Elastic Interaction of Nanostructures

9988597从纳米尺度过渡到连续介质的性质将被特别研究，以获得准连续介质的公式。许多薄膜/衬底系统最初以二维（2D）或原子平面模式生长，但最终经历粗糙化过渡，在二维层的顶部产生三维（3D）岛屿。规划了理论与数值模拟相结合的研究项目。其目标是获得表面缺陷附近的弹性场及其弹性相互作用的定量精确图像。有必要在连续和原子（离散）尺度上解决这个问题。只要缺陷之间的距离足够大（远程相互作用），连续体模型的预测应该是准确的。随着相互作用缺陷之间的分离距离减小，原子/连续体趋于发散，晶格模型的必要性变得明显。如果没有离散弹性模型，就不能确定缺陷的短程相互作用。

9988597The nature of the transition from the nanoscale to the continuum will be specifically examined in an effort to obtain a quasi-continuum formulation. Many thin-film/substrate systems initially grow in a two-dimensional (2D) or atomically flat mode but eventually undergo a roughening transition, yielding three-dimensional (3D) islands on the top of the 2D layers. A research program that combines theory and numerical simulations is planned. Its goal is to obtain a quantitatively accurate picture of the elastic field in the vicinity of surface defects and their elastic interactions. It is necessary that the problem be addressed at both the continuum and atomic (discrete) scale. The predictions of continuum models should be accurate, as long as the distance between defects remains sufficiently large (long-range interaction). As the separation distance between interacting defects diminishes, the atomic/continuum approaches diverge and the necessity of a lattice model becomes apparent. The short-range interaction of defects cannot be determined without a discrete elastic model.