Crystallization in a one-dimensional periodic landscape

TL;DR

This paper investigates how a finite chain of identical hard spheres arranges itself in a periodic landscape, revealing that crystallization is generally unlikely in long chains due to the landscape's properties.

Contribution

The study provides a theoretical analysis of crystallization in one-dimensional periodic landscapes, highlighting conditions that prevent crystallization in long chains.

Findings

Crystallization depends on the sphere's radius and landscape period.

Crystallization is generally not expected in arbitrarily long chains.

The work connects crystallization phenomena with lattice mismatch in epitaxial growth.

Abstract

We consider the crystallization problem for a finite one-dimensional collection of identical hard spheres in a periodic energy landscape. This issue arises in connection with the investigation of crystalline states of ionic dimers, as well as in epitaxial growth on a crystalline substrate in presence of lattice mismatch. Depending on the commensurability of the radius of the sphere and the period of the landscape, we discuss the possible emergence of crystallized states. In particular, we prove that crystallization in arbitrarily long chains is generically not to be expected.