Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Phys Rev Lett. 2014 Jun 6;112(22):225502. doi: 10.1103/PhysRevLett.112.225502. Epub 2014 Jun 4.
We study the structural features and underlying principles of multidislocation ground states of a crystalline spherical cap. In the continuum limit where the ratio of crystal size to lattice spacing W/a diverges, dislocations proliferate and ground states approach a characteristic sequence of structures composed of radial grain boundaries ("neutral scars"), extending radially from the boundary and terminating in the bulk. Employing a combination of numerical simulations and asymptotic analysis of continuum elasticity theory, we prove that an energetic hierarchy gives rise to a structural hierarchy, whereby dislocation number and scar number diverge as a/W→0 while scar length and dislocation number per scar become independent of lattice spacing. We characterize a secondary transition occurring as scar length grows, where the n-fold scar symmetry is broken and ground states are characterized by polydisperse, forked-scar morphologies.
我们研究了晶体球冠的多位错基态的结构特征和潜在原理。在晶体尺寸与晶格间距之比 W/a 发散的连续体极限下，位错大量增殖，基态趋近于由径向晶界（“中性疤痕”）组成的特征结构序列，从边界径向延伸并终止于内部。通过数值模拟和连续弹性理论的渐近分析相结合，我们证明了一个能量层次结构导致了结构层次结构，其中位错数量和疤痕数量随着 a/W→0 而发散，而疤痕长度和每个疤痕的位错数量与晶格间距无关。我们描述了随着疤痕长度的增长而发生的二次转变，其中 n 重疤痕对称性被打破，基态的特征是多分散的、叉状疤痕形态。
