Interstitial Fractionalization and Spherical Crystallography

TL;DR

This paper explores how vacancies and interstitials behave in spherical crystals, revealing their tendency to fragment into dislocations influenced by the sphere's topology and elastic properties.

Contribution

It provides a detailed analysis of interstitial fractionalization in spherical crystals using computational methods and compares results with continuum elastic theory predictions.

Findings

Interstitials fragment into dislocation groups influenced by disclinations.

Vacancies are attracted to disclinations, while interstitials are repelled.

The study confirms theoretical predictions about defect interactions on spheres.

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.