Curved features are ubiquitous on solid surfaces, but the effect of surface curvatures on growth of two-dimensional (2D) materials has not yet been established. Using a newly developed method based on the Metropolis algorithm and taking graphene as a prototype, we find that a curved feature on substrates can result in a variety of topological defects in 2D materials. As the feature's size increases by just nanometers, the defects can vary from adatoms, dislocation pairs, and grain boundary scars to long-range grain boundaries, in contrast to previously reported defect-free modes of rigid colloidal crystals growing on spheres. We identify an important role of curvature-induced lattice stress in lowering the growth rate over the curved features and driving a plastic instability in the materials. When the feature's size increases to several nanometers, the stress effect is compromised by an enhanced effect of geodesic curvature, yielding long-range grain boundaries as a result of increased local growth rate on the feature with respect to that on flat regions. We further provide a ‘phase diagram’ of defects that helps to guide a rational choice of geometrical parameters of features towards the growth of high-quality 2D materials as well as controllable creation of topological defects.

曲面特征在固体表面上无处不在，但尚未确定表面曲率对二维 (2D) 材料生长的影响。使用基于 Metropolis 算法的新方法并以石墨烯为原型，我们发现基板上的弯曲特征会导致二维材料中的各种拓扑缺陷。随着特征尺寸仅增加纳米级，缺陷可以从吸附原子、位错对和晶界疤痕到长程晶界变化，这与之前报道的在球体上生长的刚性胶体晶体的无缺陷模式形成对比。我们确定了曲率引起的晶格应力在降低弯曲特征上的生长速率和驱动材料的塑性不稳定性方面的重要作用。当特征' s 尺寸增加到几个纳米，应力效应受到测地曲率增强效应的影响，由于相对于平坦区域的特征局部生长速率增加，产生长程晶界。我们进一步提供了缺陷的“相图”，有助于指导合理选择特征的几何参数，以实现高质量 2D 材料的生长以及拓扑缺陷的可控创建。