Topological vacancies in spherical crystals

Abstract

Understanding geometric frustration of ordered phases in two-dimensional condensed matter on curved surfaces is closely related to a host of scientific problems in condensed matter physics and materials science. Here, we show how two-dimensional Lennard-Jones crystal clusters confined on a sphere resolve geometric frustration and form pentagonal vacancy structures. These vacancies, originating from the combination of curvature and physical interaction, are found to be topological defects and they can be further classified into dislocational and disclinational types. We analyze the dual role of these crystallographic defects as both vacancies and topological defects, illustrate their formation mechanism, and present the phase diagram. The revealed dual role of the topological vacancies may find applications in the fabrication of robust nanopores. This work also shows the promising potential of exploiting richness in both physical interactions and substrate geometries to create new types of crystallographic defects, which have strong connections with the design of crystalline materials.

Random Batch Methods (RBM) for interacting particle systems

“…The traditional Thomson problem is to determine the stable configuration of N electrons on a sphere. When N becomes large, this could lead to the so-called spherical crystals ( [60,61,62]). The configuration may have some meta-states (local minimizers of the energy surface).…”

“…The configuration may have some meta-states (local minimizers of the energy surface). When the number of particles is large, the spherical crystals have defects due to the topology of the sphere [61,62]. In the N → ∞ limit, hopefully, we will have a continuous distribution of charges on the sphere ρ(·).…”

Phase transitions on non-uniformly curved surfaces: coupling between phase and location

“…So far, most studies on the effects of curvature have focused on the case of constant curvature, such as spheres. Even in this simplest scenario, a wide range of phenomena are observed which are absent on flat surfaces, including the presence of defects and branching in the ground-state crystals, 12,15,16 and of modified nucleation pathways. 17,18 These studies have been successful in describing natural phenomena such as the structure and formation of virus capsids, 11 and the packing of particles on a Pickering emulsion droplet.…”

Stress driven fractionalization of vacancies in regular packings of elastic particles

“…Topological defects are emergent structures commonly seen in various ordered condensed media [1][2][3][4][5]. As a fundamentally important crystallographic defect, vacancies are highly involved in several important physical processes in both two- [6][7][8] and three-dimensional systems, [9,10] such as in facilitating migration of atoms, [11,12] and crystallization of DNA-programmable nanoparticles, [13,14] and in resolving geometric frustrations in curved crystals [7,8,[15][16][17]. Vacancies, together with other defects, are crucial for the characteristic of heterogeneous stress distributions in the packing of particles, [7,8,13,18] which has connections with the formation of force chain structures and the resulting jamming transition in granular media [19][20][21][22][23].…”