Local Bond-orientational Order Parameter 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.

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.

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.

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).

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.

Induced crystallization of single-chain polyethylene on a graphite surface: Molecular dynamics simulation

Molecular dynamics (MD) simulations have been carried out on the crystallization of single-chain polyethylene (PE) which was adsorbed on a graphite (001) surface on one side and exposed to vacuum on the other at different temperatures. The MD simulation data have been analyzed to provide information about the crystallization process of polymer adsorbed on the solid substrate. The isothermal crystallization of PE proceeds in two steps: (1) adsorption and (2) orientation. The results detail the radial density distribution function, ordered parameters, local bond-orientational order parameters, and the local properties displayed in layers of the polymer parallel to the graphite and vacuum interfaces. It was also shown that the film thickness affected the critical crystallization temperature of the adsorbed polymer on the substrate surface. Furthermore, the influence of the graphite surface area on the crystallization of PE is discussed by comparing the crystallinity evolution of PE on graphite with different coverage.

Molecular dynamics study of two-dimensional melting transition in copper via the embedded atom method

We report detailed molecular dynamics results for the two-dimensional (2D) melting transition using embed atomic method. The simulations are performed in the $NPT$ ensemble. Under different temperatures, the orientational correlation functions ${g}_{6}(r)$ and the pair distribution functions are measured and compared with the prediction of KTHNY theory. The size effect of distribution of the second moment of the local bond-orientational order parameter ${\ensuremath{\mid}{\ensuremath{\psi}}_{6,i}\ensuremath{\mid}}^{2}$ is studied. All results prove the existence of an intermediate hexatic phase during 2D melting. The dependence of average potential energy per atom on temperature and evidences from observations on the global bond-orientational order parameter and global translational order parameter show that the melting contains two stages and is a first-order transition as a whole. By exploring the evolution of topological defects, along with observations on the distributions of defects in inherent structures of typical crystalline phase, hexatic liquid, and isotropic liquid, we find that, instead of disclinations, the formation of defect chains and the correlation between them play an important role in both steps, which is rather different from the prediction of KTHNY theory.

Lindemann measures for the solid-liquid phase transition

A set of Lindemann measures, based on positional deviations or return distances, defined with respect to mechanically stable inherent structure configurations, is applied to understand the solid-liquid phase transition in a Lennard-Jones-type system. The key quantity is shown to be the single-particle return distance-squared distribution. The first moment of this distribution is related to the Lindemann parameter which is widely used to predict the melting temperature of a variety of solids. The correlation of the single-particle return distance and local bond orientational order parameter in the liquid phase provides insights into mechanisms for melting. These generalized Lindemann measures, especially the lower order moments of the single-particle return distance distribution, show clear signatures of the transition of the liquid from the stable to the metastable, supercooled regime and serve as landscape-based indicators of the thermodynamic freezing transition for the Lennard-Jones-type system investigated.

Computer simulations of the two-dimensional melting transition using hard disks

We present detailed Monte Carlo results for the two-dimensional melting transition of various systems up to N=65536 hard disks. The simulations are performed in the NVT ensemble, using a new updating scheme. In the isotropic phase the bond orientational correlation length xi_6 and the susceptibility chi_6 are measured and compared with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. From the scaling relation of xi_6 and chi_6 we calculate the critical exponent eta_6. In the phase transition region we use finite-size scaling methods to locate the disclination binding transition point and compare the results with the values obtained from the behaviour in the isotropic phase. Additionally, we measure the topological defect density, the pressure and the distribution of the second moment of the local bond orientational order parameter. All results are in good agreement with the KTHNY theory, while a first-order phase transition with small correlation length and a one-stage continuous transition can be ruled out.

Bond-orientational correlation in liquids and glasses

The nature of atomic bond-orientational anisotropy and order in liquids and glasses is considered based upon recent molecular dynamics studies. A possibility of spin-glass-like freezing of the local bond-orientational order (BOO) parameter is demonstrated. A close relationship between the anelasticity of metallic glasses and BOO through the response of BOO to stresses is discussed. It is suggested that stresses may be in part mediating interactions between the local BOO parameters.