Method for Predicting the Effective Conductivity of Textured Polycrystals Taking Intergranular Gaps into Consideration.

Сrystallites in real polycrystals are separated from each other by intergranular space, which affects the effective conductivity of polycrystals. This effect increases with decreasing crystal size. A method for predicting the effective conductivity of polycrystalline media, taking the intergranular space into consideration is developed. The method is constructed using the polycrystal model in which crystallites are considered to be inhomogeneous, consisting of a uniform crystalline anisotropic core and a uniform isotropic shell. In this model, the role of the intergranular gaps is played by crystallite shells. The effective polycrystal conductivity is calculated using the generalized effective-field approximation; the effective medium conductivity is taken as the reference parameter of the medium; i.e., the self-consistent solution method is used. Based on the developed method, a formula for the effective conductivity of polycrystals depending on the conductivity tensor of the crystalline core, shell conductivity, and the core volume fraction in crystallites is derived for the case of spherical crystallites with spherical shells. This formula is applied to particular cases of a polycrystalline medium, i.e., a polycrystal with similar crystallites with isotropic core; in this case, the expression for the effective conductivity is identical to the classical Maxwell–Garnett formula; polycrystals with similar crystallites with anisotropic cores at identical orientations of their crystallographic axes; polycrystals with similar crystallites with anisotropic cores at the uniform distribution of orientations of their crystallographic axes in space; and polycrystals with conductive crystallite cores and absolutely nonconductive shells. In the latter case, the effective polycrystal conductivity vanishes, which is completely consistent with the physical meaning. [ABSTRACT FROM AUTHOR]