Local Bond-orientational Order Research Articles

Binary salt structure classification with convolutional neural networks: Application to crystal nucleation and melting point calculations

Convolutional neural networks are constructed and validated for the crystal structure classification of simple binary salts such as the alkali halides. The inputs of the neural network classifiers are the local bond orientational order parameters of Steinhardt, Nelson, and Ronchetti [Phys. Rev. B 28, 784 (1983)], which are derived solely from the relative positions of atoms surrounding a central reference atom. This choice of input gives classifiers that are invariant to density, increasing their transferability. The neural networks are trained and validated on millions of data points generated from a large set of molecular dynamics (MD) simulations of model alkali halides in nine bulk phases (liquid, rock salt, wurtzite, CsCl, 5-5, sphalerite, NiAs, AntiNiAs, and β-BeO) across a range of temperatures. One-dimensional time convolution is employed to filter out short-lived structural fluctuations. The trained neural networks perform extremely well, with accuracy up to 99.99% on a balanced validation dataset constructed from millions of labeled bulk phase structures. A typical analysis using the neural networks, including neighbor list generation, order parameter calculation, and class inference, is computationally inexpensive compared to MD simulations. As a demonstration of their accuracy and utility, the neural network classifiers are employed to follow the nucleation and crystal growth of two model alkali halide systems, crystallizing into distinct structures from the melt. We further demonstrate the classifiers by implementing them in automated MD melting point calculations. Melting points for model alkali halides using the most commonly employed rigid-ion interaction potentials are reported and discussed.

Connections between structural characteristics and crystal nucleation of Al–Sm glasses near glass transition temperature

A systematic investigation on connections between structural characteristics and crystal nucleation during isothermal devitrification of Al–Sm glasses has been carried out by utilizing molecular dynamics simulations combined with an effective data-driven approach named principal component analysis. The results suggest that icosahedral order dominants the local orders in Al–Sm liquids and glasses, whereas the development of crystal-like clusters has been greatly suppressed. Doping of Sm not only increases the population of icosahedral order in Al–Sm alloys, but also promotes the tendency of formation of icosahedral medium range order. Based on the calculation of local density and bond-orientational order parameters, a distinct decoupling in spatial distributions of fluctuations in local density and bond-orientational order is observed, and an obvious lagging of densification behind structural ordering is unveiled. These facts unambiguously evidence that the bond-orientational order instead of local density is the determinant factor for the origin of crystal nucleation in Al–Sm glass.

Accelerated annealing of colloidal crystal monolayers by means of cyclically applied electric fields

External fields are commonly applied to accelerate colloidal crystallization; however, accelerated self-assembly kinetics can negatively impact the quality of crystal structures. We show that cyclically applied electric fields can produce high quality colloidal crystals by annealing local disorder. We find that the optimal off-duration for maximum annealing is approximately one-half of the characteristic melting half lifetime of the crystalline phase. Local six-fold bond orientational order grows more rapidly than global scattering peaks, indicating that local restructuring leads global annealing. Molecular dynamics simulations of cyclically activated systems show that the ratio of optimal off-duration for maximum annealing and crystal melting time is insensitive to particle interaction details. This research provides a quantitative relationship describing how the cyclic application of fields produces high quality colloidal crystals by cycling at the fundamental time scale for local defect rearrangements; such understanding of dynamics and kinetics can be applied for reconfigurable colloidal assembly.

Evolution of local atomic structure during solidification of Fe-RE (RE=La, Ce) alloy

For the study of metallic materials, it is vitally important to understand the mechanism involved in the liquid-solid transition in terms of alloying elements. In the present work, the evolution of the short-range order (SRO) of liquid Fe, Fe-La and Fe-Ce systems upon supercooling were investigated using ab initio molecular dynamics simulations. The local structures analyses indicate that the addition of La enhances the glass-forming ability (GFA) of Fe-based alloys by stabilizing the icosahedral SRO, while Ce has no significant effect on it. The effect of Ce on the crystalline nucleation of melting Fe was further examined by isothermal annealing in combination with the analyses of the local bond orientation order parameters. The results reveal that the presence of Ce promotes the formation of the random hexagonal close packing structures during the nuclei formation process, thus helps to reduce the nucleation free energy.

Liquid-hexatic-solid phase transition of a hard-core lattice gas with third neighbor exclusion.

The determination of phase behavior and, in particular, the nature of phase transitions in two-dimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using an alternative route to deriving the equation of state of a two-dimensional hard-core particle system, based on kinetic arguments and the Gibbs adsorption isotherm, by the use of the random sequential adsorption with a surface diffusion model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at any fractional surface coverage via local bond orientation order. The analysis of the bond orientation correlation function for each individual configuration confirms that first-order phase transition occurs in a two-step liquid-hexatic-solid transition at high surface coverage.

Clusters of Local Bond-Orientational Order in Liquid Gallium: Studies of ab initio and Classical MD Simulations

The structure of liquid Ga at ambient pressure (AP) were generated separately via ab initio and classical molecular dynamics simulations, and analysed with a cluster approach developed in terms of the local bond-orientational order (LBOO) parameters. Two types of cluster structures were found in both simulated liquids, one typified by sixfold orientational symmetry and the other showing fourfold orientational symmetry: The static structure factors (SSF) of the former are akin to that of the hard-sphere (HS) fluid; however, the SSFs of the latter display either an asymmetric first peak with a shape different from that of the HS fluid or even a shoulder on the high-q side of the first peak, similar as the anomalous SSF of liquid Ga at AP.

Polymorph selection during crystallization of a model colloidal fluid with a free energy landscape containing a metastable solid

The free energy landscape responsible for crystallization can be complex even for relatively simple systems like hard sphere and charged stabilized colloids. In this work, using hard-core repulsive Yukawa model, which is known to show complex phase behavior consisting of fluid, FCC and BCC phases, we studied the interplay between the free energy landscape and polymorph selection during crystallization. When the stability of the BCC phase with respect to the fluid phase is gradually increased by changing the temperature and pressure at a fixed fluid-FCC stability, the final phase formed by crystallization is found to undergo a switch from the FCC to the BCC phase, even though FCC remains thermodynamically the most stable phase. We further show that the nature of local bond-orientational order parameter fluctuations in the metastable fluid phase as well as the composition of the critical cluster depend delicately on the free energy landscape, and play a decisive role in the polymorph selection during crystallization.

Uniform and decoupled shape effects on the maximally dense random packings of hard superellipsoids

The superellipsoid model is a rich geometric model and is convenient to study the particle shape effects on random packings. The particle shape significantly influences the macroscopic and microscopic structure properties of random packings. In this work, we find uniform and decoupled shape effects on the maximally dense random packings (MDRPs) of hard superellipsoids. Slightly changing the surface shape or elongating (compressing) the particles may influence the random packing density significantly. The influences of surface shape parameter p and aspect ratio w on the random packing densities are decoupled. For the aspect ratio effects, all the packing density curves show “M” type with various p. Meanwhile, the aspect ratio effects are applicable to all the symmetric particles with three equal main cross sections when w = 1.0. For the surface shape effects, the packing density curve is also in “M” type with various w. The maximum of the random packing density is obtained at p ≈ 0.7, 2.0 and w ≈ 0.7, 1.5. Moreover, we obtain the MDRPs of hard superellipsoids via the inverse Monte Carlo packing method with a wide range of the surface shape parameter. The normalized local cubatic order parameter and a new normalized local bond-orientational order parameter are used to evaluate the order degrees of orientations and bond-orientations in random packings, respectively. The local analyses of the MDRPs of superellipsoids are carried out via the Voronoi tessellation. Two linear relationships between the mean and standard deviation of the reduced Voronoi cell volumes are obtained. Our findings should lead to a better understanding of random packings and are helpful in guiding the granular material design.

Micro-structure and motion of two-dimensional dense short spherocylinder liquids

We numerically investigate the micro-structure and motion of 2D liquids composed of dense short spherocylinders, by reducing the shape aspect ratio from 3. It is found that reducing shape aspect ratio from 3 causes a smooth transition from heterogeneous structures composed of crystalline ordered domains with good tetratic alignment order to those with good hexagonal bond-orientational order at an aspect ratio equaling 1.35. In the intermediate regime, both structural orders are strongly deteriorated, and the translational hopping rate reaches a maximum due to the poor particle interlocking of the disordered structure. Shortening rod length allows easier rotation, induces monotonic increase of rotational hopping rates, and resumes the separation of rotational and translational hopping time scales at the small aspect ratio end, after the crossover of their rates in the intermediate regime. At the large shape aspect ratio end, the poor local tetratic order has the same positive effects on facilitating local rotational and translational hopping. In contrast, at the small shape aspect ratio end, the poor local bond orientational order has the opposite effects on facilitating local rotational and translational hopping.

Interfacial energetics of two-dimensional colloidal clusters generated with a tunable anharmonic interaction potential

Interfacial characteristics are critical to various properties of two-dimensional (2D) materials such as band alignment at a heterojunction and nucleation kinetics in a 2D crystal. Despite the desire to harness these enhanced interfacial properties for engineering new materials, unexpected phase transitions and defects, unique to the 2D morphology, have left a number of open questions. In particular, the effects of configurational anisotropy, which are difficult to isolate experimentally, and their influence on interfacial properties are not well understood. In this work, we begin to probe this structure-thermodynamic relationship, using a rotating magnetic field to generate an anharmonic interaction potential in a 2D system of paramagnetic particles. At low magnetic field strengths, weakly interacting colloidal particles form non-close-packed, fluidlike droplets, whereas, at higher field strengths, crystallites with hexagonal ordering are observed. We examine spatial and interfacial properties of these 2D colloidal clusters by measuring the local bond orientation order parameter and interfacial stiffness as a function of the interaction strength. To our knowledge, this is the first study to measure the tunable interfacial stiffness of a 2D colloidal cluster by controlling particle interactions using external fields.

Sidewall-friction-driven ordering transition in granular channel flows: Implications for granular rheology.

We report a transition from a disordered state to an ordered state in the flow of nearly monodisperse granular matter flowing in an inclined channel with planar slide walls and a bumpy base, using discrete element method simulations. For low particle-sidewall friction coefficients, the flowing particles are disordered, however, for high sidewall friction, an ordered state is obtained, characterized by a layering of the particles and hexagonal packing of the particles in each layer. The extent of ordering, quantified by the local bond-orientational order parameter, varies in the cross section of the channel, with the highest ordering near the sidewalls. The flow transition significantly affects the local rheology-the effective friction coefficient is lower, and the packing fraction is higher, in the ordered state compared to the disordered state. A simple model, incorporating the extent of local ordering, is shown to describe the rheology of the system.

Analysis of local bond-orientational order for liquid gallium at ambient pressure: Two types of cluster structures.

In terms of the local bond-orientational order (LBOO) parameters, a cluster approach to analyze local structures of simple liquids was developed. In this approach, a cluster is defined as a combination of neighboring seeds having at least nb local-orientational bonds and their nearest neighbors, and a cluster ensemble is a collection of clusters with a specified nb and number of seeds ns. This cluster analysis was applied to investigate the microscopic structures of liquid Ga at ambient pressure (AP). The liquid structures studied were generated through ab initio molecular dynamics simulations. By scrutinizing the static structure factors (SSFs) of cluster ensembles with different combinations of nb and ns, we found that liquid Ga at AP contained two types of cluster structures, one characterized by sixfold orientational symmetry and the other showing fourfold orientational symmetry. The SSFs of cluster structures with sixfold orientational symmetry were akin to the SSF of a hard-sphere fluid. On the contrary, the SSFs of cluster structures showing fourfold orientational symmetry behaved similarly as the anomalous SSF of liquid Ga at AP, which is well known for exhibiting a high-q shoulder. The local structures of a highly LBOO cluster whose SSF displayed a high-q shoulder were found to be more similar to the structure of β-Ga than those of other solid phases of Ga. More generally, the cluster structures showing fourfold orientational symmetry have an inclination to resemble more to β-Ga.

Structure of inactive states of a binary Lennard-Jones mixture

We study the structure of inactive states in a prototypical model glass, the Kob–Andersen binary Lennard-Jones mixture. These inactive states are obtained by transition path sampling and are at dynamical phase coexistence with an active equilibrium state. Configurations in the inactive states are kinetically stable and are located in deeper basins of the energy landscape than their active counterparts. By analyzing trajectory-to-trajectory fluctuations within the inactive state, we assess correlations between kinetic stability, energy and other structural properties. We show that measures of local order associated to stable local packings and bond-orientational order are weakly correlated with energy and kinetic stability. We discuss what kinds of structural measurement might capture the relevant dynamical features of the inactive state.

Unveiling atomic-scale features of inherent heterogeneity in metallic glass by molecular dynamics simulations

Heterogeneity is commonly believed to be intrinsic to metallic glasses (MGs). Nevertheless, how to distinguish and characterize the heterogeneity at the atomic level is still debated. Based on the extensive molecular dynamics simulations that combine isoconfigurational ensemble and atomic pinning methods, we directly reveal that MG contains flow units and the elastic matrix which can be well distinguished by their distinctive atomic-level responsiveness and mechanical performance. The microscopic features of the flow units, such as the shape, spatial distribution dimensionality, and correlation length, are characterized from atomic position analyses. Furthermore, the correlation between the flow units and the landscape of energy state, free volume, atomic-level stress, and especially the local bond orientational order parameter is discussed.

A study to investigate phase transitions and nucleation kinetics of nickel and copper

In this study, we investigate the homogeneous nucleation kinetics of copper and nickel system during cooling process using molecular dynamics simulation (MDS). The calculation is carried out for a different number of atoms consisting of 500, 2048, 8788 and 13,500 based on embedded atom method (EAM). It is observed that the melting points for the both model increases with increasing the size of systems (i.e. the number of atoms) as expected from Parrinello and Rahman MD method. The interfacial free energies and critical nucleus radius of nickel and copper are also determined by molecular dynamics, and the results are consistent with the classical nucleation theory. The structural development and phase transformation are also determined from the radial distribution function (RDF) and local bond orientational order parameters (LBOO).

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.

Upscaling and microstructural analysis of the flow-structure relation perpendicular to random, parallel fiber arrays

Owing largely to multiscale heterogeneity in the underlying fibrous structure, the physics of fluid flow in and through fibrous media is incredibly complex. Using fully resolved finite element (FE) simulations of Newtonian, incompressible fluid flow perpendicular to the fibers, the macroscopic permeability is calculated in the creeping flow regime for arrays of random, ideal, perfectly parallel fibers.On the micro-scale, several order parameters, based on Voronoi and Delaunay tessellations, are introduced to characterize the structure of the randomly distributed, parallel, non-overlapping fiber arrays. In particular, by analyzing the mean and the distribution of the topological and metrical properties of Voronoi polygons, we observe a smooth transition from disorder to (partial) order with decreasing porosity, i.e., increasing packing fraction.On the macro-scale, the effect of fiber arrangement and local crystalline regions on the macroscopic permeability is discussed. For both permeability and local bond orientation order parameter, the deviation from a fully random configuration can be well represented by an exponential term as function of the mean gap width, which links the macro- and the micro-scales.Finally, we verify the validity of the, originally, macroscopic Darcy's law at various smaller length scales, using local Voronoi/Delaunay cells as well as uniform square cells, for a wide range of porosities. At various cell sizes, the average value and probability distributions of macroscopic quantities, such as superficial fluid velocity, pressure gradient or permeability, are obtained. These values are compared with the macroscopic permeability in Darcy's law, as the basis for a hierarchical upscaling methodology.

Statistical assessment of order within systems of nanoparticles: Determining the efficacy of patterned substrates to facilitate ordering within nanoparticle monolayers fabricated through electrophoretic deposition

The degree of order within nanoparticle monolayers deposited through electrophoretic deposition on lithographically patterned and unpatterned substrates was analyzed using four complementary measures of order: Voronoi-cell edge-fraction entropy, local bond-orientation order parameter, translational order parameter, and anisotropy order parameter. From these measures of order, we determined that the pattern had an influence on some aspects of the ordering within the nanoparticle monolayer but had no effect on others. The Voronoi-cell edge-fraction entropy did not measurably change due to the pattern, indicating that the pattern has no effect on the number of defects present. The translational order parameter also had no change due to the pattern. The local bond-orientation order parameter had a measurable change, indicating the pattern increased the bond ordering slightly. Also, the anisotropy order parameter developed herein indicated an increase in order. The direction of the increased order corresponded with the direction of the anisotropy designed on the patterned substrate, strongly suggesting that the pattern drives the particles to become more ordered.

Non-equilibrium ionic assemblies of oppositely charged nanoparticles

Structure and evolution kinetics of non-equilibrium clusters formed in a solution of oppositely charged nanoparticles are studied using a recently developed kinetic Monte Carlo simulation scheme (Jha et al., Soft Matter, 2012, 8, 227–234). A diverse range of dynamic cluster configurations are obtained by varying the interaction strength between nanoparticles, screening length, and packing density of nanoparticles. Structural details of the resulting clusters are obtained using the correlations of local bond orientational order parameters. At low-salt concentrations (weak screening), clusters with structures ranging from NaCl-type cubic aggregates to fibril-like chains are observed, while at high-salt concentrations (strong screening), disordered compact clusters are observed. A chain-folding barrier model is proposed to explain the kinetically trapped fibril-like assemblies. In higher-density solutions, large ionic clusters or percolated gel structures are observed. Our work demonstrates the structural richness of non-equilibrium ionic assemblies of oppositely charged nanoparticles and elucidates the effect of ion correlations on the determination of the structure of assemblies of oppositely charged nanoparticles. These “nanoionic composites” hold great promise in a variety of emerging applications such as templated polymerization of charged molecules and assembly of charged nano-objects.

Jammed spheres: Minkowski tensors reveal onset of local crystallinity

The local structure of disordered jammed packings of monodisperse spheres without friction, generated by the Lubachevsky-Stillinger algorithm, is studied for packing fractions above and below 64%. The structural similarity of the particle environments to fcc or hcp crystalline packings (local crystallinity) is quantified by order metrics based on rank-four Minkowski tensors. We find a critical packing fraction φ(c)≈0.649, distinctly higher than previously reported values for the contested random close packing limit. At φ(c), the probability of finding local crystalline configurations first becomes finite and, for larger packing fractions, increases by several orders of magnitude. This provides quantitative evidence of an abrupt onset of local crystallinity at φ(c). We demonstrate that the identification of local crystallinity by the frequently used local bond-orientational order metric q(6) produces false positives and thus conceals the abrupt onset of local crystallinity. Since the critical packing fraction is significantly above results from mean-field analysis of the mechanical contacts for frictionless spheres, it is suggested that dynamic arrest due to isostaticity and the alleged geometric phase transition in the Edwards framework may be disconnected phenomena.