Phase Diagram and Structural Diversity of a Family of Truncated Cubes: Degenerate Close-Packed Structures and Vacancy-Rich States

Abstract

Using Monte Carlo simulations and free-energy calculations, we determine the phase diagram of a family of truncated hard cubes, where the shape evolves smoothly from a cube via a cuboctahedron to an octahedron. A remarkable diversity in crystal phases and close-packed structures is found, including a fully degenerate crystal structure, several plastic crystals, as well as vacancy-stabilized crystal phases, all depending sensitively on the precise particle shape. Our results illustrate the intricate relation between phase behavior and building-block shape, and can guide future experimental studies on polyhedral-shaped nanoparticles. DOI: 10.1103/PhysRevLett.111.015501 PACS numbers: 61.46.Df, 64.70.MÀ, 64.75.Yz, 82.70.Dd Recent advances in experimental techniques to synthesize polyhedron-shaped particles, such as faceted nanocrystals and colloids [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and the ability to perform self-assembly experiments with these particles [15][16][17][18][19][20][21][22], have attracted the interest of physicists, mathematicians, and computer scientists [23][24][25][26][27]. Additionally, predicting the densest packings of hard polyhedra has intrigued mathematicians since the time of the early Greek philosophers, such as Plato and Archimedes [28,29]. Modern computer platforms have made it possible to perform simulations of these systems, which has resulted not only in an improved understanding of the experimentally observed phenomenology in colloidal suspensions of such particles, but also in improved Ansätze for the morphology of their closepacked configurations [24,[30][31][32][33][34][35].The self-assembly of the basic building blocks at finite pressures may differ substantially from the packings achieved at high (sedimentation and solvent-evaporation) pressures. For instance, liquid-crystal, plastic-crystal, vacancy-rich simple-cubic, and quasicrystalline mesophases are stabilized by entropy alone under non-closepacked conditions of hard anisotropic particle systems [30][31][32][33][34]36,37]. Predicting the phase behavior from the shape of the building blocks alone is therefore a major challenge in materials science and is crucial for the design of new functional materials. It is thus not surprising that numerous studies have been devoted to providing simple guidelines for predicting the self-assembly from the particle shape alone [32][33][34].Recently, Henzie et al.[15] reported the shapecontrolled synthesis of truncated cubes. In their research, the close-packed crystals of these particles were studied using sedimentation experiments and simulations. They created exotic superlattices, and their results also tested several conjectures on the densest packings of hard polyhedra [23,[25][26][27]. However, Henzie et al. did not examine the finite-pressure behavior of the system. Mapping the full phase diagram for the system of truncated cubes is thus important, not only from a fundamental perspective but also to guide future experimental self-assembly studies to fabricate new func...

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“…S1 and S2, and Table S4). Cubes densely pack into a simple cubic (SC) crystalline phase, with slight distortions in orientation for mildly truncated or rounded corners, or a plastic or crystalline FCC phase for high degrees of imperfection (20,(27)(28)(29)(30)(36)(37)(38). Indeed, a smaller zone of anisotropy was observed for cubes relative to octahedra and rhombic dodecahedra, consistent with the above hypothesis.…”

“…S1, and Table S3). The dense packing of hard octahedra varies based on corner truncation or rounding (27)(28)(29), where body-centered cubic (BCC) or bodycentered tetragonal (BCT) crystalline phases are favored for truncated octahedra (26,29), and BCC or FCC plastic crystals are favored for rounded octahedra (28,30). In experimental systems, the hydrodynamic particle shape deviates from an ideal octahedron in favor of a BCC crystalline phase (13).…”

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Heuristic Rule for Binary Superlattice Coassembly: Mixed Plastic Mesophases of Hard Polyhedral Nanoparticles

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