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Unformatted text preview: Since the activation for diffusion along extended defects is smaller than that in the bulk, the diffusion along extended defects become increasingly important as temperature decreases Example ln D 1/ T Polycrystalline Ag Single crystal Ag d=2R δ δ The ratio of the number of atoms in the GB region to that in the bulk: R R δ δ ~ 2 If ' ~ Γ Γ R δ The contribution form the lattice diffusion and that form the GB are about the same If Γ >> Γ R ' δ GB diffusion dominates s s m 8 10 3- 10 ~ , 10 ~ ' , 10 ~ e.g. Γ Γ µ δ m s s m R µ µ δ 1 . 10 10 10 ~ ' 8 10 3 = × Γ Γ = − If R < 0.1 µ m, GB diffusion dominates Analytical Solutions for GB Diffusion (B-Type Kinetics) surface diffusion species t D ' Dt d δ z ( ) 2 2 2 2 2 z c x c D c D t c ∂ ∂ + ∂ ∂ = ∇ = ∂ ∂ For | x | > δ /2 ∂ ∂ + ∂ ∂ = ∂ ∂ + 2 2 2 2 ' ' ' δ δ x c D z c D t c For | x | < δ /2 c c = ' at | x | = δ /2 x J x J dz z J + z J dz δ 2 δ =...
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- Spring '02
- Trigraph, Atomic diffusion, surface diffusion, GB Diffusion