A new analysis for the determination of ternary interdiffusion coefficients from a single diffusion couple

Concentration profiles that develop in a ternary diffusion couple during an isothermal anneal can be analyzed directly for average ternary interdiffusion coefficients. A new analysis is presented for the determination of average values for the main and cross-interdiffusion coefficients over selected regions in the diffusion zone from an integration of interdiffusion fluxes, which are calculated directly from experimental concentration profiles. The analysis is applied to selected isothermal diffusion couples investigated with α (fcc) Cu-Ni-Zn alloys at 775 °C, β (bcc) Fe-Ni-Al alloys at 1000 °C, and γ (fcc) Ni-Cr-Al alloys at 1100 °C. Average ternary interdiffusion coefficients treated as constants are calculated over composition ranges on either side of the Matano plane and examined for the diffusional interactions among the diffusing components. The ternary interdiffusion coefficients determined from the new analysis are observed to be consistent with those determined by the Boltzmann-Matano analysis at selected compositions in the diffusion zone. The ternary interdiffusion coefficients are also employed in analytical solutions based on error functions for the generation of concentration profiles for the selected diffusion couples. The generated profiles are a good representation of the experimental profiles including those exhibiting uphill diffusion or zero-flux plane (ZFP) development for the individual components. Uncertainties in the values of the interdiffusion coefficients calculated on the basis of the new analysis are found to be minimal.

[1]  David J. Young,et al.  Diffusion in the Condensed State , 1988 .

[2]  R. Dehoff,et al.  Diffusion composition path patterns in ternary systems , 1974, Metallurgical and Materials Transactions B.

[3]  Y. Sohn,et al.  Average effective interdiffusion coefficients and their applications for isothermal multicomponent diffusion couples , 1996 .

[4]  L. Onsager,et al.  THEORIES AND PROBLEMS OF LIQUID DIFFUSION , 1945, Annals of the New York Academy of Sciences.

[5]  R. Sisson,et al.  Diffusional and thermodynamic interactions in the Cu-Ni-Zn system at 775°C , 1977 .

[6]  L. Onsager.  Reciprocal Relations in Irreversible Processes. II. , 1931 .

[7]  M. Dayananda,et al.  EFFECTIVE INTERDIFFUSION COEFFICIENTS AND PENETRATION DEPTHS , 1991 .

[8]  M. Dayananda,et al.  Zero-flux planes and flux reversals in the Cu- Ni- Zn System at 775 °C , 1984 .

[9]  M. Dayananda.  Average Effective Interdiffusion Coefficients in Binary and Multicomponent Alloys , 1993 .

[10]  M. Dayananda,et al.  Diffusion in β2 Fe-Ni-Al alloys , 1976 .

[11]  M. Dayananda,et al.  Identification of zero-flux planes and flux reversals in several studies of ternary diffusion , 1983 .

[12]  M. Dayananda.  Average effective interdiffusion coefficients and the Matano plane composition , 1996 .

[13]  J. Kirkaldy.  DIFFUSION IN MULTICOMPONENT METALLIC SYSTEMS: I. PHENOMENOLOGICAL THEORY FOR SUBSTITUTIONAL SOLID SOLUTION ALLOYS , 1958 .

[14]  M. Dayananda,et al.  Zero-flux planes and flux reversals in Cu−Ni−Zn diffusion couples , 1979 .

[15]  A. Nowick,et al.  Diffusion in solids: recent developments , 1975 .

[16]  M. Dayananda.  An analysis of concentration profiles for fluxes, diffusion depths, and zero-flux planes in multicomponent diffusion , 1983 .

[17]  H. Fujita,et al.  An Exact Solution of the Equations for Free Diffusion in Three-component Systems with Interacting Flows, and its Use in Evaluation of the Diffusion Coefficients , 1956 .