Grand-potential formulation for multicomponent phase transformations combined with thin-interface asymptotics of the double-obstacle potential

Abstract

In this paper, we describe the derivation of a model for the simulation of phase transformations in multicomponent real alloys starting from a grand-potential functional. We first point out the limitations of a phase-field model when evolution equations for the concentration and the phase-field variables are derived from a free energy functional. These limitations are mainly attributed to the contribution of the grand-chemical-potential excess to the interface energy. For a range of applications, the magnitude of this excess becomes large and its influence on interface profiles and dynamics is not negligible. The related constraint regarding the choice of the interface thickness limits the size of the domain that can be simulated and, hence, the effect of larger scales on microstructure evolution can not be observed. We propose a modification to the model in order to decouple the bulk and interface contributions. Following this, we perform the thin-interface asymptotic analysis of the phase-field model. Through this, we determine the thin-interface kinetic coefficient and the antitrapping current to remove the chemical potential jump at the interface. We limit our analysis to the Stefan condition at lowest order in ε (parameter related to the interface width) and apply results from previous literature that the corrections to the Stefan condition (surface diffusion and interface stretching) at higher orders are removed when antisymmetric interpolation functions are used for interpolating the grand-potential densities and the diffusion mobilities.

Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion

“…Then the time evolution equations for φ and c (or c l ) are obtained from the functional derivatives of F. In doing so, the steady-state profile of φ can be decoupled from c, which yields the interface properties independent of c. This approach was first proposed by Kim, Kim, and Suzuki (KKS model) [36]. A different approach has recently been developed on the basis of the grand potential functional instead of the free-energy functional [34,38]. In these approaches, importantly, the antitrapping current does not appear and therefore it is added in a phenomenological manner to remove the abnormal interface effects after the derivation of the time evolution equations.…”

Numerical and Experimental Investigations on the Growth of the Intermetallic Mg2Si Phase in Mg Infiltrated Si‐Foams

“…In the following, we employ a state-of-the-art phase-field model [30] to investigate the growth of the intermetallic layer. The thickness of the intermetallic layer from the simulation results is compared with the experimental data.…”

Concepts of modeling surface energy anisotropy in phase-field approaches

“…Due to this constraint, and according to the conservation law, the evolution equations of Cahn-Hilliard type are written as follows (Nestler et al 2005;Eiken et al 2006;Choudhury and Nestler 2012): In contrast to conserved variables, the Allen-Cahn-type equation…”

“…Furthermore, the real interfacial energy σ and the modeling parameter γ should not be the same (Choudhury and Nestler 2012). However, according to our approach, the isotropic surface energy can be used directly as modeling parameter Note that the locus φ = 0.5 typically represents the sharp interface contour, since by converging the model parameter ǫ to zero, the phase-field profile in Eq.…”