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首页> 外文期刊>Crystal growth & design >Phase-Field Modeling of Step Dynamics on Growing Crystal Surface: Direct Integration of Growth Units to Step Front
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Phase-Field Modeling of Step Dynamics on Growing Crystal Surface: Direct Integration of Growth Units to Step Front

机译：生长晶体表面上阶跃动力学的相场建模：生长单元直接集成到阶跃前沿

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摘要

We propose a new formulation for numerically simulating step dynamics on growing crystal surfaces in the framework of a phase-field technique. The step advancement rate is proportional to a supersaturation at the crystal surface when the growth units in the ambient phase are integrated to the step front directly (direct integration hypothesis). We conduct numerical simulations of some standard step dynamics problems: the advancement of a straight step, the growth or dissolution of a two-dimensional island, and the vertical growth of the crystal surface due to single or multiple screw dislocations. During evaluations, our phase-field model accurately calculated the rate of advancement of a straight step for various supersaturations. The calculated time variation of the radius of the two-dimensional island showed good agreement with the exact solution. The vertical growth rate due to screw dislocations qualitatively agreed with the predictions of the classical theory of Burton, Cabrera, and Frank. Our simple formulation requires only a single parabolic partial differential equation to be solved numerically. Thus, our phase-field model provides a simple numerical tool for a quantitative step-by-step trajectory calculation, when the advancing velocity of each step follows the direct integration hypothesis.
机译：我们提出了一种新的公式，用于在相场技术的框架内数值模拟生长晶体表面上的阶跃动力学。当环境相中的生长单元直接整合到阶梯前沿时，阶梯前进速率与晶体表面的过饱和度成正比（直​​接积分假设）。我们对一些标准的阶跃动力学问题进行了数值模拟：直线阶跃的进展，二维岛的生长或溶解，以及由于单个或多个螺旋位错而导致的晶体表面的垂直生长。在评估过程中，我们的相场模型可以准确地计算出各种过饱和度的直线步长。计算出的二维岛半径随时间的变化与精确解吻合良好。螺钉位错引起的垂直增长率在质量上与伯顿，卡布雷拉和弗兰克的经典理论的预测一致。我们的简单公式仅需单个抛物型偏微分方程即可进行数值求解。因此，当每一步的前进速度遵循直接积分假设时，我们的相场模型为定量的逐步轨迹计算提供了一个简单的数值工具。

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