The pinning force density,
, is one of the main parameters that characterize the resilience of a superconductor to carrying a dissipative-free transport current in an applied magnetic field. Kramer (1973) and Dew-Hughes (1974) proposed a widely used scaling law for this quantity, where one of the parameters is the pinning force density maximum,
, which represents the maximal performance of a given superconductor in an applied magnetic field at a given temperature. Since the late 1970s to the present, several research groups have reported experimental data on the dependence of
on the average grain size,
, in Nb
3Sn-based conductors.
datasets were analyzed and a scaling law for the dependence
was proposed. Despite the fact that this scaling law is widely accepted, it has several problems; for instance, according to this law, at
and
, Nb
3Sn should lose its superconductivity, which is in striking contrast to experiments. Here, we reanalyzed the full inventory of publicly available
data for Nb
3Sn conductors and found that the dependence can be described by the exponential law, in which the characteristic length,
, varies within a remarkably narrow range of
for samples fabricated using different technologies. The interpretation of this result is based on the idea that the in-field supercurrent flows within a thin surface layer (thickness of
) near 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,
, and the surface is a superconductor–vacuum surface). An alternative interpretation is that
represents the characteristic length of the exponential decay flux pinning potential from the dominant defects in Nb
3Sn superconductors, which are grain boundaries.
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