An improved procedure for determining grain boundary diffusion coefficients from averaged concentration profiles

Whipple's solution of the problem of grain boundary diffusion and Le Claire's relation, which is often used to determine grain boundary diffusion coefficients, are examined for a broad range of ratios of grain boundary to bulk diffusivities Δ and diffusion times t. Different reasons leading to errors in determining the grain boundary diffusivity (DGB) when using Le Claire's relation are discussed. It is shown that nonlinearities of the diffusion profiles in ln Cav - y65 plots and deviations from "Le Claire's constant" (-0.78) are the major error sources (Cav =averaged concentration, y=coordinate in diffusion direction). An improved relation (replacing Le Claire's constant) is suggested for analyzing diffusion profiles particularly suited for small diffusion lengths (short times) as often required in diffusion experiments on nanocrystalline materials.