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vast number of phase transformation reaction kinetics in metallic materials are controlled by diffusion, and interdiffusion coefficient, which is fundamentally crucial to analyzing diffusion effects often vary with the concentration of diffusing solute. Theoretical models are used to compute isothermal concentration-dependent interdiffusion coefficients, and the reliability of calculated coefficients depends on inherent limitations and assumptions of the model.[1] Recently, a forward simulation technique was developed by Zhang et al.[2] to overcome the flaws in the conventional methods that are used to calculate interdiffusion coefficients, such as Boltzmann–Matano (B–M), Sauer–Freise (S–F) and Hall procedures. The major flaw of Boltzmann–Matano, and Sauer–Freise methods are the inherent problem of uncertainties close to the boundaries,[3] whereas the Hall method is inaccurate in cases where the interdiffusion coefficient has a strong dependence on concentration.[4,5] The approach by Zhang et al.[4,6] uses numerical simulation

OSAMUDIAMEN OLAYE and OLANREWAJU AKANBI OJO are with University of Manitoba, Winnipeg, MB R3T 5V6, Canada. Contact e-mails: [email protected], olanrewaju.ojo@ umanitoba.ca. Manuscript submitted June 23, 2020; accepted September 20, 2020.

METALLURGICAL AND MATERIALS TRANSACTIONS A

to obtain reliable interdiffusion and impurity diffusion coefficients at all regions of an experimental concentration profile. The Forward Simulation technique requires a reliable numerical model to simulate experimental concentration profiles by solving Fick’s second law with variable interdiffusion coefficient. The authors of this paper have developed a new explicit numerical model which does not involve non-trivial assumptions that reduce the accuracy of implicit models, and hence more accurate and faster compared to implicit models. The new explicit model is also more stable than the classical explicit model, conserves solute in single and multiphase systems and can incorporate variable diffusion coefficients.[7] In non-isothermal conditions, the Arrhenius equation describes the variation of diffusivity with temperature. Previous studies on diffusion have shown that the activation energy and pre-exponential factor in the Arrhenius equation can systematically vary with concentration as the interdiffusion coefficient changes with concentration.[8] Considering that concentration-dependent activation energy and frequency factor values are calculated from interdiffusion coefficient data, their accuracy and reliability depend on the method of analysis used to compute the interdiffusion coefficients. Furthermore, in reported works in the literature on concentration-dependent activation energy and frequency factor, authors generally used a single diffusion time that they kept constant at various temperatures. Although not commonly considered, it is known that

interdiffusion coefficients can change with diffusion time.[9] Therefore, the goal of the present work is to use a combination of the newly developed numerical simulation model developed by the present au