PROFILE OF A DECAYING CRYSTALLINE CONE
PROFILE OF A DECAYING CRYSTALLINE CONE
复制标题
正在腐烂的水晶锥体的轮廓
DOI：
10.1103/physrevb.60.5946
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发表时间：
1999
影响因子：
3.7
通讯作者：
D. Kandel
中科院分区：
文献类型：
--
作者：
Navot Israeli;D. Kandel
研究了晶锥在粗化转变下的衰变。我们考虑了通过表面扩散的局部质量传输，重点讨论了扩散受限和附着-剥离受限阶跃动力学两种情况。在这两种情况下，我们用阶跃流动模型来描述衰变动力学。模型的数值模拟表明，在附着-脱离受限的情况下，如果阶跃之间的排斥作用较弱，系统将经历阶跃聚束不稳定性。这种不稳定性在扩散受限的情况下不会发生。在稳定的情况下，高度分布h(r，t)在半径r<；R(T)\sim t^{1/4}处是平坦的。在该平坦区域之外，高度分布遵循缩放方案\Partial h/\Partial r={\cal F}(rt^{-1/4})。对锥体随时间变化的轮廓进行标度分析，得到标度指数的解析值和标度函数的微分方程式。在长时间范围内，该方程提供了离散阶跃动力学的精确描述。它允许一族解，并详细讨论了选择唯一的标度函数的机制。最后，我们推广了该模型，并通过允许相邻梯田之间的直接附着体跳跃来考虑可渗透步骤。我们认为，阶跃渗透率并不改变系统的标度行为，它唯一的影响是某些参数的重整化。
The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both cases, we describe the decay kinetics in terms of step flow models. Numerical simulations of the models indicate that in the attachment-detachment limited case the system undergoes a step bunching instability if the repulsive interactions between steps are weak. Such an instability does not occur in the diffusion limited case. In stable cases the height profile, h(r,t), is flat at radii r<R(t)\sim t^{1/4}. Outside this flat region the height profile obeys the scaling scenario \partial h/\partial r = {\cal F}(r t^{-1/4}). A scaling ansatz for the time-dependent profile of the cone yields analytical values for the scaling exponents and a differential equation for the scaling function. In the long time limit this equation provides an exact description of the discrete step dynamics. It admits a family of solutions and the mechanism responsible for the selection of a unique scaling function is discussed in detail. Finally we generalize the model and consider permeable steps by allowing direct adatom hops between neighboring terraces. We argue that step permeability does not change the scaling behavior of the system, and its only effect is a renormalization of some of the parameters.