  Advanced phase-field techniques have been applied to address various aspects
of polycrystalline solidification including different modes of crystal
nucleation. The height of the nucleation barrier has been determined by solving
the appropriate Euler-Lagrange equations. The examples shown include the
comparison of various models of homogeneous crystal nucleation with atomistic
simulations for the single component hard-sphere fluid. Extending previous work
for pure systems (Granasy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev.
Lett. 98 art no 035703), heterogeneous nucleation in unary and binary systems
is described via introducing boundary conditions that realize the desired
contact angle. A quaternion representation of crystallographic orientation of
the individual particles (outlined in Pusztai T, Bortel G and Granasy L 2005
Europhys. Lett. 71 131) has been applied for modeling a broad variety of
polycrystalline structures including crystal sheaves, spherulites and those
built of crystals with dendritic, cubic, rhombododecahedral, truncated
octahedral growth morphologies. Finally, we present illustrative results for
dendritic polycrystal-line solidification obtained using an atomistic
phase-field model.
