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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 The ratio of the number of atoms in the GB region to that in the bulk: R R ~ 2 If ' ~ R The contribution form the lattice diffusion and that form the GB are about the same If >> R ' GB diffusion dominates s s m 8 10 3- 10 ~ , 10 ~ ' , 10 ~ e.g. m s s m R 1 . 10 10 10 ~ ' 8 10 3 = = If R < 0.1 m, GB diffusion dominates Analytical Solutions for GB Diffusion (B-Type Kinetics) surface diffusion species t D ' Dt d z ( ) 2 2 2 2 2 z c x c D c D t c + = = For | x | > /2 + = + 2 2 2 2 ' ' ' x c D z c D t c For | x | < /2 c c = ' at | x | = /2 x J x J dz z J + z J dz 2 =...
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- Spring '02