  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.
