Talantsev, E.F.; Valova-Zaharevskaya, E.G.; Deryagina, I.L.; Popova, E.N. Characteristic Length for Pinning Force Density in Nb3Sn. Materials2023, 16, 5185.
Talantsev, E.F.; Valova-Zaharevskaya, E.G.; Deryagina, I.L.; Popova, E.N. Characteristic Length for Pinning Force Density in Nb3Sn. Materials 2023, 16, 5185.
Talantsev, E.F.; Valova-Zaharevskaya, E.G.; Deryagina, I.L.; Popova, E.N. Characteristic Length for Pinning Force Density in Nb3Sn. Materials2023, 16, 5185.
Talantsev, E.F.; Valova-Zaharevskaya, E.G.; Deryagina, I.L.; Popova, E.N. Characteristic Length for Pinning Force Density in Nb3Sn. Materials 2023, 16, 5185.
Abstract
The pinning force density FpJc,B=Jc×B (where Jc is the critical current density and B is the applied magnetic field) is one of the main parameters that characterize the resilience of a superconductor to carry a dissipative-free transport current in an applied magnetic field. Kramer (1973 J. Appl. Phys. 44 1360), and Dew-Hughes (1974 Phil. Mag. 30 293) proposed a widely used scaling law for the pinning force density amplitude: FpB=Fp,max×p+qp+qppqq×BBc2p×1-BBc2q, where Fp,max, Bc2, p, and q are free-fitting parameters. Since the late 1970-s till now, several research groups have reported experimental data on the dependence of Fp,max on the average grain size, d, in Nb3Sn-based conductors. Godeke (2006 Supercond. Sci. Techn. 19 R68) proposed that the dependence obeys the law Fp,maxd=A×ln1d+B. However, this scaling law has several problems, for instance, the logarithm is taken from a non-dimensionless variable, and Fp,maxd<0 for large grain sizes, and Fp,maxd→∞ for d→0. Here, we reanalysed the full inventory of publicly available Fp,maxd data for Nb3Sn conductors and found that the dependence can be described by Fp,maxd=Fp,max0×exp-dδ law, where the characteristic length, δ, varies within a remarkably narrow range, that is, δ=175±13 nm, for samples fabricated by different technologies. The interpretation of the result is based on the idea that the in-field supercurrent flows within a thin surface layer (thickness of δ) near the grain boundary surfaces (similar to London’s law, where the self-field supercurrent flows within a thin surface layer with a thickness of the London penetration depth, λ, and the surface is a superconductor-vacuum surface). An alternative interpretation is that δ represents the characteristic length of the exponential decay flux pinning potential from the dominant defects in Nb3Sn superconductors, which are grain boundaries.
Keywords
pinning force density in superconductors; superconducting critical current; scaling laws in superconductivity
Subject
Physical Sciences, Condensed Matter Physics
Copyright:
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