The pinning force density Fpβ(Jcβ,B)=JcβΓB (where Jcβ is the
critical current density, B is applied magnetic field) is one of main
quantities which characterizes the resilience of a superconductor to carry
dissipative-free transport current in 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:
Fpβ(B)=Fp,maxβ((p+q)(p+q)/(ppqq))(B/Bc2β)p(1βB/Bc2β)q,
where Fp,maxβ, Bc2β, p, and q are free-fitting parameters.
Since late 1970-s till now, several research groups reported experimental data
for the dependence of Fp,maxβ on the average grain size, d, in
Nb3βSn-based conductors. Godeke (2006 Supercond. Sci. Techn. 19 R68)
proposed that the dependence obeys the law β£Fp,maxβ(d)β£=AΓlog(1/d)+B. However, this scaling law has several problems, for instance, the
logarithm is taken from a non-dimensionless variable, and β£Fp,maxβ(d)β£<0 for large grain sizes and β£Fp,maxβ(d)β£ββ for dβ0. Here we reanalysed full inventory of publicly available
β£Fp,maxβ(d)β£ data for Nb3βSn conductors and found that the dependence
can be described by Fp,maxβ(d)=Fp,maxβ(0)exp(βd/Ξ΄) law, where the
characteristic length, Ξ΄, is varying within a remarkably narrow range,
i.e. Ξ΄=(175Β±13)nm, for samples fabricated by different
technologies. The interpretation of the result is based on an idea that the
in-field supercurrent is flowing within a thin surface layer (the thickness of
Ξ΄) near the grain boundary surfaces. Alternative interpretation is
that Ξ΄ represents characteristic length for the exponentially decay
flux pinning potential from dominant defects in Nb3βSn superconductors,
which are grain boundaries.Comment: 22 pages, 8 figure