Equilibrium behavior and critical current density in polycrystalline MgB/sub 2/

A simple "effective media" approach is used to calculate the constitutive equilibrium field B/sup e/(H), and hence also the equilibrium magnetization M/sup 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/sup e/(H) relation, for an as-prepared polycrystalline MgB/sub 2/ specimen, allows for the determination of a self-consistent set of values for the anisotropic G-L parameters and for the critical fields H/sub c1/(T), H/sub c/(T), and H/sub c2/(T) for the material. The calculated B/sup e/(H) relation, together with explicit critical current density, J/sub c/(B), trial functions, allows for the determination of flux density profiles [B(r)]/sub 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/sub c/(B,T)/spl prop/H/sub c1//sup n/(T)(1-B/B/sub 0/)/sup 2/B/sup -1/2/, where B/sub 0/(T)/spl ap//spl mu//sub 0/H/sub 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/sub c/ in polycrystalline MgB/sub 2/ is determined by vortex pinning at grain boundaries.