Hexagonal Ice Research Articles

Light scattering by hexagonal ice crystal in the Wentzel–Kramers–Brillouin approximation

The Wentzel–Kramers–Brillouin (WKB) method is applied for hexagonal ice crystal. A closed form expression of the form factor is derived for an hexagonal ice crystal. The other approximations, such as the Rayleigh–Gans–Debye approximation (RGD) and the anomalous diffraction (AD), are deducted as particular cases from our formula. Furthermore, the coefficient of extinction is also given. This study is made for two special cases of the incidence (flat incident and edge-on incidence). To illustrate our analytical results, some numerical examples are analyzed.

Backscatter by azimuthally oriented ice crystals of cirrus clouds.

The backscattering Mueller matrix has been calculated for the first time for the hexagonal ice columns and plates with both zenith and azimuth preferential orientations. The possibility of a vertically pointing polarization lidar measuring the full Mueller matrix for retrieving the orientation distributions of the crystals is considered. It is shown that the element m44 or, equivalently, the circular depolarization ratio distinguishes between the low and high zenith tilts of the crystals. Then, at their low or high zenith tilts, either the element m22 or m34, respectively, should be measured to retrieve the azimuth tilts.

Diameter-dependent hydrophobicity in carbon nanotubes

Single-wall carbon nanotubes (SWCNTs) are a good model system that provides atomically smooth nanocavities. It has been reported that water-SWCNTs exhibit hydrophobicity depending on the temperature T and the SWCNT diameter D. SWCNTs adsorb water molecules spontaneously in their cylindrical pores around room temperature, whereas they exhibit a hydrophilic-hydrophobic transition or wet-dry transition (WDT) at a critical temperature Twd ≈ 220-230 K and above a critical diameter Dc ≈ 1.4-1.6 nm. However, details of the WDT phenomenon and its mechanism remain unknown. Here, we report a systematic experimental study involving X-ray diffraction, optical microscopy, and differential scanning calorimetry. It is found that water molecules inside thick SWCNTs (D > Dc) evaporate and condense into ice Ih outside the SWCNTs at Twd upon cooling, and the ice Ih evaporates and condenses inside the SWCNTs upon heating. On the other hand, residual water trapped inside the SWCNTs below Twd freezes. Molecular dynamics simulations indicate that upon lowering T, the hydrophobicity of thick SWCNTs increases without any structural transition, while the water inside thin SWCNTs (D < Dc) exhibits a structural transition, forming an ordered ice. This ice has a well-developed hydrogen bonding network adapting to the cylindrical pores of the SWCNTs. Thus, the unusual diameter dependence of the WDT is attributed to the adaptability of the structure of water to the pore dimension and shape.

Adsorption of Fluorinated Methane Derivatives at the Surface of Ice under Tropospheric Conditions, As Seen from Grand Canonical Monte Carlo Simulations

The adsorption of the fluorinated methane derivatives, CHnF4–n, at the (0001) surface of Ih ice is studied by grand canonical Monte Carlo computer simulation at the tropospheric temperature of 200 K. It is found that CH4 and CF4 adsorbs rather weakly, while CH3F, CH2F2, and CHF3 exhibit multilayer adsorption. The vapor phase of CH4 and CF4 turns out to be rather dense, in accordance with the fact that CF4 is already rather close to, while CH4 is already above, its critical point. Adsorbed CH3F molecules, being in contact with the ice phase, turn with their H atoms toward the ice surface, forming several weak, C–H donated hydrogen bonds with the surface water molecules. By contrast, CH2F2 and CHF3 molecules are found to turn at least one of their F atoms toward the ice phase, forming strong, O–H donated hydrogen bonds with surface waters, in accordance with former infrared (IR) spectroscopy data. Once all hydrogen-bonding positions are occupied, the first molecular layer of these molecules is not yet satur...

Vibrational effects on surface energies and band gaps in hexagonal and cubic ice.

Surface energies of hexagonal and cubic water ice are calculated using first-principles quantum mechanical methods, including an accurate description of anharmonic nuclear vibrations. We consider two proton-orderings of the hexagonal and cubic ice basal surfaces and three proton-orderings of hexagonal ice prism surfaces, finding that vibrations reduce the surface energies by more than 10%. We compare our vibrational densities of states to recent sum frequency generation absorption measurements and identify surface proton-orderings of experimental ice samples and the origins of characteristic absorption peaks. We also calculate zero point quantum vibrational corrections to the surface electronic band gaps, which range from -1.2 eV for the cubic ice basal surface up to -1.4 eV for the hexagonal ice prism surface. The vibrational corrections to the surface band gaps are up to 12% smaller than for bulk ice.

How important is thermal expansion for predicting molecular crystal structures and thermochemistry at finite temperatures?

Molecular crystals expand appreciably upon heating due to both zero-point and thermal vibrational motion, yet this expansion is often neglected in molecular crystal modeling studies. Here, a quasi-harmonic approximation is coupled with fragment-based hybrid many-body interaction calculations to predict thermal expansion and finite-temperature thermochemical properties in crystalline carbon dioxide, ice Ih, acetic acid and imidazole. Fragment-based second-order Möller-Plesset perturbation theory (MP2) and coupled cluster theory with singles, doubles and perturbative triples [CCSD(T)] predict the thermal expansion and the temperature dependence of the enthalpies, entropies and Gibbs free energies of sublimation in good agreement with experiment. The errors introduced by neglecting thermal expansion in the enthalpy and entropy cancel somewhat in the Gibbs free energy. The resulting ∼ 1-2 kJ mol(-1) errors in the free energy near room temperature are comparable to or smaller than the errors expected from the electronic structure treatment, but they may be sufficiently large to affect free-energy rankings among energetically close polymorphs.

Thin Ice Films at Mineral Surfaces.

Ice films formed at mineral surfaces are of widespread occurrence in nature and are involved in numerous atmospheric and terrestrial processes. In this study, we studied thin ice films at surfaces of 19 synthetic and natural mineral samples of varied structure and composition. These thin films were formed by sublimation of thicker hexagonal ice overlayers mostly produced by freezing wet pastes of mineral particles at -10 and -50 °C. Vibration spectroscopy revealed that thin ice films contained smaller populations of strongly hydrogen-bonded water molecules than in hexagonal ice and liquid water. Thin ice films at the surfaces of the majority of minerals considered in this work [i.e., metal (oxy)(hydr)oxides, phyllosilicates, silicates, volcanic ash, Arizona Test Dust] produced intense O-H stretching bands at ∼3400 cm(-1), attenuated bands at ∼3200 cm(-1), and liquid-water-like bending band at ∼1640 cm(-1) irrespective of structure and composition. Illite, a nonexpandable phyllosilicate, is the only mineral that stabilized a form of ice that was strongly resilient to sublimation in temperatures as low as -50 °C. As mineral-bound thin ice films are the substrates upon which ice grows from water vapor or aqueous solutions, this study provides new constraints from which their natural occurrences can be understood.

What Determines the Ice Polymorph in Clouds?

Ice crystals in the atmosphere nucleate from supercooled liquid water and grow by vapor uptake. The structure of the ice polymorph grown has strong impact on the morphology and light scattering of the ice crystals, modulates the amount of water vapor in ice clouds, and can impact the molecular uptake and reactivity of atmospheric aerosols. Experiments and molecular simulations indicate that ice nucleated and grown from deeply supercooled liquid water is metastable stacking disordered ice. The ice polymorph grown from vapor has not yet been determined. Here we use large-scale molecular simulations to determine the structure of ice that grows as a result of uptake of water vapor in the temperature range relevant to cirrus and mixed-phase clouds, elucidate the molecular mechanism of the formation of ice at the vapor interface, and compute the free energy difference between cubic and hexagonal ice interfaces with vapor. We find that vapor deposition results in growth of stacking disordered ice only under conditions of extreme supersaturation, for which a nonequilibrium liquid layer completely wets the surface of ice. Such extreme conditions have been used to produce stacking disordered frost ice in experiments and may be plausible in the summer polar mesosphere. Growth of ice from vapor at moderate supersaturations in the temperature range relevant to cirrus and mixed-phase clouds, from 200 to 260 K, produces exclusively the stable hexagonal ice polymorph. Cubic ice is disfavored with respect to hexagonal ice not only by a small penalty in the bulk free energy (3.6 ± 1.5 J mol(-1) at 260 K) but also by a large free energy penalty at the ice-vapor interface (89.7 ± 12.8 J mol(-1) at 260 K). The latter originates in higher vibrational entropy of the hexagonal-terminated ice-vapor interface. We predict that the free energy penalty against the cubic ice interface should decrease strongly with temperature, resulting in some degree of stacking disorder in ice grown from vapor in the tropical tropopause layer, and in polar stratospheric and noctilucent clouds. Our findings support and explain the evolution of the morphology of ice crystals from hexagonal to trigonal symmetry with decreasing temperature, as reported by experiments and in situ measurements in clouds. We conclude that selective growth of the elusive cubic ice polymorph by manipulation of the interfacial properties can likely be achieved at the ice-liquid interface but not at the ice-vapor interface.

Polarized radiative transfer of a cirrus cloud consisting of randomly oriented hexagonal ice crystals: The 3×3 approximation for non-spherical particles

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6×103 so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling–adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5% for I and within 1.5% for Q for all viewing angles. In 1971 Hansen [1] showed that for scattering by spherical particles the 3×3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen׳s conjecture for the cirrus cloud particles considered in this study. It was found that the 3×3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3×3 approximation leads to an absolute error <2×10−6 for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

The normal modes of lattice vibrations of ice XI.

The vibrational spectrum of ice XI at thermal wavelengths using the CASTEP code, a first-principles simulation method, is investigated. A dual-track approach is constructed to verify the validity for the computational phonon spectrum: collate the simulated spectrum with inelastic neutron scattering experiments and assign the photon scattering peaks according to the calculated normal vibration frequencies. The 33 optical normal vibrations at the Brillouin center are illustrated definitely from the ab initio outcomes. The depolarizing field effect of the hydrogen bond vibrations at frequencies of 229 cm−1 and 310 cm−1 is found to agree well with the LST relationship. It is a convincing evidence to manifest the LO-TO splitting of hydrogen bonds in ice crystal. We attribute the two hydrogen bond peaks to the depolarization effect and apply this viewpoint to ordinary ice phase, ice Ih, which is difficult to analyse their vibration modes due to proton disorder.

Relationship between the line of density anomaly and the lines of melting, crystallization, cavitation, and liquid spinodal in coarse-grained water models.

Liquid water has several anomalous properties, including a non-monotonous dependence of density with temperature and an increase of thermodynamic response functions upon supercooling. Four thermodynamic scenarios have been proposed to explain the anomalies of water, but it is not yet possible to decide between them from experiments because of the crystallization and cavitation of metastable liquid water. Molecular simulations provide a versatile tool to study the anomalies and phase behavior of water, assess their agreement with the phenomenology of water under conditions accessible to experiments, and provide insight into the behavior of water in regions that are challenging to probe in the laboratory. Here we investigate the behavior of the computationally efficient monatomic water models mW and mTIP4P/2005(REM), with the aim of unraveling the relationships between the lines of density extrema in the p-T plane, and the lines of melting, liquid-vapor spinodal and non-equilibrium crystallization and cavitation. We focus particularly on the conditions for which the line of density maxima (LDM) in the liquid emerges and disappears as the pressure is increased. We find that these models present a retracing LDM, same as previously found for atomistic water models and models of other tetrahedral liquids. The low-pressure end of the LDM occurs near the pressure of maximum of the melting line, a feature that seems to be general to models that produce tetrahedrally coordinated crystals. We find that the mW water model qualitatively reproduces several key properties of real water: (i) the LDM is terminated by cavitation at low pressures and by crystallization of ice Ih at high pressures, (ii) the LDM meets the crystallization line close to the crossover in crystallization from ice Ih to a non-tetrahedral four-coordinated crystal, and (iii) the density of the liquid at the crossover in crystallization from ice Ih to a four-coordinated non-tetrahedral crystal coincides with the locus of maximum in diffusivity as a function of pressure. The similarities in equilibrium and non-equilibrium phase behavior between the mW model and real water provide support to the quest to find a compressibility extremum, and determine whether it presents a maximum, in the doubly metastable region.

Self-diffusion of protons in H2O ice VII at high pressures: Anomaly around 10 GPa.

The self-diffusion of ice VII in the pressure range of 5.5-17 GPa and temperature range of 400-425 K was studied using micro Raman spectroscopy and a diamond anvil cell. The diffusion was monitored by observing the distribution of isotope tracers: D2O and H2 (18)O. The diffusion coefficient of hydrogen reached a maximum value around 10 GPa. It was two orders of magnitude greater at 10 GPa than at 6 GPa. Hydrogen diffusion was much faster than oxygen diffusion, which indicates that protonic diffusion is the dominant mechanism for the diffusion of hydrogen in ice VII. This mechanism is in remarkable contrast to the self-diffusion in ice Ih that is dominated by an interstitial mechanism for the whole water molecule. An anomaly around 10 GPa in ice VII indicates that the rate-determining process for the proton diffusion changes from the diffusion of ionic defects to the diffusion of rotational defects, which was suggested by proton conductivity measurements and molecular dynamics simulations.

Microscopic Mechanism and Kinetics of Ice Formation at Complex Interfaces: Zooming in on Kaolinite

Most ice in nature forms because of impurities which boost the exceedingly low nucleation rate of pure supercooled water. However, the microscopic details of ice nucleation on these substances remain largely unknown. Here, we have unraveled the molecular mechanism and the kinetics of ice formation on kaolinite, a clay mineral playing a key role in climate science. We find that the formation of ice at strong supercooling in the presence of this clay is about 20 orders of magnitude faster than homogeneous freezing. The critical nucleus is substantially smaller than that found for homogeneous nucleation and, in contrast to the predictions of classical nucleation theory (CNT), it has a strong two-dimensional character. Nonetheless, we show that CNT describes correctly the formation of ice at this complex interface. Kaolinite also promotes the exclusive nucleation of hexagonal ice, as opposed to homogeneous freezing where a mixture of cubic and hexagonal polytypes is observed.

Effects of surface roughness with two scales on light scattering by hexagonal ice crystals large compared to the wavelength: DDA results

The effect of ice crystal surface roughness on light scattering by ice crystals which are large compared to the wavelength was studied, in particular changes to the 2D scattering patterns, azimuthally averaged phase functions, degree of linear polarisation patterns and asymmetry parameters for a range of orientations and roughness scales. It was found that roughness has an effect on light scattering by hexagonal prisms, particularly when the roughness features are of comparable size to the wavelength. The roughness model that has the most effect on light scattering takes account of more than one roughness scale.Rough geometry was implemented by a Gaussian roughness method that took roughness parameters derived from sand grains, which have been reported to be suitable proxies for rough ice crystals. Light scattering data for these geometries was computed using the ADDA discrete dipole approximation method.

Ice Ih anomalies: Thermal contraction, anomalous volume isotope effect, and pressure-induced amorphization.

Ice Ih displays several anomalous thermodynamic properties such as thermal contraction at low temperatures, an anomalous volume isotope effect (VIE) rendering the volume of D2O ice greater than that of H2O ice, and a pressure-induced transition to the high-density amorphous (HDA) phase. Furthermore, the anomalous VIE increases with temperature, despite its quantum-mechanical origin. Here, embedded-fragment ab initio second-order many-body perturbation (MP2) theory in the quasiharmonic approximation (QHA) is applied to the Gibbs energy of an infinite, proton-disordered crystal of ice Ih at wide ranges of temperatures and pressures. The quantum effect of nuclei moving in anharmonic potentials is taken into account from first principles without any empirical or nonsystematic approximation to either the electronic or vibrational Hamiltonian. MP2 predicts quantitatively correctly the thermal contraction at low temperatures, which is confirmed to originate from the volume-contracting hydrogen-bond bending modes (acoustic phonons). It qualitatively reproduces (but underestimates) the thermal expansion at higher temperatures, caused by the volume-expanding hydrogen-bond stretching (and to a lesser extent librational) modes. The anomalous VIE is found to be the result of subtle cancellations among closely competing isotope effects on volume from all modes. Consequently, even ab initio MP2 with the aug-cc-pVDZ and aug-cc-pVTZ basis sets has difficulty reproducing this anomaly, yielding qualitatively varied predictions of the sign of the VIE depending on such computational details as the choice of the embedding field. However, the temperature growth of the anomalous VIE is reproduced robustly and is ascribed to the librational modes. These solid-state MP2 calculations, as well as MP2 Born-Oppenheimer molecular dynamics, find a volume collapse and a loss of symmetry and long-range order in ice Ih upon pressure loading of 2.35 GPa or higher. Concomitantly, rapid softening of acoustic phonons is observed starting around 2 GPa. They constitute a computational detection of a mechanical instability in ice Ih and the resulting pressure-induced amorphization to HDA.

Self-diffusion of polycrystalline ice Ih under confining pressure: Hydrogen isotope analysis using 2-D Raman imaging

We have developed a high-resolution technique based on micro Raman spectroscopy to measure hydrogen isotope diffusion profiles in ice Ih. The calibration curve for quantitative analysis of deuterium in ice Ih was constructed using micro Raman spectroscopy. Diffusion experiments using diffusion couples composed of dense polycrystalline H2O and D2O ice were carried out under a gas confining pressure of 100MPa (to suppress micro-fracturing and pore formation) at temperatures from 235K to 245K and diffusion times from 0.2 to 94 hours. Two-dimensional deuterium profiles across the diffusion couples were determined by Raman imaging. The location of small spots of frost from room air could be detected from the shapes of the Raman bands of OH and OD stretching modes, which change because of the effect of the molar ratio of deuterium on the molecular coupling interaction. We emphasize the validity for screening the impurities utilizing the coupling interaction. Some recrystallization and grain boundary migration occurred in recovered diffusion couples, but analysis of two-dimensional diffusion profiles of regions not affected by grain boundary migration allowed us to measure a volume diffusivity for ice at 100MPa of (2.8±0.4)×10-3exp-57.0±15.4kJ/molRTm2/s (R is the gas constant, T is temperature). Based on ambient pressure diffusivity measurements by others, this value indicates a high (negative) activation volume for volume diffusivity of −29.5cm3/mol or more. We can also constrain the value of grain boundary diffusivity in ice at 100MPa to be <104 that of volume diffusivity.

Study of clathrate hydrates via equilibrium molecular-dynamics simulation employing polarisable and non-polarisable, rigid and flexible water models.

Equilibrium molecular-dynamics (MD) simulations have been performed on metastable sI and sII polymorphs of empty hydrate lattices, in addition to liquid water and ice Ih. The non-polarisable TIP4P-2005, simple point charge model (SPC), and polarisable Thole-type models (TTM): TTM2, TTM3, and TTM4 water models were used in order to survey the differences between models and to see what differences can be expected when polarisability is incorporated. Rigid and flexible variants were used of each model to gauge the effects of flexibility. Power spectra are calculated and compared to density-of-states spectra inferred from inelastic neutron scattering (INS) measurements. Thermodynamic properties were also calculated, as well as molecular-dipole distributions. It was concluded that TTM models offer optimal fidelity vis-à-vis INS spectra, together with thermodynamic properties, with the flexible TTM2 model offering optimal placement of vibrational modes.

Ice–Water Interfacial Free Energy for the TIP4P, TIP4P/2005, TIP4P/Ice, and mW Models As Obtained from the Mold Integration Technique

The freezing of water is greatly influenced by the ice–water interfacial free energy. Yet, no consistent experimental measures of this thermodynamic parameter can be found. In this work we provide estimates for the ice Ih–water interfacial free energy at the normal melting temperature for different crystal planes (basal, primary prismatic, and secondary prismatic) using some widely used water models: TIP4P, TIP4P/2005, TIP4P/Ice, and mW. To compute the interfacial free energy, we use the mold integration method. It consists in calculating the work needed to induce the formation of a crystal slab in the fluid at coexistence conditions with the aid of a mold of potential energy wells whose structure is that of the crystal plane under study. The basal plane has the lowest interfacial free energy in all models of the TIP4P family. For the mW model we could not resolve differences in interfacial free energy between different orientations. The interfacial free energies averaged over all crystal orientations we ...

Microstructural evolution of polycrystalline ice during confined creep testing

The mechanical properties of polycrystalline ice Ih have been observed to change under an applied hydrostatic pressure comparable to that present near the bottom of kilometer-thick ice sheets. To help determine the cause of these changes, we conducted confined creep testing of laboratory-prepared polycrystalline ice at pressures up to 20MPa (equivalent to ∼2000m of overburden) and subsequent microstructural analysis of specimens deformed by creep using optical microscopy and scanning electron microscopy, including extensive electron backscatter diffraction mapping of crystal orientations. Microstructural observations of the creep-deformed specimens revealed smaller median grain sizes, less regular, and more interlocked grain shapes in specimens deformed at higher pressure compared with those deformed at atmospheric pressure. Variable pressure testing reveals little change in strain rate for pressures less than 15MPa, leading to alternative hypotheses regarding the influence of confining pressure on the dislocation dynamics and associated creep behavior of polycrystalline ice. Our central hypothesis is that widely dissociated basal dislocations in ice begin to constrict after the confining pressure reaches a critical value. This critical pressure depends strongly on the (currently unknown) lattice dilatation induced in ice by the presence of stacking faults.

Classical and quantum theories of proton disorder in hexagonal water ice

It has been known since the pioneering work of Bernal, Fowler and Pauling that common, hexagonal (Ih) water ice is the archetype of a frustrated material : a proton-bonded network in which protons satisfy strong local constraints - the "ice rules" - but do not order. While this proton disorder is well established, there is now a growing body of evidence that quantum effects may also have a role to play in the physics of ice at low temperatures. In this Article we use a combination of numerical and analytic techniques to explore the nature of proton correlations in both classical and quantum models of ice Ih. In the case of classical ice Ih, we find that the ice rules have two, distinct, consequences for scattering experiments - singular "pinch points", reflecting a zero-divergence condition on the uniform polarization of the crystal, and broad, asymmetric features, coming from its staggered polarisation. In the case of the quantum model, we find that the collective quantum tunnelling of groups of protons can convert states obeying the ice rules into a quantum liquid, whose excitations are birefringent, emergent photons. We make explicit predictions for scattering experiments on both classical and quantum ice Ih, and show how the quantum theory can explain the "wings" of incoherent inelastic scattering observed in recent neutron scattering experiments [Bove et al., Phys. Rev. Lett. 103, 165901 (2009)]. These results raise the intriguing possibility that the protons in ice Ih could form a quantum liquid at low temperatures, in which protons are not merely disordered, but continually fluctuate between different configurations obeying the ice rules.