Unveiling a common phase transition pathway of high-density amorphous ices through time-resolved x-ray scattering.

Here, we investigate the hypothesis that despite the existence of at least two high-density amorphous ices, only one high-density liquid state exists in water. We prepared a very-high-density amorphous ice (VHDA) sample and rapidly increased its temperature to around 205 ± 10 K using laser-induced isochoric heating. This temperature falls within the so-called "no-man's land" well above the glass-liquid transition, wherein the IR laser pulse creates a metastable liquid state. Subsequently, this high-density liquid (HDL) state of water decompresses over time, and we examined the time-dependent structural changes using short x-ray pulses from a free electron laser. We observed a liquid-liquid transition to low-density liquid water (LDL) over time scales ranging from 20 ns to 3 µs, consistent with previous experimental results using expanded high-density amorphous ice (eHDA) as the initial state. In addition, the resulting LDL derived both from VHDA and eHDA displays similar density and degree of inhomogeneity. Our observation supports the idea that regardless of the initial annealing states of the high-density amorphous ices, the same HDL and final LDL states are reached at temperatures around 205 K.

Melting domain size and recrystallization dynamics of ice revealed by time-resolved x-ray scattering.

The phase transition between water and ice is ubiquitous and one of the most important phenomena in nature. Here, we performed time-resolved x-ray scattering experiments capturing the melting and recrystallization dynamics of ice. The ultrafast heating of ice I is induced by an IR laser pulse and probed with an intense x-ray pulse which provided us with direct structural information on different length scales. From the wide-angle x-ray scattering (WAXS) patterns, the molten fraction, as well as the corresponding temperature at each delay, were determined. The small-angle x-ray scattering (SAXS) patterns, together with the information extracted from the WAXS analysis, provided the time-dependent change of the size and the number of liquid domains. The results show partial melting (~13%) and superheating of ice occurring at around 20 ns. After 100 ns, the average size of the liquid domains grows from about 2.5 nm to 4.5 nm by the coalescence of approximately six adjacent domains. Subsequently, we capture the recrystallization of the liquid domains, which occurs on microsecond timescales due to the cooling by heat dissipation and results to a decrease of the average liquid domain size.

Liquid-liquid phase separation in supercooled water from ultrafast heating of low-density amorphous ice.

Recent experiments continue to find evidence for a liquid-liquid phase transition (LLPT) in supercooled water, which would unify our understanding of the anomalous properties of liquid water and amorphous ice. These experiments are challenging because the proposed LLPT occurs under extreme metastable conditions where the liquid freezes to a crystal on a very short time scale. Here, we analyze models for the LLPT to show that coexistence of distinct high-density and low-density liquid phases may be observed by subjecting low-density amorphous (LDA) ice to ultrafast heating. We then describe experiments in which we heat LDA ice to near the predicted critical point of the LLPT by an ultrafast infrared laser pulse, following which we measure the structure factor using femtosecond x-ray laser pulses. Consistent with our predictions, we observe a LLPT occurring on a time scale < 100 ns and widely separated from ice formation, which begins at times >1 µs.

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.

Anomalous temperature dependence of the experimental x-ray structure factor of supercooled water.

The structural changes of water upon deep supercooling were studied through wide-angle x-ray scattering at SwissFEL. The experimental setup had a momentum transfer range of 4.5 Å-1, which covered the principal doublet of the x-ray structure factor of water. The oxygen-oxygen structure factor was obtained for temperatures down to 228.5 ± 0.6 K. Similar to previous studies, the second diffraction peak increased strongly in amplitude as the structural change accelerated toward a local tetrahedral structure upon deep supercooling. We also observed an anomalous trend for the second peak position of the oxygen-oxygen structure factor (q2). We found that q2 exhibits an unprecedented positive partial derivative with respect to temperature for temperatures below 236 K. Based on Fourier inversion of our experimental data combined with reference data, we propose that the anomalous q2 shift originates from that a repeat spacing in the tetrahedral network, associated with all peaks in the oxygen-oxygen pair-correlation function, gives rise to a less dense local ordering that resembles that of low-density amorphous ice. The findings are consistent with that liquid water consists of a pentamer-based hydrogen-bonded network with low density upon deep supercooling.

Long-Range Structures of Amorphous Solid Water.

High-energy X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) of amorphous solid water (ASW) were studied during vapor deposition and the heating process. From the diffraction patterns, the oxygen-oxygen pair distribution functions (PDFs) were calculated up to the eighth coordination shell and an r = 23 Å. The PDF of ASW obtained both during vapor deposition at 80 K as well as the subsequent heating are consistent with that of low-density amorphous ice. The formation and temperature-induced collapse of micropores were observed in the XRD data and in the FTIR measurements, more specifically, in the OH stretch and the dangling mode. Above 140 K, ASW crystallizes into a stacking disordered ice, Isd. It is observed that the fourth, fifth, and sixth peaks in the PDF, corresponding to structural arrangements between 8 and 12 Å, are the most sensitive to the onset of crystallization.

Enhancement and maximum in the isobaric specific-heat capacity measurements of deeply supercooled water using ultrafast calorimetry.

Knowledge of the temperature dependence of the isobaric specific heat (Cp) upon deep supercooling can give insights regarding the anomalous properties of water. If a maximum in Cp exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid-liquid critical point model that can explain the anomalous increase in thermodynamic response functions. The challenge is that the relevant temperature range falls in the region where ice crystallization becomes rapid, which has previously excluded experiments. Here, we have utilized a methodology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infrared laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. Evaporative cooling of ∼15-µm diameter droplets in vacuum enabled us to reach a temperature down to ∼228 K with a small fraction of the droplets remaining unfrozen. We observed a sharp increase in Cp, from 88 J/mol/K at 244 K to about 218 J/mol/K at 229 K where a maximum is seen. The Cp maximum is at a similar temperature as the maxima of the isothermal compressibility and correlation length. From the Cp measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties decrease rapidly below 235 K.

Experimental observation of the liquid-liquid transition in bulk supercooled water under pressure.

We prepared bulk samples of supercooled liquid water under pressure by isochoric heating of high-density amorphous ice to temperatures of 205 ± 10 kelvin, using an infrared femtosecond laser. Because the sample density is preserved during the ultrafast heating, we could estimate an initial internal pressure of 2.5 to 3.5 kilobar in the high-density liquid phase. After heating, the sample expanded rapidly, and we captured the resulting decompression process with femtosecond x-ray laser pulses at different pump-probe delay times. A discontinuous structural change occurred in which low-density liquid domains appeared and grew on time scales between 20 nanoseconds to 3 microseconds, whereas crystallization occurs on time scales of 3 to 50 microseconds. The dynamics of the two processes being separated by more than one order of magnitude provides support for a liquid-liquid transition in bulk supercooled water.

Anisotropic X-Ray Scattering of Transiently Oriented Water.

We study the structural dynamics of liquid water by time-resolved anisotropic x-ray scattering under the optical Kerr effect condition. In this way, we can separate the anisotropic scattering decay of 160 fs from the delayed temperature increase of ∼0.1 K occurring at 1 ps and quantify transient changes in the O-O pair distribution function. Polarizable molecular dynamics simulations reproduce well the experiment, indicating transient alignment of molecules along the electric field, which shortens the nearest-neighbor distances. In addition, analysis of the simulated water local structure provides evidence that two hypothesized fluctuating water configurations exhibit different polarizability.

Brine rejection and hydrate formation upon freezing of NaCl aqueous solutions.

Studying the freezing of saltwater on a molecular level is of fundamental importance for improving freeze desalination techniques. In this study, we investigate the freezing process of NaCl solutions using a combination of X-ray diffraction and molecular dynamics simulations (MD) for different salt-water concentrations, ranging from seawater conditions to saturation. A linear superposition model reproduces well the brine rejection due to hexagonal ice Ih formation and allows us to quantify the fraction of ice and brine. Furthermore, upon cooling at T = 233 K, we observe the formation of NaCl·2H2O hydrates (hydrohalites), which coexist with ice Ih. MD simulations are utilized to model the formation of NaCl crystal hydrates. From the simulations, we estimate that the salinity of the newly produced ice is 0.5% mass percent (m/m) due to ion inclusions, which is within the salinity limits of fresh water. In addition, we show the effect of ions on the local ice structure using the tetrahedrality parameter and follow the crystallite formation using the ion coordination parameter and cluster analysis.

Intermediate range O-O correlations in supercooled water down to 235 K.

Wide angle x-ray scattering of supercooled water down to 234.8 K was studied using high energy x rays at the European Synchrotron Radiation Facility. The oxygen-oxygen pair distribution function (PDF) was calculated from the scattering pattern out to the 5th peak at an intermolecular distance, r ≈ 11 Å. We observe that the 4th peak and the 5th peak in the PDF increase in height upon supercooling. We also observe that the 4th peak position (r4) shifts to shorter distances upon supercooling consistent with previous studies, but we see a more rapid change at the lowest temperature. The running oxygen-oxygen coordination number is calculated for 5 different temperatures, and an isosbestic point at riso = 3.31 ± 0.05 Å was found corresponding to a coordination number of 4.39 ± 0.15. The comparison of the PDF of the coldest water with that of amorphous ice shows distinct differences. We propose that there are 5-member pentamer rings in low density liquid-like structures giving rise to the sharp correlations at r ≈ 9 Å and r ≈ 11 Å.

X-ray studies of the transformation from high- to low-density amorphous water.

Here we report about the structural evolution during the conversion from high-density amorphous ices at ambient pressure to the low-density state. Using high-energy X-ray diffraction, we have monitored the transformation by following in reciprocal space the structure factor SOO( Q) and derived in real space the pair distribution function gOO( r). Heating equilibrated high-density amorphous ice (eHDA) at a fast rate (4 K min-1), the transition to the low-density form occurs very rapidly, while domains of both high- and low-density coexist. On the other hand, the transition in the case of unannealed HDA (uHDA) and very-high-density amorphous ice is more complex and of continuous nature. The direct comparison of eHDA and uHDA indicates that the molecular structure of uHDA contains a larger amount of tetrahedral motives. The different crystallization behaviour of the derived low-density amorphous states is interpreted as emanating from increased tetrahedral coordination present in uHDA. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.

Apparent power-law behavior of water's isothermal compressibility and correlation length upon supercooling.

The isothermal compressibility and correlation length of supercooled water obtained from small-angle X-ray scattering (SAXS) were analyzed by fits based on an apparent power-law in the temperature range from 280 K down to the temperature of maximum compressibility at 229 K. Although the increase in thermodynamic response functions is not towards a critical point, it is still possible to obtain an apparent power law all the way to the maximum values with best-fit exponents of γ = 0.40 ± 0.01 for the isothermal compressibility and ν = 0.26 ± 0.03 for the correlation length. The ratio between these exponents is close to a value of ≈0.5, as expected for a critical point, indicating the proximity of a potential second critical point. Comparison of γ obtained from experiment with molecular dynamics simulations on the iAMOEBA water model shows that it would be located at pressures in the neighborhood of 1 kbar. The high value and sharpness of the compressibility maximum observed in the experiment are not reproduced by any of the existing classical water models, thus inviting further development of simulation models of water.

X-ray Scattering and O-O Pair-Distribution Functions of Amorphous Ices.

The structure factor and oxygen-oxygen pair-distribution functions of amorphous ices at liquid nitrogen temperature ( T = 77 K) have been derived from wide-angle X-ray scattering (WAXS) up to interatomic distances of r = 23 Å, where local structure differences between the amorphous ices can be seen for the entire range. The distances to the first coordination shell for low-, high-, and very-high-density amorphous ice (LDA, HDA, VHDA) were determined to be 2.75, 2.78, and 2.80 Å, respectively, with high accuracy due to measurements up to a large momentum transfer of 23 Å-1. Similarities in pair-distribution functions between LDA and supercooled water at 254.1 K, HDA and liquid water at 365.9 K, and VHDA and high-pressure liquid water were found up to around 8 Å, but beyond that at longer distances, the similarities were lost. In addition, the structure of the high-density amorphous ices was compared to high-pressure crystalline ices IV, IX , and XII, and conclusions were drawn about the local ordering.

Coherent X-rays reveal the influence of cage effects on ultrafast water dynamics.

The dynamics of liquid water feature a variety of time scales, ranging from extremely fast ballistic-like thermal motion, to slower molecular diffusion and hydrogen-bond rearrangements. Here, we utilize coherent X-ray pulses to investigate the sub-100 fs equilibrium dynamics of water from ambient conditions down to supercooled temperatures. This novel approach utilizes the inherent capability of X-ray speckle visibility spectroscopy to measure equilibrium intermolecular dynamics with lengthscale selectivity, by measuring oxygen motion in momentum space. The observed decay of the speckle contrast at the first diffraction peak, which reflects tetrahedral coordination, is attributed to motion on a molecular scale within the first 120 fs. Through comparison with molecular dynamics simulations, we conclude that the slowing down upon cooling from 328 K down to 253 K is not due to simple thermal ballistic-like motion, but that cage effects play an important role even on timescales over 25 fs due to hydrogen-bonding.

Response to Comment on "Maxima in the thermodynamic response and correlation functions of deeply supercooled water".

Caupin et al have raised several issues regarding our recent paper on maxima in thermodynamic response and correlation functions in deeply supercooled water. We show that these issues can be addressed without affecting the conclusion of the paper.

Maxima in the thermodynamic response and correlation functions of deeply supercooled water.

Femtosecond x-ray laser pulses were used to probe micrometer-sized water droplets that were cooled down to 227 kelvin in vacuum. Isothermal compressibility and correlation length were extracted from x-ray scattering at the low-momentum transfer region. The temperature dependence of these thermodynamic response and correlation functions shows maxima at 229 kelvin for water and 233 kelvin for heavy water. In addition, we observed that the liquids undergo the fastest growth of tetrahedral structures at similar temperatures. These observations point to the existence of a Widom line, defined as the locus of maximum correlation length emanating from a critical point at positive pressures in the deeply supercooled regime. The difference in the maximum value of the isothermal compressibility between the two isotopes shows the importance of nuclear quantum effects.

Temperature-Independent Nuclear Quantum Effects on the Structure of Water.

Nuclear quantum effects (NQEs) have a significant influence on the hydrogen bonds in water and aqueous solutions and have thus been the topic of extensive studies. However, the microscopic origin and the corresponding temperature dependence of NQEs have been elusive and still remain the subject of ongoing discussion. Previous x-ray scattering investigations indicate that NQEs on the structure of water exhibit significant temperature dependence [Phys. Rev. Lett. 94, 047801 (2005)PRLTAO0031-900710.1103/PhysRevLett.94.047801]. Here, by performing wide-angle x-ray scattering of H_{2}O and D_{2}O droplets at temperatures from 275 K down to 240 K, we determine the temperature dependence of NQEs on the structure of water down to the deeply supercooled regime. The data reveal that the magnitude of NQEs on the structure of water is temperature independent, as the structure factor of D_{2}O is similar to H_{2}O if the temperature is shifted by a constant 5 K, valid from ambient conditions to the deeply supercooled regime. Analysis of the accelerated growth of tetrahedral structures in supercooled H_{2}O and D_{2}O also shows similar behavior with a clear 5 K shift. The results indicate a constant compensation between NQEs delocalizing the proton in the librational motion away from the bond and in the OH stretch vibrational modes along the bond. This is consistent with the fact that only the vibrational ground state is populated at ambient and supercooled conditions.

Diffusive dynamics during the high-to-low density transition in amorphous ice.

Water exists in high- and low-density amorphous ice forms (HDA and LDA), which could correspond to the glassy states of high- (HDL) and low-density liquid (LDL) in the metastable part of the phase diagram. However, the nature of both the glass transition and the high-to-low-density transition are debated and new experimental evidence is needed. Here we combine wide-angle X-ray scattering (WAXS) with X-ray photon-correlation spectroscopy (XPCS) in the small-angle X-ray scattering (SAXS) geometry to probe both the structural and dynamical properties during the high-to-low-density transition in amorphous ice at 1 bar. By analyzing the structure factor and the radial distribution function, the coexistence of two structurally distinct domains is observed at T = 125 K. XPCS probes the dynamics in momentum space, which in the SAXS geometry reflects structural relaxation on the nanometer length scale. The dynamics of HDA are characterized by a slow component with a large time constant, arising from viscoelastic relaxation and stress release from nanometer-sized heterogeneities. Above 110 K a faster, strongly temperature-dependent component appears, with momentum transfer dependence pointing toward nanoscale diffusion. This dynamical component slows down after transition into the low-density form at 130 K, but remains diffusive. The diffusive character of both the high- and low-density forms is discussed among different interpretations and the results are most consistent with the hypothesis of a liquid-liquid transition in the ultraviscous regime.