Dielastic interaction of the flux line lattice with internal stresses of crystal imperfections. I. The change of elastic constants in an inhomogeneous,type II superconductor

Analytical expressions for the change of the elastic constants due to the superconducting phase transition are derived within the framework of the micromagnetic theory of superconductivity. In particular, the variation of the shear modulus in the environment of a single vortex is discussed, which is important for the second-order interaction (E effect) between flux lines and crystal dislocations. Furthermore, the change of elastic moduli in the mixed state, as caused by the periodic flux line lattice, is investigated, and its field dependence is studied. Numerical values for the material parameters that describe the strain dependence of the critical fieldH _c and the critical temperatureT _c are presented for Nb and Nb ₃ Sn.