Phase field theory of crystal nucleation and polycrystalline growth: A review
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Review
Phase field theory of crystal nucleation and polycrystalline growth: A review L. Gránásy,a) T. Pusztai, T. Börzsönyi, G. Tóth, and G. Tegze Research Institute for Solid State Physics and Optics, H-1525 Budapest, Hungary
J.A. Warren and J.F. Douglas National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (Received 17 June 2005; accepted 6 October 2005)
We briefly review our recent modeling of crystal nucleation and polycrystalline growth using a phase field theory. First, we consider the applicability of phase field theory for describing crystal nucleation in a model hard sphere fluid. It is shown that the phase field theory accurately predicts the nucleation barrier height for this liquid when the model parameters are fixed by independent molecular dynamics calculations. We then address various aspects of polycrystalline solidification and associated crystal pattern formation at relatively long timescales. This late stage growth regime, which is not accessible by molecular dynamics, involves nucleation at the growth front to create new crystal grains in addition to the effects of primary nucleation. Finally, we consider the limit of extreme polycrystalline growth, where the disordering effect due to prolific grain formation leads to isotropic growth patterns at long times, i.e., spherulite formation. Our model of spherulite growth exhibits branching at fixed grain misorientations, induced by the inclusion of a metastable minimum in the orientational free energy. It is demonstrated that a broad variety of spherulitic patterns can be recovered by changing only a few model parameters. I. INTRODUCTION
Most of our structural materials are polycrystalline, i.e., composed of a large number of crystallites, whose size, shape, and composition distributions determine their properties and failure characteristics. Polycrystalline patterns play an important role in classical materials science and nanotechnology and have biological relevance as well. Specifically, semi-crystalline spherulites of amyloid fibrils are found in association with Alzheimer and Creutzfeldt–Jakob diseases, type II diabetes, and a range of systemic and neurotic disorders.1 Despite intensive research, the formation of polycrystalline matter (technical alloys, polymers, minerals, etc.) is poorly understood. One of the sources of theoretical difficulty in modeling these materials is modeling the process of nucleation by which crystallites form via fluctuations. While nucleation takes place on the nanometer scale, its influence extends to larger size a)
Address all correspondence to this author. e-mail: [email protected] This paper was selected as the Outstanding Meeting Paper for the 2004 MRS Fall Meeting Symposium JJ Proceedings, Vol. 859E. DOI: 10.1557/JMR.2006.0011 J. Mater. Res., Vol. 21, No. 2, Feb 2006
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scales. Controlled nucleation2 is an established tool for tailoring the microstructure of matter for specific applications. The crystallization of homogeneous underco
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