Critical current and pinning-force densities in a series of niobium alloys subjected to severe plastic deformation have been determined from measurements of complete hysteretic magnetization curves on alloys with Ginzburg-Landau parameter K between 1.3 and 13 at temperatures from the critical temperature T c down to 0.147V Systematic scaling rules were found that accurately describe all of the results over the entire range of fields and temperatures. The pinning-force density scales with magnetic induction as a single function of B/H C 2', it scales with temperature as the f power of the upper critical field # c2 (r), is roughly proportional to K~V, where 1<7<3, and is otherwise independent of T. A model for the pinning process that takes into account deformation of the fluxoid lattice by the pinning forces is proposed to account for the observed scaling rules. The results are consistent with a pinning interaction based on a second-order elastic interaction between dislocations and the fluxoid lattice, but other mechanisms are not excluded. Cooperative effects seem to be an essential feature of the pinning process, leading to a dependence of the pinning-force density on the square of the pinning-point strength, and on the arrangement of pinning points. 7

Very high critical current densities (Jc=8×105 A/cm2 at 4.2 K and 6 T) have been achieved in commercial Nb3Sn tape and more recently in multifilamentary Nb3Sn superconductors. The relative contributions of two types of pinning centers, grain boundaries and second phase particles, to flux pinning have been determined by correlating Jc with microstructure. It was found that grain boundaries were the only defect present in sufficient density to account for flux pinning in the multifilamentary Nb3Sn material. The dependence of Jc on grain size was measured, and the relationship between pinning force and grain size is discussed in terms of current theories for flux pinning in type-II superconductors.

The magnetization and critical transport-current densities of samples of superconducting niobium-25% zirconium cold-worked wire have been measured quantitatively up to 40 kOe applied field. All of the magnetization characteristics, as measured by several techniques, and the critical transport currents conform to critical-state concepts provided that the equilibrium magnetization is included in the analysis. The equilibrium magnetization curves could be deduced from the hysteretic measured magnetization data, and the results agree with the theory of Abrikosov for type-II superconductors. The irreversible magnetization-current densities J C (B), where B is the local magnetic induction, just equal the critical transport-current densities Jt(H) in the range 4 to 40 kOe applied field. They are accurately fitted by an empirical criticalstate expression of the form J c {B)-a 0 exp (-B/b Q )+c 0 where a 0 , b 0 , and c 0 are measured constants of the material. The methods used appear to be generally applicable to the study of hysteretic superconducting 9 M.

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