Spinodal decomposition and droplets entrapment in monotectic solidification

Abstract

In this article, we present two models to simulate solidification morphologies in monotectic alloys. With the first model, we investigate the morphological evolution under the influence of spinodal decomposition. The model requires that a gradient energy contribution for the concentration field should be incorporated, in order to stabilize phase separation when the liquid concentration is inside the region of miscibility gap. The free energy of the system in this model is derived from direct interpolation of the bulk energy densities. This, however, results in simulation regions in nanometer scale due to contributions from the chemical free energy of the system to the total surface excess. With the second model, our purpose is to develop a phase-field model to simulate scales that are larger than nanometer, where the departures from equilibrium are very small resulting in phase concentrations outside the spinodal region. In view of this, we exclude the concentration gradient contribution to the grand chemical potential functional, and develop a model based on [M. Plapp, Phys. Rev. E 84, 031601 (2011); A. Choudhury and B. Nestler, Phys. Rev. E 85, 021602 (2012)]. The advantage is that the free energy excess across the interface at equilibrium disappears, and hence it is easier to derive the required surface energies with higher interface widths. Due to this benefit, we employ the method to simulate the dynamic entrapment process in the monotectic reaction and study the influence of liquid(1) - liquid(2) surface energy and undercooling on the entrapment process.