Equilibrium behavior and critical current density in polycrystalline MgB2

A simple "effective media" approach is used to calculate the constitutive equilibrium field B^e(H), and hence also the equilibrium magnetization M^e(H), relations for a polycrystalline, anisotropic Type II superconductor with random grain orientation. Mutually-consistent scaling of experimental M versus H isotherms to the calculated M^e(H) relation, for an as-prepared polycrystalline MgB₂ specimen, allows for the determination of a self-consistent set of values for the anisotropic G-L parameters and for the critical fields H_c1(T), H_c(T), and H_c2(T) for the material. The calculated B^e(H) relation, together with explicit critical current density, J_c(B), trial functions, allows for the determination of flux density profiles [B(r)]_H and also the nonequilibrium magnetization M(H) behavior, which is compared with the experimental M versus H isotherms. Optimum fits are obtained with a Kramer-like relation of the form: J_c(B,T)∝H_c1ⁿ(T)(1-B/B₀)²B^-12/, where B₀(T)≈μ₀H_irr(T) is the irreversibility field, and n=0.75 and 2.25 for T below and above 28 K, respectively. The general form of this relation suggests that J_c in polycrystalline MgB₂ is determined by vortex pinning at grain boundaries.