title: Emergent structure of multidislocation ground States in curved crystals.
abstract: 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.
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
authors.forename: Amir
authors.initials: A
authors.lastname: Azadi
authors.affiliation: Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
authors.forename: Gregory M
authors.initials: GM
authors.lastname: Grason