Strain Dependence of the Critical Temperature $T_{c}$ of Polycrystalline ${\rm Nb}_{3}{\rm Sn}$ Superconductors

Abstract

The polycrystalline nature of Nb 3 Sn introduces crystal orientation as a possible variable in the strain dependence of the critical properties. It is shown that a dependence of strain sensitivity on crystal orientation implies a dependence on strain of the distribution of , with implications for the functional dependence of strain sensitivity on the strain tensor. The distribution of is found to have an influence on the characteristics of the resistive transition of . Calculations of the resistive transition are done under alternative assumptions for the crystal orientation dependence of strain sensitivity. Available data on the strain dependence of the transition of are contradictory and inconclusive. If strain sensitivity were found to be independent of grain orientation, that would imply a strain dependence on the entire deviatoric strain tensor, through the scalar invariants, including the tetragonal and shear parts. This would be a surprising conclusion given the emphasis on tetragonal strain in Nb 3 Sn.Index Terms-Critical temperature, polycrystalline Nb3Sn, strain dependence.

Analysis of the strain dependence of the superconducting critical properties of single-crystal and polycrystalline Nb3Sn

“…In this section, in order to numerically analyze the critical properties of polycrystalline Nb 3 Sn, the strain-dependent T c model for single-crystal Nb 3 Sn presented in the above section is introduced into the simulated strain field of polycrystalline Nb 3 Sn. In Markiewicz et al [16], the polycrystalline model is viewed as a collection of individual elements, each of which has a T c , and in which, the T c values of the individual elements form a distribution. Considering the inhomogeneous T c distribution, the T c of polycrystalline Nb 3 Sn has been calculated by integral methods.…”

“…The responses of the superconducting properties to mechanical loading depend on the operating temperature, magnetic field, and loading mode. In order to characterize the coupling behaviors of the mechanical and superconducting properties, several constitutive models including empirical formulae, semiempirical formulae, and intrinsic models have been proposed in previous research [8,[15][16][17][18][19][20][21][22][23][24][25][26]. For example, the Ekin power-law model [15] and the Ten Haken-Godeke deviatoric strain model [21] were established, based on the experimental results.…”

Magnetic characterization of Nb3Sn strands under applied strain conditions

“…When a Nb 3 Sn strand undergoes a compressive strain, J c , B c2 , and T c reduce with strain [10,17,24,30]. The larger thermal contraction of the Cu matrix compared to the thermal contraction of the superconductor results in a precompression of Nb 3 Sn when cooled down to the cryogenic test temperatures.…”

“…In their samples, in which the bronze core introduces a radial stress similar to that induced by the jacket in our samples, both a narrowing of the transition and a T c enhancement are observed when the bronze is etched away. Such behaviour could be ascribed to a strain sensitivity to grain orientation [24], provided that the sample is homogeneous. These experimental observations can in principle imply that crystal orientation could play the role of a further variable in the 3D strain dependence descriptions for the critical properties of Nb 3 Sn.…”

“…In fact, we have recently obtained some not completely clear results in transport measurements with bending strain [21,22] on a pre-strained Nb 3 Sn wire, in relation to Ekin's model [23] and current transfer mechanisms within the strand cross section, which we ascribed to this inconsistency. On the other hand, models [24] are available for superconducting parameters, like T c and B c2 , as function of an applied 3D strain. Therefore, we have carried an experimental characterization, through magnetization measurements, of the critical field and temperature of wires to which strain is applied, coupling longitudinal and radial components.…”