Khenner Mikhail
Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):022402. doi: 10.1103/PhysRevE.88.022402. Epub 2013 Aug 13.
A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the "one-sided" model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed the nonlinear dynamics. Linear stability depends on whether the stiffness is minimum or maximum in the direction of the step growth. It also depends nontrivially on the combination of the anisotropy strength parameter and the atomic flux from the terrace to the step. Computations show formation and coarsening of a hill-and-valley structure superimposed onto a long-wavelength profile, which independently coarsens. Coarsening laws for the hill-and-valley structure are computed for two principal orientations of a maximum step stiffness, the increasing anisotropy strength, and the varying atomic flux.
建立并分析了一个具有强各向异性线能量的单步动力学连续介质模型。台阶通过从较低平台吸附吸附原子而生长，原子从气相或分子束吸附到该平台上，并且解吸不可忽略（“单边”模型）。通过多尺度展开，我们推导出了一个用于台阶轮廓的长波、强非线性和强各向异性演化偏微分方程。用台阶斜率表示时，该偏微分方程可以表示为类似于对流Cahn-Hilliard方程的形式。我们进行了线性稳定性分析并计算了非线性动力学。线性稳定性取决于在台阶生长方向上刚度是最小还是最大。它还非平凡地取决于各向异性强度参数和从平台到台阶的原子通量的组合。计算表明，在一个独立粗化的长波长轮廓上叠加形成并粗化了一个丘陵-山谷结构。针对最大台阶刚度的两个主要取向、不断增加的各向异性强度以及变化的原子通量，计算了丘陵-山谷结构的粗化规律。
