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

Abstract

We include the effects of Sn content β in the scaling law to generalize the upper critical field B c 2 ( T , ε ) 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 c 2 , 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 c 2 ( T , ε , β ) = B c 2 ( T 0 , ε 0 , β ) s ( ε ) ( 1 − t 1.52 ) where the strain function s ( ε ) and t ≡ T / T c ( ε ) are affected only by strain and temperature, respectively, and the variation of tin content β enters in the function B c 2 through B c 2 ( T 0 , ε 0 , β ) . This separable form of B c 2 ( T , ε , β ) allows one to incorporate Sn content β 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.