ASSESSMENT OF THE ACCURACY OF LE CLAIRES EQUATION FOR DETERMINATION OF GRAIN-BOUNDARY DIFFUSION-COEFFICIENTS FROM SOLUTE CONCENTRATION GRADIENTS

The accuracy with which Le Claire's equation may be used to evaluate g rain-boundary diffusion coefficients from an experimentally measured s olute distribution was determined for ranges of the experimental varia bles beta = [(D'/D)-1]a/root Dt and eta=y/root Dt. The assessment was performed by obtaining the value, beta(c), calculated upon application of Le Claire's relation to a distribution of solute that had been num erically evaluated from Whipple's exact solution to the diffusion prob lem. The calculated value, beta(c), was then compared with the true va lue, beta, from which the gradient had been computed. The relative err ors that resulted from the application of Le Claire's equation were fo und to be less than +/-10% in the range of conditions beta greater tha n or equal to 10 and 2 less than or equal to eta/beta less than or equ al to 20 that were stated as its field of applicability. The method yi elded very inaccurate grain-boundary diffusivity in the ranges beta le ss than or equal to 10 or eta/root beta less than or equal to 2. Speci al care should be taken in selecting a range of beta and eta/root beta for an experiment if the application of Le Claire's relation is to pr ovide a reliable value of the grain-boundary diffusion product aD' fro m the measured diffusion gradient.