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

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.