Hexagonal Ice Research Articles

An Implementation of the SIESTA code for Electronic Simulations and Its Application in Ordinary Hexagonal Ices

We consider descriptions of a Density Functional Theory (DFT), a flexible LCAO method, and an implementation of the SIESTA code for electronic simulations in crystalline solids. We have defined equilibrium lattice parameters and relaxed atomic positions of ordinary hexagonal iccs(disordered and ordered) with 16 water molecules by an Ab Initio total energy calculation using the SIESTA code. These results will be compared with the results of a plane wave (PW) ultrasoft-pscudopotential method by the CASTEP code.

Following the Crystallization of Amorphous Ice after Ultrafast Laser Heating.

Using time-resolved wide-angle X-ray scattering, we investigated the early stages (10 μs–1 ms) of crystallization of supercooled water, obtained by the ultrafast heating of high- and low-density amorphous ice (HDA and LDA) up to a temperature T = 205 K ± 10 K. We have determined that the crystallizing phase is stacking disordered ice (Isd), with a maximum cubicity of χ = 0.6, in agreement with predictions from molecular dynamics simulations at similar temperatures. However, we note that a growing small portion of hexagonal ice (Ih) was also observed, suggesting that within our timeframe, Isd starts annealing into Ih. The onset of crystallization, in both amorphous ice, occurs at a similar temperature, but the observed final crystalline fraction in the LDA sample is considerably lower than that in the HDA sample. We attribute this discrepancy to the thickness difference between the two samples.

Adsorption of acetamide on crystalline and amorphous ice under atmospheric conditions. A grand canonical Monte Carlo simulation study

The adsorption of acetamide at the surface of crystalline (Ih) and low density amorphous (LDA) ices under tropospheric conditions is investigated by performing a set of grand canonical Monte Carlo simulations at the temperature of 200 K. Our results show that the adsorption is governed by the possibility of new H-bond formation. Further, acetamide-water and acetamide-acetamide hydrogen bonds are found to be of rather similar strengths, and hence these H-bonds are exchangeable with each other around an adsorbed molecule for practically no energy cost. In the case of monolayers being well below the saturation surface concentration, acetamide molecules prefer to stay parallel with the ice surface and form 3H-bonds with the surface waters. The energy of the adsorption at infinitely low surface concentration is estimated to be –64.5 kJ/mol on LDA and –63.7 kJ/mol on Ih ice. Increasing saturation of the surface triggers a marked change in the orientational preference of the adsorbed molecules, thus, once the interaction between the adsorbed molecules is no longer negligible (which occurs already at mildly unsaturated coverages) they prefer to stay perpendicular to the surface, forming 2 H-bonds with the ice phase and another 2 with each other. As a consequence, the ice and adsorbed phases give similar contributions to the adsorption energy at this coverage, which results in a remarkable stability of the adsorption monolayer. Indeed, after their initial rise the adsorption isotherms exhibit a plateau, corresponding to the more or less saturated adsorption monolayer, in a rather broad range of chemical potential values. The surface concentration of the saturated adsorption monolayer is estimated to be 10.2 μmol/m2 on LDA and 8.1 μmol/m2 on Ih ice. Besides adsorption, non-negligible dissolution of the acetamide molecules is found in both ice phases; however, the concentration of the dissolved molecules is still low enough that the solution exhibits ideal behaviour.

Mean path length in refractive regular polygons and prisms

We analytically derive the mean path length of light rays diffusely incident on refractive regular polygons of $n$ sides ($n$-gons), analyzed from the dynamical billiards perspective and from ray optics. In polygons with sufficiently low refractive index, the mean path length is found to be equal to that in the invariant scattering case, i.e., the product of the mean chord length with the refractive index. If the refractive index is higher than some critical value, the mean path length is lower than the scattering value due to inaccessibility of trapped modes. Regular odd $n$-gons are found to have the same mean path length as $2n$-gons, when normalized against their mean chord length. There is a discontinuity between the mean path length in high $n$-gons and that in a circle, attributed to quasitrapped modes in high $n$-gons. This difference is removed with a small amount of absorption. We extend the results to refractive prisms with a regular polygon base, for example, hexagonal ice crystals. For prisms with any ergodic shaped base, we derive a simple formula for the mean path length.

Description of the Interfacial Behavior of Benzonitrile at Icy Surfaces by Grand Canonical Monte Carlo Simulations.

The adsorption of benzonitrile at the surface of crystalline (Ih) and low-density amorphous (LDA) ice has been investigated by grand canonical Monte Carlo simulations at temperatures ranging from 50 to 200 K. It is found that, in spite of its rather large dipole moment of 4.5 D, benzonitrile molecules can only form a highly unsaturated monolayer on LDA ice, reaching not more than 50% of the surface concentration of the saturated monolayer even at the lowest temperature considered, and they practically do not adsorb on Ih ice. In spite of the observed weak ability of the benzonitrile molecules for being adsorbed, the estimated heat of adsorption at an infinitely low surface concentration of -66.8 ± 2.2 kJ/mol is rather large. This value includes the contribution of roughly -30 to -35 kJ/mol of a benzene ring, about -10 kJ/mol of a large molecular dipole moment, and about -20 to -25 kJ/mol of a benzonitrile-water H-bond, as estimated from comparisons with the heat of adsorption values of similar molecules. The surprisingly weak ability of benzonitrile for adsorption is thus attributed to the unusually strong cohesion between the molecules, considerably exceeding their adhesion to ice, as reflected in the 70-80 kJ/mol difference of the lateral and ice contributions to the binding energy of surface benzonitrile molecules in the presence of condensed benzonitrile.

Analysis of Guest Adsorption on Crystal Surfaces Based on the Fragment Molecular Orbital Method.

For gaining insights into interactions in periodic systems, an analysis is developed based on the fragment molecular orbital method combined with periodic boundary conditions. The adsorption energy is decomposed into guest and surface polarization and deformation energy, guest-surface and guest-guest interactions, and the vibrational free energy. The analysis is applied to the adsorption of guest molecules to Ih (001) ice surface. The cooperativity effects result in a non-linear change in the adsorption energy with coverage due to many-body effects. The role of dispersion is found to be dominant for guests with long hydrophobic tails. A rule is proposed relating the length of the alkyl tail with the formation of the guest layer. The computed binding enthalpies are in good agreement with experimental values. For high coverage, adsorbed molecules can form an ordered layer known as self-assembled monolayer.

Freezing mechanism of NaCl solution ultra-confined on surface of calcium-silicate-hydrate: A molecular dynamics study

Cement-based materials in cold regions usually suffer deicer-frost deterioration. To better understand the frozen behavior of the calcium silicate hydrate (C-S-H), molecular dynamics is utilized to investigate the freezing processes of gel surface NaCl solution. The presence of C-S-H substrate significantly reduces the freezing temperature of water molecules ultra-confined on the C-S-H surface, which is 17 K lower than that of bulk water. While majority of random distributed water molecules crystalize to hexagonal ice (Ih) structure, molecules within 0.6 nm of C-S-H substrate cannot form ordered ice crystal at 225 K. The non-icing water layer and lower freezing point are mainly due to oxygen atoms on the silicate chains that provide strong hydrogen bonds with neighboring water and restrict the water orientation. Ionic clusters formed in unfrozen solution are important influence factor for water freezing. Hopefully, this work can provide molecular insights of cement-based materials design in cold regions.

High cubicity of D2O ice inside spherical nanopores of MIL-101(Cr) framework: a neutron diffraction study.

Although cubic ice (ice Ic) is considered to be an important phase of water that impacts ice cloud formation in the Earth's upper atmosphere, its properties have not been studied to the same extent as those of hexagonal ice (ice Ih). This is because pristine ice Ic is not formed in simple laboratory conditions. Ice Ic formed in ambient conditions has a stacking disordered array of both hexagonal and cubic-structured hydrogen-bonded water molecules. It is therefore an active area of research to find ways of developing stacking disorder-free pure ice Ic. We demonstrate the evolution of almost pure ice Ic structure within the spherical nanopores of a hydrostable Cr-based metal-organic framework MIL-101(Cr) with an average pore size of 1 nm by low-temperature neutron diffraction study on D2O. It is observed that at temperatures below 230 K a fraction of liquid D2O transforms into ice and more than 94% of ice crystals evolved inside the pore are cubic in shape. This is a significantly high fraction of ice Ic formed under simple conditions inside the spherical pores of a Cr-based MOF. It is also observed that upon increasing the temperature, ice Ic remains stable until its melting point, without being transformed into ice Ih. This observation is in contrast to our previous observation of ice structure in the 2D cylindrical nanopores of MCM-41, where H2O ice after creeping out from the cylindrical channel was seen to be dominated by hexagonal shape. In the present study, the D2O molecules were confined into well-defined spherical nanopores, which hindered the growth of crystals above a certain size, thus minimizing the stacking disordered array. Nanoconfinement of water inside uniform spherical pores is therefore a promising method for the evolution of a significantly large fraction of cubic ice by minimizing the stacking disorder. This finding may open up the possibility of forming ice Ic with 100% cubicity under simple laboratory conditions, which will help in exploring the microphysics of ice cloud formation in the upper atmosphere.

Ice 0: the experimental proof of its existence – the result of combining approaches used in radiophysics, geology and geography

The experience of combining the efforts of researchers working at the interface of radiophysics, geology and geography is discussed. The effectiveness of such collaboration of researchers is shown by the example of the experimental proof of the existemce of a new crystalline modiciation of ice, ice 0. This kind of ice is formed at the temperature below –23 °C out of supercooled water, and, together with ice Ih and ice Ic, may be formed at the temperatures and pressures corresponding to the surface layers of the Earth’s atmosphere. For this reason, this study is of great interest for understanding the natural processes taking place in the geospheres (atmosphere, cryosphere, biosphere, and hydrosphere).

Quasi-water layer sandwiched between hexagonal ice and wall and its influences on the ice tensile stress.

The presence of a quasi-water/premelting layer at the interface between wall and ice when the temperature (T) is below the melting point was extensively observed in experiments. In this work, molecular dynamics simulations are performed to analyze the underlying physics of the quasi-water layer and the effects of the layer on the ice tensile stress. The results indicate that each molecule and its four nearest neighbours in the quasi-water layer representing an equilibrium structure gradually form a tetrahedral ice-like arrangement from an unstructured liquid-like structure along the direction away from the wall. The average density of the quasi-water layer is equal to or higher than the bulk density of water at T ≥ 240 K or T ≤ 240 K respectively, and reaches 1.155 g cm-3 at T = 210 K, suggesting a structural correlation with the high-density liquid phase of water. Depending on the temperature and wall wettability, the thickness of the quasi-water layer (Hq) ranges from ∼2 Å to ∼25 Å. For prescribed hydrophilic walls, Hq increases monotonically with temperature, and is almost proportional to(Tm - T)-1/3, where Tm is the melting temperature of ice. Hq keeps an almost constant value (2 Å) as the temperature increases and rises sharply after passing a threshold temperature of T ≈ 250 K. In the joint effects of the wall wettability and quasi-water layer's thickness, the ice tensile stress decreasing monotonically at a larger temperature shows an upward trend and then reduces to almost a constant value as the wall changes from a hydrophobic to a hydrophilic one. The results reveal the potential development of anti-icing/de-icing techniques by heating the wall or modifying its surface to increase Hq.

Investigating the quasi-liquid layer on ice surfaces: a comparison of order parameters.

Ice surfaces are characterized by pre-melted quasi-liquid layers (QLLs), which mediate both crystal growth processes and interactions with external agents. Understanding QLLs at the molecular level is necessary to unravel the mechanisms of ice crystal formation. Computational studies of the QLLs heavily rely on the accuracy of the methods employed for identifying the local molecular environment and arrangements, discriminating between solid-like and liquid-like water molecules. Here we compare the results obtained using different order parameters to characterize the QLLs on hexagonal ice (Ih) and cubic ice (Ic) model surfaces investigated with molecular dynamics (MD) simulations in a range of temperatures. For the classification task, in addition to the traditional Steinhardt order parameters in different flavours, we select an entropy fingerprint and a deep learning neural network approach (DeepIce), which are conceptually different methodologies. We find that all the analysis methods give qualitatively similar trends for the behaviours of the QLLs on ice surfaces with temperature, with some subtle differences in the classification sensitivity limited to the solid-liquid interface. The thickness of QLLs on the ice surface increases gradually as the temperature increases. The trends of the QLL size and of the values of the order parameters as a function of temperature for the different facets may be linked to surface growth rates which, in turn, affect crystal morphologies at lower vapour pressure. The choice of the order parameter can be therefore informed by computational convenience except in cases where a very accurate determination of the liquid-solid interface is important.

Light backscattering properties of atmospheric hexagonal ice particles with distorted shape within physical optics approximation

Light backscattering properties of atmospheric hexagonal ice particles with distorted shape within physical optics approximation

Studying Ice with Environmental Scanning Electron Microscopy.

Scanning electron microscopy (SEM) is a powerful imaging technique able to obtain astonishing images of the micro- and the nano-world. Unfortunately, the technique has been limited to vacuum conditions for many years. In the last decades, the ability to introduce water vapor into the SEM chamber and still collect the electrons by the detector, combined with the temperature control of the sample, has enabled the study of ice at nanoscale. Astounding images of hexagonal ice crystals suddenly became real. Since these first images were produced, several studies have been focusing their interest on using SEM to study ice nucleation, morphology, thaw, etc. In this paper, we want to review the different investigations devoted to this goal that have been conducted in recent years in the literature and the kind of information, beyond images, that was obtained. We focus our attention on studies trying to clarify the mechanisms of ice nucleation and those devoted to the study of ice dynamics. We also discuss these findings to elucidate the present and future of SEM applied to this field.

Ring population statistics in an ice lattice model.

We calculate the distribution probability of hexagonal six-site rings in the disordered state of a cubic or hexagonal ice lattice model with ice rules perfectly obeyed. The mean-field distribution obtained is in significant agreement with those, slightly different among them, obtained by Monte Carlo simulations of the cubic or hexagonal model. The results are discussed in connection with the equilibrium and non-equilibrium transition from disorder to ferroelectric proton order.

UV-Induced Formation of Ice XI Observed Using an Ultra-High Vacuum Cryogenic Transmission Electron Microscope and its Implications for Planetary Science.

The occurrence of hydrogen atom-ordered form of ice Ih, ice XI, in the outer Solar System has been discussed based on laboratory experiments because its ferroelectricity influences the physical processes in the outer Solar System. However, the formation of ice XI in that region is still unknown due to a lack of formation conditions at temperatures higher than 72 K and the effect of UV-rays on the phase transition from ice I to ice XI. As a result, we observed the UV-irradiation process on ice Ih and ice Ic using a newly developed ultra-high vacuum cryogenic transmission electron microscope. We found that ice Ih transformed to ice XI at temperatures between 75 and 140 K with a relatively small UV dose. Although ice Ic partially transformed to ice XI at 83 K, the rate of transformation was slower than for ice Ih. These findings point to the formation of ice XI at temperatures greater than 72 K via UV irradiation of ice I crystals in the Solar System; icy grains and the surfaces of icy satellites in the Jovian and Saturnian regions.

Effects of partial crystallization on the glassy slowdown of aqueous ethylene glycol solutions

Combining differential scanning calorimetry, nuclear magnetic resonance, and broadband dielectric spectroscopy studies, we ascertain the glass transition of aqueous ethylene glycol (EG) solutions, in particular the effects of partial crystallization on their glassy slowdown. For the completely liquid solutions in the weakly supercooled regime, it is found that the dynamics of the components occur on very similar time scales, rotational and translational motions are coupled, and the structural (α) relaxation monotonously slows down with increasing EG concentration. Upon cooling, partial crystallization strongly alters the glassy dynamics of EG-poor solutions; in particular, it strongly retards the α relaxation of the remaining liquid fraction, causing a non-monotonous concentration dependence, and it results in a crossover from non-Arrhenius to Arrhenius temperature dependence. In the deeply supercooled regime, a recrossing of the respective α-relaxation times results from the Arrhenius behaviors of the partially frozen EG-poor solutions together with the non-Arrhenius behavior of the fully liquid EG-rich solutions. Exploiting the isotope selectivity of nuclear magnetic resonance, we observe different rotational dynamics of the components in this low-temperature range and determine the respective contributions to the ν relaxation decoupling from the α relaxation when the glass transition is approached. The results suggest that the ν process, which is usually regarded as a water process, actually also involves the EG molecules. In addition, we show that various kinds of partially crystalline aqueous systems share a common relaxation process, which is associated with the frozen fraction and differs from that of bulk hexagonal ice.

On the role of intermolecular vibrational motions for ice polymorphs. III. Mode characteristics associated with negative thermal expansion.

Low-pressure ice forms, such as hexagonal and cubic ice, expand on cooling below temperature 60K. This negative thermal expansivity has been explored in terms of phonon frequency modulation with varying volume and attributed to the negative Grüneisen parameters unique mostly to tetrahedrally coordinated substances. However, an underlying mechanism for the negative Grüneisen parameters has not been known except some schematic analyses. We investigate in this study the characteristics of the intermolecular vibrational modes whose Grüneisen parameters are negative by examining the individual vibrational modes rigorously. It is found that the low frequency modes below 100cm-1, which we explicitly show are mostly bending motions of three hydrogen-bonded molecules, necessarily accompany elongation of the hydrogen bond length at peak amplitudes compared with that at the equilibrium position in executing the vibrational motions. The elongation gives rise to a decrease in the repulsive interaction while an increase in the Coulombic one. The decrease in the repulsive interaction is relaxed substantially by expansion due to its steep slope against molecular separation compared with the sluggish increase in the Coulombic one, and therefore, the negative Grüneisen parameters are obtainable. This scenario is tested against some variants of cubic ice with various water potential models. It is demonstrated that four interaction-site models are suitable to describe the intermolecular vibrations and the thermal expansivity because of the moderate tendency to favor the tetrahedral coordination.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory-Based Ab Initio Molecular Dynamics II: Extensions to the Isobaric-Isoenthalpic and Isobaric-Isothermal Ensembles.

In the previous paper of this series [Ko, H.-Y. et al. J. Chem. Theory Comput. 2020, 16, 3757-3785], we presented a theoretical and algorithmic framework based on a localized representation of the occupied space that exploits the inherent sparsity in the real-space evaluation of the exact exchange (EXX) interaction in finite-gap systems. This was accompanied by a detailed description of exx, a massively parallel hybrid message-passing interface MPI/OpenMP implementation of this approach in Quantum ESPRESSO (QE) that enables linear scaling hybrid density functional theory (DFT)-based ab initio molecular dynamics (AIMD) in the microcanonical/canonical (NVE/NVT) ensembles of condensed-phase systems containing 500-1000 atoms (in fixed orthorhombic cells) with a wall time cost comparable to semi-local DFT. In this work, we extend the current capabilities of exx to enable hybrid DFT-based AIMD simulations of large-scale condensed-phase systems with general and fluctuating cells in the isobaric-isoenthalpic/isobaric-isothermal (NpH/NpT) ensembles. The theoretical extensions to this approach include an analytical derivation of the EXX contribution to the stress tensor for systems in general simulation cells with a computational complexity that scales linearly with system size. The corresponding algorithmic extensions to exx include optimized routines that (i) handle both static and fluctuating simulation cells with non-orthogonal lattice symmetries, (ii) solve Poisson's equation in general/non-orthogonal cells via an automated selection of the auxiliary grid directions in the Natan-Kronik representation of the discrete Laplacian operator, and (iii) evaluate the EXX contribution to the stress tensor. Using this approach, we perform a case study on a variety of condensed-phase systems (including liquid water, a benzene molecular crystal polymorph, and semi-conducting crystalline silicon) and demonstrate that the EXX contributions to the energy and stress tensor simultaneously converge with an appropriate choice of exx parameters. This is followed by a critical assessment of the computational performance of the extended exx module across several different high-performance computing architectures via case studies on (i) the computational complexity due to lattice symmetry during NpT simulations of three different ice polymorphs (i.e., ice Ih, II, and III) and (ii) the strong/weak parallel scaling during large-scale NpT simulations of liquid water. We demonstrate that the robust and highly scalable implementation of this approach in the extended exx module is capable of evaluating the EXX contribution to the stress tensor with negligible cost (<1%) as well as all other EXX-related quantities needed during NpT simulations of liquid water (with a very tight 150 Ry planewave cutoff) in ≈5.2 s ((H2O)128) and ≈6.8 s ((H2O)256) per AIMD step. As such, the extended exx module presented in this work brings us another step closer to routinely performing hybrid DFT-based AIMD simulations of sufficient duration for large-scale condensed-phase systems across a wide range of thermodynamic conditions.

Research of seawater freezing based on TIP4P/ICE potential: A new algorithm for generating proton disordered ice Ih

We proposed a new algorithm to generate proton disordered ice Ih, which greatly improves the operation efficiency. The direct coexistence technology was used to simulate the freezing of aqueous solution of TIP4P/Ice water and NaCl under seawater concentration. Taking the water freezing point at normal pressure of 273.15 K as the reference point of the simulated temperature, the doping of salt ions and the growth of ice were observed at three temperatures. The results presented that only a small amount of chloride ions were found to be doped into the structure of the growing ice, no sodium ions were observed.

Tunneling of Hydrogen and Deuterium Atoms on Interstellar Ices (Ih and ASW)

Model calculations are performed to investigate the kinetic isotope effect of hydrogen and deuterium atom diffusion on hexagonal ice and amorphous solid water. Comparisons with experimental results by Kuwahata et al. (Phys. Rev. Lett., Sep. 2015, 115 (13), 133201) at 10 K are made. The experimentally derived kinetic isotope effect on amorphous solid water is reproduced by transition state theory. The experimentally found kinetic isotope effect on hexagonal ice is much larger than on amorphous solid water and is not reproduced by transition state theory. Additional calculations using model potentials are made for the hexagonal ice, but the experimental kinetic isotope effect is not fully reproduced. A strong influence of temperature is observed in the calculations. The influence of tunnelling is discussed in detail and related to the experiments. The calculations fully support the claims by the Kuwahata et al. (Phys. Rev. Lett., Sep. 2015, 115 (13), 133201) that on amorphous solid water the diffusion is predominantly by thermal hopping while on the polycrystalline ice tunnelling diffusion contributes significantly.