Melting conditions and entropies of superionic water ice: Free-energy calculations based on hybrid solid/liquid reference systems.

Superionic (SI) water ices-high-temperature, high-pressure phases of water in which oxygen ions occupy a regular crystal lattice whereas the protons flow in a liquid-like manner-have attracted a growing amount of attention over the past few years, in particular due to their possible role in the magnetic anomalies of the ice giants Neptune and Uranus. In this paper, we consider the calculation of the free energies of such phases, exploring hybrid reference systems consisting of a combination of an Einstein solid for the oxygen ions occupying a crystal lattice and a Uhlenbeck-Ford potential for the protonic fluid that avoids irregularities associated with possible particle overlaps. Applying this approach to a recent neural-network potential-energy landscape for SI water ice, we compute Gibbs free energies as a function of temperature for the SI fcc and liquid phases to determine the melting temperature Tm at 340 GPa. The results are consistent with previous estimates and indicate that the entropy difference between both phases is comparatively small, in particular due to the large amplitude of vibration of the oxygen ions in the fcc phase at the melting temperature.

Absence of Off-Diagonal Long-Range Order in hcp

The mass transport properties along dislocation cores in hcp ^{4}He are revisited by considering two types of edge dislocations as well as a screw dislocation, using a fully correlated quantum simulation approach. Specifically, we employ the zero-temperature path-integral ground state (PIGS) method together with ergodic sampling of the permutation space to investigate the fundamental dislocation core structures and their off-diagonal long-range order properties. It is found that the Bose-Einstein condensate fraction of such defective ^{4}He systems is practically null (≤10^{-6}), just as in the bulk defect-free crystal. These results provide compelling evidence for the absence of intrinsic superfluidity in dislocation cores in hcp ^{4}He and challenge the superfluid dislocation-network interpretation of the mass-flux-experiment observations, calling for further experimental investigation.

Plastic deformation of superionic water ices.

Due to their potential role in the peculiar geophysical properties of the ice giants Neptune and Uranus, there has been a growing interest in superionic (SI) phases of water ice. So far, however, little attention has been given to their mechanical properties, even though plastic deformation processes in the interiors of planets are known to affect long-term processes, such as plate tectonics and mantle convection. Here, using density functional theory calculations and machine learning techniques, we assess the mechanical response of high-pressure/temperature solid phases of water in terms of their ideal shear strength (ISS) and dislocation behavior. The ISS results are well described by the renormalized Frenkel model of ideal strength and indicate that the SI ices are expected to be highly ductile. This is further supported by deep neural network molecular dynamics simulations for the behavior of lattice dislocations for the SI face-centered cubic (fcc) phase. Dislocation velocity data indicate effective shear viscosities that are orders of magnitude smaller than that of Earth's lower mantle, suggesting that the plastic flow of the internal icy layers in Neptune and Uranus may be significantly faster than previously foreseen.

Is It Possible to Follow the Structural Evolution of Water in "No-Man's Land" Using a Pulsed-Heating Procedure?

The anomalous increase in compressibility and heat capacity of supercooled water has been attributed to its structural transformation of into a four-coordinated liquid. Experiments revealed that κT and Cp peak at TWthermo ≈ 229 K [Kim et al. Science 2017, 358, 1589; Pathak et al. Proc. Natl. Acad. Sci. 2021, 118, e2018379118]. Recently, a pulsed heating procedure (PHP) was employed to interrogate the structure of water, reporting a steep increase in tetrahedrality around TWPHP = 210 ± 3 K [Kringle et al. Science 2020, 369, 1490]. This discrepancy questions whether water structure and thermodynamics are decoupled, or if the shift in TW is an artifact of PHP. Here we implement PHP in molecular simulations. We find that the stationary states captured at the bottom of the pulse are not representative of the thermalized liquid or its inherent structure. Our analysis reveals a temperature-dependent distortion that shifts TWPHP to ∼20 K below TWthermo. We conclude that 2 orders of magnitude faster rates are required to sample water's inherent structure with PHP.

Advances in the study of supercooled water.

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Crystal imperfections in ice Ih.

In this paper, we present an overview of crystal imperfections in ice Ih. Due to its molecular nature, the fundamental asymmetry of the hydrogen bond, and proton disorder, crystal defects in this condensed form of water reveal a complexity not usually seen in atomic crystalline solids. The discussion is organized in terms of the spatial extent of the defects. We start with zero-dimensional imperfections such as the molecular vacancy and interstitial, Bjerrum, and ionic defects, as well as possible defect complexes that can be formed from them. Subsequently, we turn to the properties of dislocations, which are the one-dimensional disturbances that carry plastic deformation in crystalline solids. Finally, we discuss two-dimensional defects such as stacking faults and grain boundaries and discuss to what extent the latter are similar to other interfaces in ice Ih such as the free surface. We conclude with an outlook at the road ahead, discussing future challenges toward understanding the role of crystal defects in the macroscopic behavior of ice Ih.

Nonequilibrium processes in repulsive binary mixtures.

We consider rapid cooling processes in classical, three-dimensional, purely repulsive binary mixtures in which an initial infinite-temperature (ideal-gas) configuration is instantly quenched to zero temperature. It is found that such systems display two kinds of ordering processes, the type of which can be controlled by tuning the interactions between unlike particles. While strong inter-species repulsion leads to chemical ordering in terms of an unmixing process, weak repulsion gives rise to spontaneous crystallization, maintaining chemical homogeneity. This result indicates the existence of a transition in the topography of the underlying potential-energy landscape as the intra-species interaction strength is varied. Furthermore, the dual-type behavior appears to be universal for repulsive pair-interaction potential-energy functions in general, with the propensity for the crystallization process being related to their behavior in the neighborhood of zero separation.

Density-functional theory prediction of the elastic constants of ice Ih.

We assess the elastic stiffness constants of hexagonal proton-disordered ice Ih as described by density-functional theory calculations. Specifically, we compare the results for a set of nine exchange-correlation functionals, including standard generalized-gradient approximations (GGAs), the strongly constrained and appropriately normed (SCAN) metaGGA functional, and a number of dispersion-corrected versions based on the van der Waals (vdW) and VV10 schemes. Compared to the experimental data, all functionals predict an excessively stiff response to tensile and compressive distortions, as well as shear deformations along the basal plane, with the SCAN metaGGA functional displaying the largest deviations as compared to the experimental values. These discrepancies are found to correlate with underestimates of inter-molecular distances, on the one hand, and overestimates of intra-molecular separations, on the other. The inclusion of non-local vdW corrections according to the vdW approach generally improves these structural parameters and softens the elastic response functions compared to their parent GGA functionals. The dispersion-corrected SCAN-rVV10 functional, however, acts in the opposite direction, further worsening the comparison to experiment. In this view, it appears useful that the database employed to gauge the quality of exchange-correlation functionals for water includes an assessment of their elastic response of ice Ih and possibly other crystalline phases.

Elastic constants of ice Ih as described by semi-empirical water models.

Using molecular dynamics simulations, we compute the elastic constants of ice Ih for a set of 8 frequently used semi-empirical potentials for water, namely, the rigid-molecule SPC/E, TIP4P, TIP4P2005, TIP4P/Ice, and TIP5P models, the flexible-molecule qTIP4P/Fw and SPC/Fw models, and the coarse-grained atomic mW potential. In quantitative terms, the mW description gives values for the individual stiffness constants that are closest to the experiment, whereas the explicit-proton models display substantial discrepancies. On the other hand, in contrast to all explicit-proton potentials, the mW model is unable to reproduce central qualitative trends such as the anisotropy in Young's modulus and the shear modulus. This suggests that the elastic behavior of ice Ih is closely related to its molecular nature, which has been coarse-grained out in the mW model. These observations are consistent with other recent manifestations concerning the limitations of the mW model in the description of mechanical properties of ice Ih.

Uniaxial-deformation behavior of ice I h as described by the TIP4P/Ice and mW water models.

Using molecular dynamics simulations, we assess the uniaxial deformation response of ice I h as described by two popular water models, namely, the all-atom TIP4P/Ice potential and the coarse-grained mW model. In particular, we investigate the response to both tensile and compressive uniaxial deformations along the [0001] and [ 0 1 ¯ 10 ] crystallographic directions for a series of different temperatures. We classify the respective failure mechanisms and assess their sensitivity to strain rate and cell size. While the TIP4P/Ice model fails by either brittle cleavage under tension at low temperatures or large-scale amorphization/melting, the mW potential behaves in a much more ductile manner, displaying numerous cases in which stress relief involves the nucleation and subsequent activity of lattice dislocations. Indeed, the fact that mW behaves in such a malleable manner even at strain rates that are substantially higher than those applied in typical experiments indicates that the mW description of ice I h is excessively ductile. One possible contribution to this enhanced malleability is the absence of explicit protons in the mW model, disregarding the fundamental asymmetry of the hydrogen bond that plays an important role in the nucleation and motion of lattice dislocations in ice I h .

Anomalous diffusion of water molecules at grain boundaries in ice Ih.

Using ab initio and classical molecular dynamics simulations, we study pre-melting phenomena in pristine coincident-site-lattice grain boundaries (GBs) in proton-disordered hexagonal ice Ih at temperatures just below the melting point Tm. Concerning pre-melt-layer thicknesses, the results are consistent with the available experimental estimates for low-disorder impurity-free GBs. With regard to molecular mobility, the simulations provide a key new insight: the translational motion of the water molecules is found to be subdiffusive for time scales from ∼10 ns up to at least 0.1 µs. Moreover, the fact that the anomalous diffusion occurs even at temperatures just below Tm where the bulk supercooled liquid still diffuses normally suggests that it is related to the confinement of the GB pre-melt layers by the surrounding crystalline environment. Furthermore, we show that this behavior can be characterized by continuous-time random walk models in which the waiting-time distributions decay according to power-laws that are very similar to those describing dynamics in glass-forming systems.

Uhlenbeck-Ford model: Phase diagram and corresponding-states analysis.

Using molecular dynamics simulations and nonequilibrium thermodynamic-integration techniques we compute the Helmholtz free energies of the body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal close-packed, and fluid phases of the Uhlenbeck-Ford model (UFM) and use the results to construct its phase diagram. The pair interaction associated with the UFM is characterized by an ultrasoft, purely repulsive pair potential that diverges logarithmically at the origin. We find that the bcc and fcc are the only thermodynamically stable crystalline phases in the phase diagram. Furthermore, we report the existence of two reentrant transition sequences as a function of the number density, one featuring a fluid-bcc-fluid succession and another displaying a bcc-fcc-bcc sequence near the triple point. We find strong resemblances to the phase behavior of other soft, purely repulsive systems such as the Gaussian-core model (GCM), inverse-power-law, and Yukawa potentials. In particular, we find that the fcc-bcc-fluid triple point and the phase boundaries in its vicinity are in good agreement with the prediction supplied by a recently proposed corresponding-states principle [J. Chem. Phys. 134, 241101 (2011)JCPSA60021-960610.1063/1.3605659; Europhys. Lett. 100, 66004 (2012)EULEEJ0295-507510.1209/0295-5075/100/66004]. The particularly strong resemblance between the behavior of the UFM and GCM models are also discussed.

Erratum: Dislocation Structure and Mobility in hcp

This corrects the article DOI: 10.1103/PhysRevLett.117.045301.

The Uhlenbeck-Ford model: Exact virial coefficients and application as a reference system in fluid-phase free-energy calculations.

The Uhlenbeck-Ford (UF) model was originally proposed for the theoretical study of imperfect gases, given that all its virial coefficients can be evaluated exactly, in principle. Here, in addition to computing the previously unknown coefficients B11 through B13, we assess its applicability as a reference system in fluid-phase free-energy calculations using molecular simulation techniques. Our results demonstrate that, although the UF model itself is too soft, appropriately scaled Uhlenbeck-Ford (sUF) models provide robust reference systems that allow accurate fluid-phase free-energy calculations without the need for an intermediate reference model. Indeed, in addition to the accuracy with which their free energies are known and their convenient scaling properties, the fluid is the only thermodynamically stable phase for a wide range of sUF models. This set of favorable properties may potentially put the sUF fluid-phase reference systems on par with the standard role that harmonic and Einstein solids play as reference systems for solid-phase free-energy calculations.

Dislocation Structure and Mobility in hcp

Using path-integral Monte Carlo simulations, we assess the core structure and mobility of the screw and edge basal-plane dislocations in hcp ^{4}He. Our findings provide key insights into recent interpretations of giant plasticity and mass flow junction experiments. First, both dislocations are dissociated into nonsuperfluid Shockley partial dislocations separated by ribbons of stacking fault, suggesting that they are unlikely to act as one-dimensional channels that may display Lüttinger-liquid-like behavior. Second, the centroid positions of the partial cores are found to fluctuate substantially, even in the absence of applied shear stresses. This implies that the lattice resistance to motion of the partial dislocations is negligible, consistent with the recent experimental observations of giant plasticity. Further results indicate that both the structure of the partial cores and the zero-point fluctuations play a role in this extreme mobility.

On the nature of the solvated electron in ice Ih.

The water-solvated excess electron (EE) is a key chemical agent whose hallmark signature, its asymmetric optical absorption spectrum, continues to be a topic of debate. While nearly all investigation has focused on the liquid-water solvent, the fact that the crystalline-water solvated EE shows a very similar visible absorption pattern has remained largely unexplored. Here, we present spin-polarized density-functional theory calculations subject to periodic boundary conditions of the interplay between an EE and a number of intrinsic lattice defects in ice Ih. Our results show that the optical absorption signatures in the presence of three unsaturated hydrogen bonds (HB) are very similar to those observed experimentally. Its low-energy side can be attributed to transitions between the EE ground state and a single localized excited level, in a picture that is different from that for the liquid solvent, where this portion has been associated with hydrogen-like s → p excitations. The blue tail, on the other hand, relates to transitions between the EE ground state and delocalized excited states, which is in line with the bound-to-continuum transition interpretations for the EE in liquid water. Finally, we find that, depending on the number of dangling HBs participating in the EE trap, its charge density may spontaneously break the spin degeneracy through exchange interactions with the surrounding electrons, displaying the many-electron quantum nature of the EE problem in ice Ih.

Nuclear quantum fluctuations in ice I(h).

We discuss the role of nuclear quantum fluctuations in ice Ih, focusing on the hydrogen-bond (HB) structure and the molecular dipole-moment distribution. For this purpose we carry out DFT-based first-principles molecular dynamics and path-integral molecular dynamics simulations at T = 100 K. We analyze the HB structure in terms of a set of parameters previously employed to characterize molecular structures in the liquid phase and compute the molecular dipole moments using the maximally-localized Wannier functions. The results show that the protons experience very large digressions driven by quantum fluctuations, accompanied by major rearrangements in the electronic density. As a result of these protonic quantum fluctuations the molecular dipole-moment distribution is substantially broadened as well as shifted to a larger mean value when compared to the results obtained when such fluctuations are neglected. In terms of dielectric constants, the reconciliation between the greater mean dipole moment and experimental indications that the dielectric constant of H2O ice is lower than that of D2O ice would indicate that the topology of the HB network is sensitive to protonic quantum fluctuations.

Ideal shear strength of a quantum crystal.

Using path-integral Monte Carlo simulations, we compute the ideal shear strength (ISS) on the basal plane of hcp (4)He. The failure mode upon reaching the ISS limit is characterized by the homogeneous nucleation of a stacking fault and it is found to be anisotropic, consistent with Schmid's law of resolved shear stress. Comparing the ISS of hcp (4)He to a large set of classical crystals shows that it closely fits the approximately universal modified Frenkel model of ideal strength. In addition to giving quantitative stress levels for the homogeneous nucleation of extended defects in hcp (4)He, our findings lend support to assumptions in the literature that inherently classical models remain useful for the description of mechanical behavior in quantum crystals.

Revisiting dynamics near a liquid-liquid phase transition in Si and Ga: the fragile-to-strong transition.

Using molecular dynamics simulations we analyze the dynamics of two atomic liquids that display a liquid-liquid phase transition (LLPT): Si described by the Stillinger-Weber potential and Ga as modeled by the modified embedded-atom model. In particular, our objective is to investigate the extent to which the presence of a dip in the self-intermediate scattering function is a manifestation of an excess of vibrational states at low frequencies and may be associated with a fragile-to-strong transition (FTST) across the LLPT, as suggested recently. Our results suggest a somewhat different picture. First, in the case of Ga we observe the appearance of an excess of vibrational states at low frequencies, even in the absence of the appearance of a dip in the self-intermediate scattering function across the LLPT. Second, studying the behavior of the shear viscosities traversing the LLPTs we find that both substances are fragile in character above and below their respective LLPT temperatures. Instead of a FTST in an absolute sense these findings are more in line with a view in which the LLPTs are accompanied by a transition from a more fragile to a less fragile liquid. Furthermore, we do not find this transition to correlate with the presence of a dip in the intermediate scattering function.