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Unformatted text preview: Kirkendall Effect and Chemical Diffusion Up to this point, we have considered selfdiffusion, tracer atom diffusion, and diffusion of small interstitial atoms in a host lattice of larger atoms. We usually assumed that the diffusion coefficient is a constant. What about diffusion in substitutional alloys, AB, in which both A and B atoms can diffuse or A and B go through interdiffusion? A B The Kirkendall experiment: Cu brass d Mo marker wires Cu J Zn J Mo is insoluble in both Cu and Brass No Mo diffusion. Anneal the sample at different t and d is measured Observations from the Kirkendall experiment: the decrease in the distance d , i.e. ∆ d is proportional to t 1/2 2 1 t d ∝ ∆ Kirkendall effect Two possible reasons for the effect: (a) Difference in the atomic volumes of Zn and Cu (b) Difference in selfdiffusion coefficients of Cu and Zn However, even the atomic volume difference between Zn and Cu is taken into account, there is a definite Mo marker movement d decreases Cu Zn J J > To understand the Kirkendall effect, let’s consider an infinite diffusion couple A B original interface inert markers Let’s assume that atomic volumes of A and B are the same, and that D B > D A We need two coordinate systems: (a) Lattice system – fixed to inert markers or lattice planes (b) Lab system – fixed relative to the ends of the couple Movement of A and B atoms in the lattice system is caused by diffusion down a concentration gradient: x c D J A A A ∂ ∂ − = x c D J B B B ∂ ∂ − = D A and D B are the intrinsic diffusion coefficients of A and B In the lab reference system (note: near the ends of the sample, there is no concentration gradient, no diffusion took place) A A A A Vc x c D J + ∂ ∂ − = ' B B B B Vc x c D J + ∂ ∂ − = ' marker velocity Rewrite the flux in the form of Fick’s first law, we have x c D J A A ∂ ∂ − = ~ ' x c D J B B ∂ ∂ − = ~ ' Chemical diffusion coefficient or interdiffusion coefficient ( ) ~ ~ ~ ' ' = ∂ ∂ − = ∂ + ∂ − = ∂ ∂ + ∂ ∂ − = + x c D x c c D x c x c D J J B A B A B A c total atom concentration, which is independent of composition if the atomic volumes of A and B are the same B B B A A A B A Vc x c D Vc x c D J J + ∂ ∂ − + ∂ ∂ − = = + ' ' ( ) x c D D c x c D x c D c V A B A B B A A ∂ ∂ − = ∂ ∂ + ∂ ∂ = 1 1 ( ) ( ) ( ) x c D x D x x c D D x x c D x c D D c c x c D Vc x c D J A B A A B A B A A A A A B A A A A A A A A ∂ ∂ + − = ∂ ∂ − + ∂ ∂ − = ∂ ∂ − + ∂ ∂ − = + ∂ ∂ − = 1 ' D ~ B A A B D x D x D + = ~ D ~ Chemical diffusion coefficient A D Intrinsic diffusion coefficient B D Intrinsic diffusion coefficient ( ) x c D D c V A B A ∂ ∂ − = 1 B A A B D x D x D + = ~ The direction for marker velocity depends on the difference...
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This note was uploaded on 01/19/2010 for the course MAT SCI 503 taught by Professor Chen during the Spring '02 term at Pennsylvania State University, University Park.
 Spring '02
 CHEN

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