Disorder In Ice Research Articles

Effect of ammonium fluoride doping on the ice III to ice IX phase transition.

Ice III is a hydrogen-disordered phase of ice that is stable between about 0.2 and 0.35 GPa. Upon cooling, it transforms to its hydrogen-ordered counterpart ice IX within the stability region of ice II. Here, the effect of ammonium fluoride doping on this phase transition is investigated, which is followed for the first time with in situ neutron diffraction. The a and c lattice constants are found to expand and contract, respectively, upon hydrogen ordering, yielding an overall negative volume change. Interestingly, the anisotropy in the lattice constants persists when ice IX is fully formed, and negative thermal expansion is observed. Analogous to the isostructural keatite and β-spodumenes, the negative thermal expansion can be explained through the buildup of torsional strain within the a-b plane as the helical "springs" within the structure expand upon heating. The reversibility of the phase transition was demonstrated upon heating. As seen in diffraction and Raman spectroscopy, the ammonium fluoride doping induces additional residual hydrogen disorder in ice IX and is suggested to be a chemical way for the "excitation" of the configurational ice-rules manifold. Compared to ice VIII, the dopant-induced hydrogen disorder in ice IX is smaller, which suggests a higher density of accessible configurational states close to the ground state in ice IX. This study highlights the importance of dopants for exploring the water's phase diagram and underpins the highly complex solid-state chemistry of ice.

Analysis of stacking disorder in ice I using pair distribution functions

Stacking-disordered materials display crystalline order in two dimensions but are disordered along the direction in which layered structural motifs are stacked. Countless examples of stacking disorder exist, ranging from close-packed metals, ice I and diamond to open-framework materials and small-molecule pharmaceuticals. In general, the presence of stacking disorder can have profound consequences for the physical and chemical properties of a material. Traditional analyses of powder diffraction data are often complicated by the presence of memory effects in the stacking sequences. Here it is shown that experimental pair distribution functions of stacking-disordered ice I can be used to determine local information on the fractions of cubic and hexagonal stacking. Ice is a particularly challenging material in this respect, since both the stacking disorder and the orientational disorder of the water molecules need to be described. Memory effects are found to contribute very little to the pair distribution functions, and consequently, the analysis of pair distribution functions is the method of choice for characterizing stacking-disordered samples with complicated and high-order memory effects. In the context of this work, the limitations of current structure-reconstruction approaches are also discussed.

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.

Proton disorder in cubic ice: Effect on the electronic and optical properties.

The proton disorder in ice has a key role in several properties such as the growth mode, thermodynamical properties, and ferroelectricity. While structural phase transitions from proton disordered to proton ordered ices have been extensively studied, much less is known about their electronic and optical properties. Here, we present ab initio many body perturbation theory-based calculations of the electronic and optical properties of cubic ice at different levels of proton disorder. We compare our results with those from liquid water, that acts as an example of a fully (proton- and oxygen-)disordered system. We find that by increasing the proton disorder, a shrinking of the electronic gap occurs in ice, and it is smallest in the liquid water. Simultaneously, the excitonic binding energy decreases, so that the final optical gaps result to be almost independent on the degree of proton disorder. We explain these findings as an interplay between the local dipolar disorder and the electronic correlation.

Stacking disorder in ice I.

Traditionally, ice I was considered to exist in two well-defined crystalline forms at ambient pressure: stable hexagonal ice (ice Ih) and metastable cubic ice (ice Ic). However, it is becoming increasingly evident that what has been called cubic ice in the past does not have a structure consistent with the cubic crystal system. Instead, it is a stacking-disordered material containing cubic sequences interlaced with hexagonal sequences, which is termed stacking-disordered ice (ice Isd). In this article, we summarise previous work on ice with stacking disorder including ice that was called cubic ice in the past. We also present new experimental data which shows that ice which crystallises after heterogeneous nucleation in water droplets containing solid inclusions also contains stacking disorder even at freezing temperatures of around -15 °C. This supports the results from molecular simulations, that the structure of ice that crystallises initially from supercooled water is always stacking-disordered and that this metastable ice can transform to the stable hexagonal phase subject to the kinetics of recrystallization. We also show that stacking disorder in ice which forms from water droplets is quantitatively distinct from ice made via other routes. The emerging picture of ice I is that of a very complex material which frequently contains stacking disorder and this stacking disorder can vary in complexity depending on the route of formation and thermal history.

Approximations to the full description of stacking disorder in ice I for powder diffraction

Abstract Different descriptions of the stacking disorder of the so-called “cubic” phase “ice Ic” and stacking-faulted hexagonal ice Ih exist. We present an overview of the effect of different stacking disorder interaction ranges s from s = 2 to s = 4 after Jagodzinski on the (neutron) powder diffraction patterns of stacking-disordered ice I, which we propose to name ice Ich. We fit in a systematic approach simulated diffraction data of ice Ich for s up to 4 with a multi-peak approach. In this way we allow for estimating the relative proportion of cubic sequences in the stacking sequences by using readily accessible observables of a diffraction pattern.

Spectroscopic Signature of Stacking Disorder in Ice I.

There is a growing realization that the presence of stacking disorder in ice I strongly influences its physical and chemical properties. Using Raman spectroscopy, we gain new fundamental insights into the spectroscopic properties of ice. We show that stacking disorder can be detected and quantified by comparing the spectra of stacking disordered ice with spectra of the "ordinary" hexagonal ice Ih. The spectral signature of stacking disorder is thought to arise from a greater structural diversity on the local length scale, vibrational modes that appear due to the lower-symmetry environments, and a strengthening of the covalent bonds. Our findings are compared to results from diffraction and calorimetry, and we discuss the advantages and disadvantages of the three techniques with respect to detecting stacking disorder in ice I. Apart from characterizing stacking disordered ice in the research lab, our new method is perfectly suited for remote or telescopic applications aiming at the identification of stacking disordered ice in nature.

The phase diagram of ice Ih, II, and III: A quasi-harmonic study

The phase diagram of ice Ih, II, and III is studied by a quasi-harmonic approximation. The results of this approach are compared to phase diagrams previously derived by thermodynamic integration using path integral and classical simulations, as well as to experimental data. The studied models are based on both flexible (q-TIP4P/F) and rigid (TIP4P/2005, TIP4PQ/2005) descriptions of the water molecule. Many aspects of the simulated phase diagrams are reasonably reproduced by the quasi-harmonic approximation. Advantages of this simple approach are that it is free from the statistical errors inherent to computer simulations, both classical and quantum limits are easily accessible, and the error of the approximation is expected to decrease in the zero temperature limit. We find that the calculated phase diagram of ice Ih, II, and III depends strongly on the hydrogen disorder of ice III, at least for cell sizes typically used in phase coexistence simulations. Either ice II (in the classical limit) or ice III (in the quantum one) may become unstable depending upon the proton disorder in ice III. The comparison of quantum and classical limits shows that the stabilization of ice II is the most important quantum effect in the phase diagram. The lower vibrational zero-point energy of ice II, compared to either ice Ih or III, is the microscopic origin of this stabilization. The necessity of performing an average of the lattice energy over the proton disorder of ice III is discussed.

Comparison of selected polarizable and nonpolarizable water models in molecular dynamics simulations of ice Ih

We present a molecular dynamics simulation study in which we determined the melting point of ice I(h) for the polarizable SWM4-NDP water model (Lamoureux et al., Chem. Phys. Lett., 2006, 418, 245-249) and compared the performance of several popular water force fields, both polarizable and nonpolarizable, in terms of melting temperature, stability and orientational structuring of ice. The simulations yield the melting temperature of SWM4-NDP ice as low as T(m) = 185 ± 10 K, despite the quadrupole moment of a SWM4-NDP water molecule being close to the experimental gas phase value. The results thus show that the dependence of T(m) on the molecular quadrupole, observed for the three- and four-site water models, is generally lost if polarization is explicitly included. The study also shows that adding polarizability to a planar three-charge water model increases orientational disorder in hexagonal ice. In addition, analysis of the tetrahedral order in bulk ice reveals a correlation between the pre-existing degree of orientational disorder in ice simulated using different polarizable and nonpolarizable models and the melting temperature of the models. Our findings thus suggest some new considerations regarding the role of polarization forces in a crystalline solid that may guide future development of reliable polarizable water models for ice.

Oxygen disorder in ice probed by x-ray Compton scattering

We use electron momentum density in ice as a tool to quantify order-disorder transitions by comparing Compton profiles differences of ice VI, VII, VIII, and XII with respect to ice Ih. Quantitative agreement is found between theory and experiment for ice VIII, which is the fully hydrogen ordered phase. Robust signatures of the oxygen disorder are identified in the momentum density for the VIII-VII ice phase transition. The unique aspect of this work is the determination of the fraction ${n}_{e}$ of electron directly involved in phase transitions as well as the use of position space signatures for quantifying oxygen site disorder.

Site Disorder in Ice VII Arising from Hydrogen Bond Fluctuations

Recently, multisite models used for the refinement of neutron diffraction data have suggested that the structure of ice VII is quite unlike that of its ordered counterpart, ice VIII. We investigate the oxygen site disorder by modeling the site displacement, obtained from periodic DFT calculations, as a function of the local hydrogen bond network. Then, using graph invariants to describe hydrogen bond fluctuations in the thermodynamic limit, we perform statistical mechanical calculations using the oxygen site displacement model developed here. We find that the probability distribution of the oxygen atom about its perfect lattice site more closely resembles the 100 model rather than the recently suggested 111 model, although both models represent a simplification of the actual site distribution. We also find a unimodel distribution for the hydrogen bonded oxygen-oxygen distance and a trimodel distribution for the nearest nonbonded oxygen-oxygen distance with a peak separation of approximately 0.1 A.

Picosecond ir hole-burning spectroscopy on HDO iceIh

Transient hole-burning experiments using picosecond ir pulses in the region of the OH stretching vibration of crystalline HDO (in ${\mathrm{D}}_{2}\mathrm{O}$) ice are reported; holes with a minimum width of $26{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are measured, proving the OH band to be inhomogeneously broadened. The inhomogeneous distribution having a half width of approximately $25{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ can be related to structural disorder in ice. A vibrational lifetime of $0.5\mathrm{ps}<~{T}_{1}<~2\mathrm{ps}$ is found for the OH stretching mode. Additional features in the transient data are attributed to the dissipation of excess energy; particularly microscopic energy flow in the immediate surroundings of primarily excited OH groups can be monitored.

Analysis of Single-Crystal Neutron Diffuse Scattering from Ice Ih

The single-crystal neutron diffuse scattering from ice contains a great deal of information, not only on the disorder of the hydrogen atoms but also on the instantaneous atomic positions. It is difficult to extract this information, and a series of reverse Monte Carlo (RMC) techniques have been developed for this purpose, with mixed success. The present paper presents new constrained RMC methods used to try and obtain more reliable information on the static and thermal disorder in ice. However it has been found that the RMC results depend strongly on the starting configuration, meaning that some of the conclusions of the earlier paper of Nield and Whitworth (Nield, V. M.; Whitworth, R. W. J. Phys.: Condens. Matter 1995, 7, 8258) are invalid.

Frustration model of proton disorder in ice

A pseudospin model is proposed to describe the proton disorder in ice, which includes only the two-particle interaction of protons. It is shown that the proton disorder is a result of pseudospin lattice frustrations. Connection is considered between the type of oxygen lattice and the existence of disordered and ordered proton configurations.

Intrinsic surface disorder in ice near the melting point

The crystalline perfection of the basal plane of ice Ih in thermodynamic equilibrium with its own vapour, is studied between -130 degrees C and -2 degrees C by means of 100 keV proton channelling. An intrinsically disordered surface region is found. The disorder extends into the bulk, and increases rapidly with temperature above -40 degrees C. A partial order is retained, however, at least up to -1.8 degrees C. The results are compatible with the postulated existence of large-amplitude surface vibrations. At -1.8 degrees C the square of the mean surface-vibration amplitude of oxygen is 3.3 times larger than the bulk value deduced from past x-ray measurements. The thickness t of an amorphous layer, which has the same dechannelling effect as the partially disordered region, increases with temperature as t(nm)=(94+or-17)-(54+or-14)lg(273-T). This is the functional dependence predicted by Fletcher's theory, and found experimentally by Volta effect and NMR measurements. The order of magnitude of the thickness near 0 degrees C agrees with the results of measurements of electrical and mechanical surface properties of ice, and with Weyl's original suggestion, but is ten times larger than the value estimated from NMR measurements and predicted by Fletcher.

Thermal effects of the transformation ice III–IX

The heat and entropy of the transformation ice III–IX has been measured by a differential calorimetric technique as −0.32 cal K−1 mol, compared with the value −0.805 cal K−1 mol expected if ice III were fully disordered and ice IX were fully ordered within the limitations of the ice rules. It seems likely that there is significant disorder in ice IX, as found in a recent neutron diffraction investigation.