Continuum Relaxation of Interacting Steps on Crystal Surfaces in 2+1 Dimensions
Continuum Relaxation of Interacting Steps on Crystal Surfaces in 2+1 Dimensions
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2 1 维晶体表面相互作用台阶的连续弛豫
DOI：
10.1137/06065297x
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
R. Kohn
中科院分区：
文献类型：
--
作者：
D. Margetis;R. Kohn
本文研究了2 +1维晶体表面通过相互作用的原子台阶运动的弛豫。我们的目标是严格推导连续极限。起点是来自Burton、Cabrera和Frank模型的离散方案，该方案考虑了台阶上点缺陷（“吸附原子”）的扩散和台阶边缘原子的附着-分离。结果表明，宏观吸附原子电流涉及张量流动性，它描述了不同的通量在平行和横向的步骤边缘的方向，虽然假设每个平台的物理各向同性。当台阶处处平行（直的或圆的）时，迁移率的张量特征并不重要;然而，在一般的$（2+1）$维设置中，它是至关重要的。我们的方法包括（i）的解决方案的扩散方程的吸附原子通过分离的局部空间变量成“快”和“慢”，和（ii）的治疗的步骤化学势的一个广泛的类的步骤能量和排斥…
We study the relaxation of crystal surfaces in $2+1$ dimensions via the motion of interacting atomic steps. The goal is the rigorous derivation of the continuum limit. The starting point is a discrete scheme from the Burton, Cabrera, and Frank model, which accounts for diffusion of point defects (“adatoms”) on terraces and attachment‐detachment of atoms at step edges. It is shown that the macroscopic adatom current involves a tensor mobility, which describes different fluxes in directions parallel and transverse to step edges, although the physics of each terrace is assumed isotropic. When the steps are everywhere parallel (straight or circular) the tensor character of the mobility is unimportant; in the general $(2+1)$‐dimensional setting, however, it is crucial. Our methods consist of (i) the solution of the diffusion equation for adatoms via the separation of local space variables into “fast” and “slow,” and (ii) the treatment of the step chemical potential for a wide class of step energies and repulsi...