Self-assembly of a space-tessellating structure in the binary system of hard tetrahedra and octahedra

TL;DR

This study demonstrates the entropic self-assembly of a binary crystal composed of tetrahedra and octahedra, forming a space-tessellating structure, which had not been previously observed in simulations.

Contribution

It is the first simulation evidence of a binary crystal of hard polyhedra self-assembling into a space-tessellating structure due to entropy.

Findings

Binary crystal of tetrahedra and octahedra formed via entropic forces

Coexistence of known phases with the binary crystal

No other crystalline phases observed

Abstract

We report the formation of a binary crystal of hard polyhedra due solely to entropic forces. Although the alternating arrangement of octahedra and tetrahedra is a known space-tessellation, it had not previously been observed in self-assembly simulations. Both known one-component phases - the dodecagonal quasicrystal of tetrahedra and the densest-packing of octahedra in the Minkowski lattice - are found to coexist with the binary phase. No additional crystalline phases were observed.