It was recalled that Le Claire’s equation was widely used to deduce the value, of a grain-boundary diffusion product, from measured solute concentration gradients which were produced under conditions of constant surface concentration in grain-boundary diffusion experiments. However, numerical assessments of the accuracy of this equation revealed errors which could be as large as 70% when applied to the shallow gradients (some 100nm) that were used in high-resolution analytical methods. In order to provide a relationship that was applicable to this region, a numerical analysis was made of the variation in tabulated values of lnC/6/5 as a function of . This was used to develop an improved expression of the form, D3/2t1/2[10A(-lnC/6/5)B], where A and B were parameters whose values depended upon the experimental value of lnC/6/5. The relationship was valid for an experimentally useful range of solute penetrations, and was shown to yield a grain-boundary diffusion product which was accurate to within 1% throughout this domain. As the accuracy of the relationship did not change systematically with  or , it avoided the introduction of errors (into the activation energy for boundary diffusion) that would result from inappropriate use of Le Claire’s equation in this region.

Y.C.Chung, B.J.Wuensch: Journal of Applied Physics, 1996, 79[11], 8323-9