Percolation and the resistive transition of the critical temperature Tc of Nb3Sn

The relationship between the distribution of the critical temperature, the percolation function, and the resistive transition of the critical temperature is explored for polycrystalline Nb₃Sn. In the neighborhood of the critical temperature, Nb₃Sn is assumed to be a random mixture of superconducting and normal grains. Percolation concepts are applied to a study of the resistivity. A general analysis is made showing that the onset and shape of the resistive transition for composite conductors are determined by the percolation function and the distribution of the critical temperature. An approximate form of the percolation function is determined based on a linear FEM analysis. Example resistive transitions are calculated for an assumed normal distribution of the critical temperature. An argument is presented that relates grain orientation and strain dependence in Nb₃Sn. It is noted that a dependence of the distribution of T_c with strain, in addition to the usual shift in T_c with strain, would be the result of a strain dependence that is a function of grain orientation. The analysis shows the extent to which the slope of the resistive transition is a measure of the distribution of the critical temperature, and therefore a measure of the grain orientation strain sensitivity. Finally, a method is described to determine the percolation function experimentally.