2013/12/17 by Amir Azadi, Gregory M. Grason
Engineering · Materials Science · Physics and Astronomy · #Advanced Materials and Mechanics #Atomic physics #Condensed matter physics #Force Microscopy Techniques and Applications #Ground state #Materials science #Nonlocal and gradient elasticity in micro/nano structures #Physics #cond-mat.mtrl-sci #cond-mat.soft
paper · pdf · doi:10.1103/physrevlett.112.225502
10 pages, 3 figures + supporting info
arxiv created 2013/12/17 · openalex publication_date 2014/06/04 · arxiv updated 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.