  A full understanding of polycrystalline materials requires studying the
process of nucleation, a thermally activated phase transition that typically
occurs at atomistic scales. The numerical modeling of this process is
problematic for traditional numerical techniques: commonly used phase-field
methods' resolution does not extend to the atomic scales at which nucleation
takes places, while atomistic methods such as molecular dynamics are incapable
of scaling to the mesoscale regime where late-stage growth and structure
formation takes place following earlier nucleation. Consequently, it is of
interest to examine nucleation in the more recently proposed phase-field
crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes
in microstructure simulations. In this work, we numerically calculate
homogeneous liquid-to-solid nucleation rates and incubation times in the
simplest version of the PFC model, for various parameter choices. We show that
the model naturally exhibits qualitative agreement with the predictions of
classical nucleation theory (CNT) despite a lack of some explicit atomistic
features presumed in CNT. We also examine the early appearance of lattice
structure in nucleating grains, finding disagreement with some basic
assumptions of CNT. We then argue that a quantitatively correct nucleation
theory for the PFC model would require extending CNT to a multi-variable
theory.
