Precursor-mediated crystallization process in suspensions of hard spheres

Role of Salt, Pressure, and Water Activity on Homogeneous Ice Nucleation

Pure water can be substantially supercooled below the melting temperature without transforming into ice. The achievable supercooling can be enhanced by adding solutes or by applying hydrostatic pressure. Avoiding ice formation is of great importance in the cryopreservation of food or biological samples. In this Letter, we investigate the similarity between the effects of pressure and salt on ice formation using a combination of state-of-the-art simulation techniques. We find that both hinder ice formation by increasing the energetic cost of creating the ice-fluid interface. Moreover, we examine the widely accepted proposal that the ice nucleation rate for different pressures and solute concentrations can be mapped through the activity of water [ Koop , L. ; Tsias , P. Nature , 2000 , 406 , 611 ]. We show that such a proposal is not consistent with the nucleation rates predicted in our simulations because it does not include all parameters affecting ice nucleation. Therefore, even though salt and pressure have a qualitatively similar effect on ice formation, they cannot be quantitatively mapped onto one another.

Dislocation-free growth of quasicrystals from two seeds due to additional phasonic degrees of freedom

We explore the growth of two-dimensional quasicrystals, i.e., aperiodic structures that possess long-range order, from two seeds at various distances and with different orientations by using dynamical phase-field crystal calculations. We compare the results to the growth of periodic crystals from two seeds. There, a domain border consisting of dislocations is observed in case of large distances between the seed and large angles between their orientation. Furthermore, a domain border is found if the seeds are placed at a distance that does not fit to the periodic lattice. In the case of the growth of quasicrystals, we only observe domain borders for large distances and different orientations. Note that all distances do inherently not match to a perfect domain wall-free quasicrystalline structure. Nevertheless, we find dislocation-free growth for all seeds at a small enough distance and for all seeds that approximately have the same orientation. In periodic structures, the stress that occurs due to incommensurate distances between the seeds results in phononic strain fields or, in the case of too large stresses, in dislocations. In contrast, in quasicrystals an additional phasonic strain field can occur and suppress dislocations. Phasons are additional degrees of freedom that are unique to quasicrystals. As a consequence, the additional phasonic strain field helps to distribute the stress and facilitates the growth of dislocation-free quasicrystals from multiple seeds. In contrast, in the periodic case the growth from multiple seeds most likely leads to a structure with multiple domains. Our work lays the theoretical foundations for growing perfect quasicrystals from different seeds and is therefore relevant for many applications.

Assembly of hard spheres in a cylinder: a computational and experimental study

Hard spheres are an important benchmark of our understanding of natural and synthetic systems. In this work, colloidal experiments and Monte Carlo simulations examine the equilibrium and out-of-equilibrium assembly of hard spheres of diameter σ within cylinders of diameter σ≤D≤ 2.82σ. Although phase transitions formally do not exist in such systems, marked structural crossovers can nonetheless be observed. Over this range of D, we find in simulations that structural crossovers echo the structural changes in the sequence of densest packings. We also observe that the out-of-equilibrium self-assembly depends on the compression rate. Slow compression approximates equilibrium results, while fast compression can skip intermediate structures. Crossovers for which no continuous line-slip exists are found to be dynamically unfavorable, which is the main source of this difference. Results from colloidal sedimentation experiments at low diffusion rate are found to be consistent with the results of fast compressions, as long as appropriate boundary conditions are used.

Hydrodynamic theory of freezing: Nucleation and polycrystalline growth

Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Tóth et al., J. Phys.: Condens. Matter 26, 055001 (2014)JCOMEL0953-898410.1088/0953-8984/26/5/055001], which is based on combining fluctuating hydrodynamics with the phase-field crystal theory. We show that in this hydrodynamic approach not only homogeneous and heterogeneous nucleation processes are accessible, but also growth front nucleation, which leads to the formation of new (differently oriented) grains at the solid-liquid front in highly undercooled systems. Formation of dislocations at the solid-liquid interface and interference of density waves ahead of the crystallization front are responsible for the appearance of the new orientations at the growth front that lead to spherulite-like nanostructures.

The role of fivefold symmetry in suppressing crystallization

Although long assumed to have an important role in the suppression of crystallization and the development of glassformers, the effect of local fivefold symmetry has never been directly tested. Here we consider whether such suppression of crystallization has a kinetic or thermodynamic nature and investigate its mechanism. We introduce a model in which the degree of fivefold symmetry can be tuned by favouring arrangements of particles in pentagonal bipyramids. We thus show that fivefold symmetry has both kinetic and thermodynamic effects on the mechanism of crystallization to a face-centred cubic crystal. Our results suggest that the mechanism of crystallization suppression is related to the surface tension between fluid and crystal. Interestingly, the degree of fivefold symmetry has little effect on crystal growth rate, suggesting that growth may be only weakly coupled to fluid structure in hard sphere like systems. Upon increasing the fivefold symmetry, we find a first-order transition to an alternative icosahedra-rich phase. At intermediate bias strengths we find a one-component glassformer.

The suppression of crystallization due to the appearance of structures with fivefold symmetry is widely adopted, but its kinetic and thermodynamic origin remains elusive. Taffs et al. show that fivefold symmetry substantially slows down the nucleation rate but not the crystal growth rate as expected.

Polymorph selection and nucleation pathway in the crystallization of Hertzian spheres

The crystallization process of Hertzian spheres is studied by means of molecular dynamics simulations in an NPT ensemble where the total number of particles N, the pressure P, and the temperature T are kept constant. It has been observed that the bond orientational ordering rather than the translational ordering (density) plays a primary role. The crystal polymorphs are determined by the state points. Under the conditions of small supercooling, the system is likely to be nucleated into crystals that have a preference for the metastable bcc structure, which can be regarded as a manifestation of the Alexander-McTague mechanism. In contrast, small nuclei are found to have a preference for fcc symmetry under conditions of a high degree of supercooling. Prestructured precursors that act as seeds and wet on the nuclei during nucleation always have a high degree of bcc-like ordering, despite different state points. The results above may provide a clue to the understanding of the crystallization process in core-softened particles.

Two-step crystal growth mechanism during crystallization of an undercooled Ni50Al50 alloy

Crystallization processes are always accompanied by the emergence of multiple intermediate states, of which the structures and transition dynamics are far from clarity, since it is difficult to experimentally observe the microscopic pathway. To insight the structural evolution and the crystallization dynamics, we perform large-scale molecular dynamics simulations to investigate the time-dependent crystallization behavior of the NiAl intermetallic upon rapid solidification. The simulation results reveal that the crystallization process occurs via a two-step growth mechanism, involving the formation of initial non-equilibrium long range order (NLRO) regions and of the subsequent equilibrium long range order (ELRO) regions. The formation of the NLRO regions makes the grains rather inhomogeneous, while the rearrangement of the NLRO regions into the ELRO regions makes the grains more ordered and compact. This two-step growth mechanism is actually controlled by the evolution of the coordination polyhedra, which are characterized predominantly by the transformation from five-fold symmetry to four-fold and six-fold symmetry. From liquids to NLRO and further to ELRO, the five-fold symmetry of these polyhedra gradually fades, and finally vanishes when B2 structure is distributed throughout the grain bulk. The energy decrease along the pathway further implies the reliability of the proposed crystallization processes.

Pathways to self-organization: Crystallization via nucleation and growth

Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In the initial stages of the transformation, a localized nucleus of the new phase forms in the old one due to a random fluctuation. Most of these nuclei disappear after a short time, but rarely a crystalline embryo may reach a critical size after which further growth becomes thermodynamically favorable and the entire system is converted into the new phase. In this article, we will discuss several theoretical concepts and computational methods to study crystallization. More specifically, we will address the rare event problem arising in the simulation of nucleation processes and explain how to calculate nucleation rates accurately. Particular attention is directed towards discussing statistical tools to analyze crystallization trajectories and identify the transition mechanism.

Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations

The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

Seeding approach to crystal nucleation

We present a study of homogeneous crystal nucleation from metastable fluids via the seeding technique for four different systems: mW water, Tosi-Fumi NaCl, Lennard-Jones, and Hard Spheres. Combining simulations of spherical crystal seeds embedded in the metastable fluid with classical nucleation theory, we are able to successfully describe the nucleation rate for all systems in a wide range of metastability. The crystal-fluid interfacial free energy extrapolated to coexistence conditions is also in good agreement with direct calculations of such parameter. Our results show that seeding is a powerful technique to investigate crystal nucleation.

The relationship between local density and bond-orientational order during crystallization of the Gaussian core model

Whether nucleation is triggered by density or by bond-orientational order is one of the most hotly debated issues in recent investigations of the crystallization process. Here, we present a numerical study of the relationship between them for soft particles within the isothermal-isobaric ensemble. We compress the system and thus obtain the fluid-solid transition. By investigating locally dense-packed particles and particles with a relatively high bond-orientational order in the compressing process, we find a sharp increase of the spatial correlations for both densely packed particles and highly bond-orientational ordered particles at the phase transition point, which provide new characterization methods for the liquid-crystal transition. We also find that it is the bond-orientational order rather than density that triggers the nucleation process. The relationship between the local density and the bond-orientational order parameter is strongly affected by the characterization methods used. The local bond order parameter (q6) shows clear correlation with the local density (ρ) in the fluid stage, while the coarse-grained form (q[combining macron]6) does not correlate with ρ at all, owing to the comparable spatial scales of q6 and ρ. Nevertheless, q[combining macron]6 shows an obvious advantage in distinguishing between solid and liquid particles in our work. These results may elevate our understanding of the mechanism of the crystallization process.

Equilibrium fluid-crystal interfacial free energy of bcc-crystallizing aqueous suspensions of polydisperse charged spheres

The interfacial free energy is a central quantity in crystallization from the metastable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from these data effective nonequilibrium values for the interfacial free energy between the emerging bcc nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory (CNT). A strictly linear increase of the interfacial free energy was observed as a function of increased metastability. Here, we further analyze these data for five aqueous suspensions of charged spheres and one binary mixture. We utilize a simple extrapolation scheme and interpret our findings in view of Turnbull's empirical rule. This enables us to present the first systematic experimental estimates for a reduced interfacial free energy, σ(0,bcc), between the bcc-crystal phase and the coexisting equilibrium fluid. Values obtained for σ(0,bcc) are on the order of a few k(B)T. Their values are not correlated to any of the electrostatic interaction parameters but rather show a systematic decrease with increasing size polydispersity and a lower value for the mixture as compared to the pure components. At the same time, σ(0) also shows an approximately linear correlation to the entropy of freezing. The equilibrium interfacial free energy of strictly monodisperse charged spheres may therefore be still greater.

Challenges in modelling nanoparticles for drug delivery

Although there have been significant advances in the fields of theoretical condensed matter and computational physics, when confronted with the complexity and diversity of nanoparticles available in conventional laboratories a number of modeling challenges remain. These challenges are generally shared among application domains, but the impacts of the limitations and approximations we make to overcome them (or circumvent them) can be more significant one area than another. In the case of nanoparticles for drug delivery applications some immediate challenges include the incompatibility of length-scales, our ability to model weak interactions and solvation, the complexity of the thermochemical environment surrounding the nanoparticles, and the role of polydispersivity in determining properties and performance. Some of these challenges can be met with existing technologies, others with emerging technologies including the data-driven sciences; some others require new methods to be developed. In this article we will briefly review some simple methods and techniques that can be applied to these (and other) challenges, and demonstrate some results using nanodiamond-based drug delivery platforms as an exemplar.

Atomic-Level Mechanisms of Nucleation of Pure Liquid Metals during Rapid Cooling

To obtain a material with the desired performance, the atomic-level mechanisms of nucleation from the liquid to solid phase must be understood. Although this transition has been investigated experimentally and theoretically, its atomic-level mechanisms remain debatable. In this work, the nucleation mechanisms of pure Fe under rapid cooling conditions are investigated. The local atomic packing stability and liquid-to-solid transition-energy pathways of Fe are studied using molecular dynamics simulations and first-principle calculations. The results are expressed as functions of cluster size in units of amorphous clusters (ACs) and body-centered cubic crystalline clusters (BCC-CCs). We found the prototypes of ACs in supercooled liquids and successfully divided these ACs to three categories according to their transition-energy pathways. The information obtained in this study could contribute to our current understanding of the crystallization of metallic melts during rapid cooling.

The role of shear in crystallization kinetics: From suppression to enhancement

In many technical applications crystallization proceeds in the presence of stresses and flows, hence the importance to understand the crystallization mechanism in simple situations. We employ molecular dynamics simulations to study the crystallization kinetics of a nearly hard sphere liquid that is weakly sheared. We demonstrate that shear flow both enhances and suppresses the crystallization kinetics of hard spheres. The effect of shear depends on the quiescent mechanism: suppression in the activated regime and enhancement in the diffusion-limited regime for small strain rates. At higher strain rates crystallization again becomes an activated process even at densities close to the glass transition.

Dynamic decoupling and local atomic order of a model multicomponent metallic glass-former

The dynamics of multicomponent metallic alloys is spatially heterogeneous near glass transition. The diffusion coefficient of one component of the metallic alloys may also decouple from those of other components, i.e., the diffusion coefficient of each component depends differently on the viscosity of metallic alloys. In this work we investigate the dynamic heterogeneity and decoupling of a model system for multicomponent Pd43Cu27Ni10P20 melts by using a hard sphere model that considers the size disparity of alloys but does not take chemical effects into account. We also study how such dynamic behaviors would relate to the local atomic structure of metallic alloys. We find, from molecular dynamics simulations, that the smallest component P of multicomponent Pd43Cu27Ni10P20 melts becomes dynamically heterogeneous at a translational relaxation time scale and that the largest major component Pd forms a slow subsystem, which has been considered mainly responsible for the stabilization of amorphous state of alloys. The heterogeneous dynamics of P atoms accounts for the breakdown of Stokes-Einstein relation and also leads to the dynamic decoupling of P and Pd atoms. The dynamically heterogeneous P atoms decrease the lifetime of the local short-range atomic orders of both icosahedral and close-packed structures by orders of magnitude.

Monte Carlo simulation of kinetically slowed down phase separation

Supercooled colloidal or molecular systems at low densities are known to form liquid, crystalline or glassy drops, which may remain isolated for a long time before they aggregate. This paper analyses the properties of this large time window, and how it can be tackled by computer simulation. We use single-particle and virtual move Monte Carlo simulations of short-range attractive spheres which are undercooled to the temperature region, where the spinodal intersects the attractive glass line. We study two different systems and we report the following kinetic behavior. A low-density system is shown to exhibit universal linear growth regimes under single-particle Monte Carlo correlating the growth rate to the local structure. These regimes are suppressed under collective motion, where droplets aggregate into a single large disordered domain. It is shown that the aggregation can be avoided and linear regimes recovered, if long-range repulsion is added to the short-range attraction. The results provide an insight into the behavior of the virtual move algorithm generating cluster moves according to the local forcefields. We show that different choices of maximum Monte Carlo displacement affect the dynamical trajectories but lead to the same kinetically slowed down or arrested states.

Crystallization seeds favour crystallization only during initial growth

Crystallization represents the prime example of a disorder-order transition. In realistic situations, however, container walls and impurities are frequently present and hence crystallization is heterogeneously seeded. Rarely the seeds are perfectly compatible with the thermodynamically favoured crystal structure and thus induce elastic distortions, which impede further crystal growth. Here we use a colloidal model system, which not only allows us to quantitatively control the induced distortions but also to visualize and follow heterogeneous crystallization with single-particle resolution. We determine the sequence of intermediate structures by confocal microscopy and computer simulations, and develop a theoretical model that describes our findings. The crystallite first grows on the seed but then, on reaching a critical size, detaches from the seed. The detached and relaxed crystallite continues to grow, except close to the seed, which now prevents crystallization. Hence, crystallization seeds facilitate crystallization only during initial growth and then act as impurities.

On the question of two-step nucleation in protein crystallization

We report a real-time study on protein crystallization in the presence of multivalent salts using small angle X-ray scattering (SAXS) and optical microscopy, focusing particularly on the nucleation mechanism as well as on the role of the metastable intermediate phase (MIP). Using bovine beta-lactoglobulin as a model system in the presence of the divalent salt CdCl2, we have monitored the early stage of crystallization kinetics which demonstrates a two-step nucleation mechanism: protein aggregates form a MIP, which is followed by the nucleation of crystals within the MIP. Here we focus on characterizing and tuning the structure of the MIP using salt and the related effects on the two-step nucleation kinetics. The results suggest that increasing the salt concentration near the transition zone pseudo-c** enhances the energy barrier for both MIPs and crystal nucleation, leading to slow growth. The structural evolution of the MIP and its effect on subsequent nucleation is discussed based on the growth kinetics. The observed kinetics can be well described, using a rate-equation model based on a clear physical two-step picture. This real-time study not only provides evidence for a two-step nucleation process for protein crystallization, but also elucidates the role and the structural signature of the MIPs in the nonclassical process of protein crystallization.

Two-stage crystallization of charged colloids under low supersaturation conditions

We report simulations on the homogeneous liquid-fcc nucleation of charged colloids for both low and high contact energy values. As a precursor for crystal formation, we observe increased local order at the position where the crystal will form, but no correlations with the local density. Thus, the nucleation is driven by order fluctuations rather than density fluctuations. Our results also show that the transition involves two stages in both cases, first a transition of liquid → bcc, followed by a bcc → hcp/fcc transition. Both transitions have to overcome free energy barriers, so that a spherical bcc-like cluster is formed first, in which the final fcc structure is nucleated mainly at the surface of the crystallite. This means that the second stage bcc-fcc phase transition is a heterogeneous nucleation in the partially grown solid phase, even though we start from a homogeneous bulk liquid. The height of the bcc → hcp/fcc free energy barrier strongly depends on the contact energies of the colloids. For low contact energy this barrier is low, so that the bcc → hcp/fcc transition occurs spontaneously. For the higher contact energy, the second barrier is too high to be crossed spontaneously by the colloidal system. However, it was possible to ratchet the system over the second barrier and to transform the bcc nuclei into the stable hcp/fcc phase. The transitions are dominated by the first liquid-bcc transition and can be described by classical nucleation theory using an effective surface tension.

Crystal-liquid interfacial free energy of hard spheres via a thermodynamic integration scheme

The hard-sphere crystal-liquid interfacial free energy γcl is determined from molecular dynamics simulations using a thermodynamic integration (TI) scheme. The advantage of this TI scheme compared to previous methods is to successfully circumvent hysteresis effects due to the movement of the crystal-liquid interface. This is accomplished by the use of extremely-short-range and impenetrable Gaussian flat walls that prevent the drift of the interface while imposing a negligible free-energy penalty. We find that it is crucial to analyze finite-size effects in order to obtain reliable estimates of γcl in the thermodynamic limit.

Asymmetric crystallization during cooling and heating in model glass-forming systems

We perform molecular dynamics (MD) simulations of the crystallization process in binary Lennard-Jones systems during heating and cooling to investigate atomic-scale crystallization kinetics in glass-forming materials. For the cooling protocol, we prepared equilibrated liquids above the liquidus temperature Tl and cooled each sample to zero temperature at rate Rc. For the heating protocol, we first cooled equilibrated liquids to zero temperature at rate Rp and then heated the samples to temperature T>Tl at rate Rh. We measured the critical heating and cooling rates Rh* and Rc*, below which the systems begin to form a substantial fraction of crystalline clusters during the heating and cooling protocols. We show that Rh*>Rc* and that the asymmetry ratio Rh*/Rc* includes an intrinsic contribution that increases with the glass-forming ability (GFA) of the system and a preparation-rate dependent contribution that increases strongly as Rp→Rc* from above. We also show that the predictions from classical nucleation theory (CNT) can qualitatively describe the dependence of the asymmetry ratio on the GFA and preparation rate Rp from the MD simulations and results for the asymmetry ratio measured in Zr- and Au-based bulk metallic glasses (BMG). This work emphasizes the need for and benefits of an improved understanding of crystallization processes in BMGs and other glass-forming systems.

Ligand-induced fate of embryonic species in the shape-controlled synthesis of rhodium nanoparticles

The shapes of noble metal nanoparticles directly impact their properties and applications, including in catalysis and plasmonics, and it is therefore important to understand how multiple distinct morphologies can be controllably synthesized. Solution routes offer powerful capabilities for shape-controlled nanoparticle synthesis, but the earliest stages of the reaction are difficult to interrogate experimentally and much remains unknown about how metal nanoparticle morphologies emerge and evolve. Here, we use a well-established polyol process to synthesize uniform rhodium nanoparticle cubes, icosahedra, and triangular plates using bromide, trifluoroacetate, and chloride ligands, respectively. In all of these systems, we identified rhodium clusters with diameters of 1-2 nm that form early in the reactions. The colloidally stable metal cluster intermediates served as a stock solution of embryonic species that could be transformed predictably into each type of nanoparticle morphology. The anionic ligands that were added to the embryonic species determined their eventual fate, e.g., the morphologies into which they would ultimately evolve. Extensive high-resolution transmission electron microscopy experiments revealed that the growth pathway-monomer addition, coalescence, or a combination of the two-was different for each of the morphologies, and was likely controlled by the interactions of each specific anionic adsorbate with the embryonic species. Similar phenomena were observed for related palladium and platinum nanoparticle systems. These studies provide important insights into how noble metal nanoparticles nucleate, the pathways by which they grow into several distinct morphologies, and the imperative role of the anonic ligand in controlling which route predominates in a particular system.

Real-time observation of nonclassical protein crystallization kinetics

We present a real-time study of protein crystallization of bovine β-lactoglobulin in the presence of CdCl(2) using small-angle X-ray scattering and optical microscopy. From observing the crystallization kinetics, we propose the following multistep crystallization mechanism that is consistent with our data. In the first step, an intermediate phase is formed, followed by the nucleation of crystals within the intermediate phase. During this period, the number of crystals increases with time, but the crystal growth is slowed down by the surrounding dense intermediate phase due to the low mobility. In the next step, the intermediate phase is consumed by nucleation and slow growth, and the crystals are exposed to the dilute phase. In this stage, the number of crystals becomes nearly constant, whereas the crystals grow rapidly due to access to the free protein molecules in the dilute phase. This real-time study not only provides evidence for a two-step nucleation process for protein crystallization but also elucidates the role and the structural signature of the metastable intermediate phase in this process.

The atomic-scale nucleation mechanism of NiTi metallic glasses upon isothermal annealing studied via molecular dynamics simulations

The nucleation of devitrified metallic glasses is induced either by the inherited ordered atoms or by the nucleus precursor evolved directly from the liquid.

Exposing a dynamical signature of the freezing transition through the sound propagation gap

The conventional view of freezing holds that nuclei of the crystal phase form in the metastable fluid through purely stochastic thermal density fluctuations. The possibility of a change in the character of the fluctuations as the freezing point is traversed is beyond the scope of this perspective. Here we show that this perspective may be incomplete by examination of the time autocorrelation function of the longitudinal current, computed by molecular dynamics for the hard-sphere fluid around its freezing point. In the spatial window where sound is overdamped, we identify a change in the long-time decay of the correlation function at the known freezing points of monodisperse and moderately polydisperse systems. The fact that these findings agree with previous experimental studies of colloidal systems in which particle are subject to diffusive dynamics, suggests that the dynamical signature we identify with the freezing transition is a consequence of packing effects alone.

Computer simulation of epitaxial nucleation of a crystal on a crystalline surface

We present results of computer simulations of crystal nucleation on a crystalline surface, in the Lennard-Jones model. Motivated by the pioneering work of Turnbull and Vonnegut [Ind. Eng. Chem. 44, 1292 (1952)], we investigate the effects of a mismatch between the surface lattice constant and that of the bulk nucleating crystal. We find that the nucleation rate is maximum close to, but not exactly at, zero mismatch. The offset is due to the finite size of the nucleus. In agreement with a number of experiments, we find that even for large mismatches of 10% or more, the formation of the crystal can be epitaxial, meaning that the crystals that nucleate have a fixed orientation with respect to the surface lattice. However, nucleation is not always epitaxial, and loss of epitaxy does affect how the rate varies with mismatch. The surface lattice strongly influences the nucleation rate. We show that the epitaxy observed in our simulations can be predicted using calculations of the potential energy between the surface and the first layer of the nucleating crystal, in the spirit of simple approaches such as that of Hillier and Ward [Phys. Rev. B 54, 14037 (1996)].

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.

Solidification of a colloidal hard sphere like model system approaching and crossing the glass transition

We investigated the process of vitrification and crystallization in a model system of colloidal hard spheres. The kinetics of the solidification process was measured using time resolved static light scattering, while the time evolution of the dynamic properties was determined using time resolved dynamic light scattering. By performing further analysis we confirm that solidification of hard sphere colloids is mediated by precursors. Analyzing the dynamic properties we can show that the long time dynamics and thus the shear rigidity of the metastable melt is highly correlated with the number density of solid clusters (precursors) nucleated. In crystallization these objects convert into highly ordered crystals whereas in the case of vitrification this conversion is blocked and the system is (temporarily) locked in the metastable precursor state. From the early stages of solidification one cannot clearly conclude whether the melt will crystallize or vitrify. Furthermore our data suggests that colloidal hard sphere glasses can crystallize via homogeneous nucleation.

Nested sampling for materials: the case of hard spheres

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three-dimensional hard-sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered.

Kinetically driven ordered phase formation in binary colloidal crystals

The aggregation of binary colloids of the same size and balanced charges is studied by Brownian dynamics simulations for dilute suspensions. It is shown that, under appropriate conditions, the formation of colloidal crystals is dominated by kinetic effects leading to the growth of well-ordered crystallites of the sodium-chloride (NaCl) bulk phase. These crystallites form with very high probability even when the cesium-chloride (CsCl) phase is more stable thermodynamically. Global optimization searches show that this result is not related to the most favorable structures of small clusters, which are either amorphous or of the CsCl structure. The formation of the NaCl phase is related to the specific kinetics of the crystallization process, which takes place by a two-step mechanism. In this mechanism, dense fluid aggregates form at first and then crystallization follows. It is shown that the type of short-range order in these dense fluid aggregates determines which phase is finally formed in the crystallites. The role of hydrodynamic effects in the aggregation process is analyzed by stochastic rotation dynamics - molecular dynamics simulations, and we find that these effects do not play a major role in the formation of the crystallites.