# Grain coarsening in two-dimensional phase-field models with an orientation field

## TL;DR

This study investigates the limiting grain size distribution in two-dimensional phase-field models with an orientation field, revealing that resolution of small angle grain boundaries critically influences the observed distribution, aligning some models with experimental results.

## Contribution

It demonstrates that insufficient resolution of small angle grain boundaries in orientation field models leads to lognormal distributions similar to experimental findings.

## Key findings

- LGSD is sensitive to the resolution of small angle grain boundaries.
- Insufficient resolution can cause models to produce lognormal distributions.
- Differences in LGSD across studies may stem from boundary detection methods.

## Abstract

In the literature, contradictory results have been published regarding the form of the limiting (long-time) grain size distribution (LGSD) that characterizes the late stage grain coarsening in two-dimensional and quasi-two-dimensional polycrystalline systems. While experiments and the phase-field crystal (PFC) model (a simple dynamical density functional theory) indicate a lognormal distribution, other works including theoretical studies based on conventional phase-field simulations that rely on coarse grained fields, like the multi-phase-field (MPF) and orientation field (OF) models, yield significantly different distributions. In a recent work, we have shown that the coarse grained phase-field models (whether MPF or OF) yield very similar limiting size distributions that seem to differ from the theoretical predictions. Herein, we revisit this problem, and demonstrate in the case of OF models [by R. Kobayashi et al., Physica D 140, 141 (2000) and H. Henry et al. Phys. Rev. B 86, 054117 (2012)] that an insufficient resolution of the small angle grain boundaries leads to a lognormal distribution close to those seen in the experiments and the molecular scale PFC simulations. Our work indicates, furthermore, that the LGSD is critically sensitive to the details of the evaluation process, and raises the possibility that the differences among the LGSD results from different sources may originate from differences in the detection of small angle grain boundaries.