Strain scaling law for flux pinning in NbTi, Nb<inf>3</inf>Sn, Nb-Hf/Cu-Sn-Ga, V<inf>3</inf>Ga and Nb<inf>3</inf>Ge

Abstract

Critical current and flux pinning densities have been determined for a series of practical conductors as a function of uniaxial tensile strain in magnetic fields ranging from 4 T to 19 T. An empirical relation has been found at 4.2 K that accurately describes these data over the entire range of field under both compressive and tensile strain. The pinning force F has been found to obey a scaling law of the form: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F = [B*_{c2}(\varepsilon)]^{n} f(b)</tex> where f(b) is a function only of the reduced magnetic field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b \equiv B/B*_{c2}</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B*_{c2}</tex> is the strain dependent upper-critical field determined from high-field critical-current measurements. This strain scaling law was found to hold for all superconductors examined thus far, including commercial multifilamentary wire, mono-filamentary conductors, CVD tapes, extremely fine-filament conductors, partially-reacted specimens, and "in-situ" cast conductors. For Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n \cong 1.0</tex> , for Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn with Hf and Ga additions, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n \cong 1.2</tex> , for V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Ga, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n \cong 1.4</tex> , for Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Ge, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n \cong 1.6</tex> , and for NbTi, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n \cong 4</tex> . The importance of this relationship is that, for these conductors at least, it is possible to measure F at one strain and then immediately be able to predict F (and thus J <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> ) at other strain levels simply by scaling the results by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[B*_{c2}(\varepsilon)]^{n}</tex> . The relation between strain scaling and temperature scaling is discussed as it relates to flux pinning theories.