Interstitial Fractionalization and Spherical Crystallography

Abstract

Finding the ground states of identical particles packed on spheres has relevance for stabilizing emulsions and a venerable history in the literature of theoretical physics and mathematics. Theory and experiment have confirmed that defects such as disclinations and dislocations are an intrinsic part of the ground state. Here we discuss the remarkable behavior of vacancies and interstitials in spherical crystals. The strain fields of isolated disclinations forced in by the spherical topology literally rip interstitials and vacancies apart, typically into dislocation fragments that combine with the disclinations to create small grain boundary scars. The fractionation is often into three charge-neutral dislocations, although dislocation pairs can be created as well. We use a powerful, freely available computer program to explore interstitial fractionalization in some detail, for a variety of power law pair potentials. We investigate the dependence on initial conditions and the final state energies, and compare the position dependence of interstitial energies with the predictions of continuum elastic theory on the sphere. The theory predicts that, before fragmentation, interstitials are repelled from 5-fold disclinations and vacancies are attracted. We also use vacancies and interstitials to study low energy states in the vicinity of "magic numbers" that accommodate regular icosadeltahedral tessellations.

21 pages, 9 figures

References in corpus (10)

• Grain Boundary Scars and Spherical Crystallography
• Virus shapes and buckling transitions in spherical shells
• Crystalline Order on a Sphere and the Generalized Thomson Problem
• Direct Visualization of Dislocation Dynamics in Grain Boundary Scars
• Diffusion of Point Defects in Two-Dimensional Colloidal Crystals
• Equilibrium Configurations and Energetics of Point Defects in Two-Dimensional Colloidal Crystals
• Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials
• Point Defect Dynamics in Two-Dimensional Colloidal Crystals
• Dynamics and Instabilities of Defects in Two-Dimensional Crystals on Curved Backgrounds
• Defect free global minima in Thomson's problem of charges on a sphere

Cited by in corpus (6)

• Two-Dimensional Matter: Order, Curvature and Defects
• Fractionalization of Interstitials in Curved Colloidal Crystals
• Topological vacancies in spherical crystal clusters
• Stress driven fractionalization of vacancies in regular packings of elastic particles
• Relaxation of interstitials in spherical colloidal crystals
• Intrinsic statistical regularity of topological charges revealed in dynamical disk model