Experimental and Theoretical Investigation of the Diffusion of Sn in Internal-Tin Nb$_{3}$ Sn

The diffusion of Sn through the interfilamentary matrix within a subelement and the formation the of associated Cu-Sn phases was observed experimentally for several different Nb
₃
Sn internal-Sn type strand subelements during the pre-reaction part of a heat treatment. Two different pre-reaction heat treatment schedules were investigated (10degC/hr ramp up, pausing at 185degC/24 hr + 25degC/hr ramp up, pausing at 340degC/48 hr as well as 10degC/hr ramp up, pausing at 210degC/48 hr + 25degC/hr ramp up, pausing at 400degC/48 hr). Four subelement types were measured, one without Ti, the others with Ti added either as NbTi rod replacements for selected Nb(Ta) filaments, or as wraps around each individual Nb(Ta) filament. In all but one case the majority of the filaments were a Nb-7.5 wt%Ta. A simple model was developed to determine the time and temperature dependence of Sn-diffusion through the Cu matrix of the subelements. The output of the model, in the form of radial positions of eta, epsiv, and a phases as a function of time during the pre-reaction heat treatment process, was compared to the experimental results.