Phase field method

Abstract

In an ideal scenario, a phase field model is able to compute quantitative aspects of the evolution of microstructure without explicit intervention. The method is particularly appealing because it provides a visual impression of the development of structure, one which often matches observations. The essence of the technique is that phases and the interfaces between the phases are all incorporated into a grand functional for the free energy of a heterogeneous system, using an order parameter which can be translated into what is perceived as a phase or an interface in ordinary jargon. There are, however, assumptions which are inconsistent with practical experience and it is important to realise the limitations of the method. The purpose of this review is to introduce the essence of the method, and to describe, in the context of materials science, the advantages and pitfalls associated with the technique.

Pulsed Laser Heating and Melting

“…It has also been applied to rapid solidification (Kim & Kim, 2001), including excimer laser processing of silicon (La Magna, 2004;Shih et al, 2006;Steinbach & Apel, 2007). Despite its success in replicating many experimentally observed features in solidification (see for example, Pusztai, 2008, and references therein) and the phase field itself is not necessarily associated with any physical property of the interface (Qin & Bhadeshia, 2010). Moreover, even though it can be adapted to apply to the numerical solution of the 1-D heat diffusion equation, it is essentially a method for looking at 2-D structures such as dendrites and is not well suited to planar interfaces.…”

“…for the interphase region (Qin & Bhadeshia, 2010;Sekerka, 2004). In essence, gradients within the thermodynamic quantities drive the process of crystallisation.…”

Phase-Field Simulation of Microsegregation and Dendritic Growth During Solidification of Hypoeutectic Al-Cu alloys

“…The evolution of the solid region with time is assumed to be proportional to the variation of the free energy functional with respect to the order parameter. So, in this present paper, the phase-field model is briefly summarized, readers can refer to literatures [19][20] for more details of the formulation. For simulation of microstructures in binary alloys during solidification, we used two equations: one for solute concentrations, the other for the phase field itself.…”

Thermodynamic properties of phase separation in shear flow

“…The method was based on the idea of bounceback of the nonequilibrium part. For those lattices located on the bottom boundary where the boundary is moving with speed y u x u y x , the mass density and the unknown particle distribution functions are given by proper method should be developed to convert all the parameters to dimensionless variables in the calculation so that the occurrence of very small or very large numbers is avoided [21]. The equilibrium phase diagrams for the system with all round periodic boundary conditions have been studied and found in good agreement with the result based on free energy minimization methods [4] lattices in x and y directions are to ensure that flat interface will form during the phase separation.…”