Phase and vacancy behaviour of hard "slanted" cubes

TL;DR

This study uses simulations to explore how hard, slanted cubes organize into different crystal phases, revealing unexpected simple cubic structures with high vacancy levels across various shapes and densities.

Contribution

It provides the first detailed phase diagram for hard rhombic prisms, showing the stability of simple cubic phases despite non-cubic particle shapes.

Findings

Simple cubic crystal is the equilibrium phase over a wide range of angles and densities.

Vacancy concentration in the cubic phase is extremely high and shape-independent.

Rhombic crystals emerge at higher densities.

Abstract

We use computer simulations to study the phase behaviour for hard, right rhombic prisms as a function of the angle of their rhombic face (the "slant" angle). More specifically, using a combination of event-driven molecular dynamics simulations, Monte Carlo simulations, and free-energy calculations, we determine and characterize the equilibrium phases formed by these particles for various slant angles and densities. Surprisingly, we find that the equilibrium crystal structure for a large range of slant angles and densities is the simple cubic crystal - despite the fact that the particles do not have cubic symmetry. Moreover, we find that the equilibrium vacancy concentration in this simple cubic phase is extremely high and depends only on the packing fraction, and not the particle shape. At higher densities, a rhombic crystal appears as the equilibrium phase. We summarize the phase behaviour of this system by drawing a phase diagram in the slant angle - packing fraction plane.