Characteristic length for pinning force density in $Nb{}_{3}Sn$

Abstract

The pinning force density $F{}_p(J{}_c,B)=J{}_c\times B$ (where $J_c$ is the critical current density and $B$ is the 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: $F{}_p(B)=F{}_{p,max}((p+q){}^{(p+q)}/(p^p{q}^q))(B/B_{c2}){}^p(1-B/B{}_{c2}{)}^q$, where $F{}_{p,max}$, $B{}_{c2}$, $p$, and $q$ are free-fitting parameters. Since the late 1970-s till now, several research groups have reported experimental data on the dependence of $F_{p,max}$ on the average grain size, $d$, in $Nb{}_{3}Sn$-based conductors. Godeke (2006 Superc.Sci.Techn. 19 R68) proposed that the dependence obeys the law $|F{}_{p,max}(d)|=A\times ln(1/d)+B$. However, this scaling law has several problems, for instance, the logarithm is taken from a non-dimensionless variable, and $|F{}_{p,max}(d)|<0$ for large grain sizes and $|F{}_{p,max}(d)|\to \infty$ for $d\to 0$. Here we reanalysed the full inventory of publicly available $|F{}_{p,max}(d)|$ data for $Nb{}_{3}Sn$ conductors and found that the dependence can be described by $F_{p,max}(d)=F_{p,max}(0)exp(-d/\delta )$ law, where the characteristic length, $\delta$, varies within a remarkably narrow range, that is, $\delta =(175\pm 13)nm$, 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 $\delta$) near the grain boundary surfaces. An alternative interpretation is that $\delta$ represents characteristic length of the exponential decay flux pinning potential from the dominant defects in $Nb{}_{3}Sn$ superconductors, which are grain boundaries.

arXiv comment27 pages, 12 figures

References in corpus (7)

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Cited by in corpus (1)

• A-15 type superconducting hydride $L{a}_4{H}_{23}$: Nanograined structure with low strain, strong electron-phonon interaction, and moderate level of nonadiabaticity