Effect of Varying Molar Volume on Interdiffusion Analysis in a Binary System

Abstract

There are seven approaches of determination of interdiffusion coefficients with respect to volume-fixed frame given in the literature. These methods are by Boltzmann–Matano, Sauer–Freise, den Broeder, Wagner, Balluffi, Guy et al. and Danielewski et al. It is important to verify the applicability of these approaches under real conditions such as when molar volume $\left( {V_{m} } \right)$ is a function of composition. This is one of the primary objectives of the present study and to achieve this goal, both qualitative and quantitative analyses of the said methods are carried out. These seven methods are examined critically for possible errors and implicit assumptions, if any, in their derivation. Subsequently, quantitative estimation of errors in these approaches is done through MATLAB simulation. Five hypothetical cases of variation of $V_{m}$ with composition are treated including constant, ideal and non-ideal dependence on composition. Concentration profiles are generated for each of these cases in a hypothetical binary diffusion couple by employing a code written in MATLAB. Using the concentration profiles, errors are evaluated in the diffusion coefficients determined based on the seven approaches. Based on the error analysis, methods which give the least error in interdiffusion coefficients are finally proposed. Effect of assuming constant $V_{m}$ in alloy systems which show dependence of $V_{m}$ on composition is also investigated.