Ring Statistics Research Articles

Structural and dynamical properties of two dimensional disordered metal chalcogenides AB (A [formula omitted] Zn, Cd; B [formula omitted] S, Se): A classical molecular dynamic study

In recent years, the synthesis of two-dimensional (2D) materials, particularly the crystalline and disordered phases of 2D transition metal chalcogenides (TMCs), has gained considerable attention due to their wider electronic band gaps. This distinctive feature is pivotal in shaping their potential applications in solar cells, sensors, field-effect transistors (FETs), and photocatalysis for water decomposition. In the present study, we report molecular dynamics simulation of 2d disordered configuration of ZnX and CdX (X: S, Se) compounds using the Stillinger–Weber potential. We have explored their structural features by calculating their radial distribution functions and ring statistics. These systems are thermodynamically stable. The disordered network with numerous voids in these compounds play a pivotal role in lowering their melting temperature compared to their 2D crystalline counterparts, which falls within the range of 600 K to 700 K. The phonon density of states for all these systems shows a higher number of lower frequency (acoustic) modes than optical modes, which is understandably due to the presence of open regions and 2-fold sites in such systems.

Comparative structural study of Al2O3–SiO2 glasses and amorphous thin films

AbstractWe compared the impact of alumina doping on the structure of Al2O3–SiO2 amorphous thin films and bulk glasses using Raman spectroscopy and x‐ray diffraction. In both thin films and bulk glasses, the addition of Al2O3 is accompanied by an increase in the mean Si–O–T angle and an evolution of the ring statistics with a decrease in the proportion of small rings. We evidenced structural differences between sputtered films and fused bulk glasses. Sputtered Al2O3–SiO2 thin films are about 6%–7% denser than their equivalent Al2O3–SiO2 bulk glasses. This difference is mainly due to a change in ring statistics with the formation of small rings within the sputtered thin films. These structural differences in atomic structural organization highlight the impact of the synthesis conditions and open the door to further investigation of the structure–functional property relationships in sputtered Al2O3–SiO2 thin films.

Melting Process of the Two-Dimensional Material BN: Insights from Molecular Dynamics Simulations

The structure of the two-dimensional BN containing 9941 atoms has been studied by classical molecular dynamics simulation with Tersoff potential. The periodic boundary condition is applied to the two x and y directions, while the z direction is free. The analysis results of the function of total energy per atom and heat capacity, mean squared displacement, diffusion coefficient, radial distribution function, distribution of coordination number, angle distribution, and ring statistics show that the melting point of the material is about 4600 K. This value is higher than the experimental value as well as the previous simulation results. The observations also show that the melting process begins at the corners and edges and then spreads across the face of the model. The breakage of the B-N bond leads to the formation of clusters of N2 molecules and B with different sizes.

Analysis of Structural Change across the Liquid-Liquid Transition and the Widom Line in Supercooled Stillinger-Weber Silicon.

We consider the changes in the structure of supercooled Stillinger-Weber silicon at pressures at which the studied range of temperatures traverses the liquid-liquid transition or the "Widom line" (at which the isothermal compressibility or the specific heat exhibits a maximum). In addition to the conventional characterizations in terms of the pair-correlation function and bond orientational order, we analyze the statistics of rings in the bond network as well as the statistics of clusters of low density liquid (LDL)- and high density liquid (HDL)-like atoms. We investigate the nature of the change in these structural characterizations when the liquid-liquid transition line or the Widom line is crossed. We find that the isobaric temperature variation of these structural features reveals clear indications of maximal structural heterogeneity or frustration upon crossing the liquid-liquid transition or the Widom line, as in the case of water, but with some differences in detail, which we discuss.

Ring compaction as a mechanism of densification in amorphous silica

The structure of permanently densified silica glass is investigated by neutron and x-ray diffraction, and by the production of atomistic models that reproduce the diffraction results. The focus is on the nature of the ordering on an intermediate length scale that originates from the formation of $n$-rings, where $n$ is the number of Si or O atoms within a ring. The densification process has a large effect on this ordering, as identified by pronounced changes to the first sharp diffraction peak (FSDP) in the measured structure factors. A clear and systematic dependence of the distribution of ring sizes on the position and shape of the FSDP could not be found, i.e., the ring statistics are not directly encoded into the form of this peak. Instead, a significant contribution to the glass densification originates from compaction of the $n$-rings, a metric that is quantified by the radius of gyration and lifetime of the rings. We thereby uncover and quantify a key densification mechanism in amorphous materials.

Study of the structure of MgSiO3 system under compression by using ring statistics and voronoi analysis

The structural change of MgSiO3 liquid under compression is still one of the most interesting challenges. In this paper, we perform the molecular dynamics simulation to study the structural change of MgSiO3 liquid from 0 to 200 GPa. Ring statistics are analyzed to clarify the intermediate-range order, to explain why the second peak of Si–Si PRDFs splits into 2 subpeaks at 200 GPa, and to show the heterogeneity of MgSiO3. Large rings which form at high pressures would capture the oxygen atoms. Oxygen atoms which have negative charge attract Mg2+ ions, creating magnesium-rich regions. Besides, the Voronoi and Q n distribution changes on the ring with pressure are clarified to give more information about the rings.

Simulation and experimental study on the effect of iron on the structure and flow properties of coal ash slag

Slag fluidity is an important parameter affecting the stable operation of the gasifier. Above liquid temperature, slag fluidity is closely related to its structure. In the present study, the effect of iron on the three-dimensional connection state between [SiO4]4- and [AlO4]5- tetrahedrons in the SiO2-Al2O3-FeO-CaO slag system at 1773 K was deeply discussed by applying molecular dynamics (MD) simulation and ring statistics methods, and the slag network structure was divided into three rings with different functions according to the three-dimensional connection state. It was found that Fe2+ operated as a network modifier ion and substituted Si4+ and Al3+ in the slag and combined with O2–, thereby continuously depolymerizing higher-order rings into lower-order rings. This phenomenon simplified slag structure, reduced internal friction force, and improved fluidity. Finally, the ring distribution coefficient (Rdc) was defined and it was found that there was a linear relationship between Rdc and viscosity.

Role of Al in Cu-Zr-Al thin film metallic glasses: Molecular dynamics and experimental study

The paper deals with the role of Al in thin film metallic glasses based on Cu and Zr. We employ a combination of molecular-dynamics simulations of the atom-by-atom growth process with magnetron sputtering. We use the previously studied composition Cu0.46Zr0.54 as a starting point, and focus on the effect of Al incorporation into Cu0.46Zr0.54 (simulations) and Cu0.46(Zr + Hf)0.54 (sputtering). We go beyond the state-of-the-art by quantifying the homogeneity, densification, short-range order (bonding preferences and coordination numbers), medium-range order (common neighbor and network ring statistics) and functional properties (hardness, Young's modulus, glass transition temperature and crystallization temperature) in a wide range of Al contents (0to20at.%) and growth conditions. We identify the key building blocks of Cu-Zr-Al: icosahedral clusters (12 vertices) centered around Cu and Al, and supraicosahedral clusters (16 vertices) centered around Zr. The atomic-scale simulations provide a lot of information not accessible experimentally and explain the experimental data. Theresults are important for understanding the structures and properties of this class of metallic glasses, and for optimizing their compositions and pathways for their preparation for various technological applications.

The Evolution of Hydrogen Bond Network in Nafion via Molecular Dynamics Simulation

The hydrogen bond network (HBN) is of primary importance to the proton transport in Nafion. However, the evolution of the HBN in Nafion with water content and the underlying thermodynamics have not been revealed. In this study, the free energy of hydrogen bond formation is calculated based on an information-theoretic approach, indicating the formation of HBN in Nafion is a thermodynamically favorable process as the water content increases. In addition, the evolution of HBN in Nafion with water content including the topology and basic building blocks has been visualized and quantified by a ring statistics approach based on graph theory. Finally, the rearrangement dynamics and heterogeneity of HBN are also disclosed. This study provides a fundamental and comprehensive understanding of HBN in Nafion including the formation thermodynamics, topology, and rearrangement dynamics, which is useful for the design of high-performance proton exchange membranes.

Quantum-corrected thickness-dependent thermal conductivity in amorphous silicon predicted by machine learning molecular dynamics simulations

Amorphous silicon (a-Si) is an important thermal-management material and also serves as an ideal playground for studying heat transport in strongly disordered materials. Theoretical prediction of the thermal conductivity of a-Si in a wide range of temperatures and sample sizes is still a challenge. Herein we present a systematic investigation of the thermal transport properties of a-Si by employing large-scale molecular dynamics (MD) simulations with an accurate and efficient machine-learned neuroevolution potential (NEP) trained against abundant reference data calculated at the quantum-mechanical density-functional-theory level. The high efficiency of NEP allows us to study the effects of finite size and quenching rate in the formation of a-Si in great detail. We find that it requires a simulation cell up to $64,000$ atoms (a cubic cell with a linear size of 11 nm) and a quenching rate down to $10^{11}$ K s$^{-1}$ for fully convergent thermal conductivity. Structural properties, including short- and medium-range order as characterized by the pair correlation function, angular distribution function, coordination number, ring statistics and structure factor are studied to demonstrate the accuracy of NEP and to further evaluate the role of quenching rate. Using both the heterogeneous and the homogeneous nonequilibrium MD methods and the related spectral decomposition techniques, we calculate the temperature- and thickness-dependent thermal conductivity values of a-Si and show that they agree well with available experimental results from 10 K to room temperature. Our results also highlight the importance of quantum effects in the calculated thermal conductivity and support the quantum correction method based on the spectral thermal conductivity.

Ge136 type-II clathrate as precursor for the synthesis of metastable germanium polymorphs: A computational study

The response to compression of the clathrate type-II structure Ge(cF136) is investigated by means of \textit{ab initio} small-cell metadynamics at different temperatures and pressures. At lower pressure $p$=2.5 GPa the metastable metallic bct-5 phase competes against $\beta$-Sn Ge(tI4), which forms at higher pressures. On lowering temperature, the presence of amorphous intermediates obtained from Ge$_{136}$ is more pronounced and is instrumental to the formation of denser structural motifs, from which metallic bct-5 can form. Therein, anisotropic box fluctuations promote phase formation. The metadynamics runs are analysed in depth using a set of topological descriptors, including coordination sequence and ring statistics. Differences in the structural landscape history and amorphous intermediates are critical for the selective formation of particular metastable polymorphs, towards turning crystal structure predictions into actual materials.

Structural Evolution of Single-Walled Carbon Nanotubes: Molecular Dynamics Simulation

We investigate the structural evolution of the single-walled carbon nanotubes (SWNTs) by molecular dynamics (MD) simulation using the Gao-Weber potential. The structural evolution of SWNTs is analyzed through the total energy per atom, the radial distribution function, coordination number, bond angle and the distribution of ring statistics. The results show that the melting temperature of SWNTs occurs at around Tm=5620 K. This value is in good agreement with the result of Zhang and co-workers. The visualization indicates that the initially perfect SWNTs is broken resulting in the ring of various.

Robust coverless steganography using limited mapping images

Coverless image steganography (CIS) has attracted significant attention because it can fundamentally resist steganalysis tools. Available CIS schemes are mainly divided into synthesis-based and mapping-based schemes. Compared with the former, mapping-based methods ensure lossless information extraction and stronger attack robustness. However, these methods still face the challenges of incomplete secret information mapping, trade-off between robustness and distinguishability of mapping features, and demand for huge numbers of mapping images. To tackle these issues, a novel robust coverless steganography using limited mapping images is proposed in this paper. In our scheme, we extract ring statistics to ensure both the distinguishability and robustness of mapping features. Moreover, different from conventional CIS schemes, we further design a chaotic system for scrambling image features to map secret information. Using this system, a single image is mapped to multiple secret information instances using different scrambled features, which reduces the demand on the numbers of images and avoids incomplete mapping. Furthermore, the scrambled features also enhance the security of secret information. Experimental results demonstrate that our scheme has superior performance in terms of distinguishability and robustness against geometrical attacks, the required number of mapping images, and mapping completeness.

Relationship between local coordinates and thermal conductivity in amorphous carbon

To determine the correlation between local structure and thermal conductivity of amorphous carbon, we investigated heat conduction in 216-atom systems with different densities (2.0–3.4 g/cm3) using the ab initio molecular dynamics approach. By applying the Allen–Feldman theory with interatomic force constants from ab initio calculations, we report a significant correlation between the thermal conductivity and the density. To clarify which structural characteristics in the high- and low-density cases determine the magnitude of thermal conductivity, we performed geometrical and topological analyses. Coordination number analysis and ring statistics revealed that the sp/sp2/sp3 bond ratios and topological characteristics correlate with density. We also demonstrated that these structural characteristics can be quantified using persistent homology analysis, providing a predictive model of thermal conductivity.

Internal structure of localized quantized vortex tangles

In this study, we numerically investigate the internal structure of localized quantum turbulence in superfluid $^4$He at zero temperature with the expectation of self-similarity in the real space. In our previous study, we collected the statistics of vortex rings emitted from a localized vortex tangle. As a result, the power law between the minimum size of detectable vortex rings and the emission frequency is obtained, which suggests that the vortex tangle has self-similarity in the real space [Nakagawa $et$ $al.$, Phys. Rev. B $\boldsymbol{101}$, 184515 (2020)]. In this work, we study the fractal dimension and vortex length distribution of localized vortex tangles, which can show their self-similar structure. We generate statistically steady and localized vortex tangles by injecting vortex rings with a fixed size. We used two types of injection methods that produce anisotropic or isotropic tangles. The injected vortex rings develop into a localized vortex tangle consisting of vortex rings of various sizes through reconnections (fusions and splitting of vortices). The fractal dimension is an increasing function of the vortex line density and becomes saturated to a value of approximately 1.8, as the density increases sufficiently. The behavior of the fractal dimension was independent of the anisotropy of the vortex tangles. The vortex length distribution indicates the number of vortex rings of each size that are distributed in a tangle. The distribution of the anisotropic vortex tangle shows the power law in the range above the injected vortex size, although the distribution of the isotropic vortex does not.

Persistent homology in two-dimensional atomic networks.

The topology of two-dimensional network materials is investigated by persistent homology analysis. The constraint of two dimensions allows for a direct comparison of key persistent homology metrics (persistence diagrams, cycles, and Betti numbers) with more traditional metrics such as the ring-size distributions. Two different types of networks are employed in which the topology is manipulated systematically. In the first, comparatively rigid networks are generated for a triangle-raft model, which are representative of materials such as silica bilayers. In the second, more flexible networks are generated using a bond-switching algorithm, which are representative of materials such as graphene. Bands are identified in the persistence diagrams by reference to the length scales associated with distorted polygons. The triangle-raft models with the largest ordering allow specific bands Bn (n = 1, 2, 3, …) to be allocated to configurations of atoms separated by n bonds. The persistence diagrams for the more disordered network models also display bands albeit less pronounced. The persistent homology method thereby provides information on n-body correlations that is not accessible from structure factors or radial distribution functions. An analysis of the persistent cycles gives the primitive ring statistics, provided the level of disorder is not too large. The method also gives information on the regularity of rings that is unavailable from a ring-statistics analysis. The utility of the persistent homology method is demonstrated by its application to experimentally-obtained configurations of silica bilayers and graphene.

Topology and complexity of the hydrogen bond network in classical models of water

Over the years, plenty of classical interaction potentials for water have been developed and tested against structural, dynamical and thermodynamic properties. On the other hands, it has been recently observed (F. Martelli et al., ACS Nano, 14, 8616–8623, 2020) that the topology of the hydrogen bond network (HBN) is a very sensitive measure that should be considered when developing new interaction potentials. Here we report a thorough comparison of 11 popular non polarizable classical water models against their HBN, which is at the root of water properties. We probe the topology of the HBN using the ring statistics and we evaluate the quality of the network inspecting the percentage of broken and intact HBs. For each water model, we assess the tendency to develop hexagonal rings (that promote crystallization at low temperatures) and pentagonal rings (known to frustrate against crystallization at low temperatures). We then introduce the network complexity index, a general descriptor to quantify how much the topology of a given network deviates from that of the ground state, namely of hexagonal or cubic ice. Remarkably, we find that the network complexity index allows us to relate, for the first time, the dynamical properties of different water models with their underlying topology of the HBN. Our study provides a benchmark against which the performances of new models should be tested against, and introduces a general way to quantify the complexity of a network which can be transferred to other materials and that links the topology of the HBN with dynamical properties. Finally, our study introduces a new perspective that can help in rationalizing the transformations among the different phases of water and of other materials.

Modeling glassy SiC nanoribbon by rapidly cooling from the liquid: An affirmation of appropriate potentials

Modeling glassy SiC nanoribbon by cooling rapidly the SiC liquid from 8000K to 300K is carried out by molecular dynamics (MD) simulations. Two separated MD simulations are performed, one of which uses the Tersoff potential and the other one uses the Vashishta potential. The temperature dependence of various structural and thermodynamic properties of the systems is analyzed and discussed via the radial distribution functions (RDFs), the coordination number distributions, and the ring statistics. We find that the Tersoff potential is clearly more appropriate in order to obtain the glassy SiC when rapidly cooling is employed.

A novel zero-watermarking scheme with enhanced distinguishability and robustness for volumetric medical imaging

The authenticity and copyright protection of volumetric medical images has become extremely important when these images are distributed online for diagnosis and education purpose. Compared to the authenticity and copyright protection of conventional images, there are two additional challenges for protecting the volumetric medical images. On one hand, the content of the protected medical images must be distortion-free to ensure unbiased diagnosis. On the other hand, it requires enhanced distinguishability to avoid misclassification of non-protected images into the protected set because volumetric medical images of different persons in the same modality share similar visual structures. To address these issues, a novel multi-slice feature based zero-watermarking scheme with enhanced distinguishability and robustness for volumetric medical imaging is proposed. In this scheme, ring statistics are deployed to guarantee both the watermarking distinguishability and robustness. In addition, an intra-slice variation based mechanism is designed to further enhance the watermarking distinguishability. Finally, a logistic-logistic system based chaotic map is used to ensure the watermarking security. Our experimental results demonstrate that the proposed scheme not only satisfies the lossless quality requirement but also ensures the watermarking distinguishability and robustness, which outperforms the state-of-the-art schemes.

Gaining insights on high-temperature thermal conductivity and structure of oxide melts through experimental and molecular dynamics simulation study

The high-temperature thermal conductivity of CaO–Al2O3–B2O3 melts was measured using the hot-wire method between 1550 and 1850 K. From the structural analysis of the as-quenched melts based on Raman spectra, X-ray photoelectron spectroscopy (XPS), magic-angle spinning nuclear magnetic resonance (MAS-NMR) and molecular dynamics simulation, the relationship between thermal conductivity and melt structure was discussed. When the Al2O3/B2O3 ratio was fixed at unity, the CaO increments from 40 to 60 mol pct lowered the thermal conductivity. The three-dimensional network structures were depolymerized, resulting in more orthoborates and fewer bridging oxygens. Al[4] population increased with the CaO addition, while the fraction of B[4] species decreased relative to B[3] species. When the CaO content was fixed at 50 mol pct, the thermal conductivity initially decreased with B2O3 increments up to 25 mol pct. The proportion of Al–O–Al linkages dropped, while the borate units mostly remained in two-dimensional forms. Greater addition of B2O3 over 25 mol pct enhanced the thermal conductivity mainly due to the conversion of BO3 triangular units to BO4 tetrahedral units. The structural changes are consistent with the topological network connectivity evaluated from the ring statistics.