Particles on curved surfaces - a dynamic approach by a phase field crystal model

TL;DR

This paper introduces a dynamic phase field crystal model to study particle ordering on curved surfaces, analyzing defect dynamics and energy configurations, with applications to spherical geometries.

Contribution

It presents a novel dynamic PDE-based approach for modeling particle arrangements on curved surfaces, including defect interactions and energy scaling laws.

Findings

Dislocation annihilation dynamics on curved surfaces analyzed.

Scaling laws for excess dislocations derived.

Comparison with existing results confirms model validity.

Abstract

We present a dynamic model to study ordering of particles on arbitrary curved surfaces. Thereby the particles are represented as maxima in a density field and a surface partial differential equation for the density field is solved to the minimal energy configuration. We study annihilation of dislocations within the ordered sytem and premelting along grain boundary scars. The obtained minimal energy configurations on a sphere are compared with existing results and scaling laws are computed for the number of excess dislocations as a function of system size.