Equilibrium at stationary solid-liquid interface during phase-field modeling of alloy solidification

The phase-field parameters (coefficient of gradient energy and double-well potential height) were obtained for a binary solid-liquid (SL) interface with a finite thickness (thin interface). The parameters were compared with those obtained at a sharp interface condition in order to test the maintenance of equilibrium condition at a stationary SL interface. The phase-field parameters determined at the thin interface condition account for the chemical energy contribution to the interface energy. They reproduce the interface energy, interface thickness, and capillary effect during phase-field calculation at a wide interface thickness range, even though there still exists interface thickness limitation. The phase-field parameters at the sharp interface ignore the chemical energy contribution to the interface energy. When the interface thickness is small enough, the parameters generate the same interface energy and interface thickness as the corresponding input values since the chemical energy contribution increases with increasing interface thickness. However, regardless of interface models, the equilibrium shape of solid particles embedded in a liquid, obtained from the phase-field equation with different interface anisotropy constants, is in good agreement with theoretical two-dimensional (2-D) prediction. This is due to the equilibrium shape of solid particles being dependent only on anisotropy constant.