Influence of the phase diagram on the diffuse interface thickness and on the microstructure formation in a phase-field model for binary alloy
In this paper, the authors give very interesting investigations that are referred to a phase-field model, which is used to show the responses of planar interfaces and of eutectic microstructures on the different shapes of the phase diagram in binary alloy systems. The paper consists of four sections. In the first section we have a short introduction to the considered topic with the note that in phase-field models, the thermodynamic state of regions in a system is described by a continuous order parameter (phase field) \(\varphi(x)\). The bulk solid and liquid phases are represented by \(\varphi=1\) and \(\varphi =0\) -- other cases (especially those with planar interface in a pure substance under thermodynamic equilibrium conditions) are described by the equation \(\varphi_0(x)=\frac{1}{2}(1-\tanh\frac{3x}{2\varepsilon})\) where \(\varepsilon\) parameter is related to the width of the diffuse interface layer. The profile \(\varphi_0(x)\) gives a stationary solution of a nonlinear partial differential equation giving the description of the evolution and dynamics of the solid-liquid interface. The parameter \(\varepsilon\) is also related to the thickness of the transition layer and plays a very important role in numerical solutions. Usually one tries to keep \(\varepsilon\) as large as possible in order to cover larger microstructure during the simulation; on the other hand very thick interface leads to a number of undesirable effects. In section 2, the authors give a simplified version of a general multiphase and multicomponent phase-field model, which is reduced to the case of binary alloy in isothermal approximation in order to provide detailed study of the nonuniform concentration profile at the diffuse solid-liquid interface on the thickness of the phase-field profile. Having a characteristic length scale \(d\) related to the interfacial entropy the authors show the results of numerical analysis of the dependence of a reduced interface \(\delta\varepsilon/d\) on the parameter \(\varepsilon/d\). Section 3 shows the three-phase eutectic system with 2D numerical simulations. A phase-field \(\varphi\) is a function of spatial coordinates \(x\), \(y\) and time \(t\) -- we have a list of figures with the results of authors work. These results demonstrate the dependence of the diffuse interface thickness and of the microstructure on the segregation of the alloy components. The thickness of the interface in the phase-field solution depends not only on the parameter \(\varepsilon\), but also on the properties of the phase diagram. The paper is concluded in section 4 where the author show how one should interpret the results of their work.
scientific article; zbMATH DE number 5718139