# Phase-field modeling of crystal nucleation in undercooled liquids -- A review

## TL;DR

This review discusses how phase-field models, including classical and crystal-specific variants, have advanced understanding of crystal nucleation and microstructure evolution in undercooled liquids, covering various nucleation phenomena and morphologies.

## Contribution

It provides a comprehensive overview of phase-field modeling approaches and their applications to diverse crystal nucleation processes in undercooled liquids.

## Key findings

- Phase-field models capture homogeneous and heterogeneous nucleation.
- Crystal growth morphologies depend on nucleation and growth dynamics.
- Recent models operate on molecular scales using density functional theories.

## Abstract

We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the conventional phase-field approaches that rely on spatially averaged (coarse grained) order parameters in capturing freezing, and by the recently developed phase-field crystal models that work on the molecular scale, while employing time averaged particle densities, and are regarded as simple dynamical density functional theories of classical particles. Besides simpler cases of homogeneous and heterogeneous nucleation, phenomena addressed by these techniques include precursor assisted nucleation, nucleation in eutectic and phase separating systems, phase selection via competing nucleation processes, growth front nucleation (a process, in which grains of new orientations form at the solidification front) yielding crystal sheaves and spherulites, and transition between the growth controlled cellular and the nucleation dominated equiaxial solidification morphologies.