Bond Orientational Order Parameters Research Articles

Study of phase transition and local order in equiatomic and nonequiatomic mixtures of HfNbTaTi under uniaxial loading from molecular dynamics simulations

We simulate an alloy of HfNbTaTi mixed in six different proportions and also of the equiatomic system under uniaxial tensile loading at 300 K. Molecular dynamics simulation trajectories are analyzed using radial distribution functions, OVITO, bond-orientational order parameters, and coordination numbers. Equiatomic and the two other alloys (Hf0.31Nb0.23Ta0.23Ti0.23 and Hf0.23Nb0.31Ta0.23Ti0.23) containing comparable fraction of elements deform similarly through the formation of an amorphous state. Two alloys rich in Nb (Hf0.17Nb0.50Ta0.16Ti0.17) and Ta (Hf0.17Nb0.16Ta0.50Ti0.17) deform similarly resulting in the formation of bcc atoms, which transform to fcc at higher loading. Finally, alloys rich in Hf (Hf0.50Nb0.16Ta0.17Ti0.17) and Ti (Hf0.17Nb0.16Ta0.17Ti0.50) deform resulting in high dislocation densities and hcp atoms. These two hcp-rich alloys also undergo strain hardening. In each mixture during loading, local orientational order of all the different elements changes similarly. Atoms prefer to pair with other atoms than to themselves during tensile loading.

Understanding melting of Ti crystals with spherical voids from molecular dynamics simulations

Titanium (Ti) is one of the most important metals used in several industrial applications, and the presence of spherical defect reduces its strength and stability. We simulate the melting of Ti crystals with a spherical void of radii 0.6, 0.8, 1.0, and 1.5 nm and also of the crystal without it. Ti is modeled using embedded atom method ,and all crystals are heated at 1 atm from 300 to 2200 K till it melts completely. All molecular dynamics trajectories are analyzed using radial distribution functions, bond-orientational order parameters, Voronoi tessellation, and velocity auto-correlation functions. The results show that 0.6, 0.8, 1.0, and 1.5 nm voids fill before the crystals melt and they fill immediately within few picoseconds; thereafter, atoms rearrange/order to crystal like arrangements, wherein overall crystallinity remains hcp for crystals with 0.6 and 0.8 nm void and changes to bcc for the crystals with 1.0 and 1.5 nm voids. For all crystals with and without void, melting takes place with the loss of both long- and short-range orders and not from liquid like nuclei as proposed by classical nucleation theory.

Structures and energies of twist grain boundaries in Mg[formula omitted]SiO4 forsterite

In this work, we investigate twist grain boundary (GB) energies and structures in Mg2SiO4 forsterite using atomistic simulations. We first present a new bond orientational order parameter allowing to highlight disordered regions in this low-symmetry crystal for which classical visualization tools are ineffective. Then we examine three GB planes, (010), (120) and (001), corresponding to the most favorable free surfaces of this crystal. We show that twist GB follow the same energy ordering as corresponding free surfaces. In addition, except for some misorientation angles and for the (120) GB plane, GB energies and structures are quite insensitive to microscopic translational degrees of freedom. The dislocation composition of low-angle twist GB can be related to γ-surfaces in the corresponding planes, and are in good agreement with first-principle calculations. It is also shown that the dislocation core structures in low angle twist GB can strongly differ from the ones of intracrystalline dislocations.

Atomistically informed hierarchical modeling for revisiting the constituent structures from heredity and nano-micro mechanics of sheath-core carbon fiber.

To better understand the heterogeneous anisotropic nanocomposite features and provide reliable underlying constitutive parameters of carbon fiber for continuum-level simulations, hierarchical modeling approaches combining quantum chemistry, molecular dynamics, numerical and analytical micromechanics are employed for studying the structure-performance relationships of the precursor-inherited sheath-core carbon fiber layers. A robust debonding force field is derived from energy matching protocols, including bond dissociation enthalpy calculations and rigid-constraint potential energy surface scan. Logistic long range bond stretching curves with exponential parameters and shifted force vdW curves are designed to diminish energy perturbations. The pseudo-crystalline microstructure is proposed and validated using virtual wide angle X-ray diffraction patterns and bond-orientational order parameters. The distribution or alignment features of the nanocomposite microstructures are collected from quantum chemical topology analysis and normal vector extractions. Non-equilibrium tensile loading simulation predicts the decomposed strain energy contributions, principal-axis modulus, strength limit, localized stress, and fracture morphologies of the model. Finally, an atomistically-informed stiffness prediction model combining numerical homogenization and analytical self-consistent Eshelby-Mori-Tanaka-type effective mean field micromechanics theory is proposed, giving a successful estimation of the overall stiffness matrix of the sheath-core carbon fiber system. The hierarchical models in combination with the carbonization reaction template will help in providing efficient and feasible schemes for the synergistic process-performance control of distinct types of carbon fiber.

The influence of engineering strain rates on the atomic structure, crack propagation and cavitation formation in Al based metallic glass

To enhance the toughness of metallic glasses (MGs), considerable scientific efforts have been made to investigate the physical mechanism of fracture behavior of MGs in past few years. However, many unresolved puzzles remain about the fracture mechanisms of MGs at present. In this paper, Molecular Dynamics (MD) simulations have been used to investigate the tensile fracture behavior of Al based MGs under nine different Engineering strain rates. Our results show that the higher the Engineering strain rate is, the longer the period of plastic deformation, the shorter the crack length. We have observed that Al amorphous with notch gradually crystallizes during tensile fracture, however, there are differences in the degree of crystallization and atomic arrangement as well as micro-structure in different regions with different Engineering strain rates. In the process of tensile fracture of Al based MGs, the crack propagation mainly along the hexagonal-close-packed (HCP) grain boundaries between face-centered-cubic (FCC) crystal blocks. As the Engineering strain increases, numerous HCP atoms located at grain boundaries gradually migrate into the interior of FCC crystal blocks, the velocity of crack propagation will also increase and finally induce the brittle fracture of Al based MGs. Meanwhile, we effectively demonstrated the existence of HCP and FCC atoms in Al based MGs during tensile deformation by analyzing the bond-orientational order parameters ql. The analysis of thermodynamics (entropy) showed that there is a positive correlation between the Engineering strain rate and the strain of maximum entropy when the Engineering strain rate exceeds 0.002 ps−1. The formation of cavitation ahead of crack could be attributed to the migrate of atoms from the higher entropy cavity region to the lower entropy crystallization region. This study enriches the traditional tensile deformation theories and provides a new understanding for the physical origins of cavitation in the crack tip of MGs.

Effect of graphene on solid–liquid coexistence in Cu nanodroplets

The microstructure determines the macro properties, so the chemical and physical properties of nanoparticles can be tuned by changing their structures. A molecular dynamics simulation for the rapid solidification of Cu nanodroplets on the graphene sheet is conducted to investigate the effect of substrate on nanoparticles. The phase transition, structure evolution, and crystallinity are quantified by the potential energy, the largest standard cluster analysis, and Bond-orientation order parameters. It is found that the solidification is inhomogeneous and stepwise crystallization. Interestingly, originating from the graphene wettability, different solid–liquid coexistence states are obtained that may have the potential to modify the chemical and physical reactions on nanoparticles. The temperature of this solid–liquid coexistence state depends strongly on the structural evolution of crystallization and thus can be regulated by the wetting properties of the graphene substrate. These results significantly extend the fundamental understanding of heterogeneous nucleation in nanodroplets, providing important insights for designing and fabricating composite materials with multifunctional properties.

Entropic stabilization and descriptors of structural transformation in high entropy alloys

With first-principles theoretical analysis of the local structure using Bond-Orientational Order parameters and Voronoi partitioning, we establish (a) HCP→BCC structural transformation in high-entropy alloys (HEAs) Nbx(HfZrTi)y at 16% Nb-concentration, and (b) that the internal lattice distortions (ILDs) peak at the transition. We demonstrate that the relative stability of HCP and BCC structures is driven by energetics, while the overall stability is achieved with contribution from the vibrational entropy that exceeds the configurational entropy of mixing. We show that along with atomic size mismatch, low average number (<5) of valence electrons and disparity in the crystal structures of constituent elements are responsible for larger ILDs in Nbx(HfZrTi)y than in HEAs like NbaMobWcTad.

Disordering two-dimensional magnet-particle configurations using bidispersity.

In various types of many-particle systems, bidispersity is frequently used to avoid spontaneous ordering in particle configurations. In this study, the relation between bidispersity and disorder degree of particle configurations is investigated. By using magnetic dipole-dipole interaction, magnet particles are dispersed in a two-dimensional cell without any physical contact between them. In this magnetic system, bidispersity is introduced by mixing large and small magnets. Then, the particle system is compressed to produce a uniform particle configuration. The compressed particle configuration is analyzed by using Voronoi tessellation for evaluating the disorder degree, which strongly depends on bidispersity. Specifically, the standard deviation and skewness of the Voronoi cell area distribution are measured. As a result, we find that the peak of standard deviation is observed when the numbers of large and small particles are almost identical. Although the skewness shows a non-monotonic behavior, a zero skewness state (symmetric distribution) can be achieved when the numbers of large and small particles are identical. In this ideally random (disordered) state, the ratio between pentagonal, hexagonal, and heptagonal Voronoi cells becomes roughly identical, while hexagons are dominant under monodisperse (ordered) conditions. The relation between Voronoi cell analysis and the global bond orientational order parameter is also discussed.

Phase behavior of active and passive dumbbells.

We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.

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.

Dimensionality reduction of local structure in glassy binary mixtures.

We consider unsupervised learning methods for characterizing the disordered microscopic structure of supercooled liquids and glasses. Specifically, we perform dimensionality reduction of smooth structural descriptors that describe radial and bond-orientational correlations and assess the ability of the method to grasp the essential structural features of glassy binary mixtures. In several cases, a few collective variables account for the bulk of the structural fluctuations within the first coordination shell and also display a clear connection with the fluctuations of particle mobility. Fine-grained descriptors that characterize the radial dependence of bond-orientational order better capture the structural fluctuations relevant for particle mobility but are also more difficult to parameterize and to interpret. We also find that principal component analysis of bond-orientational order parameters provides identical results to neural network autoencoders while having the advantage of being easily interpretable. Overall, our results indicate that glassy binary mixtures have a broad spectrum of structural features. In the temperature range we investigate, some mixtures display well-defined locally favored structures, which are reflected in bimodal distributions of the structural variables identified by dimensionality reduction.

Inorganic Crystal Structure Prototype Database Based on Unsupervised Learning of Local Atomic Environments.

Recognition of structure prototypes from tremendous known inorganic crystal structures has been an important subject beneficial for materials science research and new materials design. The existing databases of inorganic crystal structure prototypes were mostly constructed by classifying materials in terms of the crystallographic space group information. Herein, we employed a distinct strategy to construct the inorganic crystal structure prototype database, relying on the classification of materials in terms of local atomic environments (LAEs) accompanied by unsupervised machine learning method. Specifically, we adopted a hierarchical clustering approach onto all experimentally known inorganic crystal structure data to identify structure prototypes. The criterion for hierarchical clustering is the LAE represented by the state-of-the-art structure fingerprints of the improved bond-orientational order parameters and the smooth overlap of atomic positions. This allows us to build up a LAE-based Inorganic Crystal Structure Prototype Database (LAE-ICSPD) containing 15,613 structure prototypes with defined stoichiometries. In addition, we have developed a Structure Prototype Generator Infrastructure (SPGI) package, which is a useful toolkit for structure prototype generation. Our developed SPGI toolkit and LAE-ICSPD are beneficial for investigating inorganic materials in a global way as well as accelerating the materials discovery process in the data-driven mode.

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.

Bond Orientational Order Parameters for Classifying Solid-like Clusters in a Lennard-Jones System near Liquid-Solid Transition and at Solid States.

In this paper, we introduced an order parameter, named the local structure similarity (LSS), to measure the resemblance of a cluster structure in a liquid with respect to a perfect crystal. The LSS is based on a dot product of two bond orientational order complex vectors, with one vector associated with a particle in a liquid and the other vector with a particle in a crystal. The calculation of the LSS should scan the entire space of the Euler angles determined by the two coordinate frames describing individually the liquid and the crystal. The effectiveness of the LSS was examined by solid-like clusters in a Lennard-Jones (LJ) system near its liquid-solid phase transition and at solid states below its melting point, where the thermodynamic states of the LJ system were obtained by simulation annealing. The LSS measure was utilized to scrutinize the fcc-like, hcp-like, and bcc-like clusters classified by criteria based on W4 and W6 order parameters. As indicated by our results, the two ways of classification are consistent for fcc-like and hcp-like clusters, which are in a close resemblance to their crystalline counterparts. However, the classification with positive W6 for bcc-like clusters is inconsistent with the results of the LSS measure, which was confirmed by clusters in a LJ system confined between two parallel slabs of particles in the bcc structure arrangement.

Superstripes and quasicrystals in bosonic systems with hard-soft corona interactions

The search for spontaneous pattern formation in equilibrium phases with genuine quantum properties is a leading direction of current research. In this paper, we investigate the effect of quantum fluctuations---zero-point motion and exchange interactions---on the phases of an ensemble of bosonic particles with isotropic hard-soft corona interactions. We perform extensive path-integral Monte Carlo simulations to determine their ground-state properties. A rich phase diagram, parametrized by the density of particles and the interaction strength of the soft-corona potential, reveals supersolid stripes, kagome, and triangular crystals in the low-density regime. In the high-density limit, we observe patterns with 12-fold rotational symmetry compatible with periodic approximants of quasicrystalline phases. We characterize these quantum phases by computing the superfluid density and the bond-orientational order parameter. Finally, we highlight the qualitative and quantitative differences of our findings with the classical equilibrium phases for the same parameter regimes.

Investigation of bond orientational order of new Schiff base and theoretical study on Covid-19 activity: A molecular dynamics based on DFT and molecular docking analysis

2-(2-(3-hydroxy-4-methoxyphenyl)ethylidene)hydrazinecarbothioamide (HMHT) and 2-(2-(4-ethoxy-3-methoxyphenyl)ethylidene)hydrazinecarbothioamide (EMHT) compounds were synthesized and characterized. Some physical properties of HMHT and EMHT with increasing of temperature were determined by molecular dynamics (MD) simulations based on density functional theory (DFT). The local structure characterization of the HMHT molecule at different rotation angles were analysed the bond orientational order parameters. Results showed that EMHT becomes unstable compared to HMHT towards the end of the simulation. Finally, the effectiveness of compounds on Covid19 was theoretically tested on 6-NUR protein and protein binding detected in docking studies.

Screening toward the Development of Fingerprints of Atomic Environments Using Bond-Orientational Order Parameters.

A combination of atomic numbers and bond-orientational order parameters is considered a candidate for a simple representation that involves information on both the atomic species and their positional relation. The 504 candidates are applied as the fingerprint of the molecules stored in QM9, a data set of computed geometric, energetic, electronic, and thermodynamic properties for 133 885 stable small organic molecules made up of carbon, hydrogen, oxygen, nitrogen, and fluorine atoms. To screen the fingerprints, a regression analysis of the atomic charges given by Open Babel was performed by supervised machine learning. The regression results indicate that the 60 fingerprints successfully estimate Open Babel charges. The results of the dipole moments, an example of a property expressed by charge and position, also had a high accuracy in comparison with the values computed from Open Babel charges. Therefore, the screened 60 fingerprints have the potential to precisely describe the chemical and structural information on the atomic environment of molecules.

Controlling morphology in hybrid isotropic/patchy particle assemblies.

Brownian dynamics is used to study self-assembly in a hybrid system of isotropic particles (IPs), combined with anisotropic building blocks that represent special "designer particles." Those are modeled as spherical patchy particles (PPs) with binding only allowed between their patches and IPs. In this study, two types of PPs are considered: Octahedral PPs (Oh-PPs) and Square PPs (Sq-PPs), with octahedral and square arrangements of patches, respectively. The self-assembly is additionally facilitated by the simulated annealing procedure. The resultant structures are characterized by a combination of local correlations in cubatic ordering and a symmetry-specific variation of bond orientation order parameters (SymBOPs). By varying the PP/IP size ratio, we detected a sharp crossover between two distinct morphologies in both types of systems. High symmetry phases, NaCl crystal for Oh-PP and square lattice for Sq-PP, are observed for larger size ratios. For the smaller ones, the dominant morphologies are significantly different, e.g., Oh-PPs form a compact amorphous structure with predominantly face-to-face orientation of neighboring PPs. Unusually, for a morphology without a long-range order, it is still possible to identify well organized coherent clusters of this structure, thanks to the adoption of our SymBOP-based characterization.

Could network structures generated with simple rules imposed on a cubic lattice reproduce the structural descriptors of globular proteins?

Abstract A direct way to spot structural features that are universally shared among proteins is to find analogues from simpler condensed matter systems. In the current study, the feasibility of creating ensembles of artificial structures that can automatically reproduce a large number of geometrical and topological descriptors of globular proteins is investigated. Towards this aim, a simple cubic (SC) arrangement is shown to provide the best background lattice after a careful analysis of the residue packing trends from 210 globular proteins. It is shown that a minimalistic set of rules imposed on this lattice is sufficient to generate structures that can mimic real proteins. In the proposed method, 210 such structures are generated by randomly removing residues (beads) from clusters that have a SC lattice arrangement such that all the generated structures have single connected components. Two additional sets are prepared from the initial structures via random relaxation and a reverse Monte Carlo simulated annealing algorithm, which targets the average radial distribution function (RDF) of 210 globular proteins. The initial and relaxed structures are compared to real proteins via RDF, bond orientational order parameters and several descriptors of network topology. Based on these features, results indicate that the structures generated with 40% occupancy closely resemble real residue networks. The structure generation mechanism automatically produces networks that are in the same topological class as globular proteins and reproduce small-world characteristics of high clustering and small shortest path lengths. Most notably, the established correspondence rules out icosahedral order as a relevant structural feature for residue networks in contrast to other amorphous systems where it is an inherent characteristic. The close correspondence is also observed in the vibrational characteristics as computed from the Anisotropic Network Model, therefore hinting at a non-superficial link between the proteins and the defect laden cubic crystalline order.

Accurate force field of two-dimensional ferroelectrics from deep learning

The discovery of two-dimensional (2D) ferroelectrics with switchable out-of-plane polarization such as monolayer $\alpha$-In$_2$Se$_3$ offers a new avenue for ultrathin high-density ferroelectric-based nanoelectronics such as ferroelectric field effect transistors and memristors. The functionality of ferroelectrics depends critically on the dynamics of polarization switching in response to an external electric/stress field. Unlike the switching dynamics in bulk ferroelectrics that have been extensively studied, the mechanisms and dynamics of polarization switching in 2D remain largely unexplored. Molecular dynamics (MD) using classical force fields is a reliable and efficient method for large-scale simulations of dynamical processes with atomic resolution. Here we developed a deep neural network-based force field of monolayer In$_2$Se$_3$ using a concurrent learning procedure that efficiently updates the first-principles-based training database. The model potential has accuracy comparable with density functional theory (DFT), capable of predicting a range of thermodynamic properties of In$_2$Se$_3$ polymorphs and lattice dynamics of ferroelectric In$_2$Se$_3$. Pertinent to the switching dynamics, the model potential also reproduces the DFT kinetic pathways of polarization reversal and 180$^\circ$ domain wall motions. Moreover, isobaric-isothermal ensemble MD simulations predict a temperature-driven $\alpha \rightarrow \beta$ phase transition at the single-layer limit, as revealed by both local atomic displacement and Steinhardt's bond orientational order parameter $Q_4$. Our work paves the way for further research on the dynamics of ferroelectric $\alpha$-In$_2$Se$_3$ and related systems.