Phonon dispersion of ice under pressure

The Importance of Nuclear Quantum Effects on the Thermodynamic and Structural Properties of Low-Density Amorphous Ice: A Comparison with Hexagonal Ice

We study the nuclear quantum effects (NQE) on the thermodynamic properties of low-density amorphous ice (LDA) and hexagonal ice (I_h) at P = 0.1 MPa and T ≥ 25 K. Our results are based on path-integral molecular dynamics (PIMD) and classical MD simulations of H₂O and D₂O using the q-TIP4P/F water model. We show that the inclusion of NQE is necessary to reproduce the experimental properties of LDA and ice I_h. While MD simulations (no NQE) predict that the density ρ(T) of LDA and ice I_h increases monotonically upon cooling, PIMD simulations indicate the presence of a density maximum in LDA and ice I_h. MD and PIMD simulations also predict a qualitatively different T-dependence for the thermal expansion coefficient α_P(T) and bulk modulus B(T) of both LDA and ice I_h. Remarkably, the ρ(T), α_P(T), and B(T) of LDA are practically identical to those of ice I_h. The origin of the observed NQE is due to the delocalization of the H atoms, which is identical in LDA and ice I_h. H atoms delocalize considerably (over a distance ≈ 20-25% of the OH covalent-bond length) and anisotropically (preferentially perpendicular to the OH covalent bond), leading to less linear hydrogen bonds HB (larger HOO angles and longer OO separations) than observed in classical MD simulations.

The microscopic origin of the anomalous isotopic properties of ice relies on the strong quantum anharmonic regime of atomic vibration

Water ice is a unique material presenting intriguing physical properties, such as negative thermal expansion and anomalous volume isotope effect (VIE). They arise from the interplay between weak hydrogen bonds and nuclear quantum fluctuations, making theoretical calculations challenging. Here, we employ the stochastic self-consistent harmonic approximation to investigate how thermal and quantum fluctuations affect the physical properties of ice XI with ab initio accuracy. Regarding the anomalous VIE, our work reveals that quantum effects on hydrogen are so strong to be in a nonlinear regime: When progressively increasing the mass of hydrogen from protium to infinity (classical limit), the volume first expands and then contracts, with a maximum slightly above the mass of tritium. We observe an anharmonic renormalization of about 10% in the bending and stretching phonon frequencies probed in IR and Raman experiments. For the first time, we report an accurate comparison of the low-energy phonon dispersion with the experimental data, possible only thanks to high-level accuracy in the electronic correlation and nuclear quantum and thermal fluctuations, paving the way for the study of thermal transport in ice from first-principles and the simulation of ice under pressure.

High-Pressure Nonequilibrium Dynamics on Second-to-Microsecond Time Scales: Application of Time-Resolved X-ray Diffraction and Dynamic Compression in Ice

The study of nonequilibrium transition dynamics on structural transformation from the second to microsecond regime, a time scale between static and shock compression, is an emerging field of high-pressure research. There are ample opportunities to uncover novel physical phenomena within this time regime. Herein, we briefly review the development and application of a dynamic compression technique based on a diamond anvil cell (DAC) and time-resolved X-ray diffraction (TRXRD) for the study of time-, pressure-, and temperature-dependent structural dynamics. Applications of the techniques are illustrated with our recent investigations on the mechanisms of the interconversions between different high-pressure ice polymorphs. These examples demonstrate that a combination of dynamic compression and TRXRD is a versatile approach capable of providing information on the kinetics and thermodynamic nature associated with structural transformations. Future improvement of rapid compression and TRXRD techniques and potentially interesting research topics in this area are suggested.

Coherent thermodynamic model for ice Ih-A model case for complex behavior

New data on the variation of the thermal expansion of ice Ih with temperature at ambient pressure together with new evaluations of the bulk modulus and earlier data for the heat capacity provide the basis for a coherent thermodynamic modeling of the main thermophysical properties of ice Ih over its whole range of stability. The quasi-harmonic approximation with one Debye term and seven Einstein terms, together with explicit anharmonicity, represents the dominant contribution next to minor "anomalies" from hydrogen ordering and lattice defects. The model accurately fits the main features of all experimental data and provides a basis for the comparison with earlier determinations of the phonon density of states and the Grüneisen parameters.

Nuclear quantum effects on the thermodynamic, structural, and dynamical properties of water

We perform path-integral molecular dynamics (PIMD) simulations of H2O and D2O using the q-TIP4P/F model. Simulations are performed at P = 1 bar and over a wide range of temperatures that include the equilibrium (T≥ 273 K) and supercooled (210 ≤T < 273 K) liquid states of water. The densities of both H2O and D2O calculated from PIMD simulations are in excellent agreement with experiments in the equilibrium and supercooled regimes. We also evaluate important thermodynamic response functions, specifically, the thermal expansion coefficient αP(T), isothermal compressibility κT(T), isobaric heat capacity CP(T), and static dielectric constant ε(T). While these properties are in excellent [αP(T) and κT(T)] or semi-quantitative agreement [CP(T) and ε(T)] with experiments in the equilibrium regime, they are increasingly underestimated upon further cooling. It follows that the inclusion of nuclear quantum effects in PIMD simulations of (q-TIP4P/F) water is not sufficient to reproduce the anomalous large fluctuations in density, entropy, and electric dipole moment characteristic of supercooled water. It has been hypothesized that water may exhibit a liquid-liquid critical point (LLCP) in the supercooled regime at P > 1 bar and that such a LLCP generates a maximum in CP(T) and κT(T) at 1 bar. Consistent with this hypothesis and in particular, with experiments, we find a maximum in the κT(T) of q-TIP4P/F light and heavy water at T≈ 230-235 K. No maximum in CP(T) could be detected down to T≥ 210 K. We also calculate the diffusion coefficient D(T) of H2O and D2O using the ring-polymer molecular dynamics (RPMD) technique and find that computer simulations are in remarkable good agreement with experiments at all temperatures studied. The results from RPMD/PIMD simulations are also compared with the corresponding results obtained from classical MD simulations of q-TIP4P/F water where atoms are represented by single interacting sites. Surprisingly, we find minor differences in most of the properties studied, with CP(T), D(T), and structural properties being the only (expected) exceptions.

Temperature-dependent kinetic pathways featuring distinctive thermal-activation mechanisms in structural evolution of ice VII

Ice amorphization, low- to high-density amorphous (LDA-HDA) transition, as well as (re)crystallization in ice, under compression have been studied extensively due to their fundamental importance in materials science and polyamorphism. However, the nature of the multiple-step "reverse" transformation from metastable high-pressure ice to the stable crystalline form under reduced pressure is not well understood. Here, we characterize the rate and temperature dependence of the structural evolution from ice VII to ice I recovered at low pressure (∼5 mTorr) using in situ time-resolved X-ray diffraction. Unlike previously reported ice VII (or ice VIII)→LDA→ice I transitions, we reveal three temperature-dependent successive transformations: conversion of ice VII into HDA, followed by HDA-to-LDA transition, and then crystallization of LDA into ice I. Significantly, the temperature-dependent characteristic times indicate distinctive thermal activation mechanisms above and below 110-115 K for both ice VIII-to-HDA and HDA-to-LDA transitions. Large-scale molecular-dynamics calculations show that the structural evolution from HDA to LDA is continuous and involves substantial movements of the water molecules at the nanoscale. The results provide a perspective on the interrelationship of polyamorphism and unravel its underpinning complexities in shaping ice-transition kinetic pathways.

Thermal Expansion of Single-Crystal H_{2}O and D_{2}O Ice Ih

Thermal expansion of H_{2}O and D_{2}O ice Ih with relative resolution of 1 ppb is reported. A large transition in the thermal expansion coefficient at 101 K in H_{2}O moves to 125 K in D_{2}O, revealing one of the largest-known isotope effects. Rotational oscillatory modes that couple poorly to phonons, i.e., lattice solitons, may be responsible.

Accurate and precise lattice parameters of H2O and D2O ice Ihbetween 1.6 and 270 K from high-resolution time-of-flight neutron powder diffraction data

Accurate and precise lattice parameters for D2O and H2O varieties of hexagonal ice (ice Ih, space groupP63/mmc) have been obtained in the range 1.6 to 270 K. Precision of the lattice parameters (∼0.0002% inaand 0.0004% incfor D2O, 0.0008% inaand 0.0015% incfor H2O) is ensured by use of the time-of-flight method on one of the longest primary neutron flight-path instruments in the world, the High-Resolution Powder Diffractometer at the ISIS neutron source. These data provide a more precise description of the negative thermal expansion of the material at low temperatures than the previous synchrotron `gold standard' [Röttgeret al.(1994).Acta Cryst.B50, 644–648], including the region below 10 K where the lattice parameters saturate. The volume expansivity of both isotopologues turns negative below 59–60 K, in excellent agreement with a recent dilatometry study. The axial expansivities are highly isotropic (differing by < 1% in D2O ice Ih). Furthermore, thec/aratio of different D2O ice samples exhibit a statistically significant dispersion of ∼0.015% below 150 K that appears to depend on the thermal history of the sample, which disappears on warming above 150 K. Similarly, H2O ice exhibits a `kink' in thec/aratio at ∼115 K. The most plausible explanation is a freezing-in of the molecular reorientation process on cooling and subsequent relaxation on warming.

Kinetically Controlled Two-Step Amorphization and Amorphous-Amorphous Transition in Ice

We report the results of in situ structural characterization of the amorphization of crystalline ice Ih under compression and the relaxation of high-density amorphous (HDA) ice under decompression at temperatures between 96 and 160 K by synchrotron x-ray diffraction. The results show that ice Ih transforms to an intermediate crystalline phase at 100 K prior to complete amorphization, which is supported by molecular dynamics calculations. The phase transition pathways show clear temperature dependence: direct amorphization without an intermediate phase is observed at 133 K, while at 145 K a direct Ih-to-IX transformation is observed; decompression of HDA shows a transition to low-density amorphous ice at 96 K and ∼1  Pa, to ice Ic at 135 K and to ice IX at 145 K. These observations show that the amorphization of compressed ice Ih and the recrystallization of decompressed HDA are strongly dependent on temperature and controlled by kinetic barriers. Pressure-induced amorphous ice is an intermediate state in the phase transition from the connected H-bond water network in low pressure ices to the independent and interpenetrating H-bond network of high-pressure ices.

Is High-Density Amorphous Ice Simply a "Derailed" State along the Ice I to Ice IV Pathway?

The structural nature of high-density amorphous ice (HDA), which forms through low-temperature pressure-induced amorphization of the "ordinary" ice I, is heavily debated. Clarifying this question is important for understanding not only the complex condensed states of H₂O but also in the wider context of pressure-induced amorphization processes, which are encountered across the entire materials spectrum. We first show that ammonium fluoride (NH₄F), which has a similar hydrogen-bonded network to ice I, also undergoes a pressure collapse upon compression at 77 K. However, the product material is not amorphous but NH₄F II, a high-pressure phase isostructural with ice IV. This collapse can be rationalized in terms of a highly effective mechanism. In the case of ice I, the orientational disorder of the water molecules leads to a deviation from this mechanism, and we therefore classify HDA as a "derailed" state along the ice I to ice IV pathway.

The cold neutron chopper spectrometer at the Spallation Neutron Source-A review of the first 8 years of operation

The first eight years of operation of the Cold Neutron Chopper Spectrometer (CNCS) at the Spallation Neutron Source in Oak Ridge is being reviewed. The instrument has been part of the facility user program since 2009, and more than 250 individual user experiments have been performed to date. CNCS is an extremely powerful and versatile instrument and offers leading edge performance in terms of beam intensity, energy resolution, and flexibility to trade one for another. Experiments are being routinely performed with the sample at extreme conditions: T ≲ 0.05 K, p ≳ 2 GPa, and B = 8 T can be achieved individually or in combination. In particular, CNCS is in a position to advance the state of the art with inelastic neutron scattering under pressure, and some of the recent accomplishments in this area will be presented in more detail.

Nature of the Volume Isotope Effect in Ice

The substitution of hydrogen (H) by deuterium (D) in ice Ih and in its H-ordered version, ice XI, produces an anomalous form of volume isotope effect (VIE), i.e., volume expansion. This VIE contrasts with the normal VIE (volume contraction) predicted in ice-VIII and in its H-disordered form, ice VII. Here we investigate the VIE in ice XI and in ice VIII using first principles quasiharmonic calculations. We conclude that normal and anomalous VIEs can be produced in ice VIII and ice XI in sequence by application of pressure (ice XI starting at negative pressures) followed by a third type-anomalous VIE with zero-point volume contraction. The latter should also contribute to the isotope effect in the ice VII → ice X transition. The predicted change between normal and anomalous VIE in ice VIII at 14.3 GPa and 300 K is well reproduced experimentally in ice VII using x-ray diffraction measurements. The present discussion of the VIE is general, and conclusions should be applicable to other solid phases of H(2)O, possibly to liquid water under pressure, and to other H-bonded materials.

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C₄₄, which was proposed to trigger the transition through Born criteria B₃. However, by using density-functional theory, we surprisingly found that both C₄₄ and C₆₆ in α-quartz exhibit strong nonlinearity under compression and the Born criteria B₃ vanishes dominated by stiffening of C₁₄, instead of by decreasing of C₄₄. Further studies of archetypal quartz homeotypes (GeO₂ and AlPO₄) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed.

Future directions in high-pressure neutron diffraction

The ability to manipulate structure and properties using pressure has been well known for many centuries. Diffraction provides the unique ability to observe these structural changes in fine detail on lengthscales spanning atomic to nanometre dimensions. Amongst the broad suite of diffraction tools available today, neutrons provide unique capabilities of fundamental importance. However, to date, the growth of neutron diffraction under extremes of pressure has been limited by the weakness of available sources. In recent years, substantial government investments have led to the construction of a new generation of neutron sources while existing facilities have been revitalized by upgrades. The timely convergence of these bright facilities with new pressure-cell technologies suggests that the field of high-pressure (HP) neutron science is on the cusp of substantial growth. Here, the history of HP neutron research is examined with the hope of gleaning an accurate prediction of where some of these revolutionary capabilities will lead in the near future. In particular, a dramatic expansion of current pressure-temperature range is likely, with corresponding increased scope for extreme-conditions science with neutron diffraction. This increase in coverage will be matched with improvements in data quality. Furthermore, we can also expect broad new capabilities beyond diffraction, including in neutron imaging, small angle scattering and inelastic spectroscopy.

Temperature-induced amorphisation of hexagonal ice

We studied for the first time systematically the temperature-induced amorphisation (TIA) of hexagonal ice.

Diffuse scattering in Ih ice

Single crystals of ice Ih, extracted from the subglacial Lake Vostok accretion ice layer (3621 m depth) were investigated by means of diffuse x-ray scattering and inelastic x-ray scattering. The diffuse scattering was identified as mainly inelastic and rationalized in the frame of ab initio calculations for the ordered ice XI approximant. Together with Monte-Carlo modelling, our data allowed reconsidering previously available neutron diffuse scattering data of heavy ice as the sum of thermal diffuse scattering and static disorder contribution.

Path-integral simulation of solids

The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity.

Surface energy and surface proton order of the ice Ih basal and prism surfaces

Density-functional theory (DFT) is used to examine the basal and prism surfaces of ice Ih. Similar surface energies are obtained for the two surfaces; however, in each case a strong dependence of the surface energy on surface proton order is identified. This dependence, which can be as much as 50% of the absolute surface energy, is significantly larger than the bulk dependence (<1%) on proton order, suggesting that the thermodynamic ground state of the ice surface will remain proton ordered well above the bulk order-disorder temperature of about 72 K. On the basal surface this suggestion is supported by Monte Carlo simulations with an empirical potential and solution of a 2D Ising model with nearest neighbor interactions taken from DFT. Order parameters that define the surface energy of each surface in terms of nearest neighbor interactions between dangling OH bonds (those which point out of the surface into vacuum) have been identified and are discussed. Overall, these results suggest that proton order-disorder effects have a profound impact on the stability of ice surfaces and will most likely have an effect on ice surface reactivity as well as ice crystal growth and morphology.

Experimental evidence for a crossover between two distinct mechanisms of amorphization in ice Ih under pressure

We report neutron scattering data which reveal the central role of phonon softening leading to a negative melting line, solid-state amorphization, and negative thermal expansion of ice. We find that pressure-induced amorphization is due to mechanical melting at low temperatures, while at higher temperatures amorphization is governed by thermal melting (violations of Born's and Lindemann's criteria, respectively). This confirms earlier conjectures of a crossover between two distinct amorphization mechanisms and provides a natural explanation for the strong annealing observed in high-density amorphous ice.

A Universal Criterion of Melting

Melting is analyzed dynamically as a problem of localization at a liquid-solid interface. A Lindemann-like criterion of melting is derived in terms of particular vibrational amplitudes, which turn out to equal a universal quotient (about one-tenth) of the molecular spacing, at the interface. The near universality of the Lindemann ratio apparently arises owing to strongly overdamped dynamics near melting, and despite the anharmonic interactions being system-specific. A similar criterion is derived for structural displacements in the bulk of the solid, in particular the premelted layer; the criterion is no longer strictly universal, but still depends only on the harmonic properties of the solid. We further compute the dependence of the magnitude of the elemental molecular translations, in deeply supercooled fluids, on the temperature and the high frequency elastic constants. We show explicitly that the surface tension between distinct liquid states, near the glass transition of a supercooled liquid, is nearly evenly split between entropic and energetic contributions.

Lattice dynamics of molybdenum at high pressure

We have determined the lattice dynamics of molybdenum at high pressure to 37 GPa using high-resolution inelastic x-ray scattering. Over the investigated pressure range, we find a significant decrease in the H-point phonon anomaly. We also present calculations based on density functional theory that accurately predict this pressure dependence. Based on these results, we infer that the likely explanation for the H-point anomaly in molybdenum is strong electron-phonon coupling, which decreases upon compression due to the shift of the Fermi level with respect to the relevant electronic bands.