Ofori-Opoku N, Warren J A, Voorhees P W
Center for Hierarchical Materials Design, Northwestern University, Evanston IL 60208.
Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg MD 20899.
Phys Rev Mater. 2018;2(8). doi: https://doi.org/10.1103/physrevmaterials.2.083404.
Highly anisotropic interfaces play an important role in the development of material microstructure. Using the diffusive atomistic phase-field crystal (PFC) formalism, we determine the capability of the model to quantitatively describe these interfaces. Specifically, we coarse grain the PFC model to attain both its complex amplitude formulation and its corresponding phase-field limit. Using this latter formulation, in one-dimensional calculations, we determine the surface energy and the properties of the Wulff shape. We find that the model can yield Wulff shapes with missing orientations, the transition to missing orientations, and facet formation. We show that the corresponding phase-field limit of the complex amplitude model yields a self-consistent description of highly anisotropic surface properties that are a function of the surface orientation with respect to the underlying crystal lattice. The phase-field model is also capable of describing missing orientations on equilibrium shapes of crystals and naturally includes a regularizing contribution. We demonstrate, in two dimensions, how the resultant model can be used to study growth of crystals with varying degrees of anisotropy in the phase-field limit.
高度各向异性的界面在材料微观结构的发展中起着重要作用。利用扩散原子相场晶体（PFC）形式体系，我们确定了该模型定量描述这些界面的能力。具体而言，我们对PFC模型进行粗粒化处理，以获得其复振幅形式及其相应的相场极限。使用后一种形式，在一维计算中，我们确定了表面能和Wulff形状的性质。我们发现该模型可以产生具有缺失取向、向缺失取向的转变以及小面形成的Wulff形状。我们表明，复振幅模型的相应相场极限对高度各向异性的表面性质给出了自洽描述，这些性质是表面相对于底层晶格取向的函数。相场模型还能够描述晶体平衡形状上的缺失取向，并且自然地包含一个正则化贡献。我们在二维中展示了所得模型如何用于研究在相场极限下具有不同程度各向异性的晶体生长。
