Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces
Engel M, Damasceno PF, Glotzer SC (2012)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2012
Journal
Publisher: American Chemical Society
Book Volume: 6
Pages Range: 609-614
Journal Issue: 1
DOI: 10.1021/nn204012y
Abstract
Figure Persented: Polyhedra and their arrangements have intrigued humankind since the ancient Greeks and are today important motifs in condensed matter, with application to many classes of liquids and solids. Yet, little is known about the thermodynamically stable phases of polyhedrally shaped building blocks, such as faceted nanoparticles and colloids. Although hard particles are known to organize due to entropy alone, and some unusual phases are reported in the literature, the role of entropic forces in connection with polyhedral shape is not well understood. Here, we study thermodynamic self-assembly of a family of truncated tetrahedra and report several atomic crystal isostructures, including diamond, β-tin, and high-pressure lithium, as the polyhedron shape varies from tetrahedral to octahedral. We compare our findings with the densest packings of the truncated tetrahedron family obtained by numerical compression and report a new space-filling polyhedron, which has been overlooked in previous searches. Interestingly, the self-assembled structures differ from the densest packings. We show that the self-assembled crystal structures can be understood as a tendency for polyhedra to maximize face-to-face alignment, which can be generalized as directional entropic forces. © 2011 American Chemical Society.
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APA:
Engel, M., Damasceno, P.F., & Glotzer, S.C. (2012). Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces. Acs Nano, 6(1), 609-614. https://doi.org/10.1021/nn204012y
MLA:
Engel, Michael, Pablo F. Damasceno, and Sharon C. Glotzer. "Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces." Acs Nano 6.1 (2012): 609-614.
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