A model for phase boundary thermodynamics

Phase boundaries separate thermodynamically distinct phases and can govern microstructural stability, transformation kinetics, and property evolution. Here, we extend the density-based thermodynamic and phase-field (DPF) framework developed for grain boundaries to phase boundaries (PBs). We consider a planar PB in a single-component system and characterize it through the minimum atomic density across the boundary region and phase-specific relative density fields referenced to the homogeneous bulk state of each adjoining phase. The PB Gibbs free energy functional is derived across the boundary width, defined as the region over which the atomic density varies. We present a numerical scheme for determining the equilibrium density profile across the PB and systematically identifying the model parameters. The effects of local stiffness, gradient-energy penalties, bulk-density mismatch, PB plane density, and reduced-traction contrasts on the PB localization lengths and the excess free energy are discussed. The connection between the continuum model and atomistics is demonstrated through Gaussian coarse-graining of an atomistic BCC-FCC Fe PB, from which the bulk densities, PB plane density, and geometric half-widths are extracted. A base-case calibration is used to identify the key coefficients of the PB free energy functional by fitting the model to the coarse-grained atomistic reference profile. The present framework provides an efficient route for studying segregation and interfacial phase behavior in multiphase systems. It enables the construction of phase boundary phase diagrams grounded in bulk reference states and parameterized from atomistic calculations.