Crystallization in a one-dimensional periodic landscape

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.

References in corpus (4)

• Stable crystalline lattices in two-dimensional binary mixtures of dipolar particles
• Binary crystals in two-dimensional two-component Yukawa mixtures
• Finite crystallization and Wulff shape emergence for ionic compounds in the square lattice
• Crystalline structures in a one-dimensional two-component lattice gas with $1/r^{\alpha }$ interactions

Cited by in corpus (3)

• Emergence of rigid Polycrystals from atomistic Systems with Heitmann-Radin sticky disk energy
• Typical ground states for large sets of interactions
• Uniform distribution of dislocations in Peierls-Nabarro models for semi-coherent interfaces