PART XII – December 1967 – Papers - Analysis of Ternary Diffusion Curves Using a Second Integration of the Fick Law

A second intepation of the Fick law has been developed and applied to three-place data generated from the Gosting and Fujita solution of the diffusion equation. This integration provides new mathematical techniques for the analysis of experimental data. Through use of the synthetic data it is shown that for concentration-independent interdifiusion coefficients these techniques permit a more accurate determination of the coefficients than does the usual Boltzmann-Alatano analysis. Another technique, applicable to the most general concentration-dependent diffusion coefficients , can be used to determine whether given sets of coefficients are consistent with the experimental ternary concentration-distance curves. DURING the past 10 years the subject of three-component diffusion has advanced from the stage of a laboratory curiosity to the status of an accepted portion of physical metallurgy.1 In the course of this development the underlying treatment for two-component sys- tems was extended and generalized to accommodate the added component, but fundamentally the analyses currently employed for ternary systems are analogous to those previously developed for binary systems. There are several indications that an improved analysis is needed for the ternary case. First, the two cross coefficients, D312 and D321 are typically an order of magnitude smaller than the direct coefficients and consequently are difficult to determine with adequate precision. Second, instead of a single concentration-penetration curve (as in binary diffusion), there are four such curves in the usual determination of ternary diffusion coefficients. These curves have definite theoretical interrelationships, but actual experimental curves exhibit significant departures from these relationships. Finally, the amount of data needed to adequately describe the diffusion behavior of a ternary system is so large that radically new methods are needed to facilitate the gathering of these data. ICirkaldy2j4 has proposed several possible analyses of ternary diffusion data, including some of the methods in current use. A "second-integration" procedure proposed by him4 differed in important respects from that presented here and was not carried to the point of application. Two other methods have been explored by the authors and will be published separately; these are a numerical analysis technique and a method for the analysis of a single ternary diffusion couple. Still other analyses are being explored by various investigators. At present it seems likely that the final analysis of ternary diffusion that evolves will be a composite