It was recalled that Boltzmann and Matano had developed a method for solving Fick’s second law when the diffusivity was a function of concentration. This procedure required the determination of the so-called Matano interface, and the accuracy of the resultant solution depended sensitively upon its precise location. The determination of the latter was laborious and often inaccurate. However, 3 alternative procedures (Sauer-Freise, Wagner, den Breeder) had been developed such that the diffusivity could be calculated without having to locate the Matano interface. None of these derivations quantified the extent to which the other methods approached the result which was obtained by using a standard Boltzmann-Matano analysis. The latter method, and the den Breeder modification, were applied here to various analytical concentration profiles which contained various degrees of noise and to concentration profiles which had arisen during interdiffusion experiments. The 2 methods were shown to be equivalent in terms of accuracy.

Evaluation of Methods for Calculating the Concentration-Dependent Diffusivity in Binary Systems. S.K.Kailasam, J.C.Lacombe, M.E.Glicksman: Metallurgical and Materials Transactions A, 1999, 30[10], .2605-10