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Combined Surface and Grain‐Boundary Diffusion

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1 Author(s)
Stark, J.P. ; Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712

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A mathematical analysis for the accumulation of tracer as diffused through a thin metallic slab by grain‐boundary diffusion is presented. Boundary conditions on the side where the tracer is deposited consist of a small depletable source, and the grain‐boundary concentration is enhanced by surface diffusion. Due to the mathematical difficulty associated with boundary conditions for combined grain‐boundary and surface diffusion, two cases are studied: No accelerated surface diffusion and infinite surface diffusivity along with finite grain‐boundary diffusivity. The difference between the accumulated tracer for the two cases is similar to the contribution from lattice diffusion only. Thus, for a relatively short diffusion time, grain‐boundary diffusion analyses without surface diffusion complications are correct.

Published in:

Journal of Applied Physics  (Volume:40 ,  Issue: 8 )