How does tetrahedral structure grow in liquid silicon upon supercooling?

Ab Initio Characterization of the CO2-Water Interface Using Unsupervised Machine Learning for Dimensionality Reduction

Precise characterization of the supercritical CO2-water interface under high pressure and temperature conditions is crucial for the geological storage of carbon dioxide (CO2) in deep saline aquifers. Molecular dynamics (MD) simulations offer a valuable approach to gaining insight into the CO2-water interface at a microscopic level. However, no attempt has been made to characterize the CO2-water interface with the accuracy afforded by ab initio calculations. In this study, we performed ab initio MD (AIMD) simulations to investigate the structural and dynamical properties of the CO2-water interface, comparing the results with those obtained from classical force-field MD (FF-MD) simulations. Molecular orientation at the interface was well reproduced in both AIMD and FF-MD simulations. Characteristic structural fluctuations of water at the interface were unveiled by applying multidimensional scaling and time-dependent principal component analysis to the AIMD trajectories; however, they were not prominent in the FF-MD simulations. Furthermore, our study demonstrated a marked difference in the residence time of molecules in the interface region between AIMD and FF-MD simulations, indicating that time-dependent properties of the CO2-water interface strongly depend on the description of the intermolecular forces.

Atomic-Scale Insights into the Phase Behavior of Carbon Dioxide and Water from 313 to 573 K and 8 to 30 MPa

We performed molecular dynamics (MD) simulations of CO2 + H2O systems by employing widely used force fields (EPM2, TraPPE, and PPL models for CO2; SPC/E and TIP4P/2005 models for H2O). The phase behavior observed in our MD simulations is consistent with the coexistence lines obtained from previous experiments and SAFT-based theoretical models for the equations of state. Our structural analysis reveals a pronounced correlation between phase transitions and the structural orderliness. Specifically, the coordination number of Ow (oxygen in H2O) around other Ow significantly correlates with phase changes. In contrast, coordination numbers pertaining to the CO2 molecules show less sensitivity to the thermodynamic state of the system. Furthermore, our data indicate that a predominant number of H2O molecules exist as monomers without forming hydrogen bonds, particularly in a CO2-rich mixture, signaling a breakdown in the hydrogen bond network's orderliness, as evidenced by a marked decrease in tetrahedrality. These insights are crucial for a deeper atomic-level understanding of phase behaviors, contributing to the well-grounded design of CO2 injection under high-pressure and high-temperature conditions, where an atomic-scale perspective of the phase behavior is still lacking.

Observation of plasmon excitation in liquid silicon by inelastic x-ray scattering

Inelastic x-ray scattering (IXS) measurements were performed for observing the excitation of bulk plasmons in metallic liquid silicon (Si). The peak due to plasmon excitation was observed within the energy loss around 17 eV. Combined with IXS data of crystalline Si measured at several elevated temperatures, it was found that temperature dependence of the excitation energy in the crystalline solid state is explained by the electron gas including the band gap effect, whereas in the metallic liquid state near the melting point, it exhibits a departure from the electron gas; the plasmon energy takes a lower value than that of the electron gas. Such lowering of plasmon energies is reasonably explained by a model incorporating semiconducting component to the electron gas. Non-simple metallic nature in liquid silicon is highlighted by the observation of electron collective dynamics.

Relationship between diffraction peak, network topology, and amorphous-forming ability in silicon and silica

The network topology in disordered materials is an important structural descriptor for understanding the nature of disorder that is usually hidden in pairwise correlations. Here, we compare the covalent network topology of liquid and solidified silicon (Si) with that of silica (SiO2) on the basis of the analyses of the ring size and cavity distributions and tetrahedral order. We discover that the ring size distributions in amorphous (a)-Si are narrower and the cavity volume ratio is smaller than those in a-SiO2, which is a signature of poor amorphous-forming ability in a-Si. Moreover, a significant difference is found between the liquid topology of Si and that of SiO2. These topological features, which are reflected in diffraction patterns, explain why silica is an amorphous former, whereas it is impossible to prepare bulk a-Si. We conclude that the tetrahedral corner-sharing network of AX2, in which A is a fourfold cation and X is a twofold anion, as indicated by the first sharp diffraction peak, is an important motif for the amorphous-forming ability that can rule out a-Si as an amorphous former. This concept is consistent with the fact that an elemental material cannot form a bulk amorphous phase using melt quenching technique.

Time-dependent principal component analysis: A unified approach to high-dimensional data reduction using adiabatic dynamics

Systematic reduction of the dimensionality is highly demanded in making a comprehensive interpretation of experimental and simulation data. Principal component analysis (PCA) is a widely used technique for reducing the dimensionality of molecular dynamics (MD) trajectories, which assists our understanding of MD simulation data. Here, we propose an approach that incorporates time dependence in the PCA algorithm. In the standard PCA, the eigenvectors obtained by diagonalizing the covariance matrix are time independent. In contrast, they are functions of time in our new approach, and their time evolution is implemented in the framework of Car-Parrinello or Born-Oppenheimer type adiabatic dynamics. Thanks to the time dependence, each of the step-by-step structural changes or intermittent collective fluctuations is clearly identified, which are often keys to provoking a drastic structural transformation but are easily masked in the standard PCA. The time dependence also allows for reoptimization of the principal components (PCs) according to the structural development, which can be exploited for enhanced sampling in MD simulations. The present approach is applied to phase transitions of a water model and conformational changes of a coarse-grained protein model. In the former, collective dynamics associated with the dihedral-motion in the tetrahedral network structure is found to play a key role in crystallization. In the latter, various conformations of the protein model were successfully sampled by enhancing structural fluctuation along the periodically optimized PC. Both applications clearly demonstrate the virtue of the new approach, which we refer to as time-dependent PCA.

Structure of levitated Si-Ge melts studied by high-energy x-ray diffraction in combination with reverse Monte Carlo simulations

The short-range order in liquid Si, Ge and binary Si_x-Ge_1-xalloys (x= 0.25, 0.50, 0.75) was studied by x-ray diffraction and reverse Monte Carlo simulations. Experiments were performed in the normal and supercooled liquid states by using the containerless technique of aerodynamic levitation with CO₂laser heating, enabling deeper supercooling of liquid Si and Si-Ge alloys than previously reported. The local atomic structure of liquid Si and Ge resembles theβ-tin structure. The first coordination numbers of about 6 for all compositions are found to be independent of temperature indicating the supercooled liquids studied retain this high-density liquid (HDL) structure. However, there is evidence of developing local tetrahedral ordering, as manifested by a shoulder on the right side of the first peak inS(Q) which becomes more prominent with increasing supercooling. This result is potentially indicative of a continuous transition from the stable HDLβ-tin (high pressure) phase, towards a metastable low-density liquid phase, reminiscent of the diamond (ambient pressure) structure.

Liquid-Liquid Phase Transitions in Silicon

We use computationally simple neutral pseudoatom ("average atom") density functional theory (DFT) and standard DFT to elucidate liquid-liquid phase transitions (LPTs) in liquid silicon. An ionization-driven transition and three LPTs including the known LPT near 2.5  g/cm^{3} are found. They are robust even to 1 eV. The pair distributions functions, pair potentials, electrical conductivities, and compressibilites are reported. The LPTs are elucidated within a Fermi liquid picture of electron scattering at the Fermi energy that complements the transient covalent bonding picture.

Abnormal separation of the silicon–oxygen bond in the liquid layering transition of silicon dioxide in a nanoslit

Layering transition and separation of silicon and oxygen in liquid SiO₂ become obvious due to the strengthening of the nanoconfined effect.

Liquid-liquid phase transition in quasi-two-dimensional supercooled silicon

Anomalies of the local structural order in quasi-two-dimensional liquid silicon upon cooling are investigated. Results show that the appearance of the left subpeak in pair correlation functions is the signature of the liquid-liquid phase transition (LLPT). The structural origin of the LLPT is the formation of a crystal-like ordered structure with a short-range scale, which in turn forms the local well-organized paracrystalline region. Unlike in the bulk liquid silicon, the stages of the LLPT and liquid-solid phase transition (LSPT) in the quasi-two-dimensional liquid silicon do not overlap. The crystal-like ordered structures formed in the LLPT are precursors which are prepared for the subsequent LSPT. Also observed was a strong interconnection between the local well-organized paracrystalline region and the transition from the typical metal to the semimetal in the two-dimensional silicon. This study will aid in better understanding of the essential phase change in two-dimensional liquid silicon.

Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.

A tetrahedral entropy for water

We introduce the space-dependent correlation function C (Q)(r) and time-dependent autocorrelation function C (Q)(t) of the local tetrahedral order parameter Q identical with Q(r,t). By using computer simulations of 512 waterlike particles interacting through the transferable interaction potential with five points (TIP5 potential), we investigate C (Q)(r) in a broad region of the phase diagram. We find that at low temperatures C (Q)(t) exhibits a two-step time-dependent decay similar to the self-intermediate scattering function and that the corresponding correlation time tau(Q) displays a dynamic cross-over from non-Arrhenius behavior for T > T (W) to Arrhenius behavior for T < T (W), where T (W) denotes the Widom temperature where the correlation length has a maximum as T is decreased along a constant-pressure path. We define a tetrahedral entropy S (Q) associated with the local tetrahedral order of water molecules and find that it produces a major contribution to the specific heat maximum at the Widom line. Finally, we show that tau(Q) can be extracted from S (Q) by using an analog of the Adam-Gibbs relation.

Surface-induced crystallization in supercooled tetrahedral liquids

Surfaces have long been known to have an intricate role in solid-liquid phase transformations. Whereas melting is often observed to originate at surfaces, freezing usually starts in the bulk, and only a few systems have been reported to exhibit signatures of surface-induced crystallization. These include assembly of chain-like molecules, some liquid metals and alloys and silicate glasses. Here, we report direct computational evidence of surface-induced nucleation in supercooled liquid silicon and germanium, and we illustrate the crucial role of free surfaces in the freezing process of tetrahedral liquids exhibiting a negative slope of their melting lines (dT/dP|coexist<0). Our molecular dynamics simulations show that the presence of free surfaces may enhance the nucleation rates by several orders of magnitude with respect to those found in the bulk. Our findings provide insight, at the atomistic level, into the nucleation mechanism of widely used semiconductors, and support the hypothesis of surface-induced crystallization in other tetrahedrally coordinated systems, in particular water in the atmosphere.

Liquid-liquid transition in supercooled silicon determined by first-principles simulation

First-principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below Tc approximately 1232 K and above pc approximately -12 kB. The low-density phase is nearly tetracoordinated, with a pseudogap at the Fermi surface, while the high-density phase is more highly coordinated and metallic in nature. The transition is observed through the formation of van der Waals loops in pressure-volume isotherms below Tc.

Molecular dynamics calculation of thermophysical properties for a highly reactive liquid

In order to further understand the physical characteristics of liquid silicon, the thermophysical properties are required over a broad temperature range. However, its high reactivity brings about great difficulties in the experimental measurement. Here we report the thermophysical properties by molecular dynamics calculation, including density, specific heat, diffusion coefficient, and surface tension. The calculation is performed with a system consisting of 64,000 atoms, and employing the Stillinger-Weber (SW) potential model and the modified embedded atom method (MEAM) potential model. The results show that the density increases as a quadratic function of undercooling, and the value calculated by SW potential model is only 2-4 % smaller than the reported experimental data. The specific heat is obtained to be 30.95 J mol;{-1}K;{-1} by SW potential model and 32.50 J mol;{-1}K;{-1} by MEAM potential model, both of which are constants in the corresponding ranges of temperature. The self-diffusion coefficient is exponentially dependent on the temperature and consistent with the Arrhenius equation. The surface tension increases linearly with the rise of undercooling and agrees well with the reported experimental results. This work provides reasonable data in much wider temperature range, especially for the undercooled metastable state.

Structural and thermodynamic properties of different phases of supercooled liquid water

Computer simulation results are reported for a realistic polarizable potential model of water in the supercooled region. Three states, corresponding to the low density amorphous ice, high density amorphous ice, and very high density amorphous ice phases are chosen for the analyses. These states are located close to the liquid-liquid coexistence lines already shown to exist for the considered model. Thermodynamic and structural quantities are calculated, in order to characterize the properties of the three phases. The results point out the increasing relevance of the interstitial neighbors, which clearly appear in going from the low to the very high density amorphous phases. The interstitial neighbors are found to be, at the same time, also distant neighbors along the hydrogen bonded network of the molecules. The role of these interstitial neighbors has been discussed in connection with the interpretation of recent neutron scattering measurements. The structural properties of the systems are characterized by looking at the angular distribution of neighboring molecules, volume and face area distribution of the Voronoi polyhedra, and order parameters. The cumulative analysis of all the corresponding results confirms the assumption that a close similarity between the structural arrangement of molecules in the three explored amorphous phases and that of the ice polymorphs I(h), III, and VI exists.

Structural and dynamical heterogeneity in deeply supercooled liquid silicon

We report on a first-principles molecular-dynamics study of structural and dynamical heterogeneity in supercooled liquid silicon. We find that highly tetrahedral configurations are intermittently formed and that spatially heterogeneous dynamics is concurrently induced in the deeply supercooled state (1000 K). This heterogeneity is responsible for the anomalous structural relaxation characterized by the stretched-exponential function. The temporal structural fluctuation is found to give rise to the 1/f dependence in the corresponding power spectral density. In a moderately supercooled state (1600 K), the structural and dynamical heterogeneity is quite weak, in contrast to the deeply supercooled state. The applicability of the Stillinger-Weber potential to the deeply supercooled state is also discussed.

Liquid-liquid phase transformation in silicon: evidence from first-principles molecular dynamics simulations

We report results of first principles molecular dynamics simulations that confirm early speculations on the presence of liquid-liquid phase transition in undercooled silicon. However, we find that structural and electronic properties of both low-density liquid (LDL) and high-density liquid (HDL) phases are quite different from those obtained by empirical calculations, the difference being more pronounced for the HDL phase. The discrepancy between quantum and classical simulations is attributed to the inability of empirical potentials to describe changes in chemical bonds induced by density and temperature variations.