Anomalous Self-Diffusion in Solid Bismuth: The Trapping Mechanism

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Abstract
An anomalous self‐diffusion behavior has been observed in single‐crystalline bismuth. The penetration profiles do not follow Fick's laws of diffusion and disagree with the results reported by Seith. For the semi‐infinite rod configuration, the concentration of 210Bi tracer decreased exponentially with depth, but there was not necessarily an excess of tracer on the surface and the profiles did not vary with time. Penetration was correlated with mechanical twins, but was not directly amenable to a Fisher grain‐boundary analysis. Volume diffusion was not observed. The results have been interpreted by a modified grain‐boundary treatment in which the diffusing species is trapped. Integration of the trapped material over time with a Laplace transform results in the profile C=s(k/D′)1/2 exp[−y(k/D′)1/2], which is in functional agreement with observation. The quantity (k/D)′1/2 appears to be a property of Bi, and may be regarded as a characteristic inverse trapping distance.

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