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

Abstract Preserving volume in the Allen-Cahn framework is appealing as a computationally-efficient alternate for Cahn-Hilliard approach. The limitations of adopting volume-preserved Allen-Cahn treatment to analyse curvature-driven morphological transformations in chemical equilibrium is unraveled in the present work. The 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 three-dimension, indicates that preserving volume in Allen-Cahn formalism renders an inaccurate transformation mechanism and final phase-distribution, which significantly deviate from the experimental observations and theoretical predictions. Moreover, it is shown that the redistribution-energy technique, in its existing form, fails to recover the thermodynamic condition imposed on the system.

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