lecture11-12 - Atomic Theory of Diffusion (See Chapter 2 in...

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Unformatted text preview: Atomic Theory of Diffusion (See Chapter 2 in Philibert) The purpose: to relate the phenomenological diffusion coefficient to microscopic parameters such as jump distance and jump frequency Consider a simple problem of diffusion along [001] direction of a simple cubic lattice with a lattice parameter a . [001] x 1 2 n 1 n 2 J 12 J 21 a 21 2 12 1 21 12 Γ − Γ = − = n n J J J The net flux from plane 1 to 2 where is the jump frequency from plan i to plane j , and n i is the number of atoms per unit area on plane i . ij Γ In terms of average concentration, or the concentration, n , at the middle of the plane 1 and 2, dx dn a n n 2 1 1 − = dx dn a n n 2 1 2 + = The net flux is now: ( ) ( ) 21 12 21 12 2 1 Γ − Γ + Γ + Γ − = n dx dn a J Please note that c = n/a . Therefore ( ) ( ) a c dx dc a J 21 12 21 12 2 2 1 Γ − Γ + Γ + Γ − = v c dx dc D J + − = Compare to ( ) 2 2 21 12 2 1 a a D s Γ = Γ + Γ = ( ) a 21 12 v Γ − Γ = where Γ s is the jump frequency to a particular direction. is the jump frequency to a particular direction....
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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 Penn State.

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lecture11-12 - Atomic Theory of Diffusion (See Chapter 2 in...

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