An improved method, based on Whipple's exact solution, for obtaining accurate grain-boundary diffusion coefficients from shallow solute concentration gradients

An equation developed by Le Claire is widely used to obtain a grain-boundary diffusion product, aD', from the measured solute concentration gradients produced under conditions of constant surface concentration in grain-boundary diffusion experiments. However, a numerical assessment of the accuracy of Le Claire's equation has revealed errors as large as 70% when applied outside of its range of validity to the shallow gradients (similar to 10(2) nm) that are provided by high-resolution analytical methods. To provide a relation applicable to this region, a numerical analysis of the variation of computed values of partial derivative ln (C) over bar/partial derivative eta(6/5) with beta has been used to develop a new and greatly improved expression of the form aD ' = D(3/2)t(1/2)[10(A)(-partial derivative ln (C) over bar/partial derivative eta(6/5))(B)], where A and B are parameters whose value depends on the experimental value of partial derivative ln (C) over bar/partial derivative eta/(6/5). The relation is valid for the experimentally useful range of solute penetrations 6 root Dt similar to 10 root Dt and for 1 less than or equal to beta less than or equal to 10(5) and has been shown to produce a grain-boundary diffusion product accurate to within 1% throughout this domain. As the accuracy of the relation does not change systematically with eta or beta, it avoids introduction of an error in the activation energy for boundary diffusion that would result from inappropriate use of Le Claire's equation in this region. (C) 1996 American Institute of Physics.