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621.762The percolation approach is used in an analytic relationship between the electrical conductivity and the porosity, which represents a combination of equations previously proposed by Skorokhod for determining the porosity dependence of the electrical conductivity and the relative linear size of the contacts. Equations proposed by the authors use the shaking porosity as the most stable characteristic. The dependence gives better agreement with experiment than do certain analytic relationships given by others.The theory of conductivity for a porous sintered body is a particular case of the general theory of physical properties for heterophase bodies, whose principles are presented in [1][2][3][4]. There is difficulty in describing the properties of such systems because the conductivity is dependent not only on the volume content of the nonconducting phase (pores) but also on the perfection of the contacts between particles. Also, our experiments show that for a given porosity and sintering temperature, the conductivity is substantially dependent on the pore-space geometry: pore sizes and porous structure type [5,6].Up till now, the most effective principle for calculating the dependence of the conductivity on the volume pore concentration has been a combination of model and continuum approaches. Odelevskii [7] proposed the following dependence from a particular structural model in the approximation of a statistically homogeneous isotropic medium:in which λ is the conductivity of the porous body, λ 0 the conductivity of the material, and θ the porosity.This linear dependence fits well for low porosity, while for a wide porosity range and if the differentiation of (1) is correct, Skorokhod [2] obtained the expression λ = λ 0 (1 − θ) 3/2 .Although this formula gives finite values for the conductivity with any porosity, at a certain critical value of θ in a system with a random structure the connectedness is lost. The volume fraction of conducting phase should be close to the percolation threshold and be dependent to a considerable extent on the topology of the pore surfaces. Then it is necessary to modify (2) on the basis of percolation theory principles. Also, that expression does not incorporate the actual contact phenomena occurring in sintered porous bodies. Skorokhod previously proposed to estimate the effects of imperfect particle contacts on the macroscopic conductivity of a powder body on the basis of the relation between the linear dimensions of the contacts and the powder particles [8]. The corrected dependence is λ = λ 0 (1 − θ) 3/2 ξ, (3) in which ξ is the relative linear dimension of the contacts.

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