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

Abstract

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.

Phase-Field Simulation of Sintering Process: A Review

“…where ω s and ω v are the grand potential energy densities of the solid phase and gas phase, respectively, ω b and ω gb are the contributions from the bulk and the interface, and h s (φ) and h v (φ) are the interpolation functions. Assuming the vacancy concentrations in the solid phase and gas phase are c s and c v , respectively, we can further derive the chemical potential of vacancies [108,109]:…”