Grand-potential based phase-field model for systems with interstitial sites

Existing grand-potential based multicomponent phase-field model is extended to handle systems with interstitial sublattice. This is achieved by treating the concentration of alloying elements in site-fraction. Correspondingly, the chemical species are distinguished based on their lattice positions, and their mode of diffusion, interstitial or substitutional, is appropriately realised. An approach to incorporate quantitative driving-force, through parabolic approximation of CALPHAD data, is introduced. By modelling austenite decomposition in ternary Fe–C–Mn, albeit in a representative microstructure, the ability of the current formalism to handle phases with interstitial components, and to distinguish interstitial diffusion from substitutional in grand-potential framework is elucidated. Furthermore, phase transformation under paraequilibrium is modelled to demonstrate the limitation of adopting mole-fraction based formulation to treat multicomponent systems.