Dynamics and scaling of one-dimensional surface structures
Dynamics and scaling of one-dimensional surface structures
复制标题
一维表面结构的动力学和缩放
DOI：
10.1103/physrevb.61.5698
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发表时间：
1999
影响因子：
3.7
通讯作者：
J. Weeks
中科院分区：
文献类型：
--
作者：
Navot Israeli;Hyeong;D. Kandel;J. Weeks
研究了几种一维阶梯流模型。数值模拟结果表明，在所有情况下，剖面的斜率都表现出尺度化。我们对各种阶跃流模型进行了尺度分析，并研究了它们的长时间演化。这种演变是用连续阶跃密度函数来描述的，该函数根据${D(x,t)=F（xt}^{\ensuremath{-}1/\ensuremath{\gamma}}）按时间缩放。缩放指数$\ensuremath{\gamma}$的值取决于质量传递机制。当步骤与全局存储库交换原子时，$\ensuremath{\gamma}$的值为2。另一方面，当台阶只能与相邻的台阶交换原子时，$\ensuremath{\gamma}=4。我们计算了全球和本地交换机制的三种不同配置文件的步长密度缩放函数。计算得到的密度函数与离散系统的模拟结果相吻合。这些结果与Mullins的连续统方法给出的结果进行了比较。
We study several one-dimensional step flow models. Numerical simulations show that the slope of the profile exhibits scaling in all cases. We apply a scaling ansatz to the various step flow models and investigate their long time evolution. This evolution is described in terms of a continuous step density function, which scales in time according to ${D(x,t)=F(xt}^{\ensuremath{-}1/\ensuremath{\gamma}}).$ The value of the scaling exponent $\ensuremath{\gamma}$ depends on the mass transport mechanism. When steps exchange atoms with a global reservoir the value of $\ensuremath{\gamma}$ is 2. On the other hand, when the steps can only exchange atoms with neighboring terraces, $\ensuremath{\gamma}=4.$ We compute the step density scaling function for three different profiles for both global and local exchange mechanisms. The computed density functions coincide with simulations of the discrete systems. These results are compared to those given by the continuum approach of Mullins.