Geometrically Frustrated Crystals: Elastic Theory and Dislocations

TL;DR

This paper develops an elastic theory for ring-shaped crystals, explores how geometrical frustration induces dislocations, and draws analogies to vortex states in superconductors, analyzing phase diagrams based on size parameters.

Contribution

It introduces a novel elastic framework for ring crystals and investigates dislocation generation due to bending-induced frustration, linking it to vortex phenomena in condensed matter physics.

Findings

Dislocations are generated by geometrical frustration in bent ring crystals.

The phase diagram of ring crystals depends on radius and thickness.

Analogies to vortex states in superconductors are established.

Abstract

Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is pointed out and the phase diagram of the ring-crystal, which depends on radius and thickness, is discussed.