Interdiffusion in ternary Fe-Cr-AI alloys
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I.
INTRODUCTION
W H E N two dissimilar metals or alloys are clamped together and annealed, interdiffusion occurs as a result of the imposed activity gradient. From an experimental point of view, diffusion studies involve the determination of the diffusion coefficient(s) from the solution(s) of the corresponding diffusion equation(s), which adequately describe(s) the redistributions of the solute(s) during the diffusion anneal. Diffusion studies in binary systems involve the measurement of a single diffusion coefficient tl] from just one independent composition profile, which must vary monotonically through all solid solutions bracketed by the terminal alloys. In ternary systems, four independent coefficients are needed to describe the diffusion phenomena from two independent composition profiles of each independent component. The increase in the number of coefficients is due to the interactions between the two independent components in the ternary alloy systems. Diffusion theory in multicomponent systems has been the subject of several papers tg-12] and has been reviewed in considerable detail by Kirkaldy and Young. f~31 Here, the theory is briefly reviewed to help in showing the significance of the present experimental results: the treatment is essentially that of De Groot t2~ and Fitts. fig1 Diffusion is the motion (rearrangement) and, hence, flux of atoms or molecules under the influence of a driving force. In the thermodynamics of irreversible processes, t2,3~ the entropy production ~b in an n-component isotropic system undergoing isothermal diffusion can be represented as a sum of the products of the fluxes J and the corresponding forces X: n
q, = ~ JiX~
[1]
i=1
H.C. AKUEZUE, formerly with the Lawrence Berkeley Laboratories of the University of California, Berkeley, is a consultant in Mountain View, CA. J. STRINGER, Director of Technical Support, is with the Electric Power Research Institute, Palo Alto, CA 96303. At the time of this research, Dr. Stringer was on sabbatical leave at the Lawrence Berkeley Laboratories, Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720. Manuscript submitted November 18, 1987. METALLURGICAL TRANSACTIONS A
The corresponding phenomenological equations of diffusion are the linear relations: n
Ji = Z Li.iXJ (J = 1,2 . . . . . n) j--I And according to (ORR's), ta]
Onsager's
Lij = Lji
reciprocal
[2] relations [3]
The coefficients L U are called the phenomenological coefficients. The phenomenological coefficient Lii determines that part of the diffusion flux of component i arising from its own force. The off-diagonal phenomenological coefficient Lik determines that part of the i-th component diffusion flux arising from the force of component k. Relation [3] holds directly if the forces X and the fluxes J are an independent set of linearly independent vectors; otherwise, the dependent term will be subtracted from Eq. [1] to yield a new scheme of phenomenological equations which can satisfy the form of ORR' s. [2,41 In practi
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