Influence of third elements on growth of Nb3Sn compounds and on global pinning force

The crystal growth of Nb₃Sn by the bronze method has been investigated by using diffusion couples consisting of niobium and bronze with the addition of third elements. When the specimens were annealed at temperatures between 973 and 1073 K, the time-dependence of layer thickness was represented approximately by the function ofd=kt^m. The time exponent changed from 1/3 to unity depending on the annealing condition as well as on the nature of the third element. By the addition of titanium, hafnium, zirconium, indium and galium to the bronze, the growth rate of the compound layer increases. Faster layer growth corresponds to a larger time exponent. The following three processes are suggested to be important for controlling layer growth: diffusivity of tin atoms through grain boundaries in the compound layer, diffusivity of tin atoms through the matrix of the compound, and the rate of the chemical reaction to form the compound. Essentially these combined processes control the overall rate of layer growth. The grain size is found to be the most effective structural parameter to affect directly the maximum global pinning force. The critical current at a magnetic field of 5T can be scaled by both the layer thickness and the inverse grain size.