A semi-empirical formula for the dependence of upper critical field with component and strain in Nb₃Sn

Abstract

<p>We include the effects of Sn content b in the scaling law to generalize the upper critical field B<sub>c2</sub>(T, e) function of temperature and strain in Nb<sub>3</sub>Sn. The basis for this generalization comes from a theory developed by the same author [Scientific Reports 7, 1133 (2017)]. The important assumption in the current work is that, in determining the upper critical field B<sub>c2</sub>, the contributions of strain, temperature and Sn content are independent of each other. It is followed that we write down a semi-empirical expression B<sub>c2</sub>(T, e, b) = B<sub>c2</sub> (T<sub>0</sub>, e<sub>0</sub>, b)s(e)(1 - t<sup>1.52</sup>) where the strain function s(e) and t ºT/T<sub>c</sub> (e) are affected only by strain and temperature, respectively, and the variation of tin content b enters in the function B<sub>c2</sub> through B<sub>c2</sub>(T<sub>0</sub>, e<sub>0</sub>, b). This separable form of B<sub>c2</sub>(T, e, b) allows one to incorporate Sn content b in the scaling law in a natural way, while this variable is not considered by traditional scaling laws. In addition to this advance, one can see a more flexible function with triple variables which could be an effective tool to fit or predict experiments. As the last but most important outcome, this semi-empirical function instructs one how to understand the role of component content played in scaling behaviors of Nb<sub>3</sub>Sn, so as to reduce the off-stoichiometric composition inducing discrepancy between the results by scaling laws and experiments.</p>