3 research outputs found

    Grain coarsening in two-dimensional phase-field models with an orientation field

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    In the literature, contradictory results have been published regarding the form of the limiting (long-time) grain size distribution (LGSD) that characterizes the late stage grain coarsening in two-dimensional and quasi-two-dimensional polycrystalline systems. While experiments and the phase-field crystal (PFC) model (a simple dynamical density functional theory) indicate a lognormal distribution, other works including theoretical studies based on conventional phase-field simulations that rely on coarse grained fields, like the multi-phase-field (MPF) and orientation field (OF) models, yield significantly different distributions. In a recent work, we have shown that the coarse grained phase-field models (whether MPF or OF) yield very similar limiting size distributions that seem to differ from the theoretical predictions. Herein, we revisit this problem, and demonstrate in the case of OF models [by R. Kobayashi et al., Physica D 140, 141 (2000) and H. Henry et al. Phys. Rev. B 86, 054117 (2012)] that an insufficient resolution of the small angle grain boundaries leads to a lognormal distribution close to those seen in the experiments and the molecular scale PFC simulations. Our work indicates, furthermore, that the LGSD is critically sensitive to the details of the evaluation process, and raises the possibility that the differences among the LGSD results from different sources may originate from differences in the detection of small angle grain boundaries

    Orientation-field models for polycrystalline solidification: grain coarsening and complex growth forms

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    We compare two versions of the phase-field theory for polycrystalline solidification, both relying on the concept of orientation fields: one by Kobayashi et al. [Physica D 140 (2000) 141] and the other by Henry et al. [Phys. Rev. B 86 (2012) 054117]. Setting the model parameters so that the grain boundary energies and the time scale of grain growth are comparable in the two models, we first study the grain coarsening process including the limiting grain size distribution, and compare the results to those from experiments on thin films, to the models of Hillert, and Mullins, and to predictions by multiphase-field theories. Next, following earlier work by Gránásy et al. [Phys. Rev. Lett. 88 (2002) 206105; Phys. Rev. E 72 (2005) 011605], we extend the orientation field to the liquid state, where the orientation field is made to fluctuate in time and space, and employ the model for describing of multi-dendritic solidification, and polycrystalline growth, including the formation of “dizzy” dendrites disordered via the interaction with foreign particles

    Phase-field modeling of polycrystalline solidification, from needle crystals to spherulites: a review

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    Advances in the orientation-field-based phase-field (PF) models made in the past are reviewed. The models applied incorporate homogeneous and heterogeneous nucleation of growth centers and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycrystalline structures are shown as impinging symmetric dendrites, polycrystalline growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solutions associated with quantitative PF simulations are discussed briefly
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