SCALING LAWS FOR FLUX PINNING IN HARD SUPERCONDUCTORS.

For all hard, high field superconductors examined to date, there is a maximum in the pinning force density F as a function of the reduced magnetic field h.Fietz and Webb first demonstrated in dilute Nb alloys that the peak in F scales as [Hc2(T)12.5if the temperature is changed; the maximum value of F occurred at the same value of reduced field regardless of temperature.P Recent data on the temperature dependence of pinning in Nb3Sn, Nb-25% Zr and a Nb-Ti alloy, which exhibits the "peak effect", are analysed to show that similar scaling laws are obeyed by these materials.All presently available evidence indicates however that the reduced field h at which the maximum F P P occurs, as well as the height and shape of this maximum, can be altered by metallurgical treatment.Apparently weak pinning defects, or widely spaced ones, produce a small peak in F (h) at high h whereas strong, closely spaced pins produce a large peak in F (h) at low h without producing much change in P F (h) at high h.A model which predicts these metallurgical effects, as well P as the scaling laws, is proposed.According to the model at h< >h it occurs P by synchronous shear of the flux line lattice around line pins too strong to be broken.In the high field regime, where quantitative predictions are possible, the magnitude and field dependence of F are in good agreement with P experiment.In this model the anomalous "peak effect" occurs whenever line pins are relatively weak, producing a narrow peak in F (h) at high h.MASTER