Crystal-structure prediction via the Floppy-Box Monte Carlo algorithm: Method and application to hard (non)convex particles

Abstract

In this paper, we describe the way to set up the floppy-box Monte Carlo (FBMC) method [L. Filion, M. Marechal, B. van Oorschot, D. Pelt, F. Smallenburg, and M. Dijkstra, Phys. Rev. Lett. 103, 188302 (2009)] to predict crystal-structure candidates for colloidal particles. The algorithm is explained in detail to ensure that it can be straightforwardly implemented on the basis of this text. The handling of hard-particle interactions in the FBMC algorithm is given special attention, as (soft) short-range and semi-long-range interactions can be treated in an analogous way. We also discuss two types of algorithms for checking for overlaps between polyhedra, the method of separating axes and a triangular-tessellation based technique. These can be combined with the FBMC method to enable crystal-structure prediction for systems composed of highly shape-anisotropic particles. Moreover, we present the results for the dense crystal structures predicted using the FBMC method for 159 (non)convex faceted particles, on which the findings in [J. de Graaf, R. van Roij, and M. Dijkstra, Phys. Rev. Lett. 107, 155501 (2011)] were based. Finally, we comment on the process of crystalstructure prediction itself and the choices that can be made in these simulations.

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

“…The simulations by which the close-packed structures were derived, are based on the floppy-box Monte Carlo (FBMC) method [1,2] in combination with the separating-axis-based overlap algorithm [3]. We obtained * Electronic address: A.P.Gantapara@uu.nl † Electronic address: M.Dijkstra1@uu.nl the densest crystal structure and the corresponding packing fraction φ as a function of the level of particle truncation s by considering 1,000 equidistant points in s ∈ [0, 1].…”

“…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].…”

“…1(a) and the Supplemental Material [38] for the definition of the truncated cube and additional details. Two Platonic (cube and octahedron) and three Archimedean (truncated cube, cuboctahedron, and truncated octahedron) solids are members of this family.Using the floppy-box Monte Carlo method [39][40][41][42] in combination with a separating-axis-based overlap algorithm [43], we first numerically determined the densest structure and the corresponding packing fraction; see Fig. 1(b).…”

“…Using the floppy-box Monte Carlo method [39][40][41][42] in combination with a separating-axis-based overlap algorithm [43], we first numerically determined the densest structure and the corresponding packing fraction; see Fig. 1(b).…”

Phase diagram of octapod-shaped nanocrystals in a quasi-two-dimensional planar geometry

“…These particles were constrained to move in a planar quasi-2D geometry, namely that of the monolayers on a substrate observed in the experimental system. 8 Using floppy-box Monte Carlo (FBMC) simulations, 16,44,45 we constructed the highpressure crystal structures for these octapods as a function of the pod length-to-diameter ratio L/D, with L the length and D the diameter. Subsequent isothermal-isobaric (NPT) and isothermal-isochoric (NV T .…”