控制二维微观生长模型中的各向异性
Controlling anisotropy in 2D microscopic models of growth
摘要：
在晶格模型中的界面各向异性的定量知识是一个主要问题，无论是连续界面模型的参数化，并为实验观察的分析。在本文中，我们专注于线张力和刚度的各向异性，这在平衡形状和波动，以及在选择非平衡增长模式中起着重要作用。本文研究了具有第一和第二近邻相互作用的正方形晶格上的二维伊辛哈密顿量。表面刚度和线张力计算通过一个断键模型为任意取向。界面能的分析使我们能够确定刚度各向异性最小的条件。支持这些结果的定量比较动力学蒙特卡罗模拟的基础上，耦合的一个领域的流动原子的凝聚相。此外，我们引入了一个通用的平滑参数，它允许一个模仿实验显微镜技术的有限分辨率。我们的研究结果提供了一种方法来微调的纳米级非平衡过程，各向异性和波动相结合，并产生非平凡的形态模型中的界面能。
英文摘要：
The quantitative knowledge of interface anisotropy in lattice models is a major issue, both for the parametrization of continuum interface models, and for the analysis of experimental observations. In this paper, we focus on the anisotropy of line tension and stiffness, which plays a major role both in equilibrium shapes and fluctuations, and in the selection of nonequilibrium growth patterns. We consider a 2D Ising Hamiltonian on a square lattice with first and second-nearest-neighbor interactions. The surface stiffness and line tension are calculated by means of a broken-bond model for arbitrary orientations. The analysis of the interface energy allows us to determine the conditions under which stiffness anisotropy is minimal. These results are supported by a quantitative comparison with kinetic Monte Carlo simulations, based on the coupling of a field of mobile atoms to a condensed phase. Furthermore, we introduce a generic smoothing parameter which allows one to mimic the finite resolution of experimental microscopy techniques. Our results provide a method to fine-tune the interface energy in models of nanoscale non-equilibrium processes, where anisotropy and fluctuations combine and give rise to non-trivial morphologies.
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