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

We include the effects of Sn content beta in the scaling law to generalize the upper critical field Bc2 (T,E) function of temperature and strain in Nb3Sn. 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-c2, 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-c2 (T, is an element of, beta) = B-c2 (T-0, is an element of(0), beta)s (E)(1 t(1.52)) where the strain function s(E) and t equivalent to T/T-c (is an element of) are affected only by strain and temperature, respectively, and the variation of tin content beta enters in the function B-c2 through B-c2 (T-0, is an element of(0), beta). This separable form of B-c2 (T, is an element of, beta) allows one to incorporate Sn content beta 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 Nb3Sn, so as to reduce the off-stoichiometric composition inducing discrepancy between the results by scaling laws and experiments.