Hexagonal Ice Research Articles

Medium-density amorphous ice unveils shear rate as a new dimension in water’s phase diagram

Recent experiments revealed a new amorphous ice phase, medium-density amorphous ice (MDA), formed by ball-milling ice Ih at 77 K [Rosu-Finsen et al., Science 379, 474-478 (2023)]. MDA has density between that of low-density amorphous (LDA) and high-density amorphous (HDA) ices, adding to the complexity of water's phase diagram, known for its glass polyamorphism and two-state thermodynamics. The nature of MDA and its relation to other amorphous ices and liquid water remain unsolved. Here, we use molecular simulations under controlled pressure and shear rate at 77 K to produce and investigate MDA. We find that MDA formed at constant shear rate is a steady-state nonequilibrium shear-driven amorphous ice (SDA), that can be produced by shearing ice Ih, LDA, or HDA. Our results suggest that MDA could be obtained by ball-milling water glasses without crystallization interference. Increasing the shear rate at ambient pressure produces SDAs with densities ranging from LDA to HDA, revealing shear rate as a new thermodynamic variable in the nonequilibrium phase diagram of water. Indeed, shearing provides access to amorphous states inaccessible by controlling pressure and temperature alone. SDAs produced with shearing rates as high as 106 s-1 sample the same region of the potential energy landscape than hyperquenched glasses with identical density, pressure, and temperature. Intriguingly, SDAs obtained by shearing at ~108 s-1 have density, enthalpy, and structure indistinguishable from those of water "instantaneously" quenched from room temperature to 77 K over 10 ps, making them good approximants for the "true glass" of ambient liquid water.

High Resolution X-ray Diffraction Studies of the Natural Minerals of Gas Hydrates and Occurrence of Mixed Phases

The types and concentrations of gas hydrates collected from four different geological sites were analyzed using high-resolution angular dispersive X-ray powder diffraction, with synchrotron radiation as the source. Measurements were taken across a temperature range of 80 to 300 K and a pressure range of 0.1 to 80 MPa. All four gas hydrate samples showed the presence of three mixed crystal structures: structures I, II, and H. Additionally, the ice Ih structure was inherently present in all the natural gas hydrate minerals. The variation in the types and concentrations of gas hydrates can be attributed to the diversity of natural gases at different geographic locations.

Microstructure-sensitive crystal plasticity and phase-field modeling of deformation and fracture in polycrystalline ice

The formation of crevasses in Greenland and Antarctica is primarily driven by the brittle failure of ice at low strain rates. Understanding this phenomenon requires exploring the effect of microstructural heterogeneity and anisotropic elastoplastic deformation on the fracture behavior of ice. Here, we have developed a microstructure-sensitive coupled crystal plasticity and phase-field model. This model allows us to study the plastic deformation, damage initiation and propagation under various strain rates in hexagonal open-packed polycrystalline ice, the prevailing phase on Earth. By employing a Bayesian optimization method, we derived the material parameters for the micromechanical model based on experimental results. The modeling results reveal that the activation of basal dislocations results in a brittle to ductile transition in ice at a low strain rate of 10-7s-1 under tension. At higher strain rates, the intrinsic plastic anisotropy of ice leads to heterogeneous deformation among grains and stress concentration near grain boundaries, triggering crack initiation and exacerbating the brittleness of ice. Under compression, cracks usually do not propagate throughout the specimen due to a significant decrease in stress around the crack tip upon propagation. Moreover, we found that the formation of the shear-induced basal texture at the bottom of ice layers and along glacier valley sides intensifies the brittleness of ice. This study provides insights into the micromechanical deformation and fracture mechanisms of ice, elucidating the intricate process of crevasse development in polar ice sheets.

Efficient Parametrization of Transferable Atomic Cluster Expansion for Water.

We present a highly accurate and transferable parametrization of water using the atomic cluster expansion (ACE). To efficiently sample liquid water, we propose a novel approach that involves sampling static calculations of various ice phases and utilizing the active learning (AL) feature of the ACE-based D-optimality algorithm to select relevant liquid water configurations, bypassing computationally intensive ab initio molecular dynamics simulations. Our results demonstrate that the ACE descriptors enable a potential initially fitted solely on ice structures, which is later upfitted with few configurations of liquid, identified with AL to provide an excellent description of liquid water. The developed potential exhibits remarkable agreement with first-principles reference, accurately capturing various properties of liquid water, including structural characteristics such as pair correlation functions, covalent bonding profiles, and hydrogen bonding profiles, as well as dynamic properties like the vibrational density of states, diffusion coefficient, and thermodynamic properties such as the melting point of the ice Ih. Our research introduces a new and efficient sampling technique for machine learning potentials in water simulations while also presenting a transferable interatomic potential for water that reveals the accuracy of first-principles reference. This advancement not only enhances our understanding of the relationship between ice and liquid water at the atomic level but also opens up new avenues for studying complex aqueous systems.

X-ray diffraction and quasielastic neutron scattering studies of the structure and dynamic properties of water confined in ordered microporous carbon pores

The structure and dynamic properties of capillary-condensed water confined in ordered microporous carbon (OMC) of pores diameter 18.7 Å are investigated over a temperature range of 200–300 K by adsorption/desorption isotherms, X-ray diffraction (XRD), and quasielastic neutron scattering (QENS). The nitrogen adsorption/desorption isotherm of OMC pores at 77 K exhibits an I-type pattern. The water adsorption/desorption isotherm of OMC pores at 298 K is of type V. The XRD data on water confined in OMC reveal that the tetrahedral network structure of water is perturbed from the bulk water structure, but not to such an extent as found for water confined in MCM-41 and Ph-PMO previously reported. With decreasing the temperature, the ∼2.8 Å peak shifts to shorter distances, while the second-neighbor H2O– H2O interaction distances gradually increase from 3.95 Å and 4.49 Å to 4.43 Å and 4.84 Å, indicating a tendency to form a more tetrahedral-like hydrogen-bonded water structure at subzero temperatures. Below 230 K, the hexagonal ice Ih was partially formed in OMC pores. The QENS spectra were analyzed using a jump-diffusion model to translate water molecules. The translational diffusion of water molecules in OMC pores is comparable to that of bulk water at 300 K and higher than that in MCM-41, and the mobility slows as the temperature decreases. The elastic incoherent structure factor (EISF) analysis found evidence for immobile and mobile fractions of confined water. The mobile fraction exhibited jump diffusion, with a jump length consistent with a sphere of confinement radius of 4–8 Å. The results obtained in the present work are compared with those reported for MCM-41 with a hydrophilic interface and Ph-PMO with an amphiphilic interface, and the influence of interface effect on local structure and dynamic properties of confined water is discussed.

Multitwinned Ice Nanocrystals.

Multitwinned nanocrystals are commonly found in substances that preferentially adopt tetrahedral local arrangements, but not yet in water crystals. Ice nanocrystals are pivotal in cloud microphysics, and their surfaces become increasingly prominent in determining structure as crystal size decreases. Nevertheless, discussions on nanocrystal structures have predominantly centered on ice polymorphs observed in bulk: hexagonal (Ih), cubic (Ic), and stacking-disordered (Isd) ices. Here, we demonstrate, through molecular dynamics (MD) simulations, that decahedral and icosahedral nanocrystals form from liquid water droplets of a few nanometers in size without violating the ice rule. The brute force spontaneous crystallization is conducted using the mW model, and the thermodynamic stability is examined using the TIP4P/Ice model. During the crystallization process, the formation of twin boundaries precedes the emergence of centers exhibiting 5-fold and icosahedral symmetry. The free energy calculation suggests the icosahedron has comparable stability with ice Ih nanocrystal. The frequent occurrence of these unreported ice nanocrystals aligns with the fact that natural polycrystalline snow crystals predominantly display a 70.5-degree angle between the Ih c-axes of adjacent branches. Moreover, we show that the formation of multitwinned ice nanocrystals is enhanced within a fullerene, providing a potential avenue for experimental observations.

Proton-Driven Dynamic Behavior of Nanoconfined Water in Hydrophilic MXene Sheets.

Liquid water under nanoscale confinement has attracted intensive attention due to its pivotal role in understanding various phenomena across many scientific fields. MXenes serve an ideal paradigm for investigating the dynamic behaviors of nanoconfined water in a hydrophilic environment. Combining deep neural networks and an active learning scheme, here we elucidate the proton-driven dynamics of water molecules confined between V2CTx sheets using molecular dynamics simulation. Firstly, we have found that the Eigen and Zundel cations can inhibit water-induced oxidation by adjusting the orientation of water molecules, thus proposing a general antioxidant strategy. Besides, we also identified a hexagonal ice phase with abnormal bonding rules at room temperature, rather than only at ultralow temperatures as other studies reported, and further captured the proton-induced water phase transition. This highlighted the importance of protons in the maintaining stable crystal phase and phase transition of water. Furthermore, we discussed the conversions of different water structures and water diffusivity with changing proton concentrations in detail. The results provide useful guidance in practical applications of MXenes including developing antioxidant strategies, identifying novel 2D water phases and optimizing energy storage and conversion.

Hydrogen Ordering in Ice Ih Facilitates the Transition from HDA to Ice XII

Hydrogen Ordering in Ice Ih Facilitates the Transition from HDA to Ice XII

Numerical evidence for the existence of three different stable liquid water structures as indicated by local order parameter.

Structures of liquid water are controversial not only in supercooled polyamorphism but also in stable bulk liquids in the high temperature and pressure range. Several experimental studies in bulk liquid have assumed the existence of three different liquid water structures. If indeed the three liquid water structures are different, they should be clearly distinguished by some measure other than density that characterizes the difference in structural order. In this study, whether the three different bulk liquid water structures are real or not is numerically verified based on molecular simulations using a reliable water molecular model. Since these liquid water structures have been suggested to be related to three different crystal structures (i.e., ice Ih, III, and V), liquid structures are sampled from the vicinity of the ice Ih-liquid coexistence point, the ice III-V-liquid triple point, and the ice V-VI-liquid triple point, respectively. An attempt is made to introduce local order parameters (LOPs) as an indicator to distinguish these structures. A fast and exhaustive LOP search is performed by the molecular assembly structure learning package for Identifying order parameters. The selected LOP distinguishes the molecular structures of three different stable liquid waters with high accuracy, providing numerical evidence that these structural orders differ from each other. Furthermore, regions of the liquid water structures are drawn on a phase diagram using the LOP, demonstrating their consistency with experimental studies.

Data-efficient fine-tuning of foundational models for first-principles quality sublimation enthalpies.

Calculating sublimation enthalpies of molecular crystal polymorphs is relevant to a wide range of technological applications. However, predicting these quantities at first-principles accuracy - even with the aid of machine learning potentials - is a challenge that requires sub-kJ mol-1 accuracy in the potential energy surface and finite-temperature sampling. We present an accurate and data-efficient protocol for training machine learning interatomic potentials by fine-tuning the foundational MACE-MP-0 model and showcase its capabilities on sublimation enthalpies and physical properties of ice polymorphs. Our approach requires only a few tens of training structures to achieve sub-kJ mol-1 accuracy in the sublimation enthalpies and sub-1% error in densities at finite temperature and pressure. Exploiting this data efficiency, we perform preliminary NPT simulations of hexagonal ice at the random phase approximation level and demonstrate a good agreement with experiments. Our results show promise for finite-temperature modelling of molecular crystals with the accuracy of correlated electronic structure theory methods.

Molecular dynamics simulations of the effect of static electric field on progressive ice formation.

Ice accumulation under static electric fields presents a significant hazard to transmission lines and power grids. Contemporary computational studies of electrofreezing predominantly probed excessive electric fields (109 V/m) that are significantly higher than those typically encountered in proximity to transmission lines. To elucidate the influence of realistic electric fields (105 V/m) on ice crystallization, we run extensive molecular dynamics (MD) simulations across dual ice-water coexistence systems. Three aspects of work were accordingly examined. First, we investigated the influence of the effect of static electric fields, with a strength of 105 V/m, along three orthogonal axes on the phase transition during the encountered freezing and melting processes. Second, we established the mechanism of how the direction of an electric field, the initial ice crystallography, and the adjacent crystal planes influence the solidification process. Third, the results of our MD simulations were further post-processed to determine the dipole moment, radial distribution, and angle distribution resulting from the static electric field. Our results indicate that while weak electric fields do not cause complete polarization of liquid water molecules, they can induce a transition to a more structured ice-like geometry of the water molecules at the ice-water interphase region, particularly when applied perpendicular to the ice-water interphase. Notably, the interface adjacent to cubic ice exhibits a greater response to the electric fields than that adjacent to hexagonal ice. This is attributable to the intrinsic differences in their original hydrogen bonding networks.

Numerical Simulation of the Effects of Surface Roughness on Light Scattering by Hexagonal Ice Plates

Numerical Simulation of the Effects of Surface Roughness on Light Scattering by Hexagonal Ice Plates

Bridging classical nucleation theory and molecular dynamics simulation for homogeneous ice nucleation.

Water freezing, initiated by ice nucleation, occurs widely in nature, ranging from cellular to global phenomena. Ice nucleation has been experimentally proven to require the formation of a critical ice nucleus, consistent with classical nucleation theory (CNT). However, the accuracy of CNT quantitative predictions of critical cluster sizes and nucleation rates has never been verified experimentally. In this study, we circumvent this difficulty by using molecular dynamics (MD) simulation. The physical properties of water/ice for CNT predictions, including density, chemical potential difference, and diffusion coefficient, are independently obtained using MD simulation, whereas the calculation of interfacial free energy is based on thermodynamic assumptions of CNT, including capillarity approximation among others. The CNT predictions are compared to the MD evaluations of brute-force simulations and forward flux sampling methods. We find that the CNT and MD predicted critical cluster sizes are consistent, and the CNT predicted nucleation rates are higher than the MD predicted values within three orders of magnitude. We also find that the ice crystallized from supercooled water is stacking-disordered ice with a stacking of cubic and hexagonal ices in four representative types of stacking. The prediction discrepancies in nucleation rate mainly arise from the stacking-disordered ice structure, the asphericity of ice cluster, the uncertainty of ice-water interfacial free energy, and the kinetic attachment rate. Our study establishes a relation between CNT and MD to predict homogeneous ice nucleation.

Phase Transition of Cubic Ice to Hexagonal Ice during Growth and Decomposition.

Ice, one of the most enigmatic materials on Earth, exhibits diverse polymorphism, with research mainly focusing on the most commonly observed phases: hexagonal ice (Ih), cubic ice (Ic), and stacking-disordered ice (Isd). While their formation or structural changes are crucial for advancements in cloud science, climate modeling, and cryogenic technology, the molecular mechanisms driving these phenomena remain unexplored. Herein, utilizing cryogenic transmission electron microscopy, we investigate the formation of ice at two different temperatures, demonstrating a size-dependent phase shift from Ic to Isd. Furthermore, a relatively metastable cubic phase in Isd transitions to a hexagonal phase under electron beam radiation. This transition, facilitated by crystal defects, contrasts with perfect crystalline Ic, which maintains its original phase, emphasizing the importance of defects in polymorphic phase transitions. Our findings provide novel insights on phase control during the ice growth processes and polymorphic phase transitions from the cubic-to-hexagonal phases.

Proton‐Driven Dynamic Behavior of Nanoconfined Water in Hydrophilic MXene Sheets

Liquid water under nanoscale confinement has attracted intensive attention due to its pivotal role in understanding various phenomena across many scientific fields. MXenes serve an ideal paradigm for investigating the dynamic behaviors of nanoconfined water in a hydrophilic environment. Combining deep neural networks and an active learning scheme, here we elucidate the proton‐driven dynamics of water molecules confined between V2CTx sheets using molecular dynamics simulation. Firstly, we have found that the Eigen and Zundel cations can inhibit water‐induced oxidation by adjusting the orientation of water molecules, thus proposing a general antioxidant strategy. Besides, we also identified a hexagonal ice phase with abnormal bonding rules at room temperature, rather than only at ultralow temperatures as other studies reported, and further captured the proton‐induced water phase transition. This highlighted the importance of protons in the maintaining stable crystal phase and phase transition of water. Furthermore, we discussed the conversions of different water structures and water diffusivity with changing proton concentrations in detail. The results provide useful guidance in practical applications of MXenes including developing antioxidant strategies, identifying novel 2D water phases and optimizing energy storage and conversion.

Generating proton-disordered ice configurations using orientational simulated annealing.

We examine an algorithm for the creation of proton-disordered ice cells based on a simulated-annealing (SA) scheme for molecular orientations. Application to defect-free ice Ih, a clathrate-hydrate structure, and a random polycrystalline ice Ih sample demonstrates the SA technique to be effective, attaining maximum HB connectivity using relatively short cooling simulations, thus serving as an alternative method for those cases in which the application of topology-based methods is inhibited.

Molecular Dynamics Simulation Investigation of Freezing Point Depression in NaClO4 Electrolyte Solution by CaCl2.

The development of inorganic antifreeze electrolytes is of paramount importance for the application of sodium-ion batteries under low-temperature conditions. However, there is little reported about their molecular mechanism for lowering the freezing point of electrolytes. Therefore, this study explores the mechanism by which CaCl2 lowers the freezing point of the NaClO4 electrolyte. Hexagonal ice (ice Ih) was used as the ice seed, and CaCl2 was selected as the antifreeze agent. The coexistence system of ice and solution was constructed to simulate the freezing process. It was found that there is ion rejection at the ice layer, with ions predominantly distributed in the solution. Over time, ions form an ion adsorption layer at the ice-solution interface. The radial distribution function (RDF) and spatial distribution function (SDF) of Na+, ClO4-, Ca2+, and Cl- revealed that ions form the first solvation shells with water molecules. The interaction energy between ions and water molecules is greater than that between ice nuclei and water. Therefore, ions are better able to maintain the stability of their solvation shells and inhibit the growth of ice Ih through a mechanism of competition for water molecules. Furthermore, the dissolution free energy of Na+ and Ca2+ in the aqueous phase was studied. The results indicated that Ca2+ has a stronger affinity for water molecules than Na+, making it more competitive in competing for water with ice Ih. Therefore, CaCl2 in NaClO4 solution can reduce the freezing point. This work provides a molecular-level understanding of how CaCl2 reduces the freezing point of NaClO4 solution, which is beneficial for designing strategies for low-temperature electrolytes.

Direct Visualization of Molecular Stacking in Quasi-2D Hexagonal Ice.

Understanding ice nucleation and growth is of great interest to researchers due to its importance in the biological, cryopreservation, and environmental fields. However, microstructural investigations of ice on the molecular scale are still lacking. In this paper, a simple method is proposed to prepare quasi-2-dimensional ice Ih films, which have been characterized via cryogenic transmission electron microscope. The intersecting stacking faults of basal (BSF) and prismatic (PSF) types have been directly visualized and resolved with a notable first-time report of PSF in ice Ih. Moreover, the possible growth pathways of BSF, namely, the Ic phase, were elucidated by the theoretical calculations and the chair conformation of H2O molecules. This study offers valuable insights that can enhance researchers' understanding of the growth kinetics of crystalline ice.

Hirshfeld atom refinement and dynamical refinement of hexagonal ice structure from electron diffraction data.

Reaching beyond the commonly used spherical atomic electron density model allows one to greatly improve the accuracy of hydrogen atom structural parameters derived from X-ray data. However, the effects of atomic asphericity are less explored for electron diffraction data. In this work, Hirshfeld atom refinement (HAR), a method that uses an accurate description of electron density by quantum mechanical calculation for a system of interest, was applied for the first time to the kinematical refinement of electron diffraction data. This approach was applied here to derive the structure of ordinary hexagonal ice (Ih). The effect of introducing HAR is much less noticeable than in the case of X-ray refinement and it is largely overshadowed by dynamical scattering effects. It led to only a slight change in the O-H bond lengths (shortening by 0.01 Å) compared with the independent atom model (IAM). The average absolute differences in O-H bond lengths between the kinematical refinements and the reference neutron structure were much larger: 0.044 for IAM and 0.046 Å for HAR. The refinement results changed considerably when dynamical scattering effects were modelled - with extinction correction or with dynamical refinement. The latter led to an improvement of the O-H bond length accuracy to 0.021 Å on average (with IAM refinement). Though there is a potential for deriving more accurate structures using HAR for electron diffraction, modelling of dynamical scattering effects seems to be a necessary step to achieve this. However, at present there is no software to support both HAR and dynamical refinement.

Accuracy limit of non-polarizable four-point water models: TIP4P/2005 vs OPC. Should water models reproduce the experimental dielectric constant?

The last generation of four center non-polarizable models of water can be divided into two groups: those reproducing the dielectric constant of water, as OPC, and those significantly underestimating its value, as TIP4P/2005. To evaluate the global performance of OPC and TIP4P/2005, we shall follow the test proposed by Vega and Abascal in 2011 evaluating about 40 properties to fairly address this comparison. The liquid-vapor and liquid-solid equilibria are computed, as well as the heat capacities, isothermal compressibilities, surface tensions, densities of different ice polymorphs, the density maximum, equations of state at high pressures, and transport properties. General aspects of the phase diagram are considered by comparing the ratios of different temperatures (namely, the temperature of maximum density, the melting temperature of hexagonal ice, and the critical temperature). The final scores are 7.2 for TIP4P/2005 and 6.3 for OPC. The results of this work strongly suggest that we have reached the limit of what can be achieved with non-polarizable models of water and that the attempt to reproduce the experimental dielectric constant deteriorates the global performance of the water force field. The reason is that the dielectric constant depends on two surfaces (potential energy and dipole moment surfaces), whereas in the absence of an electric field, all properties can be determined simply from just one surface (the potential energy surface). The consequences of the choice of the water model in the modeling of electrolytes in water are also discussed.