Isomorph invariance of classical crystals' structure and dynamics

TL;DR

This study demonstrates through simulations that certain classical crystals exhibit isomorphs, invariant structure and dynamics along specific curves in their phase diagrams, with implications for understanding melting and crystallization.

Contribution

The paper provides the first validation of isomorph invariance in crystalline solids, expanding the concept beyond liquids to include most metallic and van der Waals crystals.

Findings

FCC crystals with Lennard-Jones interactions show isomorph invariance.

Vacancy-jump dynamics in FCC crystals are isomorph invariant.

NaCl crystals do not exhibit isomorph invariance.

Abstract

This paper shows by computer simulations that some crystalline systems have curves in their thermodynamic phase diagrams, so-called isomorphs, along which structure and dynamics in reduced units are invariant to a good approximation. The crystals are studied in a classical-mechanical framework, which is generally a good description except significantly below melting. The existence of isomorphs for crystals is validated by simulations of particles interacting via the Lennard-Jones pair potential arranged into a face-centered cubic (FCC) crystalline structure; the slow vacancy-jump dynamics of a defective FCC crystal is also shown to be isomorph invariant. In contrast, a NaCl crystal model does not exhibit isomorph invariances. Other systems simulated, though in less detail, are the Wahnstrom binary Lennard-Jones crystal with the ${\rm MgZn_2}$ Laves crystal structure, monatomic FCC crystals of particles interacting via the Buckingham pair potential and via a novel purely repulsive pair potential diverging at a finite separation, an ortho-terphenyl molecular model, and SPC/E hexagonal ice. Except for NaCl and ice, the crystals simulated all have isomorphs. Based on these findings and previous simulations of liquid models, we conjecture that crystalline solids with isomorphs include most or all formed by atoms or molecules interacting via metallic or van der Waals forces, whereas covalently- or hydrogen-bonded crystals are not expected to have isomorphs. Crystals of ions or dipolar molecules constitute a limiting case for which isomorphs are only expected when the Coulomb interactions are relatively weak. We briefly discuss the consequences of the findings for theories of melting and crystallization.