Numerical analysis of isothermal variation of concentration-dependent interdiffusion coefficient

Abstract

The accuracy of theoretical predictions and analyses of diffusion-controlled phase transformations in materials is significantly influenced by the concentration-dependent interdiffusion coefficient (D(C)). It is generally assumed in the literature that the dependence of the interdiffusion coefficient on concentration is isothermally constant. However, this may not be the case because of the evolution of diffusion stresses and strains, which result from factors that can change the concentration gradients at the same solute concentration. This work aims to theoretically and experimentally study how factors that change concentration gradient and, by implication, the diffusion-induced stress/strain (DIS) influence the solute concentration dependence of the interdiffusion coefficient. In this research work, six factors that are postulated to influence the D(C) have been theoretically studied, and the results are experimentally validated using diffusion couples. The six factors studied are time, temperature, non-uniform initial solute distribution, time-varying surface concentration (SC), solute source concentrations, and diffusion geometry. A theoretical model based on DIS and its relaxation is used to simulate concentration profiles and calculate the D(C). Key theoretical predictions are experimentally verified using a newly developed and validated numerical model to reliably extract the D(C) from experimental data. The theoretical and experimental data analyses show that the concentration dependence of interdiffusion coefficient can significantly change when any of the six factors changes. This study shows that the common practice of using a single interdiffusion coefficient to predict isothermal diffusion effects can become significantly unreliable when the dependence of diffusivity on concentration changes. Neglecting the fundamental concept elucidated in this study can lead to the consequential misidentification of the mechanism of microstructural changes through phase transformation reactions.