It was noted that up-hill diffusion of Sn took place from a binary Cu–Sn alloy to Nb3Sn during reactive diffusion between the Cu–Sn alloy and Nb at around 1000K. In order to account quantitatively for the occurrence of the up-hill diffusion, phase equilibria in the ternary Cu–Nb–Sn system were theoretically analyzed using a thermodynamic model for phases with different sub-lattices. In this ternary system, there was no ternary compound and the solubility of the third component was very small for all the phases. Consequently, the ternary interaction was assumed negligible, and thus the Gibbs energy of each phase was expressed with the thermodynamic parameters of the relevant binary systems. In an isothermal section calculated at 1053K, the 3-phase equilibrium of Cu+Nb+Nb3Sn appeared at an activity of Sn with 0.0047. If the activity aSnb of Sn for the binary Cu–Sn alloy was greater than the activity aSnc of Sn for the three-phase equilibrium of Cu+Nb+Nb3Sn, Nb3Sn was spontaneously produced owing to the reactive diffusion. As a result, the up-hill diffusion of Sn occurred from the Cu–Sn alloy to Nb3Sn. The chemical driving force, ΔGSn, for the up-hill diffusion was evaluated by the equation ΔGSn = RTln(aSnb/aSnc). This equation semi-quantitatively explained the growth behavior of Nb3Sn.

Quantitative Explanation for Up-Hill Diffusion of Sn during Reactive Diffusion between Cu–Sn Alloys and Nb. T.Yamashina, M.Kajihara: Materials Transactions, 2006, 47[3], 829-37