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Computational Simulations Using Time-Dependent Ginzburg–Landau Theory for Nb–Ti-Like Microstructures

Haddon, C.W.W.; Blair, A.I.; Schoofs, F.; Hampshire, D.P.

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Charles Haddon
PGR Student Doctor of Philosophy

A.I. Blair

F. Schoofs


Simulations based on time-dependent Ginzburg–Landau theory are employed to determine the critical current for a model system which represents a Nb–Ti-like pinning landscape at low drawing strain. The system consists of ellipsoids of normal metal, with dimensions 60ξ×3ξ×3ξ , randomly distributed throughout the superconducting bulk with their long axes parallel to the applied current and perpendicular to the field. These preciptates represent the α -Ti elongated precipitates which act as strong pinning centres in Nb–Ti alloys. We present the volume pinning force density as a function of field across the entire range of precipitate volume fractions and find that optimised material in our model system occurs at 32 vol.% ppt., whereas in real materials the optimum occurs at 25 vol.% ppt. The maximum pinning force density in our simulations is slightly higher ( 5.4×10−3JDBc2 vs. 17GN⋅m−3=4.5×10−3JDBc2 ) and occurs at a lower reduced field ( 0.2Bc2 vs. 0.5Bc2 ) than in real materials. We conclude that the broad features of Nb–Ti-like systems are captured in our model, but that the details of the precipitate pinning mechanism are not yet included properly.


Haddon, C., Blair, A., Schoofs, F., & Hampshire, D. (2022). Computational Simulations Using Time-Dependent Ginzburg–Landau Theory for Nb–Ti-Like Microstructures. IEEE Transactions on Applied Superconductivity, 32(4), Article 8800105.

Journal Article Type Article
Online Publication Date Mar 7, 2022
Publication Date 2022-06
Deposit Date Apr 1, 2022
Publicly Available Date Apr 1, 2022
Journal IEEE Transactions on Applied Superconductivity
Print ISSN 1051-8223
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 32
Issue 4
Article Number 8800105
Public URL


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