Crystallization Dynamics on Curved Surfaces

TL;DR

This paper investigates how curvature influences the crystallization process in two-dimensional systems, revealing that high curvature regions act as defect sinks and can lead to slow, glassy ordering dynamics that hinder reaching the ground state.

Contribution

It introduces a detailed study of crystallization dynamics on curved surfaces, highlighting the role of curvature in defect formation, growth, and the emergence of metastable structures.

Findings

High curvature regions promote defect relaxation.

Grain boundary pinning leads to metastable defect structures.

Ordering dynamics become slow and glassy-like due to curvature effects.

Abstract

We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is rapidly relaxed through isolated defects. Further relaxation involves a mechanism of crystal growth and defect annihilation where regions with high curvature act as sinks for the diffusion of domain walls. The pinning of grain boundaries at regions of low curvature leads to the formation of a metastable structure of defects, characterized by asymptotically slow dynamics of ordering and activation energies dictated by the largest curvatures of the system. These glassy-like ordering dynamics may completely inhibit the appearance of the ground state structures.