Most research into microstructure formation during solidification has focused on single-crystal growth ranging from faceted crystals to symmetric dendrites. However, these growth forms can be perturbed by heterogeneities, yielding a rich variety of polycrystalline growth patterns. Phase-field simulations show that the presence of particulates (for example, dirt) or a small rotational-translational mobility ratio (characteristic of high supercooling) in crystallizing fluids give rise to similar growth patterns, implying a duality in the growth process in these structurally heterogeneous fluids. Similar crystallization patterns are also found in thin polymer films with particulate additives and pure films with high supercooling. This duality between the static and dynamic heterogeneity explains the ubiquity of polycrystalline growth patterns in polymeric and other complex fluids.

We present a phase field theory for binary crystal nucleation. In the one-component limit, quantitative agreement is achieved with computer simulations (Lennard-Jones system) and experiments (ice-water system) using model parameters evaluated from the free energy and thickness of the interface. The critical undercoolings predicted for Cu-Ni alloys accord with the measurements, and indicate homogeneous nucleation. The Kolmogorov exponents deduced for dendritic solidification and for "soft-impingement" of particles via diffusion fields are consistent with experiment.PACS numbers: 81.10. Aj, 82.60.Nh, 64.60.Qb Understanding alloy solidification is of vast practical and theoretical importance. While the directional geometry in which the solidification front propagates from a cool surface towards the interior of a hot melt is understood fairly well, less is known of equiaxial solidification that takes place in the interior of the melt. The latter plays a central role in processes such as alloy casting, hibernation of biological tissues, hail formation, and crystallization of proteins and glasses. The least understood stage of these processes is nucleation, during which seeds of the crystalline phase appear via thermal fluctuations. Since the physical interface thickness is comparable to the typical size of critical fluctuations that are able to grow to macroscopic sizes, these fluctuations are nearly all interface. Accordingly, the diffuse interface models lead to a considerably more accurate description of nucleation than those based on a sharp interface [1,2].The phase field theory, a recent diffuse interface approach, emerged as a powerful tool for describing complex solidification patterns such as dendritic, eutectic, and peritectic growth morphologies [3]. It is of interest to extend this model to nucleation and post-nucleation growth including diffusion controlled "soft-impingement" of growing crystalline particles, expected to be responsible for the unusual transformation kinetics recently seen during the formation of nanocrystalline materials [4].In this Letter, we develop a phase field theory for crystal nucleation and growth, and apply it to current problems of unary and binary equiaxial solidification.Our starting point is the free energy functionaldeveloped along the lines described in [5,6]. Here φ and c are the phase and concentration fields, f (φ, c) = W T g(φ) + [1 − P (φ)]f S + P (φ)f L is the local free energy density, W = (1 − c)W A + cW B the free energy scale, the quartic function g(φ) = φ 2 (1 − φ) 2 /4 that emerges from density functional theory [7] ensures the doublewell form of f , while the function P (φ) = φ 3 (10 − 15φ + 6φ 2 ) switches on and off the solid and liquid contributions f S,L , taken from the ideal solution model. (A and B refer to the constituents.) For binary alloys the model contains three parameters ǫ, W A and W B that reduce to two (ǫ and W ) in the one-component limit. They can be fixed if the respective interface free energy γ, melting point T f , and interface thickn...