Development of different methods and their efficiencies for the estimation of diffusion coefficients following the diffusion couple technique

TL;DR

This paper compares and develops methods for estimating diffusion coefficients in diffusion couple experiments, introducing new relations with respect to concentration normalized variables and analyzing their accuracy across different alloy systems.

Contribution

It derives new relations for intrinsic and integrated diffusion coefficients based on concentration normalized variables, expanding existing methods.

Findings

Both Wagner's and den Broeder's methods are valid with small differences in estimates.

New relations with respect to concentration normalized variables are established.

Estimations with concentration-based methods require ideal molar volume variation.

Abstract

The interdiffusion coefficients are estimated either following the Wagner's method expressed with respect to the composition (mol or atomic fraction) normalized variable after considering the molar volume variation or the den Broeder's method expressed with respect to the concentration (composition divided by the molar volume) normalized variable. On the other hand, the relations for estimation of the intrinsic diffusion coefficients of components as established by van Loo and integrated diffusion coefficients in a phase with narrow homogeneity range as established by Wagner are currently available with respect to the composition normalized variable only. In this study, we have first derived the relation proposed by den Broeder following the line of treatment proposed by Wagner. Further, the relations for estimation of the intrinsic diffusion coefficients of the components and integrated interdiffusion coefficient are established with respect to the concentration normalized variable, which were not available earlier. The veracity of these methods is examined based on the estimation of data in Ni-Pd, Ni-Al and Cu-Sn systems. Our analysis indicates that both the approaches are logically correct and there is small difference in the estimated data in these systems although a higher difference could be found in other systems. The integrated interdiffusion coefficients with respect to the concentration (or concentration normalized variable) can only be estimated considering the ideal molar volume variation. This might be drawback in certain practical systems.