Role of vacancy wind effect or cross phenomenological constants of Onsager formalism considering actual (ideal or non-ideal) molar volume variation on diffusing elements in binary solid solutions

Abstract

Manning (1967-70) established the intrinsic and tracer diffusion coefficient correlation by considering both main and cross-phenomenological constants of Onsager formalism, albeit assuming constant molar volume, simplifying the analysis. He mentioned the need for correction when molar volume variation is not constant, although it has never been practiced until now. The variation in molar volume with composition in real systems is never exactly constant. This may vary (almost) ideally following the rule of mixture (Vegard's law) or deviate positively and negatively. Therefore, the correct correlation considering the actual molar volume in a real system is first derived in this study. The differences in the contribution of the vacancy wind effect (role of cross phenomenological constants of Onsager) considering actual and constant molar volume variation (which was practiced previously) are calculated and explained. This shows that the contribution was underestimated or overestimated by considering a constant molar volume variation and depending on whether the element with higher or lower partial molar volume has higher or lower relative mobility. The tracer diffusion coefficient calculated in different systems from intrinsic diffusion coefficients estimated following the Kirkendall marker experiment explains the importance of considering the ideal or non-ideal molar volume instead of the constant molar volume variation. Therefore, this study addresses a critical issue faced during the last several decades by calculating inaccurate values of the vacancy wind effect and the tracer diffusion coefficients from the diffusion couple experiments considering constant molar volume variation.