  Germanium is the base element in many phase-change materials, i.e. systems
that can undergo reversible transformations between their crystalline and
amorphous phases. They are widely used in current digital electronics and hold
great promise for the next generation of non-volatile memory devices. However,
the ultra fast phase transformations required for these applications can be
exceedingly complex even for single component systems, and a full physical
understanding of these phenomena is still lacking. In this paper we study
nucleation and growth of crystalline Ge from amorphous thin films at high
temperature using phase field models informed by atomistic calculations of
fundamental material properties. The atomistic calculations capture the full
anisotropy of the Ge crystal lattice, which results in orientation dependences
for interfacial energies and mobilities. These orientation relations are then
exactly recovered by the phase field model at finite thickness via a novel
parametrization strategy based on invariance solutions of the Allen-Cahn
equations. By means of this multiscale approach, we study the interplay between
nucleation and growth and find that the relation between the mean radius of the
crystallized Ge grains and the nucleation rate follows simple Avrami-type
scaling laws. We argue that these can be used to cover a wide region of the
nucleation rate space, hence facilitating comparison with experiments.
