We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The
focus is placed on recent applications of phase-field simulations of solid-state microstructure …

Phase-field simulations have achieved notable success in capturing characteristic details of
microstructure evolution in directional solidification of ternary eutectic alloys. In spite of the …

Significant cost savings are realized in alloy processing by using computer models of the
processes, reducing the amount of experimental effort necessary. Understanding the …

▪ Abstract The phase-field method has recently emerged as a powerful computational
approach to modeling and predicting mesoscale morphological and microstructure evolution …

Phase-field-based models have become common in material science, mechanics, physics,
biology, chemistry, and engineering for the simulation of microstructure evolution. Yet, they …

The phase-field-crystal method is a new modeling technique that incorporates the periodic
nature of a crystal lattice by considering a free energy functional that is minimized by …

We review the use of phase field methods in solidification modeling, describing their
fundamental connection to the physics of phase transformations. The inherent challenges …

Mesoscale modeling and simulation approaches provide a bridge from atomic-scale
methods to the macroscale. The phase field (PF) method has emerged as a powerful and …

Phase-field models have emerged as a successful class of models in a wide variety of
applications in computational materials science. Multiphase field theories, as a subclass of …

The phase-field method has become the method of choice for simulating microstructural
pattern formation during solidification. One of its main advantages is that time-dependent …