Lecture23-26 - Kirkendall Effect and Chemical Diffusion Up to this point we have considered self-diffusion tracer atom diffusion and diffusion of

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Unformatted text preview: Kirkendall Effect and Chemical Diffusion Up to this point, we have considered self-diffusion, 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 self-diffusion 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.

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Lecture23-26 - Kirkendall Effect and Chemical Diffusion Up to this point we have considered self-diffusion tracer atom diffusion and diffusion of

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