Diffusion in Multicomponent Metallic Systems: Vii. Solutions of the Multicomponent Diffusion Equations With Variable Coefficients

Abstract

Analytic solutions of the multicomponent diffusion equations are only available for constant diffusion coefficients, a situation which is unlikely in real systems. Using an extension of Boltzmann's treatment for binary diffusion, the multi-component diffusion equations with variable coefficients have been converted to an integral form which can be solved by iterative methods. For those multicomponent systems in which the off-diagonal Onsager L-coefficients may be approximated by zero, a simple numerical method of solution of the activity profile has been derived, which is applicable even if the D's are variable. A method is developed for designing and analyzing experimental diffusion couples to obtain the maximum amount of information about variable coefficients in ternary systems. The possibility of obtaining thermodynamic data from diffusion experiments is discussed.

Interdiffusion in β Phase of the Ternary Ti-Al-V System

“…13) On the other hand, the ternary interdiffusion coefficients in the Ti-Al-V alloys have been evaluated from the concentration profiles in ternary diffusion couples (K1, K2, K3, K4, V1, V2, V3 and V4) by using the extended the Matano-Kirkaldy method. 14,15) …”

Quaternary Diffusion in 7000 Aluminum Alloys

“…(1) and (2) to the ternary alloy system. 14,15) The effective interdiffusion coefficients in a multicomponent alloy system can be evaluated by the following equation 16,17) …”

“…Recently, the authors have reported the nine interdiffusion coefficients in the quaternary Al-Zn-Mg-Cu alloys. 13) The purposes of the present work are (a) to determine the ternary interdiffusion coefficients by Matano-Kirkaldy method 14,15) in the α-phase region of the ternary Al-Zn-Mg system at 725 K, (b) to determine the effective interdiffusion coefficients by Dayananda method 16,17) in the 7000 aluminum alloys at 755 K, (c) to clarify the relation between the interdiffusion coefficients and the effective interdiffusion coefficients on the basis of the results of quaternary interdiffusion coefficients by in the α Al-ZnMg-Cu solid solutions, and (d) to discuss the thermodynamic interactions between solute atoms in α Al-Zn-Mg-Cu solid solutions.…”

Microstructure Evolution Mechanism in Iron Aluminides/CrMo Steel Composite Prepared by Solid State Bonding

“…These results suggest that columnar grain evolves further than expected from chemical composition analyses. Interdiffusion coefficients were derived from the concentration profiles by using the Boltzmann-Matano method, 14) and those at the Matano interface are incorporated in Table 3. Alloying effect on diffusion was done with the aid of a plot of interdiffusion coefficient at the Matano interface against the content of alloying element.…”