Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

Abstract

Grand-potential based multiphase-field model is extended to include surface diffusion. Diffusion is elevated in the interface through a scalar degenerate term. In contrast to the classical Cahn-Hilliard-based formulations, the present model circumvents the related difficulties in restricting diffusion solely to the interface by combining two second-order equations, an Allen-Cahn-type equation for the phase field supplemented with an obstacletype potential and a conservative diffusion equation for the chemical potential or composition evolution. The sharp interface limiting behavior of the model is deduced by means of asymptotic analysis. A combination of surface diffusion and finite attachment kinetics is retrieved as the governing law. Infinite attachment kinetics can be achieved through a minor modification of the model, and with a slight change in the interpretation, the same model handles the cases of pure substances and alloys. Relations between model parameters and physical properties are obtained which allow one to quantitatively interpret simulation results. An extensive study of thermal grooving is conducted to validate the model based on existing theories. The results show good agreement with the theoretical sharp-interface solutions. The obviation of fourth-order derivatives and the usage of the obstacle potential make the model computationally cost-effective.

An improved grand-potential phase-field model of solid-state sintering for many particles

“…in which the thermodynamical relation c α = − ∂ψα ∂µ is exploited to arrive at the phase-specific concentration c α (µ, T). Taking the time derivative of equation (8) yields…”

Modeling intercalation in cathode materials with phase-field methods: Assumptions and implications using the example of LiFePO4

“…The model in Sec. 2.6 on the other hand, is composed of coupled second-order conservative and nonconservative equations [30,37,54]. We compute the evolution of order parameters, which are non-conserved via the Allen-Cahn equation ( 23), and secondly the evolution of chemical potential (26), which is based on mass conservation.…”

“…This framework has been sucessfully combined with elastic driving forces based on jump conditions [31,32] to model martensitic transformations [12], crack propagation [33][34][35] and the evolution of electric field to study electromigration [36]. It has further been shown that grain boundary diffusion [37] as well as the instability leading to phase separation in the miscibility gap [6] can be effectively modelled. The aim of this work is to show the potentials of both approaches for the numerical screening of promising intercalation electrode materials while also discussing their complementary range of applicability and their limitations due to modeling assumptions.…”

A phase‐field based model for coupling two‐phase flow with the motion of immersed rigid bodies

“…The interpolation function $$$ {h}^{\mathrm{ff}} $$$ exhibits a monotonic transition between zero and unity. An evident choice would be $$$ {h}^{\mathrm{ff}}=\tilde{\varphi} $$$, but also other functions meeting the conditions specified in Reference 26 are appropriate. Higher order polynomials in $$$ \tilde{\varphi} $$$ lead to a steeper transition of $$$ {h}^{\mathrm{ff}} $$$ in interface normal direction $$$ \eta $$$.…”