Universality in the Screening Cloud of Dislocations Surrounding a Disclination

TL;DR

This paper provides a comprehensive analytical and numerical study of dislocation clouds around disclinations, revealing a universal behavior characterized by an effective fractional charge and scalable energy expressions.

Contribution

It introduces a universal scaling form for the energy of dislocation clouds around disclinations, validated by high-accuracy numerical checks and applicable to arbitrary defect distributions and geometries.

Findings

Dislocation clouds behave as single disclinations with fractional charge.

Energy scales universally with Young's modulus and a universal function.

Numerical method efficiently handles arbitrary defect configurations.

Abstract

A detailed analytical and numerical analysis for the dislocation cloud surrounding a disclination is presented. The analytical results show that the combined system behaves as a single disclination with an effective fractional charge which can be computed from the properties of the grain boundaries forming the dislocation cloud. Expressions are also given when the crystal is subjected to an external two-dimensional pressure. The analytical results are generalized to a scaling form for the energy which up to core energies is given by the Young modulus of the crystal times a universal function. The accuracy of the universality hypothesis is numerically checked to high accuracy. The numerical approach, based on a generalization from previous work by S. Seung and D.R. Nelson ({\em Phys. Rev A 38:1005 (1988)}), is interesting on its own and allows to compute the energy for an {\em arbitrary} distribution of defects, on an {\em arbitrary geometry} with an arbitrary elastic {\em energy} with very minor additional computational effort. Some implications for recent experimental, computational and theoretical work are also discussed.