The authors have numerically calculated the elementary pinning force, f p and the bulk pinning force, F p , for Nb-Ti alloys containing alpha -Ti ribbon-like precipitates. The Nb-Ti microstructure is modelled as an array of parallel slabs of normal alpha -Ti of thickness d n <5 xi separated by superconducting Nb-Ti of thickness d s <5 xi . They solve the Ginzburg-Landau (G-L) equations, for each alloy, to obtain the order parameter Psi 0 (r) within the structure. The fluxon-pin interaction is calculated by overlapping Psi 0 (r) with Psi f (r) the order parameter around the fluxon core, and re-evaluating the G-L free energy. Repeating this process as a function of fluxon position, they can map out the pinning potential and calculate both f p and F p for each model alloy. f p is found to increase steadily but non-linearly for d n <1.5 xi and plateau for d n >3 xi . Additionally, they note an enhancement in f p for 1.5 xi <d n <3 xi due to the proximity effect. The authors F p calculations predict a maximum for an alloy with d n =1.0 xi and d s =1.6 xi . This result suggests that a Nb-Ti alloy with 40 vol.% alpha -Ti and 6 nm thick ribbons would maximize F p and yield an increase in J c of 40% over present alloys. In addition, their theoretical results for F p closely parallels the experimental results of Meingast and Larbalestier for F p as a function of the pin thickness and the results of Lee and Larbalestier for F p as a function of alpha -Ti volume fractions.
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Stejic et al. (1992) studied this question.
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