| Polycrystalline patterns are present in a broad variety of systems including metal alloys, polymers, minerals, and have biological relevance as well (see e.g. semi-crystalline amyloid spherulites and spherultic kidney stones). The fact that similar polycrystalline patterns are observed in systems of very different nature suggests that a minimal model based on coarse-grained fields, which neglects the details of molecular interactions, might be appropriate. Although such a field-theoretic approach disregards most of the molecular scale details of formation, some features such as crystal symmetries can be incorporated via the anisotropies of the model parameters. The rationale for developing such coarse-grained models is the current inability of fully molecular models to address the formation of large scale morphologies. Along these lines, we have developed a phase field theory of polycrystalline growth that has been applied for describing various polycrystalline growth forms in two and three dimensions including spherulites. Our model consists of several mechanisms for nucleating new grains at the perimeter of the crystallites, including homogeneous (trapping of orientational disorder and branching in certain crystallographic directions) and heterogeneous (particle-induced nucleation) processes. It will be shown that the diversity of spherulitic growth morphologies arises from a competition between the ordering effect of discrete local crystallographic symmetries and the randomization of the local crystallographic orientation that accompanies crystal grain nucleation at the growth front. We find that a wide range of observed polycrystalline morphologies can be reproduced by varying only a few model parameters. Possible extension to polymorphs will be discussed. |
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