Degenerate Quasicrystal of Hard Triangular Bipyramids

TL;DR

This paper reports the discovery of a degenerate quasicrystal formed by hard triangular bipyramids through Monte Carlo simulations, revealing unique degeneracy and phase behavior at high packing fractions.

Contribution

It introduces a new type of degenerate quasicrystal formed by hard triangular bipyramids and analyzes its structural and thermodynamic properties.

Findings

Degenerate quasicrystal forms above 54% packing fraction.

A triclinic crystal is thermodynamically favored at high densities.

Degeneracy differs from quasiperiodic random tiling degeneracy.

Abstract

We report a degenerate quasicrystal in Monte Carlo simulations of hard triangular bipyramids each composed of two regular tetrahedra sharing a single face. The dodecagonal quasicrystal is similar to that recently reported for hard tetrahedra [Haji-Akbari et al., Nature (London) 462, 773 (2009)] but degenerate in the pairing of tetrahedra, and self-assembles at packing fractions above 54%. This notion of degeneracy differs from the degeneracy of a quasiperiodic random tiling arising through phason flips. Free energy calculations show that a triclinic crystal is preferred at high packing fractions.