Assessment of the accuracy of Le Claire's equation for determination of grain boundary diffusion coefficients from solute concentration gradients

• Published in: Materials letters 1996-09, Vol.28 (1), p.47-54
• Main Authors: Chung, Yong-Chae, Wuensch, Bernhardt J.
• Format: Article
• Language: English
• Subjects: Accuracy of Le Claire's equation; Condensed matter: structure, mechanical and thermal properties; Diffusion in solids; Exact sciences and technology; Grain boundary diffusion; Le Claire's equation; Numerical integration; Physics; SIMS analysis; Theory of diffusion and ionic conduction in solids; Transport properties of condensed matter (nonelectronic); Whipple's exact solution
• ISSN: 0167-577X; 1873-4979
• DOI: 10.1016/0167-577X(96)00058-4

The accuracy with which Le Claire's equation may be used to evaluate grain-boundary diffusion coefficients from an experimentally measured solute distribution was determined for ranges of the experimental variables β = [( D′ D ) − 1]a √Dt and η = y √Dt , The assessment was performed by obtaining the value, β c, calculated upon application of Le Claire's relation to a distribution of solute that had been numerically evaluated from Whipple's exact solution to the diffusion problem. The calculated value, β c, was then compared with the true value, β, from which the gradient had been computed. The relative errors that resulted from the application of Le Claire's equation were found to be less than ± 10% in the range of conditions β ≥ 10 and 2 ≤ η √β ≤ 20 that were stated as its field of applicability. The method yielded very inaccurate grain-boundary diffusivity in the ranges β ≤ 10 or solη √β ≤ 2 . Special care should be taken in selecting a range of β and η √β for an experiment if the application of Le Claire's relation is to provide a reliable value of the grain-boundary diffusion product aD′ from the measured diffusion gradient.