Decay of one-dimensional surface modulations
Decay of one-dimensional surface modulations
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DOI：
10.1103/physrevb.62.13707
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发表时间：
2000-06
影响因子：
3.7
通讯作者：
Navot Israeli Daniel Kandel
中科院分区：
文献类型：
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作者：
Navot Israeli Daniel Kandel
重新检查一维表面调制的弛豫过程。表面演变是用标准阶梯流模型来描述的。提供了表面坡度 D(x,t) 服从缩放 ansatz D(x,t)=alpha(t)F(x) 的数值证据。我们使用缩放 ansatz 将离散阶跃模型转换为表面动力学的连续模型。该模型由函数 alpha(t) 和 F(x) 的微分方程组成。这些方程的解与离散阶跃模型的仿真结果一致。我们确定了两种可能的扩展解决方案。第一种类型的解在极值点处具有小平面，而在第二种类型的解中，小平面被尖点取代。符号相反的步骤之间的相互作用决定系统是第一类型还是第二类型。最后，我们将我们的模型与实际实验联系起来，并发现测量的 AFM 快照与我们的连续体模型的解之间具有良好的一致性。
The relaxation process of one dimensional surface modulations is re-examined. Surface evolution is described in terms of a standard step flow model. Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz D(x,t)=alpha(t)F(x) is provided. We use the scaling ansatz to transform the discrete step model into a continuum model for surface dynamics. The model consists of differential equations for the functions alpha(t) and F(x). The solutions of these equations agree with simulation results of the discrete step model. We identify two types of possible scaling solutions. Solutions of the first type have facets at the extremum points, while in solutions of the second type the facets are replaced by cusps. Interactions between steps of opposite signs determine whether a system is of the first or second type. Finally, we relate our model to an actual experiment and find good agreement between a measured AFM snapshot and a solution of our continuum model.