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    "description": "Boltzmann and Matano developed a procedure for the solution to Fick\u2019s second law when the diffusivity is a function of concentration. The procedure requires the determination of the so-called Matano interface. The accuracy of the resulting solution depends heavily on the precise location of the Matano interface, the determination of which is laborious and often inaccurate. Three alternative procedures by Sauer and Freise, Wagner, and den Broeder, modifications to the original Boltzmann-Matano (B-M) method, were developed such that the diffusivity can be calculated without having to determine the location of the Matano interface. However, none of these derivations quantifies the extent to which the modified methods arrive at the same result as that obtained from the standard B-M analysis. This article serves to apply the B-M method, and the modification suggested by den Broeder, to various analytical concentration profiles containing different degrees of noise and to compare the results quantitatively. In addition to these analytical functions, concentration profiles obtained from interdiffusion experiments were studied. The two methods are shown to be equivalent in terms of the accuracy of the result. The advantages or disadvantages of one method over the other are illustrated with examples.", 
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