Neutral versus charged defect patterns in curved crystals

Abstract

Characterizing the complex spectrum of topological defects in ground states of curved crystals is a long-standing problem with wide implications, from the mathematical Thomson problem to diverse physical realizations, including fullerenes and particle-coated droplets. While the excess number of "topologically-charged" 5-fold disclinations in a closed, spherical crystal is fixed, here, we study the elementary transition from defect-free, flat crystals to curved-crystals possessing an excess of "charged" disclinations in their bulk. Specifically, we consider the impact of topologically-neutral patterns of defects -- in the form of multi-dislocation chains or "scars" stable for small lattice spacing -- on the transition from neutral to charged ground-state patterns of a crystalline cap bound to a spherical surface. Based on the asymptotic theory of caps in continuum limit of vanishing lattice spacing, we derive the morphological phase diagram of ground state defect patterns, spanned by surface coverage of the sphere and forces at the cap edge. For the singular limit of zero edge forces, we find that scars reduce (by half) the threshold surface coverage for excess disclinations. Even more significant, scars flatten the geometric dependence of excess disinclination number on Gaussian curvature, leading to a transition between stable "charged" and "neutral" patterns that is, instead, critically sensitive to the compressive vs. tensile nature of boundary forces on the cap.

15 pages

References in corpus (5)

• Two-Dimensional Matter: Order, Curvature and Defects
• Crystallography on Curved Surfaces
• Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
• Emergent structure of multi-dislocation ground states in curved crystals
• Bubble Raft Model for a Paraboloidal Crystal

Cited by in corpus (15)

• Perspective: Geometrically-Frustrated Assemblies
• Ground States of Crystalline Caps: Generalized Jellium on Curved Space
• Conformal Vortex Crystals
• Topological vacancies in spherical crystal clusters
• Elasticity in Curved Topographies: Exact Theories and Linear Approximations
• Dislocation screening in crystals with spherical topology
• Plastic deformation of a permanently bonded network: stress relaxation by pleats
• Orientational ordering of lamellar structures on closed surfaces
• Sculpting liquids with ultrathin shells
• A simple, general criterion for onset of disclination disorder on curved surfaces
• Defects in Conformal Crystals: Discrete vs. Continuous Disclination Models
• Statistical Mechanics of Low Angle Grain Boundaries in Two Dimensions
• Predicting the Characteristics of Defect Transitions on Curved Surfaces
• Statistical Mechanics of Dislocation Pileups in Two Dimensions
• General Solution for Elastic Networks on Arbitrary Curved Surfaces in the Absence of Rotational Symmetry