Extractive Metallurgy Division - Diffusion in Liquid Lead-Bismuth Alloys

Diffusivity of bismuth in liquid Pb-Bi alloys has been measured by the capillary reservoir method as a function of temperature and composition. Fair agreement between theory and experiment is found for the measured diffusion coefficients and activation energies of diffusivity and viscosity in dilute lead alloys. The measured diffusion coefficients in the high bismuth alloys describe mass transport in special concentration gradients. THE study of diffusion in liquid metals has been restricted largely to the amalgams over small ranges of temperature and composition. In contrast to this, diffusion and transport of ions and molecules in aqueous and organic solvents have been studied extensively for the past 50 years. The general difficulty of measuring diffusion coefficients in both gases and liquids at high temperatures has been that of eliminating convection currents. Measuring techniques based on freezing and sectioning after the diffusion period1 are not particularly satisfactory because of the volume changes and segregation which occur during freezing. The most promising technique which is currently being developed for liquid metals is the capillary reservoir method. This eliminates convection currents from the diffusion zone and requires measurements only of the length and initial and final compositions of the alloy within the capillary. Anderson and Saddington' have measured the diffusion coefficient of tungstate anions in aqueous Na,W04; Wane4' and Hoffman- ave studied structure and self-diffusion in water and self-diffusion in mercury, respectively, by similar techniques. Selection of the Pb-Bi system for initial study was made for several reasons: I—It afforded a low temperature system for development of techniques which would be suitable for high temperature measurements in liquid iron. This research on diffusion in liquid iron is now in progress as a part of a general program on the rates and mechanisms of slag-metal reactions. 2—Activity data on liquid Pb-Bi alloys of all compositions are available from the emf meas- urements of Strickler and Seltz.9 3—Some data are available on the diffusion of bismuth into solid lead. The measurements on solid alloys were made by von Hevesy and Seith7 for the concentration range of 0 to 2 pct Bi. An appropriate solution to Fick's law (unsteady state) for the capillary reservoir has been found by considering the mass flow which passes through a unit area of surface on a slab of infinite thickness as a function of time. This is the first application of this solution to diffusion measurements, although a similar solution is available for identical boundary conditions.' By analogy with heat conduction, the problem reduces to a perfectly insulated infinite slab at temperature C,, one surface of which is quenched to C, for all times, t. Heat is permitted to flow from quenched surface of the slab to an infinite supply of coolant at C.' (see Appendix). For the corresponding solution for diffusion in liquids, these terms become Where Cu is the initial concentration of component A" in entire capillary at t - 0, C, is the final con- In this case. component A is bismuth, and C, = 0. centration of component A in entire capillary at t = t, C, is the concentration of component A in bath for all t, 1 is the length of the capillary in centimeters, t is the time of diffusion period in seconds, and D is the diffusion coefficient in square centimeters per second. By comparison with solutions to Fick's law used in the solid state, this solution for liquids is similar to the Grube solution for solids, where the change in D with chemical composition is not taken into consideration. Difficulty is to be expected if large concentration gradients are employed and if the concentration gradients extend over an appreciable length of the capillary.