Thayer G E, Hannon J B, Tromp R M
IBM Research Division, Thomas J. Watson Research Center, PO Box 218 Yorktown Heights, New York 10598, USA.
Nat Mater. 2004 Feb;3(2):95-8. doi: 10.1038/nmat1050. Epub 2004 Jan 11.
The shapes of two-dimensional (2D) nanostructures on surfaces are determined by their boundary energies as well as by long-range elastic, electrostatic or magnetic interactions. Although it is well known that long-range interactions can give rise to shape bifurcation-an abrupt change in shape symmetry at a critical size-a general description of the evolution of shape with size, systematically incorporating both the azimuthal dependence of the boundary energy and long-range interactions, has been lacking. Here we show that unconstrained shape relaxation, including previously ignored boundary curvature, leads to a novel, continuous shape change from convex at small size to concave at large size. In addition to demonstrating a method to quantitatively determine the azimuthal dependence of the boundary energy, we show that the energy gain associated with boundary curvature relaxation is a key factor in stabilizing surface nanostructures. For 7 x 7 domains on Si(111), boundary curvature reduces the formation free-energy by up to 50%.
表面二维（2D）纳米结构的形状由其边界能以及长程弹性、静电或磁相互作用决定。尽管众所周知，长程相互作用会导致形状分岔——在临界尺寸下形状对称性的突然变化——但一直缺乏对形状随尺寸演变的一般描述，该描述需系统地纳入边界能的方位依赖性和长程相互作用。在此，我们表明，不受约束的形状弛豫，包括此前被忽略的边界曲率，会导致一种新颖的、连续的形状变化，即从小尺寸时的凸形转变为大尺寸时的凹形。除了展示一种定量确定边界能方位依赖性的方法外，我们还表明，与边界曲率弛豫相关的能量增益是稳定表面纳米结构的关键因素。对于Si(111)上的7×7畴，边界曲率可将形成自由能降低多达50%。
