Limitations of preserving volume in Allen-Cahn framework for microstructural analysis

Abstract

Preserving volume in the Allen-Cahn framework is appealing as a computationally-e cient alternate for Cahn-Hilliard approach. e limitations of adopting volume-preserved Allen-Cahn treatment to analyse curvature-driven morphological transformations in chemical equilibrium is unraveled in the present work. e outcomes of redistribution-energy technique, which operates in Allen-Cahn framework, and a thermodynamically-consistent generalised quasi-Allen-Cahn (qAC) treatment, involving a conserved variable, is comparatively studied to explicate the limitations of the former. Analysis of representative microstructural evolution, in two-and threedimension, indicates that preserving volume in Allen-Cahn formalism renders an inaccurate transformation mechanism and nal phase-distribution, which signi cantly deviate from the experimental observations and theoretical predictions. Moreover, it is shown that the redistributionenergy technique, in its existing form, fails to recover the thermodynamic condition imposed on the system.

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

“…Furthermore, this technique is also combined with an elastic model, in order to analyze chemoelastic transformations [89,90]. Much different from these conventional studies, this approach has recently been adopted to investigate energy-minimizing, curvaturedriven transformations, where the phase field behaves in a conserved fashion [91][92][93][94][95]. In all analyses involving the grand-potential formalism, volume diffusion is treated as the primary mode of mass transfer.…”

“…Since the grand potentials of the different phases are equal in chemical equilibrium, the driving force for any phase transformation becomes insignificant. By assigning equilibrium compositions to the phases, despite any morphological change, induced by the interface contribution, the volume fraction of the constituent phases can be preserved [94].…”

Effect of tortuosity, porosity, and particle size on phase-separation dynamics of ellipsoid-like particles of porous electrodes: Cahn–Hilliard-type phase-field simulations

“…The inhomogeneous system consists of different phases whose identity is distinguished by its physical state or orientation. In the present description, a multi-phase Allen Cahn model is considered to study the evolution of multiphase systems whose interfacial energy decreases with preserving their volume [68]. The evolution of a general system containing N phases is governed by Ginzburg-Landau free energy,…”