title: Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra.
abstract: All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of phi = pi/ radical18 approximately 0.7405. Simple lattice packings of many shapes easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with phi = 0.7786 (ref. 4), which was subsequently compressed numerically to phi = 0.7820 (ref. 5), while compressing with different initial conditions led to phi = 0.8230 (ref. 6). Here we show that tetrahedra pack even more densely, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, which can be compressed to a packing fraction of phi = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is phi = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams and compresses to phi = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs of pentagonal dipyramids that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.
authors.affiliation: Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: Amir
authors.initials: A
authors.lastname: Haji-Akbari
authors.forename: Michael
authors.initials: M
authors.lastname: Engel
authors.forename: Aaron S
authors.initials: AS
authors.lastname: Keys
authors.forename: Xiaoyu
authors.initials: X
authors.lastname: Zheng
authors.forename: Rolfe G
authors.initials: RG
authors.lastname: Petschek
authors.forename: Peter
authors.initials: P
authors.lastname: Palffy-Muhoray
authors.forename: Sharon C
authors.initials: SC
authors.lastname: Glotzer