Nanosecond freezing of water under multiple shock wave compression: optical transmission and imaging measurements

Scaling Law for the Onset of Solidification at Extreme Undercooling

Quasi-isentropic compression enables one to study the solidification of metastable liquid states that are inaccessible through other experimental means. The onset of this nonequilibrium solidification is known to depend on the compression rate and material-specific factors, but this complex interdependence has not been well characterized. In this study, we use a combination of experiments, theory, and computational simulations to derive a general scaling law that quantifies this dependence. One of its applications is a novel means to elucidate melt temperatures at high pressures.

Spatiotemporal Control of Ice Crystallization in Supercooled Water via an Ultrashort Laser Impulse

Focused irradiation with ultrashort laser pulses realized the fine spatiotemporal control of ice crystallization in supercooled water. An effective multiphoton excitation at the laser focus generated shockwaves and bubbles, which acted as an impulse for inducing ice crystal nucleation. The impulse that was localized close to the laser focus and accompanied by a small temperature elevation allowed the precise position control of ice crystallization and its observation with spatiotemporal resolution of micrometers and microseconds using a microscope. To verify the versatility of this laser method, we also applied it using various aqueous systems (e.g., plant extracts). The systematic study of crystallization probability revealed that laser-induced cavitation bubbles play a crucial role in inducing ice crystal nucleation. This method can be used as a tool for studying ice crystallization dynamics in various natural and biological phenomena.

High-temperature and high-pressure plastic phase of ice at the boundary of liquid water and ice VII

Simultaneous high-temperature and high-pressure studies reveal phase transformation of bulk liquid water to an ice-VII-like structure having an eight coordination. It was demonstrated through this numerical study that the observed high-temperature and high-pressure phase of water obtained upon shock compression and equilibration has high rotational diffusion and thereby the hydrogen dynamics of these crystal structures are significantly complex compared with ice VII. The current work provides new characterization methods for the numerically observed plastic crystal phase of ice at the boundary of the liquid water and ice VII phases in which the molecules have a defined lattice position but rotate freely. It is anticipated that the present work will provide important data and guide new theoretical and experimental investigations in the search for plastic crystal phases of water. The power spectra plots of bulk liquid water subjected to different temperature and pressure conditions have also been presented in this numerical study, demonstrating significant differences between these high-temperature and high-pressure shock-equilibrated phases and those of pure ice VII at 10 GPa and liquid water at ambient temperature and pressure, as well as at elevated pressures and temperatures.

Structure, Properties, and Phase Transformations of Water Nanoconfined between Brucite-like Layers: The Role of Wall Surface Polarity

The interaction of water with confining surfaces is primarily governed by the wetting properties of the wall material-in particular, whether it is hydrophobic or hydrophilic. The hydrophobicity or hydrophilicity itself is determined primarily by the atomic structure and polarity of the surface groups. In the present work, we used molecular dynamics to study the structure and properties of nanoscale water layers confined between layered metal hydroxide surfaces with a brucite-like structure. The influence of the surface polarity of the confining material on the properties of nanoconfined water was studied in the pressure range of 0.1-10 GPa. This pressure range is relevant for many geodynamic phenomena, hydrocarbon recovery, contact spots of tribological systems, and heterogeneous materials under extreme mechanical loading. Two phase transitions were identified in water confined within 2 nm wide slit-shaped nanopores: (1) at p₁ = 3.3-3.4 GPa, the liquid transforms to a solid phase with a hexagonal close-packed (HCP) crystal structure, and (2) at p₂ = 6.7-7.1 GPa, a further transformation to face-centered cubic (FCC) crystals occurs. It was found that the behavior of the confined water radically changes when the partial charges (and, therefore, the surface polarity) are reduced. In this case, water transforms directly from the liquid phase to an FCC-like phase at 3.2-3.3 GPa. Numerical simulations enabled determination of the amount of hydrogen bonding and diffusivity of nanoconfined water, as well as the relationship between pressure and volumetric strain.

Metastability of Liquid Water Freezing into Ice VII under Dynamic Compression

The ubiquitous nature and unusual properties of water have motivated many studies on its metastability under temperature- or pressure-induced phase transformations. Here, nanosecond compression by a high-power laser is used to create the nonequilibrium conditions where liquid water persists well into the stable region of ice VII. Through our experiments, as well as a complementary theoretical-computational analysis based on classical nucleation theory, we report that the metastability limit of liquid water under nearly isentropic compression from ambient conditions is at least 8 GPa, higher than the 7 GPa previously reported for lower loading rates.

Metastable-solid phase diagrams derived from polymorphic solidification kinetics

Nonequilibrium processes during solidification can lead to kinetic stabilization of metastable crystal phases. A general framework for predicting the solidification conditions that lead to metastable-phase growth is developed and applied to a model face-centered cubic (fcc) metal that undergoes phase transitions to the body-centered cubic (bcc) as well as the hexagonal close-packed phases at high temperatures and pressures. Large-scale molecular dynamics simulations of ultrarapid freezing show that bcc nucleates and grows well outside of the region of its thermodynamic stability. An extensive study of crystal-liquid equilibria confirms that at any given pressure, there is a multitude of metastable solid phases that can coexist with the liquid phase. We define for every crystal phase, a solid cluster in liquid (SCL) basin, which contains all solid clusters of that phase coexisting with the liquid. A rigorous methodology is developed that allows for practical calculations of nucleation rates into arbitrary SCL basins from the undercooled melt. It is demonstrated that at large undercoolings, phase selections made during the nucleation stage can be undone by kinetic instabilities amid the growth stage. On these bases, a solidification-kinetic phase diagram is drawn for the model fcc system that delimits the conditions for macroscopic grains of metastable bcc phase to grow from the melt. We conclude with a study of unconventional interfacial kinetics at special interfaces, which can bring about heterogeneous multiphase crystal growth. A first-order interfacial phase transformation accompanied by a growth-mode transition is examined.

Numerical modeling of solid-cluster evolution applied to the nanosecond solidification of water near the metastable limit

Classical nucleation theory (CNT) is a promising way to predictively model the submicrosecond kinetics of phase transitions that occur under dynamic compression, such as the suite of experiments performed over the past two decades on the solidification of liquid water to the high-pressure ice VII phase. Myint et al. [Phys. Rev. Lett. 121, 155701 (2018)] presented the first CNT-based model for these types of rapid phase transitions, but relied on an empirical scaling parameter in their transient induction model to simulate the lag time that occurs prior to the onset of significant formation of ice VII clusters in the system. To build on that study, we model the liquid water-ice VII phase transformation using a numerical discretization scheme to solve the Zel'dovich-Frenkel partial differential equation, which is a fundamental CNT-based kinetic equation that describes the statistical time-dependent behavior of solid cluster formation. The Zel'dovich-Frenkel equation inherently accounts for transience in the nucleation kinetics and eliminates the need for the empirical scaling factor used by Myint et al. One major result of this research is that transience is found to play a relatively small role in the nucleation process for the dynamic-compression time scales of the liquid water-ice VII experiments being simulated. Instead, we show that it is possible to properly model the lag time using steady-state CNT by making small refinements to the interfacial free energy value. We have also developed a new dimensionless parameter that may be applied a priori to predict whether or not transient nucleation will be important in a given dynamic-compression experiment.

Nanosecond X-ray diffraction of shock-compressed superionic water ice

Since Bridgman's discovery of five solid water (H₂O) ice phases¹ in 1912, studies on the extraordinary polymorphism of H₂O have documented more than seventeen crystalline and several amorphous ice structures^2,3, as well as rich metastability and kinetic effects^4,5. This unique behaviour is due in part to the geometrical frustration of the weak intermolecular hydrogen bonds and the sizeable quantum motion of the light hydrogen ions (protons). Particularly intriguing is the prediction that H₂O becomes superionic^6-12-with liquid-like protons diffusing through the solid lattice of oxygen-when subjected to extreme pressures exceeding 100 gigapascals and high temperatures above 2,000 kelvin. Numerical simulations suggest that the characteristic diffusion of the protons through the empty sites of the oxygen solid lattice (1) gives rise to a surprisingly high ionic conductivity above 100 Siemens per centimetre, that is, almost as high as typical metallic (electronic) conductivity, (2) greatly increases the ice melting temperature^7-13 to several thousand kelvin, and (3) favours new ice structures with a close-packed oxygen lattice^13-15. Because confining such hot and dense H₂O in the laboratory is extremely challenging, experimental data are scarce. Recent optical measurements along the Hugoniot curve (locus of shock states) of water ice VII showed evidence of superionic conduction and thermodynamic signatures for melting¹⁶, but did not confirm the microscopic structure of superionic ice. Here we use laser-driven shockwaves to simultaneously compress and heat liquid water samples to 100-400 gigapascals and 2,000-3,000 kelvin. In situ X-ray diffraction measurements show that under these conditions, water solidifies within a few nanoseconds into nanometre-sized ice grains that exhibit unambiguous evidence for the crystalline oxygen lattice of superionic water ice. The X-ray diffraction data also allow us to document the compressibility of ice at these extreme conditions and a temperature- and pressure-induced phase transformation from a body-centred-cubic ice phase (probably ice X) to a novel face-centred-cubic, superionic ice phase, which we name ice XVIII^2,17.

Shock growth of ice crystal near equilibrium melting pressure under dynamic compression

Crystal growth and morphological transitions are crucial for fundamental science and wide applications. Nevertheless, their mechanisms under local nonequilibrium growth condition are unclear due to severe interference of thermal and mass transports on the interplay between thermodynamic driving force and interface kinetics. Here, we reveal the origin of the pressure-induced 2D shock growth of ice VI crystal by using dynamic compression, in which a dimensional transition from 3D to 2D is observed. Unlike generally expected, the 2D shock growth occurs from 3D crystal edges rather than from its corners upon fast compression, even near equilibrium growth condition. This is due to similar interface structure to the crystal edge plane facilitating the fast interface kinetics under local nonequilibrium growth.

Crystal growth is governed by an interplay between macroscopic driving force and microscopic interface kinetics at the crystal–liquid interface. Unlike the local equilibrium growth condition, the interplay becomes blurred under local nonequilibrium, which raises many questions about the nature of diverse crystal growth and morphological transitions. Here, we systematically control the growth condition from local equilibrium to local nonequilibrium by using an advanced dynamic diamond anvil cell (dDAC) and generate anomalously fast growth of ice VI phase with a morphological transition from three- to two-dimension (3D to 2D), which is called a shock crystal growth. Unlike expected, the shock growth occurs from the edges of 3D crystal along the (112) crystal plane rather than its corners, which implies that the fast compression yields effectively large overpressure at the crystal–liquid interface, manifesting the local nonequilibrium condition. Molecular dynamics (MD) simulation reproduces the faster growth of the (112) plane than other planes upon applying large overpressure. Moreover, the MD study reveals that the 2D shock crystal growth originates from the similarity of the interface structure between water and the (112) crystal plane under the large overpressure. This study provides insight into crystal growth under dynamic compressions, which makes a bridge for the unknown behaviors of crystal growth between under static and dynamic pressure conditions.

Nanosecond Freezing of Water at High Pressures: Nucleation and Growth near the Metastability Limit

The fundamental study of phase transition kinetics has motivated experimental methods toward achieving the largest degree of undercooling possible, more recently culminating in the technique of rapid, quasi-isentropic compression. This approach has been demonstrated to freeze water into the high-pressure ice VII phase on nanosecond timescales, with some experiments undergoing heterogeneous nucleation while others, in apparent contradiction, suggest a homogeneous nucleation mode. In this study, we show through a combination of theory, simulation, and analysis of experiments that these seemingly contradictory results are in agreement when viewed from the perspective of classical nucleation theory. We find that, perhaps surprisingly, classical nucleation theory is capable of accurately predicting the solidification kinetics of ice VII formation under an extremely high driving force (|Δμ/k_{B}T|≈1) but only if amended by two important considerations: (i) transient nucleation and (ii) separate liquid and solid temperatures. This is the first demonstration of a model that is able to reproduce the experimentally observed rapid freezing kinetics.

The thermodynamics of a liquid-solid interface at extreme conditions: A model close-packed system up to 100 GPa

The first experimental insight into the nature of the liquid-solid interface occurred with the pioneering experiments of Turnbull, which simultaneously demonstrated both that metals could be deeply undercooled (and therefore had relatively large barriers to nucleation) and that the inferred interfacial free energy γ was linearly proportional to the enthalpy of fusion [D. Turnbull, J. Appl. Phys. 21, 1022 (1950)]. By an atomistic simulation of a model face-centered cubic system via adiabatic free energy dynamics, we extend Turnbull's result to the realm of high pressure and demonstrate that the interfacial free energy, evaluated along the melting curve, remains linear with the bulk enthalpy of fusion, even up to 100 GPa. This linear dependence of γ on pressure is shown to be a consequence of the entropy dominating the free energy of the interface in conjunction with the fact that the entropy of fusion does not vary greatly along the melting curve for simple monoatomic metals. Based on this observation, it appears that large undercoolings in liquid metals can be achieved even at very high pressure. Therefore, nucleation rates at high pressure are expected to be non-negligible, resulting in observable solidification kinetics.

Rapid freezing of water under dynamic compression

Understanding the behavior of materials at extreme pressures is a central issue in fields like aerodynamics, astronomy, and geology, as well as for advancing technological grand challenges such as inertial confinement fusion. Dynamic compression experiments to probe high-pressure states often encounter rapid phase transitions that may cause the materials to behave in unexpected ways, and understanding the kinetics of these phase transitions remains an area of great interest. In this review, we examine experimental and theoretical/computational efforts to study the freezing kinetics of water to a high-pressure solid phase known as ice VII. We first present a detailed analysis of dynamic compression experiments in which water has been observed to freeze on sub-microsecond time scales to ice VII. This is followed by a discussion of the limitations of currently available molecular and continuum simulation methods in modeling these experiments. We then describe how our phase transition kinetics models, which are based on classical nucleation theory, provide a more physics-based framework that overcomes some of these limitations. Finally, we give suggestions on future experimental and modeling work on the liquid-ice VII transition, including an outline of the development of a predictive multiscale model in which molecular and continuum simulations are intimately coupled.

Crystallization of Lennard-Jones liquids under dynamic compression: Heterogeneous and homogeneous nucleation

We investigate crystallization of Lennard-Jones liquids on substrates under dynamic compression with large-scale molecular dynamics simulations. The substrates examined include single crystals and bicrystals with different crystallographic orientations, and the loading paths include shock and quasi-isentropic loading. Microstructure is characterized with simulated x-ray diffraction and orientation mapping. For shock loading, only heterogeneous nucleation occurs at the simulation scales. Quasi-isentropic loading induces less heating and larger supercooling; as a result, heterogeneous nucleation occurs at low loading strengths, and both heterogeneous and homogeneous nucleation occur at high loading strengths, despite the crystalline substrates. Crystallization depends on the substrate structure (crystal orientation and grain boundary) and loading characteristics. Deformation may induce grain structure change (e.g., reorientation and twinning) of substrates and affect subsequent crystallization. Crystallization rate is anisotropic, inversely proportional to the cosine of the dihedral angle between the substrate plane and a main {111} growth plane.

Compression Freezing Kinetics of Water to Ice VII

Time-resolved x-ray diffraction (XRD) of compressed liquid water shows transformation to ice VII in 6 nsec, revealing crystallization rather than amorphous solidification during compression freezing. Application of classical nucleation theory indicates heterogeneous nucleation and one-dimensional (e.g., needlelike) growth. These first XRD data demonstrate rapid growth kinetics of ice VII with implications for fundamental physics of diffusion-mediated crystallization and thermodynamic modeling of collision or impact events on ice-rich planetary bodies.

Outcomes of the collapse of a large bubble in water at high ambient pressures

Presented here are observations of the outcomes of the collapses of large single bubbles in H_{2}O and D_{2}O at high ambient pressures. Experiments were carried out in a high-pressure spherical resonator at ambient pressures of up to 30 MPa and acoustic pressures up to 35 MPa. Monitoring of the collapse events and their outcomes was accomplished using multiframe high-speed photography. Among the observations to be presented are the temporal and spatial evolution of light emissions produced by the collapse events, which were observed to last on the order of 30 ns and have time independent radii on the order of 30μm; the production of Rayleigh-Taylor jets which were observed to travel distances of up to 70μm at speeds in excess of 4500 m/s; the entrainment of the light emitting regions in the jets' remnants; the production of spheroidal objects around the collapse points of the bubbles, far from any surface of the resonator; and the traversal and emergence of the Rayleigh-Taylor jets through the spherical objects. These spheroidal objects appear to behave as amorphous solids and form at locations where hydrodynamics predicts pressures in excess of the known transition pressures of water into the high-pressure crystalline ices, Ice-VI and Ice-VII.

A time-resolved single-pass technique for measuring optical absorption coefficients of window materials under 100 GPa shock pressures

An experimental method was developed to perform time-resolved, single-pass optical absorption measurements and to determine absorption coefficients of window materials under strong shock compression up to approximately 200 GPa. Experimental details are described of (i) a configuration to generate an in situ dynamic, bright, optical source and (ii) a sample assembly with a lithium fluoride plate to essentially eliminate heat transfer from the hot radiator into the specimen and to maintain a constant optical source within the duration of the experiment. Examples of measurements of optical absorption coefficients of several initially transparent single crystal materials at high shock pressures are presented.

Viscosity of water measured to pressures of 6 GPa and temperatures of 300 degrees C

Shear viscosities of fluid water have been measured to 300 degrees C and 6 GPa (60 kbar). Measurements were made in a diamond-anvil cell with a rolling-ball technique. Enskog's equation for viscosity, coupled with an ad hoc assumption that increased collision rates are due to an "excluded volume", yield excellent matches to the data at temperatures of 100 degrees C and over, without any freely variable parameter. The data overlap the pressure-temperature range in which experiments on shocked water have previously been interpreted to indicate extremely high viscosities. It is shown conclusively that viscosities in this region are very close to those at ambient temperature. Further, it is argued that explanations of high apparent viscosities which rely on the putative formation of ice behind the shock front are probably incorrect.

Dynamic diamond anvil cell (dDAC): a novel device for studying the dynamic-pressure properties of materials

We have developed a unique device, a dynamic diamond anvil cell (dDAC), which repetitively applies a time-dependent load/pressure profile to a sample. This capability allows studies of the kinetics of phase transitions and metastable phases at compression (strain) rates of up to 500 GPa/s (approximately 0.16 s(-1) for a metal). Our approach adapts electromechanical piezoelectric actuators to a conventional diamond anvil cell design, which enables precise specification and control of a time-dependent applied load/pressure. Existing DAC instrumentation and experimental techniques are easily adapted to the dDAC to measure the properties of a sample under the varying load/pressure conditions. This capability addresses the sparsely studied regime of dynamic phenomena between static research (diamond anvil cells and large volume presses) and dynamic shock-driven experiments (gas guns, explosive, and laser shock). We present an overview of a variety of experimental measurements that can be made with this device.

Nanosecond freezing of water under multiple shock wave compression: continuum modeling and wave profile measurements

Using real time optical transmission and imaging measurements in multiple shock wave compression experiments, water was shown to solidify on nanosecond time scales [D. H. Dolan and Y. M. Gupta, J. Chem. Phys. 121, 9050 (2004)]. Continuum modeling and wave profile measurements, presented here, provide a complementary approach to examine the freezing of shocked water. The water model consisted of thermodynamically consistent descriptions of liquid and solid (ice VII) water, relationships for phase coexistence, and a time-dependent transition description to simulate freezing dynamics. Continuum calculations using the water model demonstrate that, unlike single shock compression, multiple shock compression results in pressure-temperature conditions where the ice VIII phase is thermodynamically favored over the liquid phase. Wave profile measurements, using laser interferometry, were obtained with quartz and sapphire windows at a peak pressure of 5 GPa. For water confined between sapphire windows, numerical simulations corresponding to a purely liquid response are in excellent agreement with the measured wave profile. For water confined between quartz windows (to provide a nucleating surface), wave profile measurements demonstrate a pure liquid response for an incubation time of approximately 100 ns followed by a time-dependent transformation. Analysis of the wave profiles after the onset of transformation suggests that water changes from a metastable liquid to a denser phase, consistent with the formation of a high-pressure ice phase. Continuum analyses and simulations underscore the need for multiple time scales to model the freezing transition. Findings from the present continuum work are extremely consistent with optical results reported previously. These studies constitute the first comprehensive investigation reported for freezing of a liquid at very short time scales.

Nanosecond rapid freezing of liquid benzene under shock compression studied by time-resolved coherent anti-Stokes Raman spectroscopy

Nanosecond time-resolved coherent anti-Stokes Raman spectroscopy is used to investigate the shock-induced liquid-solid phase transition and crystallization of liquid benzene. Temporal evolution of the Raman shift of the ring-breathing and C-H stretching modes is investigated. A metastable supercompressed state and a liquid-solid phase transition are observed under shock compression. Time-resolved Raman spectra reveal that the liquid state is initially a metastable state and rapidly transforms to the solid state within 25 ns under shock compression at 4.2 GPa.

Evolution of the Adsorbed Water Layer Structure on Silicon Oxide at Room Temperature

The molecular configuration of water adsorbed on a hydrophilic silicon oxide surface at room temperature has been determined as a function of relative humidity using attenuated total reflection (ATR)-infrared spectroscopy. A completely hydrogen-bonded icelike network of water grows up to three layers as the relative humidity increases from 0 to 30%. In the relative humidity range of 30-60%, the liquid water structure starts appearing while the icelike structure continues growing to saturation. The total thickness of the adsorbed layer increases only one molecular layer in this humidity range. Above 60% relative humidity, the liquid water configuration grows on top of the icelike layer. This structural evolution indicates that the outermost layer of the adsorbed water molecules undergoes transitions in equilibrium behavior as humidity varies. These transitions determine the shape of the adsorption isotherm curve. The structural transitions of the outermost adsorbed layer are accompanied by interfacial energy changes and explain many phenomena observed only for water adsorption.