Isomorph invariance of classical crystals' structure and dynamics

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 $\mathrm{MgZ}{\mathrm{n}}_2$ 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.

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Cited by in corpus (16)

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• Impact of size polydispersity on the nature of Lennard-Jones liquids
• The Lennard Jones Potential Revisited -- Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices
• Studies of the Lennard-Jones fluid in 2, 3, and 4 dimensions highlight the need for a liquid-state 1/d expansion
• Effect of Energy Polydispersity on the Nature of Lennard-Jones Liquids
• The EXP pair-potential system. I. Fluid phase isotherms, isochores, and quasiuniversality
• Isomorph theory of physical aging
• An extreme case of density scaling: The Weeks-Chandler-Andersen system at low temperatures
• Isomorph theory beyond thermal equilibrium
• Hidden scale invariance at high pressures in gold and five other fcc metal crystals
• A pair potential that reproduces the shape of isochrones in molecular liquids
• Isomorphs in nanoconfined liquids