Interdiffusion of Sn and Pb in liquid Pb-Sn alloys

Abstract

Coefficients for the interdiffusion of Sn in Pb-rich alloys and Pb in Sn-rich alloys were established using 1.5-mm-diameter capillaries and the semi-infinite rod technique. Interdiffusion coefficients are presented for the entire concentration range from pure Pb to pure Sn, for temperatures from 668 to 1031 K. The concentration dependence of the interdiffusion coefficients was determined by establishing the concentration along the length of the capillaries and calculating the coefficients using a finite-difference technique. The interdiffusion of Sn in Pb, extrapolated to 0 at, pct Sn, is given by $$D = 8.8 \times 10^{ - 8} \exp - (22,600/RT)m^2 /s$$ and that for Pb in Sn, extrapolated to 0 at. pct Pb, by $$D = 2.4 \times 10^{ - 8} \exp - (19,300/RT)m^2 /s$$ The “average” value for the interdiffusion of Sn in Pb, for the concentration range from 0 to 74 at. pct Sn, is given by $$D = 1.1 \times 10^{ - 7} \exp - (25,200/RT)m^2 /s$$ and the average value for the interdiffusion of Pb in Sn, for the concentration range from 0 to 26 at. pct Pb, is given by $$D = 1.3 \times 10^{ - 8} \exp - (22,600/RT)m^2 /s$$ The values obtained for the coefficients agree reasonably well with previous results for the diffusion of Sn in Pb-rich alloys and are consistent with solvent self-diffusion coefficients for pure Pb and pure Sn. However, while the diffusion coefficients obtained from these Arrhenius equations are likely of the right order of magnitude, it is concluded that the results are affected by fluid flow in the capillaries, resulting in higher than actual activation energies. It is suggested that, for the capillary-reservoir technique, convective flow in the reservoir across the open end of the capillaries induces “lid-driven” flow in the upper portions of the capillaries, resulting in higher than actual diffusion coefficients, particularly for the Sn-rich alloys, since the Sn-rich end of the capillaries was open to the reservoir. Because of fluid motion induced in the capillaries, all of the results for solute and self-diffusion in Pb, both present and previous, are likely erroneous because they were obtained using the capillary-reservoir technique.