Invariant formulation of the strain dependence of the critical temperature Tc of Nb3Sn in a three term approximation

It has been shown previously in a full detailed analysis that the strain dependence of the critical temperature may be obtained from a general strain invariant formulation of T-c in strong superconductivity. A physical model was presented in which the phonon frequency spectrum is represented through generalized elastic stiffness coefficients that include strain dependence. The primary purpose of the present work is to achieve a simplification of the analysis in order to facilitate calculation and reveal the essential physical content. The formulation in wave vector space of the equations for T-c in strong superconductivity is reviewed. The method of simplification employs a succession of approximations to the effective elastic constants that enter the relation between phonon frequency and wave number. It is found that the effective elastic constants in the crystal symmetry directions may be grouped into sets having similar form, and this form includes terms in common among the sets and difference terms. The difference terms are found to be in the nature of gradients and may be eliminated to good approximation. The common terms include the strain dependence in a form identified as a deformation strain parameter. The analysis treats spherical (hydrostatic) and deformation strain dependence under longitudinal and transverse applied strain for wire and tape conductor. The analysis is applicable over a full range of applied strain, including small strains often described by a power law strain dependence, and larger strains often described by a deviatoric strain approach. A comparison is provided between the results of the full detailed analysis and the results of the approximate treatment showing the degree of agreement in the various applied strain orientations. (C) 2004 Elsevier Ltd. All rights reserved.