Crystal phases of a glass-forming Lennard-Jones mixture

The Kob-Andersen model crystal structure: Genetic algorithms vs spontaneous crystallization

The crystal structure of the Kob-Andersen mixture has been probed by genetic algorithm calculations. The stable structures of the system with different molar fractions of the components have been identified, and their stability at finite temperatures has been verified. It has been found that the structures of composition ABn, where n = 2, 3, or 4, can be formed in the system. Metastable structures with compositions AB0.4 and AB0.58 have also been identified. Molecular dynamics simulations of spontaneous crystallization from liquid have been performed.

100 Years of the Lennard-Jones Potential

It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.

Critical comparison of general-purpose collective variables for crystal nucleation

The nucleation of crystals is a prominent phenomenon in science and technology that still lacks a full atomic-scale understanding. Much work has been devoted to identifying order parameters able to track the process, from the inception of early nuclei to their maturing to critical size until growth of an extended crystal. We critically assess and compare two powerful distance-based collective variables, an effective entropy derived from liquid state theory and the path variable based on permutation invariant vectors using the Kob-Andersen binary mixture and a combination of enhanced-sampling techniques. Our findings reveal a comparable ability to drive nucleation when a bias potential is applied, and comparable free-energy barriers and structural features. Yet, we also found an imperfect correlation with the committor probability on the barrier top which was bypassed by changing the order parameter definition.

MD simulations of charged binary mixtures reveal a generic relation between high- and low-temperature behavior

Experimental studies of the glassy slowdown in molecular liquids indicate that the high-temperature activation energy E_∞ of glass-forming liquids is directly related to their glass transition temperature T_g. To further investigate such a possible relation between high- and low-temperature dynamics in glass-forming liquids, we analyze the glassy dynamics of binary mixtures using molecular dynamics simulations. We consider a binary mixture of charged Lennard-Jones particles and vary the partial charges of the particles and, thus, the high-temperature activation energy and the glass transition temperature of the system. Based on previous results, we introduce a phenomenological model describing relaxation times over the whole temperature regime from high temperatures to temperatures well inside the supercooled regime. By investigating the dynamics of both particle species on molecular and diffusive length scales along isochoric and isobaric pathways, we find a quadratic charge dependence of both E_∞ and T_g, resulting in an approximately constant ratio of both quantities independent of the underlying observable, the thermodynamic ensemble, and the particle species, and this result is robust against the actual definition of T_g. This generic relation between the activation energy and the glass transition temperature indicates that high-temperature dynamics and the glassy slowdown are related phenomena, and the knowledge of E_∞ may allow us to approximately predict T_g.

Alloy, Janus and core-shell nanoparticles: numerical modeling of their nucleation and growth in physical synthesis

While alloy, core-shell and Janus binary nanoclusters are found in more and more technological applications, their formation mechanisms are still poorly understood, especially during synthesis methods involving physical approaches. In this work, we employ a very simple model of such complex systems using Lennard-Jones interactions and inert gas quenching. After demonstrating the ability of the model to well reproduce the formation of alloy, core-shell or Janus nanoparticles, we studied their temporal evolution from the gas via droplets to nanocrystalline particles. In particular, we showed that the growth mechanisms exhibit qualitative differences between these three chemical orderings. Then, we determined how the quenching rate can be used to finely tune structural characteristics of the final nanoparticles, including size, shape and crystallinity.

Dynamical solid-liquid transition through oscillatory shear

Starting from an ideal crystalline state, we numerically study a nonequilibrium dynamical order-disorder transition promoted by the application of a periodic shearing protocol at low temperatures in model systems in three dimensions. We observe a discontinuous dynamical transition from an ordered to a disordered steady state. Through the analysis of large-scale simulations, we show that the amorphization mechanism around the discontinuous transition is reminiscent of spinodal decomposition.

Assessing the utility of structure in amorphous materials

This paper presents a set of general strategies for the analysis of structure in amorphous materials and a general approach to assessing the utility of any selected structural description. Two measures of structure are defined, "diversity" and "utility," and applied to two model glass forming binary atomic alloys, Cu₅₀Zr₅₀ and a Lennard-Jones A₈₀B₂₀ mixture. We show that the change in diversity associated with selecting Voronoi structures with high localization or low energy, while real, is too weak to support claims that specific structures are the prime cause of these local physical properties. In addition, a new structure-free measure of incipient crystal-like organization in mixtures is introduced, suitable for cases where the stable crystal is a compound structure.

Glass forming phase diagram and local structure of Kob-Andersen binary Lennard-Jones nanoparticles

Molecular dynamics simulation is used to study glass formation in Kob-Andersen binary Lennard-Jones nanoparticles and determine the glass forming phase diagram for the system as a function of composition. The radial distribution function, a Steinhardt bond-orientational order parameter, and favored local structure analysis are used to distinguish between glassy and ordered systems. We find that surface enrichment of the large atoms alters the nanoparticle core composition, leading to an overall shift of the glass forming region to lower small atom mole fractions, relative to the bulk system. At small atom mole fraction, x_B = 0.1, the nanoparticles form a solid with an amorphous core, enriched with the small atoms, surrounded by a partially ordered surface region, enriched with the large atom component. The most disordered glass nanoparticles occur at x_B ≈ 0.3, but the surface-core enrichment leads to the crystallization of the nanoparticle to the CsCl crystal above x_B ≈ 0.35, which is lower than observed in the bulk. The glass transition temperatures of the nanoparticles are also significantly reduced. This allows the liquid to remain dynamic to low temperatures and sample the low energy inherent structure minima on the potential energy surface containing a high abundance of favoured local structures.

Phase Diagram of Kob-Andersen-Type Binary Lennard-Jones Mixtures

The binary Kob-Andersen (KA) Lennard-Jones mixture is the standard model for computational studies of viscous liquids and the glass transition. For very long simulations, the viscous KA system crystallizes, however, by phase separating into a pure A particle phase forming a fcc crystal. We present the thermodynamic phase diagram for KA-type mixtures consisting of up to 50% small (B) particles showing, in particular, that the melting temperature of the standard KA system at liquid density 1.2 is 1.028(3) in A particle Lennard-Jones units. At large B particle concentrations, the system crystallizes into the CsCl crystal structure. The eutectic corresponding to the fcc and CsCl structures is cutoff in a narrow interval of B particle concentrations around 26% at which the bipyramidal orthorhombic PuBr_{3} structure is the thermodynamically stable phase. The melting temperature's variation with B particle concentration at two constant pressures, as well as at the constant density 1.2, is estimated from simulations at pressure 10.19 using isomorph theory. Our data demonstrate approximate identity between the melting temperature and the onset temperature below which viscous dynamics appears. Finally, the nature of the solid-liquid interface is briefly discussed.

Self-Assembly of Mesophases from Nanoparticles

A growing number of crystalline and quasi-crystalline structures have been formed by coating nanoparticles with ligands, polymers, and DNA. The design of nanoparticles that assemble into mesophases, such as those formed by block copolymers, would combine the order, mobility, and stimuli responsive properties of mesophases with the electronic, magnetic, and optical properties of nanoparticles. Here we use molecular simulations to demonstrate that binary mixtures of unbound particles with simple short-ranged pair interactions produce the same mesophases as block copolymers and surfactants, including lamellar, hexagonal, gyroid, body-centered cubic, face-centered cubic, perforated lamellar, and semicrystalline phases. The key to forming the mesophases is the frustrated attraction between particles of different types, achieved through control over interparticle size and over strength and softness of the interaction. Experimental design of nanoparticles with effective interactions described by the potentials of this work would provide a distinct, robust route to produce ordered tunable liquid crystalline mesophases from nanoparticles.

The Perfect Glass Paradigm: Disordered Hyperuniform Glasses Down to Absolute Zero

Rapid cooling of liquids below a certain temperature range can result in a transition to glassy states. The traditional understanding of glasses includes their thermodynamic metastability with respect to crystals. However, here we present specific examples of interactions that eliminate the possibilities of crystalline and quasicrystalline phases, while creating mechanically stable amorphous glasses down to absolute zero temperature. We show that this can be accomplished by introducing a new ideal state of matter called a "perfect glass". A perfect glass represents a soft-interaction analog of the maximally random jammed (MRJ) packings of hard particles. These latter states can be regarded as the epitome of a glass since they are out of equilibrium, maximally disordered, hyperuniform, mechanically rigid with infinite bulk and shear moduli, and can never crystallize due to configuration-space trapping. Our model perfect glass utilizes two-, three-, and four-body soft interactions while simultaneously retaining the salient attributes of the MRJ state. These models constitute a theoretical proof of concept for perfect glasses and broaden our fundamental understanding of glass physics. A novel feature of equilibrium systems of identical particles interacting with the perfect-glass potential at positive temperature is that they have a non-relativistic speed of sound that is infinite.

Composition dependence of the glass forming ability in binary mixtures: The role of demixing entropy

We present a comparative study of the glass forming ability of binary systems with varying composition, where the systems have similar global crystalline structure (CsCl+fcc). Biased Monte Carlo simulations using umbrella sampling technique show that the free energy cost to create a CsCl nucleus increases as the composition of the smaller particles is decreased. We find that systems with comparatively lower free energy cost to form CsCl nucleus exhibit more pronounced pre-crystalline demixing near the liquid/crystal interface. The structural frustration between the CsCl and fcc crystal demands this demixing. We show that closer to the equimolar mixture, the entropic penalty for demixing is lower and a glass forming system may crystallize when seeded with a nucleus. This entropic penalty as a function of composition shows a non-monotonic behaviour with a maximum at a composition similar to the well known Kob-Anderson (KA) model. Although the KA model shows the maximum entropic penalty and thus maximum frustration against CsCl formation, it also shows a strong tendency towards crystallization into fcc lattice of the larger "A" particles which can be explained from the study of the energetics. Thus for systems closer to the equimolar mixture although it is the requirement of demixing which provides their stability against crystallization, for KA model it is not demixing but slow dynamics and the presence of the "B" particles make it a good glass former. The locally favoured structure around "B" particles is quite similar to the CsCl structure and the incompatibility of CsCl and fcc hinders the fcc structure growth in the KA model. Although the glass forming binary systems studied here are quite similar, differing only in composition, we find that their glass forming ability cannot be attributed to a single phenomenon.

Vapor Condensed and Supercooled Glassy Nanoclusters

We use molecular simulation to study the structural and dynamic properties of glassy nanoclusters formed both through the direct condensation of the vapor below the glass transition temperature, without the presence of a substrate, and via the slow supercooling of unsupported liquid nanodroplets. An analysis of local structure using Voronoi polyhedra shows that the energetic stability of the clusters is characterized by a large, increasing fraction of bicapped square antiprism motifs. We also show that nanoclusters with similar inherent structure energies are structurally similar, independent of their history, which suggests the supercooled clusters access the same low energy regions of the potential energy landscape as the vapor condensed clusters despite their different methods of formation. By measuring the intermediate scattering function at different radii from the cluster center, we find that the relaxation dynamics of the clusters are inhomogeneous, with the core becoming glassy above the glass transition temperature while the surface remains mobile at low temperatures. This helps the clusters sample the highly stable, low energy structures on the potential energy surface. Our work suggests the nanocluster systems are structurally more stable than the ultrastable glassy thin films, formed through vapor deposition onto a cold substrate, but the nanoclusters do not exhibit the superheating effects characteristic of the ultrastable glass states.

Mixing effects in the crystallization of supercooled quantum binary liquids

By means of Raman spectroscopy of liquid microjets, we have investigated the crystallization process of supercooled quantum liquid mixtures composed of parahydrogen (pH2) or orthodeuterium (oD2) diluted with small amounts of neon. We show that the introduction of the Ne impurities affects the crystallization kinetics in terms of a significant reduction of the measured pH2 and oD2 crystal growth rates, similarly to what found in our previous work on supercooled pH2-oD2 liquid mixtures [Kühnel et al., Phys. Rev. B 89, 180201(R) (2014)]. Our experimental results, in combination with path-integral simulations of the supercooled liquid mixtures, suggest in particular a correlation between the measured growth rates and the ratio of the effective particle sizes originating from quantum delocalization effects. We further show that the crystalline structure of the mixtures is also affected to a large extent by the presence of the Ne impurities, which likely initiate the freezing process through the formation of Ne-rich crystallites.

First-order phase transition in a model glass former: coupling of local structure and dynamics

Recently, numerical evidence for a dynamical first-order phase transition in trajectory space [L.O. Hedges et al., Science 323, 1309 (2009)] has been found. In a model glass former in which clusters of 11 particles form upon cooling, we find that the transition has both dynamical and structural character. It occurs between an active phase with a high fraction of mobile and low fraction of cluster particles, and an inactive phase with few mobile but many cluster particles. The transition can be driven both dynamically and structurally with a chemical potential, showing that local order forms a mechanism for dynamical arrest.

Decoding the energy landscape: extracting structure, dynamics and thermodynamics

Describing a potential energy surface in terms of local minima and the transition states that connect them provides a conceptual and computational framework for understanding and predicting observable properties. Visualizing the potential energy landscape using disconnectivity graphs supplies a graphical connection between different structure-seeking systems, which can relax efficiently to a particular morphology. Landscapes involving competing morphologies support multiple potential energy funnels, which may exhibit characteristic heat capacity features and relaxation time scales. These connections between the organization of the potential energy landscape and structure, dynamics and thermodynamics are common to all the examples presented, ranging from atomic and molecular clusters to biomolecules and soft and condensed matter. Further connections between motifs in the energy landscape and the interparticle forces can be developed using symmetry considerations and results from catastrophe theory.

Inherent structures of phase-separating binary mixtures: nucleation, spinodal decomposition, and pattern formation

An energy landscape view of phase separation and nonideality in binary mixtures is developed by exploring their potential energy landscape (PEL) as functions of temperature and composition. We employ molecular dynamics simulations to study a model that promotes structure breaking in the solute-solvent parent binary liquid, at low temperatures. The PEL of the system captures the potential energy distribution of the inherent structures (IS) of the system and is obtained by removing the kinetic energy (including that of intermolecular vibrations). The broader distribution of the inherent structure energy for structure breaking liquid than that of the structure making liquid demonstrates the larger role of entropy in stabilizing the parent liquid of the structure breaking type of binary mixtures. At high temperature, although the parent structure of the structure breaking binary mixture is homogenous, the corresponding inherent structure is found to be always phase separated, with a density pattern that exhibits marked correlation with the energy of its inherent structure. Over a broad range of intermediate inherent structure energy, bicontinuous phase separation prevails with interpenetrating stripes as signatures of spinodal decomposition. At low inherent structure energy, the structure is largely phase separated with one interface where as at high inherent structure energy we find nucleation type growth. Interestingly, at low temperature, the average inherent structure energy (<E{IS}>) exhibits a drop with temperature which signals the onset of crystallization in one of the phases while the other remains in the liquid state. The nonideal composition dependence of viscosity is anticorrelated with average inherent structure energy.

Stability of supercooled binary liquid mixtures

Recently, the supercooled Wahnstrom binary Lennard-Jones mixture was partially crystallized into MgZn(2) phase crystals in lengthy molecular dynamics simulations. We present molecular dynamics simulations of a modified Kob-Andersen binary Lennard-Jones mixture that also crystallizes in lengthy simulations here, however, by forming pure fcc crystals of the majority component. The two findings motivate this paper that gives a general thermodynamic and kinetic treatment of the stability of supercooled binary mixtures, emphasizing the importance of negative mixing enthalpy whenever present. The theory is used to estimate the crystallization time in a Kob-Andersen mixture from the crystallization time in a series of related systems. At T=0.40 we estimate this time to be 5x10(7) time units ( approximately 0.1 ms). A new binary Lennard-Jones mixture is proposed that is not prone to crystallization and faster to simulate than the two standard binary Lennard-Jones mixtures. This is obtained by removing the like-particle attractions by switching to Weeks-Chandler-Andersen type potentials, while maintaining the unlike-particle attraction.

Glass transitions in one-, two-, three-, and four-dimensional binary Lennard-Jones systems

We investigate the calorimetric liquid-glass transition by performing simulations of a binary Lennard-Jones mixture in one through four dimensions. Starting at a high temperature, the systems are cooled to T = 0 and heated back to the ergodic liquid state at constant rates. Glass transitions are observed in two, three and four dimensions as a hysteresis between the cooling and heating curves. This hysteresis appears in the energy and pressure diagrams, and the scanning rate dependence of the area and height of the hysteresis can be described using power laws. The one-dimensional system does not experience a glass transition but its specific heat curve resembles the shape of the D≥2 results in the supercooled liquid regime above the glass transition. As D increases, the radial distribution functions reflect reduced geometric constraints. Nearest neighbor distances become smaller with increasing D due to interactions between nearest and next-nearest neighbors. Simulation data for the glasses are compared with crystal and melting data obtained with a Lennard-Jones system with only one type of particle and we find that with increasing D crystallization becomes increasingly more difficult.

Phase diagram of model anisotropic particles with octahedral symmetry

The phase diagram for a system of model anisotropic particles with six attractive patches in an octahedral arrangement has been computed. This model for a relatively narrow value of the patch width where the lowest-energy configuration of the system is a simple cubic crystal. At this value of the patch width, there is no stable vapor-liquid phase separation, and there are three other crystalline phases in addition to the simple cubic crystal that is most stable at low pressure. First, at moderate pressures, it is more favorable to form a body-centered-cubic crystal, which can be viewed as two interpenetrating, and almost noninteracting, simple cubic lattices. Second, at high pressures and low temperatures, an orientationally ordered face-centered-cubic structure becomes favorable. Finally, at high temperatures a face-centered-cubic plastic crystal is the most stable solid phase.

Equilibrium density of states and thermodynamic properties of a model glass former

This paper presents an analysis of the thermodynamics of a model glass former. We have performed equilibrium sampling of a popular binary Lennard-Jones model, employing parallel tempering Monte Carlo to cover the crystalline, amorphous, and liquid regions of configuration space. Disconnectivity graphs are used to visualize the potential energy landscape in the vicinity of a crystalline geometry and in an amorphous region of configuration space. The crystalline global minimum is separated from the bulk of the minima by a large potential energy gap, leading to broken ergodicity in conventional simulations. Our sampling reveals crystalline global minima that are lower in potential energy than some of the previous candidates. We present equilibrium thermodynamic properties based on parallel tempering simulations, including heat capacities and free energy profiles, which depend explicitly on the crystal structure. We also report equilibrium melting temperatures.

Controlling crystallization and its absence: proteins, colloids and patchy models

The ability to control the crystallization behaviour (including its absence) of particles, be they biomolecules such as globular proteins, inorganic colloids, nanoparticles, or metal atoms in an alloy, is of both fundamental and technological importance. Much can be learnt from the exquisite control that biological systems exert over the behaviour of proteins, where protein crystallization and aggregation are generally suppressed, but where in particular instances complex crystalline assemblies can be formed that have a functional purpose. We also explore the insights that can be obtained from computational modelling, focussing on the subtle interplay between the interparticle interactions, the preferred local order and the resulting crystallization kinetics. In particular, we highlight the role played by "frustration", where there is an incompatibility between the preferred local order and the global crystalline order, using examples from atomic glass formers and model anisotropic particles.

Ordered binary crystal phases of Lennard-Jones mixtures

The lattice energies at zero temperature are calculated, using Lennard-Jones interactions, for a large number of crystal structures associated with ordered binary compounds. In units of the AA interaction length and strength (i.e., sigmaAA= epsilonAA= 1.0) we examine the lowest energy structures, including coexisting phases, across the space of cross-species interactions 0.6< or = sigmaAB< or = 1.1 and 1.0< or = epsilonAB< or = 2.0. The remaining parameters sigmaBB= 0.88 and epsilonBB= 0.5 are chosen so that the parameter space studied includes the space of binary glass-forming alloys. In addition to some large unit cell structures such as Ni3P and PuBr3 appearing among the lowest lattice energies, a number of low-energy structures based on close-packed lattices are found that do not correspond to any experimentally observed crystals. The prevalence and stability of metastable crystal phases at the compositions AB, A2B, and A3B is examined.