An exponential scaling law for the strain dependence of the Nb₃Sn critical current density

Abstract

The critical current density of the Nb 3 Sn superconductor is strongly dependent on the strain applied to the material. In order to investigate this dependence, it is a common practice to measure the critical current of Nb 3 Sn strands for different values of applied axial strain. In the literature, several models have been proposed to describe these experimental data in the reversible strain region. All these models are capable of fitting the measurement results in the strain region where data are collected, but tend to predict unphysical trends outside the range of data, and especially for large strain values. In this paper we present a model of a new strain function, together with the results obtained by applying the new scaling law on relevant datasets. The data analyzed consisted of the critical current measurements at 4.2 K that were carried out under applied axial strain at Durham University and the University of Geneva on different strand types. With respect to the previous models proposed, the new scaling function does not present problems at large strain values, has a lower number of fitting parameters (only two instead of three or four), and is very stable, so that, starting from few experimental points, it can estimate quite accurately the strand behavior in a strain region where there are no data. A relationship is shown between the proposed strain function and the elastic strain energy, and an analogy is drawn with the exponential form of the McMillan equation for the critical temperature.

A theory of the strain-dependent critical field in Nb3Sn, based on anharmonic phonon generation

“…Before turning to the fits, we note that the parametrization (14) may not be the best choice in every situation. In the case of pre-strained wires, the formula (14) generates all powers of a from zero to four, and has enough freedom to grant a good fit. For hydrostatic pressure, however, Eq.…”

Estimate of density-of-states changes with strain in A15 Nb 3 Sn superconductors

“…Several attempts at determining a generic parameterization for the critical properties (the critical temperature T c , the upper critical field l 0 H c2 , and the critical current density J c ) have been made in the past decades, which involves the empirical characterization and interpretation of uniaxial strain dependence [7][8][9], the microscopic modeling based on the strain-induced modifications in the electron-phonon spectrum [10][11][12], the electron density of states (DOS) [13,14] or both [15], and the models with a semi-empirical construction which balances the need for well-founded formalisms for the important features of the strain effects and practical engineering application to multifilamentary composite Nb 3 Sn wire measurements implementation [16][17][18]. Because of the failure to make explicit an underlying microscopic mechanisms, the description of the strain sensitivity in superconducting Nb 3 Sn offered by empirical/semi-empirical modeling and analytics exhibits its limitations in achieving the comprehensive characterizations [14,16].…”

An experimental and computational study of srain sensitivity in superconducting Nb3Sn

“…A variety of strain function descriptions are compared to experimental data, after Lu et al [90]. An additional normalization factor was added to the strain function description by Bordini et al [99].…”

“…The most recent addition is the strain function by Bordini et al [99], which describes the strain function as a function of uni-axial strain, with:…”