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.