Distinguishing interstitial and substitutional diffusion in grand-potential based phase-field model

Abstract

Grand-potential based phase-field technique is often claimed to be an efficient approach for modelling phase transformation in multicomponent systems. Since this technique largely employs mole fraction to treat concentration, it is principally restricted to simulating microstructural evolutions which are exclusively governed by substitutional diffusion. In this work, an existing grand-potential model is re-formulated to encompass interstitial diffusion. The distinction between interstitial and substitutional diffusion is achieved by adopting molar number-density (mol/m3) based description of composition. The ability of the re-formulated approach to model phase transformation accompanying interstitial and substitutional diffusion is elucidated by simulating rather straightforward decomposition of austenite into ferrite in the ternary Fe-C-Mn system. Energy-density approximations that facilitate the incorporation of CALPHAD data in the present framework are delineated for general, and in particular for Fe-C-X alloy systems. Furthermore, phase-change under para-equilibrium, which can only be imposed through the re-formulated variant of grand-potential technique, is modelled and the resulting concentration profile is discussed in comparison to the outcomes of the conventional approach. Partitioning of carbon in constrained-carbon-equilibrium condition is consistently simulated in-line with its description.