (MX-A). The mixing rule in its classical form sigma (alpha) = (1 - f) . sigma (alpha)(M) + f . sigma (alpha)(A) (where f is the volume fraction of A; sigma (M,A) are conductivity of the phases hi and A; - 1 < < 1) is applicable only for some specific morphology of the composite. This equation may be generalized by introducing the dependence (f) = alpha1 . (1 - f) + alpha2 . f in order to take variation of the morphology with f into account. For MX-A systems the general mixing rule has the form sigma (alpha (f)) = (1 - f - f(S)) . sigma (alpha (f))(MX) + f(s) .sigma (alpha (f))(S) + f . sigma (alpha (f))(A), where f(S) is the volume fraction of high-conducting interface regions estimated in terms of the brick-wall model; a, is the conductivity via the interface. The general mixing rules are rather simple, convenient, agree with effective medium models, qualitatively describe percolation effects and satisfactorily represent the experimental data in many composites. (C) 2000 Elsevier Science B.V. All rights reserved.