A new analysis for the determination of ternary interdiffusion coefficients from a single diffusion couple
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INTRODUCTION
MULTICOMPONENT diffusion is commonly encountered in most of the commercial material systems employed in a high-temperature and nuclear reactor environment. The development of multicomponent alloys also requires control of microstructures through appropriate heat treatments involving solid-state transformations, precipitation processes, and surface modifications, where the interdiffusion processes play a major role. The description of the interdiffusion behavior of the various components in a multicomponent alloy involves an understanding of the diffusional interactions among the components. Such a description is provided by the Onsager’s formalism[1,2] of Fick’s law extended to multicomponent systems and is based on a determination of (n 2 1)2 interdiffusion coefficients in an n-component system. The description of ternary diffusion requires four concentration-dependent interdiffusion coefficients, two main and two cross-coefficients. For their experimental determination, two independent diffusion couples with a common composition in their diffusion zones, where the interdiffusion coefficients can be evaluated, are needed.[3,4] Also, the ternary interdiffusion coefficients can be partially calculated from a diffusion couple, provided that the concentration profile of a component exhibits relative maxima or minina. If the interdiffusion coefficients are assumed independent of compositions, the concentration profiles developed in an isothermal ternary diffusion couple can be described with analytical solutions based on error functions.[3–7] Since these coefficients are norM.A DAYANANDA, Professor of Materials Engineering, is with the School of Materials Engineering, Purdue University, West Lafayette, IN 47907-1289. Y.H. SOHN, formerly a Graduate Student, School of Materials Engineering, Purdue University, is a Post-Doctoral Research Associate, Institute of Materials Science, University of Connecticut, Storrs, CT 06269-3136. Manuscript submitted April 24, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
mally composition dependent, the use of analytical solutions has been restricted to small concentration ranges.[8,9,10] The objective of this article is to present a new approach in which the four ternary interdiffusion coefficients are determined over selected composition ranges from a single diffusion couple experiment. In this analysis, interdiffusion fluxes of all components are determined directly from the experimental concentration profiles and integrated over selected regions in the diffusion zone; from such flux integration, independent relations are set up for the evaluation of the four ternary interdiffusion coefficients treated as constants and considered as average values over the selected composition ranges. The analysis is applied to selected single-phase isothermal diffusion couples investigated in the Cu-Ni-Zn,[11] Fe-Ni-Al,[12] and Ni-Cr-Al[8,9] systems, and the main and cross-interdiffusion coefficients are calculated as average values for the diffusion path segments on both sides of
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