Icosahedral symmetry, which is not compatible with truly long-range order, can be found in many systems, such as liquids, glasses, atomic clusters, quasicrystals and virus-capsids. To obtain arrangements with a high degree of icosahedral order from tens of particles or more, interparticle attractive interactions are considered to be essential. Here, we report that entropy and spherical confinement suffice for the formation of icosahedral clusters consisting of up to 100,000 particles. Specifically, by using real-space measurements on nanometre- and micrometre-sized colloids, as well as computer simulations, we show that tens of thousands of hard spheres compressed under spherical confinement spontaneously crystallize into icosahedral clusters that are entropically favoured over the bulk face-centred cubic crystal structure. Our findings provide insights into the interplay between confinement and crystallization and into how these are connected to the formation of icosahedral structures.

Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schätzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.

One of the main reasons for the current interest in colloidal nanocrystals is their propensity to form superlattices, systems in which (different) nanocrystals are in close contact in a well-ordered three-dimensional (3D) geometry resulting in novel material properties. However, the principles underlying the formation of binary nanocrystal superlattices are not well understood. Here, we present a study of the driving forces for the formation of binary nanocrystal superlattices by comparing the formed structures with full free energy calculations. The nature (metallic or semiconducting) and the size-ratio of the two nanocrystals are varied systematically. With semiconductor nanocrystals, self-organization at high temperature leads to superlattices (AlB 2 , NaZn 13 , MgZn 2 ) in accordance with the phase diagrams for binary hard-sphere mixtures; hence entropy increase is the dominant driving force. A slight change of the conditions results in structures that are energetically stabilized. This study provides rules for the rational design of 3D nanostructured binary semiconductors, materials with promises in thermoelectrics and photovoltaics and which cannot be reached by any other technology.KEYWORDS Nanocrystals, self-assembly, superlattices, hard spheres, thermodynamics. C olloidal, monolayer-stabilized nanocrystals (NC) can be synthesized with a nearly spherical shape and with a well-defined diameter that does not vary by more than 5% in the sample. Because of their monodisperse size and shape, such NCs show a strong propensity to assemble into NC superlattices.1 More than a decade ago, the formation of single-component superlattices that consist of CdSe semiconductor NCs was reported.1 This was followed by the demonstration of binary superlattices, consisting of NCs of different diameters and different nature, that is, semiconductor, metallic, or magnetic. [1][2][3][4][5][6][7][8][9][10][11][12][13] In such systems, novel collective properties can arise from the (quantum mechanical) interactions between the different components that are in close contact in a three-dimensional (3D) ordered geometry. Some striking examples have already been reported. 3,4,14,15 For instance, a binary superlattice of two types of insulator nanoparticles is found to become conductive due to interparticle charge transfer.3 Colloidal crystallization is the only method known to date to obtain nanostructured systems with order in three dimensions. However, for further progress in the field of designed nanostructured materials, improved control of nanocolloid crystallization is a key factor.Apart from the viewpoint of emerging nanomaterials, the formation of (binary) NC superlattices is of strong interest in colloidal science. Nanocrystals have a mass that is about a million times smaller than that of the colloidal particles commonly used in crystallization studies; hence, their thermal velocity is about a factor of thousand higher. This agrees with the fact that nanocolloid crystallization is a relatively fast process, still oc...

We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and AlB2, we predict additional crystal structures with the symmetry of CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se, and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach.

One of the most controversial hypotheses for explaining the origin of the thermodynamic anomalies characterizing liquid water postulates the presence of a metastable second-order liquid-liquid critical point [1] located in the “no-man’s land” [2]. In this scenario, two liquids with distinct local structure emerge near the critical temperature. Unfortunately, since spontaneous crystallization is rapid in this region, experimental support for this hypothesis relies on significant extrapolations, either from the metastable liquid or from amorphous solid water [3, 4]. Although the liquid-liquid transition is expected to feature in many tetrahedrally coordinated liquids, including silicon [5], carbon [6] and silica, even numerical studies of atomic and molecular models have been unable to conclusively prove the existence of this transition. Here we provide such evidence for a model in which it is possible to continuously tune the softness of the interparticle interaction and the flexibility of the bonds, the key ingredients controlling the existence of the critical point. We show that conditions exist where the full coexistence is thermodynamically stable with respect to crystallization. Our work offers a basis for designing colloidal analogues of water exhibiting liquid-liquid transitions in equilibrium, opening the way for experimental confirmation of the original hypothesis.

In this paper we examine the phase behavior of the Weeks-Chandler-Andersen (WCA) potential with βε = 40. Crystal nucleation in this model system was recently studied by Kawasaki and Tanaka [Proc. Natl. Acad. Sci. U.S.A. 107, 14036 (2010)], who argued that the computed nucleation rates agree well with experiment, a finding that contradicted earlier simulation results. Here we report an extensive numerical study of crystallization in the WCA model, using three totally different techniques (Brownian dynamics, umbrella sampling, and forward flux sampling). We find that all simulations yield essentially the same nucleation rates. However, these rates differ significantly from the values reported by Kawasaki and Tanaka and hence we argue that the huge discrepancy in nucleation rates between simulation and experiment persists. When we map the WCA model onto a hard-sphere system, we find good agreement between the present simulation results and those that had been obtained for hard spheres [L. Filion, M. Hermes, R. Ni, and M. Dijkstra, J. Chem. Phys. 133, 244115 (2010); S. Auer and D. Frenkel, Nature 409, 1020 (2001)].

We examine the effect of vacancies on the phase behavior and structure of systems consisting of hard cubes using event-driven molecular dynamics and Monte Carlo simulations. We find a firstorder phase transition between a fluid and a simple cubic crystal phase that is stabilized by a surprisingly large number of vacancies, reaching a net vacancy concentration of approximately 6.4% near bulk coexistence. Remarkably, we find that vacancies increase the positional order in the system. Finally, we show that the vacancies are delocalized and therefore hard to detect.hard polyhedra | colloids | free energy T he free energy of crystal phases is generally minimized by a finite fraction of point defects like vacancies and interstitials. However, the equilibrium number of such defects in most colloidal and atomic/molecular crystals with a single constituent is extremely low. Exemplarily, for the face-centered cubic crystal of hard spheres, one of the few colloidal systems where the vacancy and interstitial fractions have been calculated, the fraction of vacancies and interstitials is on the order of 10 −4 and 10 −8 , respectively, near coexistence (1). As such, neither the vacancies nor the interstitials strongly affect the phase behavior, and so most studies of crystals ignore the effect of these defects. Nevertheless, vacancies and interstitials have a significant effect on the dynamics in an otherwise perfect crystal, as the main mechanism for particle diffusion is hopping of particles from filled to empty sites or between interstitial sites.In this paper, we examine a system of hard cubes where, as we will demonstrate, one cannot ignore the presence of vacancies. Arguably, a cube is one of the simplest nonspherical shapes and the archetype of a space-filling polyhedron. Surprisingly, despite the simplicity of this system, we find that the stable ordered phase is strongly affected by the presence of vacancies, so much that vacancies actually increase the positional order and change the melting point. Remarkably, the fraction of vacancies in this system is more than two orders of magnitude higher than that of hard spheres or any other known typical, experimentally realizable, single-component atomic or colloidal system, reaching 6.4% near coexistence. Additionally, while purely hard (not rounded) colloidal cubes are yet to be realized, colloidal cubes with various interactions are now a reality (2-7), and it is likely that hard cubes will be realized in the future.Here, we use Monte Carlo (MC) and event-driven molecular dynamics (EDMD) (8) simulations to examine in detail the effect of vacancies on the equilibrium phase behavior of hard cubes. The model we study consists of N perfectly sharp hard cubes with edge length σ in a volume V . Aside from hard-core interactions that prevent configurations of overlapping cubes, the particles do not interact. In both types of simulation (MC and EDMD), overlaps are detected using an algorithm based on the separating axis theorem (e.g., ref. 9). More information on the EDMD impleme...

We study by computer simulations the stability of various crystal structures in a binary mixture of large and small spheres interacting either with a hard sphere or a screened-Coulomb potential. In the case of hard-core systems, we consider structures that have atomic prototypes CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se and the Laves phases (MgCu2, MgNi2, and MgZn2) as well as a structure with space group symmetry 74. By utilizing Monte Carlo simulations to calculate Gibbs free energies, we determine composition versus pressure and constant volume phase diagrams for diameter ratios of q=0.74, 0.76, 0.8, 0.82, 0.84, and 0.85 for the small and large spheres. For diameter ratios 0.76 < or = q < or = 0.84, we find the Laves phases to be stable with respect to the other crystal structures that we considered and the fluid mixture. By extrapolating to the thermodynamic limit, we show that the MgZn2 structure is the most stable one of the Laves structures. We also calculate phase diagrams for equally and oppositely charged spheres for size ratio of 0.73 taking into consideration the Laves phases and CsCl. In the case of equally charged spheres, we find a pocket of stable Laves phases, while in the case of oppositely charged spheres, Laves phases are found to be metastable with respect to the CsCl and fluid phases.