Invariant strain analysis of the critical temperature Tc of Nb3Sn

An analysis has been made that incorporates the strain dependence of the critical temperature T_c of Nb₃Sn in a calculation using the formalism of strong superconductivity. The critical temperature in the absence of strain depends on the harmonic phonon spectrum. The value of T_c can be related to the acoustic phonon modes. It is found that the phonon frequency characteristics can be determined, in a simple model, from a scalar strain energy potential that is a function of the invariants of the strain tensor under the cubic symmetry group and that includes harmonic and anharmonic terms. The strain dependent anharmonic phonon spectrum is found to result in the strain dependence of T_c. A calculation of the normalized strain dependence T_c(ε)/T_cm is presented for assumed wire and tape composite conductors and shown to agree with measurements from the literature over the full range of strain. The correspondence of the various strain scalar invariants with various aspects of the typical strain profile is discussed. The analysis contains the influence of the hydrostatic strain on T_c and relates the observed asymmetry in the strain profile between compressive and tensile intrinsic strain to the principle part of the third strain invariant.