Numerical evaluation method for the determination of grain-boundary diffusion coefficients from tracer concentration profiles for a constant boundary concentration

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Abstract
The determination of grain-boundary diffusion coefficients of tracers in polycrystals has been carried out so far by a graphical method derived by Le Claire. It is based on an approximate solution of the exact solution of Suzuoka The product D GBδ is calculated from the slope of log c against y 6/5 (where c is the tracer concentration and y the penetration depth) for a known volume diffusion coefficient Dv. It is limited to intermediate times (time stage B) and to great penetration depths y. In cases where these conditions cannot be fulfilled the exact solution of Suzuoka has to be applied for evaluation of the profiles. This cannot be done in an easy way owing to the complex form of the Suzuoka solution. Therefore for these cases this work offers numerical evaluation of the diffusion profiles based on the exact Suzuoka solution. It allows determination of D GBδ and also of Dv for a known grain size.

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