Development of a Theoretical Model for Anisotropic Polycrystalline Superconductors Using the Effective-Medium Approximation

Abstract

A study of the transport properties in the normal-state of the anisotropic polycrystalline superconductors have been developed. The presence of certain orientation order of the grains in polycrystalline (Bi,Pb)₂Sr₂Ca₂Cu₃O_10+δ superconductors is modeled taking to account a probability factor of the grain's orientation ϒ. In addition, the concentration of the pores p, which characterizes the contribution of the porosity to the conductivity's decrease in the polycrystalline superconductor have been introduced. The pores and grains are assumed as oblate ellipsoids with similar dimensions, regarding the value of conductivity in each direction in the case of the grains. The calculation is based on the application of a generalization of the effective-medium theory to the heterogeneous mediums which is denominated CoherentPotential Approximation (CPA). The results are compared with a current empiric model to low oriented YBa₂Cu₃O_7-δ (YBCO) samples, this enriches their employment and is applied to superconductor ceramics in general.