Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra

TL;DR

This study investigates the equilibrium phase behavior and maximally random jammed states of truncated tetrahedra, revealing phase transitions, absence of rotator phases, and hyperuniform dense packings with implications for glass formation.

Contribution

It provides high-precision phase diagrams for truncated tetrahedra and characterizes their jammed states, advancing understanding of shape-dependent packing and phase behavior.

Findings

Two first-order phase transitions identified: liquid-solid and solid-solid.

Maximally random jammed packings are hyperuniform with packing fraction 0.770.

No stable rotator or nematic phases observed.

Abstract

Systems of hard nonspherical particles exhibit a variety of stable phases with different degrees of translational and orientational order, including isotropic liquid, solid crystal, rotator and a variety of liquid crystal phases. In this paper, we employ a Monte Carlo implementation of the adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations to ascertain with high precision the equilibrium phase behavior of systems of congruent Archimedean truncated tetrahedra over the entire range of possible densities up to the maximal nearly space-filling density. In particular, we find that the system undergoes two first-order phase transitions as the density increases: first a liquid-solid transition and then a solid-solid transition. The isotropic liquid phase coexists with the Conway-Torquato (CT) crystal phase at intermediate densities. At higher densities, we find that the CT phase undergoes another first-order phase transition to one associated with the densest-known crystal. We find no evidence for stable rotator (or plastic) or nematic phases. We also generate the maximally random jammed (MRJ) packings of truncated tetrahedra, which may be regarded to be the glassy end state of a rapid compression of the liquid. We find that such MRJ packings are hyperuniform with an average packing fraction of 0.770, which is considerably larger than the corresponding value for identical spheres (about 0.64). We conclude with some simple observations concerning what types of phase transitions might be expected in general hard-particle systems based on the particle shape and which would be good glass formers.