Ice II is a dense, crystalline polymorph of water ice that forms under moderate high-pressure conditions, exhibiting a rhombohedral structure with space group R\overline{3} and 12 water molecules per unit cell, where hydrogen bonds are fully ordered and form distinct hexagonal rings.[1] It has a density of approximately 1.30 g/cm³ at 225 K and ambient pressure (extrapolated), making it denser than ordinary ice Ih (0.92 g/cm³) but less dense than many higher-pressure ices.[1]Discovered in 1912 by Percy Bridgman through pioneering high-pressure experiments, Ice II is stable in a specific region of water's phase diagram, typically between pressures of about 0.2 GPa and 0.5 GPa and temperatures below roughly 250 K, bordering the fields of Ice Ih at lower pressures and Ice III at higher pressures.[2][1] Unlike most ice phases, which have both hydrogen-disordered and ordered variants, Ice II is uniquely known only in its fully proton-ordered form, with no disordered counterpart observed experimentally. This ordering contributes to its thermodynamic stability even at elevated temperatures within its pressure range, and it can be formed by compressing Ice Ih at temperatures around 190–210 K or by cooling higher-pressure ices.[1]Key physical properties of Ice II include a relatively low bulk modulus of about 12.1 GPa, indicating moderate compressibility, and a volumetric thermal expansion coefficient of 2.48 × 10⁻⁴ K⁻¹ at 225 K, which influences its behavior in geophysical contexts.[1] Lattice parameters at 225 K and 0.25 GPa are a = 12.9351 Å and c = 6.2331 Å (in hexagonal setting).[1] Although it does not occur naturally on Earth's surface due to insufficient pressures, Ice II is relevant to planetary science, potentially existing in the interiors of icy moons like Europa or Ganymede where similar P-T conditions prevail.[1] Its topological constraints, where molecular orientations are interlocked over long distances, highlight water's anomalous behavior and have been studied using neutron diffraction to probe hydrogen ordering under pressure.
Discovery and History
Initial Discovery
The initial discovery of Ice II, a high-pressure polymorph of water ice, is credited to German physical chemist Gustav Heinrich Tammann in 1900. During experiments investigating the boundaries of the solid state of water, Tammann employed a hydraulic press to apply pressures up to approximately 4,000 kg/cm² (about 0.4 GPa) to supercooled liquid water at low temperatures, typically between -10°C and -80°C. He observed abrupt volume decreases during solidification, indicating the formation of denser solid phases distinct from ordinary hexagonal ice (Ice Ih). One of these phases, formed at higher pressures and lower temperatures, exhibited a reversible transition and was later identified as Ice II, characterized by its greater density and stability under compression.Tammann's apparatus, though pioneering, had limitations in precise temperature regulation and pressure measurement, leading him to initially describe two new high-pressure ices without fully distinguishing their phase boundaries or naming them systematically. His work demonstrated that water could adopt multiple crystalline forms under pressure, with the new phase (Ice II) showing a volume contraction of roughly 17% compared to Ice Ih upon formation, highlighting the role of pressure in altering hydrogen bonding networks in ice. This discovery challenged the prevailing view of ice as a single polymorphic substance and spurred further research into the pressure-temperature phase diagram of H₂O.[3]In 1912, American physicist Percy Williams Bridgman built upon Tammann's findings using an advanced opposed-anvil high-pressure device capable of sustaining up to 12,000 kg/cm² (1.2 GPa) with improved sealing and measurement accuracy. Bridgman's volumetric and thermal studies confirmed Ice II as a distinct phase stable in the pressure range of approximately 2,100 to 3,500 kg/cm² (0.21 to 0.35 GPa) at temperatures below -35°C, where it transforms from Ice Ih via a first-order phase transition. He provided the first detailed pressure-volume isotherms, noting Ice II's incompressibility relative to liquid water and its tendency to quench to atmospheric pressure without reverting, enabling easier characterization. Bridgman's comprehensive mapping of five solid ice phases, including Ice II, earned him the 1946 Nobel Prize in Physics for high-pressure techniques and established the foundational phase relations still referenced today.
Structural Determination
The initial structural analysis of Ice II was conducted by Ronald L. McFarlan in 1936 using X-ray powder diffraction on samples recovered from high-pressure conditions. McFarlan proposed a side-centered orthorhombic unit cell with dimensions a = 7.80 Å, b = 4.50 Å, and c = 5.56 Å, containing eight water molecules and suggesting an ionic-like arrangement, though this model was approximate due to the limitations of powder data and did not resolve atomic positions accurately.[3]The definitive crystal structure was established by Barclay Kamb in 1964 through single-crystal X-ray diffraction experiments on Ice II grown at pressures around 2 GPa and temperatures near 200 K. Kamb determined a rhombohedral unit cell with a = 7.78 Å and \alpha = 113.1^\circ, space group R\bar{3} (No. 148), accommodating 12 water molecules per cell and a density of 1.17 g/cm³. Although X-ray diffraction is insensitive to hydrogen positions, Kamb inferred a fully proton-ordered configuration by analyzing subtle distortions in the oxygen framework, which deviated from ideal tetrahedral geometry in a manner consistent with fixed hydrogen bonds forming two distinct types of water molecules linked in a network of puckered and planar hexagonal rings. This ordering distinguished Ice II from proton-disordered phases like Ice Ih.[4]The proton-ordered model was rigorously confirmed in 1971 by Kamb, Hamilton, La Placa, and Prakash using single-crystal neutron diffraction on fully deuterated D₂O Ice II at 110 K and ambient pressure after decompression. The neutron data directly located the four inequivalent deuterium sites, validating the R\bar{3} space group and revealing precise bond lengths (O-D ≈ 0.98 Å, O···O ≈ 2.76–2.85 Å) that supported the tetrahedral hydrogen-bonded framework with no residual disorder. This study refined the structure to an R-factor of 0.047, establishing Ice II as one of the few high-pressure ice phases with complete proton order at synthesis conditions.[5]
Crystal Structure
Lattice Parameters
Ice II adopts a trigonal crystal system with space group R\overline{3} (No. 148), featuring a rhombohedral primitive unit cell that contains 12 water molecules. Neutron diffraction studies conducted at approximately 83 K and 0.21 GPa report lattice parameters of a = 7.743 \pm 0.002 Å and \alpha = 113.09^\circ \pm 0.03^\circ, corresponding to an oxygen-oxygen distance of about 2.772 Å within the framework. These parameters reflect the compact, fully hydrogen-ordered arrangement unique to Ice II among high-pressure ice phases.[6]The structure is equivalently described using a larger hexagonal unit cell (triple the volume of the rhombohedral cell), which contains 36 water molecules and facilitates visualization of the layered hexagonal rings. At conditions near 225 K and 0.25 GPa, this hexagonal cell has parameters a = b = 12.935 Å and c = 6.233 Å.[1] Approximate values often cited in literature, such as a = 7.78 Å and \alpha = 113.1^\circ for the rhombohedral cell, represent room-temperature averages under moderate pressure.[7]Lattice parameters vary continuously with pressure and temperature across Ice II's stability range (roughly 0.2–2.1 GPa and 100–260 K). Compressibility leads to a reduction in cell volume by about 10–15% at the upper pressure limit, while thermal expansion increases the volume by similar margins at higher temperatures; oxygen-oxygen distances adjust anisotropically, with the c-axis of the hexagonal cell showing greater compressibility. These changes maintain the overall topology of the hydrogen-bonded network, contributing to Ice II's density of approximately 1.19 g/cm³ at low temperatures.
Hydrogen Bonding
In Ice II, the hydrogen bonding network is fully ordered, with each water molecule participating in four hydrogen bonds arranged in a tetrahedral coordination geometry, adhering to the Bernal-Fowler ice rules that require two hydrogen atoms covalently bonded to each oxygen and two hydrogen bonds as acceptors.[8] This ordered configuration distinguishes Ice II from proton-disordered phases like Ice Ih, as confirmed by single-crystal neutron diffraction studies revealing precise positions for all protons (or deuterons in D₂O analogs).[5] The structure features two crystallographically independent types of water molecules, forming a tetrahedrally linked network without residual disorder.[5]The hydrogen bonds in Ice II exhibit bending, with D–O–D angles measured at approximately 106° ± 3° from neutron diffraction data on deuterated samples at low temperatures, supporting a non-linear arrangement that stabilizes the overall lattice.[6] This network organizes into hexagonal rings of water molecules, comprising alternating puckered (chair-like) and nearly flat rings stacked along the c-axis to form helical channels, interconnected laterally by additional hydrogen bonds between adjacent rings.[9] In pure Ice II, typical O⋯O distances across hydrogen bonds are around 2.78–2.85 Å, with covalent O–H lengths near 0.98 Å and the hydrogen bond donor-acceptor distances (H⋯O) approximately 1.80–1.87 Å, though these vary slightly with pressure and temperature.[6] The ordered bonding enhances the phase's stability in its pressure-temperature regime, contributing to its relatively high density among ice polymorphs.[10]
Physical Properties
Density and Compressibility
Ice II possesses a density of approximately 1.17 g/cm³ (for H₂O) at ambient pressure and 225 K, representing a roughly 27% increase over the density of ice Ih (0.917 g/cm³ under similar conditions), due to its more efficiently packed rhombohedral lattice with 12 water molecules per unit cell.[1] This value is derived from neutron diffraction measurements on recovered D₂O samples, with the unit cell volume extrapolated to zero pressure yielding V = 306.95 ± 0.04 ų at 225 K.[1] At lower temperatures, such as the athermal limit near 0 K, computational studies indicate a slightly higher density of about 1.19 g/cm³, reflecting reduced thermal expansion.[11]Within its thermodynamic stability field (pressures of 0.2–2.1 GPa and temperatures below 250 K), the density of ice II reaches up to 1.20–1.25 g/cm³, depending on exact conditions, as the phase forms by compression of ice Ih or decompression of higher-pressure phases like ice V.[12] Experimental data from powder neutron diffraction confirm that density increases modestly with pressure in this range, consistent with the phase's ordered hydrogen-bond network that resists further compaction compared to disordered low-pressure ices.[1]Ice II demonstrates low compressibility, characteristic of its rigid framework, with an isothermal bulk modulus K_T of 12.13 ± 0.07 GPa at 225 K and ambient pressure (for D₂O), making it approximately 36% stiffer than ice Ih (K_T ≈ 8.9 GPa).[1] This value is obtained from Birch-Murnaghan equation fits to volume-pressure data, assuming a pressure derivative K' = 6.0, and aligns with computer simulations using water models like TIP4P/2005, which reproduce experimental compressibility to within a few percent across the stability range above 150 K.[12] At higher pressures within the stability field (e.g., 0.35 GPa), K_T rises to 14.23 ± 0.07 GPa, indicating moderate stiffening.[1]Quantum mechanical calculations reveal that nuclear quantum effects slightly reduce the bulk modulus at low temperatures, transitioning from anomalous to normal isotope effects (H₂O vs. D₂O) as density increases, with a zero-temperature value of approximately 17.3 GPa for H₂O ice II under vdW-DF approximations.[11] Overall, the compressibility of ice II underscores its role as a dense, mechanically stable phase in high-pressure environments, with minimal volume change (less than 1% per GPa) under typical geological pressures.[12]
Thermal Expansion and Conductivity
Ice II displays positive thermal expansion throughout its stability field, unlike the low-temperature negative expansivity observed in ice Ih. Measurements on metastable samples recovered to ambient pressure reveal that the volumetric thermal expansion coefficient \alpha_V increases monotonically with temperature, with no evidence of negative values. For D₂O ice II at ambient pressure and 225 K, \alpha_V = 2.48 \times 10^{-4} K^{-1}, as determined by powder neutron diffraction over the range 4.2–160 K.[1] Similar behavior is reported for H₂O ice II, where neutron diffraction data from 5–175 K at ambient pressure show a positive and isotropic expansivity, fitted using a third-order Birch-Murnaghan equation of state.[13] The linear thermal expansion is largely isotropic due to the stable c/a lattice ratio under compression, contrasting with more anisotropic high-pressure phases like ice V.The thermal conductivity of ice II is lower than that of the low-pressure ice Ih phase, consistent with trends across denser high-pressure polymorphs where phonon scattering increases. Early measurements using steady-state techniques confirmed this reduction for ice II under pressures up to 0.5 GPa and temperatures around 200–250 K.[14] Subsequent transient hot-wire experiments on multiple ice phases, including ice II, quantified the conductivity in the range 100–300 K and up to 2.5 GPa, revealing values that scale inversely with density compared to ice Ih (typically ~2 W m^{-1} K^{-1} near 273 K). This diminished conductivity arises from increased phonon scattering in the denser lattice structure, impacting heat transport in planetary interiors where ice II may occur.[15]
Thermodynamic Stability
Pressure-Temperature Range
Ice II exhibits thermodynamic stability within a region of the water phase diagram, spanning pressures from approximately 0.2 GPa to 0.6 GPa (wider at lower temperatures) and temperatures from near 0 K up to a maximum of about 256 K. This field is delimited by key phase boundaries: the lower pressure limit corresponds to the transition with Ice Ih, occurring near 0.2 GPa over much of the temperature range, while the upper pressure boundary marks the transition to Ice III or Ice V, varying with temperature—the boundary with Ice III gently increases from 0.29 GPa at 238 K. The structure's stability at low temperatures underscores its role as a proton-ordered phase persistent down to cryogenic conditions, with no lower temperature limit other than absolute zero.[16]The precise boundaries are defined by three significant triple points involving Ice II. The Ice Ih–Ice II–Ice III triple point lies at 0.29 GPa and 238 K, where the three phases coexist in equilibrium; below this temperature along the Ih–II line, Ice II becomes the stable form under compression. At higher temperatures, the Ice II–Ice III–Ice V triple point occurs at approximately 0.35 GPa and 256 K, and the Ice II–Ice V–Ice VI triple point at 0.62 GPa and 218 K, beyond which Ice V or Ice VI dominates depending on conditions. These points were established through high-pressure piston-cylinder experiments and calorimetric measurements in the early 20th century, with refinements from later thermodynamic modeling.[17][18]Above the relevant temperatures within this pressure interval, Ice II undergoes melting to liquid water, following a short segment of the water melting curve that connects the Ih–II–III triple point to the II–III–L triple point near 0.35 GPa and 256 K. This melting boundary slopes positively, with melting temperatures rising from 238 K at 0.29 GPa to about 256 K at 0.35 GPa, reflecting the phase's higher density compared to Ice Ih but lower than Ice III. Outside this P-T envelope, Ice II can persist metastably, particularly upon decompression to ambient conditions at low temperatures below 170 K, where it resists transformation back to Ice Ih. Such metastability has been observed in laboratory recovery experiments, highlighting kinetic barriers to phase reversion.[17]
Phase Transitions
Ice II, a proton-ordered high-pressure polymorph of water, exhibits solid-solid phase transitions to adjacent ice phases within the complex water phase diagram. Its stability field spans pressures from approximately 0.2 GPa to 0.6 GPa and temperatures below about 256 K, where it forms from Ice Ih upon compression in the range of 170–230 K.[13][17] At higher pressures up to around 2 GPa, Ice II remains metastable at low temperatures below 100 K.[7] These transitions are first-order, involving rearrangements of the hydrogen-bonded network, and are influenced by compression rates; for instance, slow compression at 10 MPa/min facilitates the sequence Ice Ih → Ice II → Ice VI near 200 K.[19]The boundary with Ice III occurs at higher temperatures around 250 K and pressures of 0.25–0.3 GPa, marking a transition from the ordered structure of Ice II to the partially disordered Ice III; further ordering of Ice III yields Ice IX at lower temperatures.[20] Ice II borders Ice V along a boundary from approximately 0.35 GPa and 256 K to 0.62 GPa and 218 K, with compression driving the shift to this denser, disordered phase. At the II–V–VI triple point (0.62 GPa, 218 K), Ice II meets Ice VI but does not share an extended boundary with it.[20] A triple point involving Ice II, Ice III, and Ice V lies at 0.35 GPa and 256 K, near the melting curve.[21] Unlike many ice phases, Ice II lacks an observed hydrogen-disordered counterpart, transforming directly to Ice Ih, III, V, or VI upon heating depending on pressure, without intermediate disordering.[21]At low temperatures below 140 K and pressures of 0.2–0.4 GPa, Ice II can transition to Ice IX, the fully proton-ordered variant of Ice III, via cooling or quenching processes that promote hydrogen ordering.[22][23] This transition is evidenced by changes in spin relaxation rates in muon studies, indicating structural reconfiguration around 140 K.[23] Metastable persistence of Ice II or related phases, such as Ice III in the Ice II field, can occur due to kinetic barriers, affecting deformation and recovery behaviors under varying pressure-temperature paths.[24]
Comparisons with Other Phases
Relation to Ice Ih and Ice III
Ice II is thermodynamically connected to Ice Ih (the common hexagonal ice phase) and Ice III through key phase boundaries in the water phase diagram. The three phases coexist at a triple point located at approximately 238 K and 0.29 GPa, where Ice Ih transforms to either Ice II at lower temperatures or Ice III at higher temperatures under increasing pressure.[17] This triple point marks the boundary of stability for Ice Ih up to about 0.2 GPa at low temperatures, beyond which compression of Ice Ih leads to the formation of Ice II below roughly 245 K, while above this temperature, Ice III is favored.[21] Upon decompression from high pressures, Ice II can revert to Ice Ih, often via a reconstructive transition that involves significant atomic rearrangement.The transition between Ice II and Ice III occurs along a phase boundary extending from the Ih-II-III triple point to higher pressures and temperatures, up to about 0.35 GPa and 250 K, where Ice III meets Ice V.[25] This boundary is characterized by a small volume change, on the order of 0.00002 m³/kg, reflecting the similar densities of Ice II (approximately 1.19 g/cm³) and Ice III (1.16 g/cm³) compared to the less dense Ice Ih (0.92 g/cm³ at ambient conditions).[26] The stability of Ice II relative to these phases arises from its lower vibrational zero-point energy, which provides a microscopic driving force for its formation under cold, high-pressure conditions.[25]Structurally, Ice II differs markedly from the hydrogen-disordered frameworks of Ice Ih and Ice III. Ice Ih features a wurtzite-like hexagonal lattice with tetrahedral coordination and randomly oriented hydrogen bonds, while Ice III adopts a more compact tetragonal structure with similar disorder.[21] In contrast, Ice II has a rhombohedral lattice (space group R-3) with 12 water molecules per unit cell, featuring fully ordered hydrogen bonds that form four distinct bond types, including open nanotube-like channels composed of alternating six-membered rings.[21] This ordering distinguishes Ice II as the only fully proton-ordered phase among low-pressure ices, enabling direct transitions to disordered phases like Ice Ih and Ice III without an intermediate disordered counterpart, unlike other ice pairs.[21]
Hydrogen Ordering Differences
Ice II is characterized by a fully proton-ordered crystal structure, in which the positions of hydrogen atoms relative to oxygen atoms are fixed in a specific arrangement that adheres to the Bernal-Fowler rules—each oxygen has two hydrogens close (covalent bonds) and two distant (hydrogen bonds), with no net dipole moment per molecule. This ordering results in zero residual entropy at absolute zero temperature, distinguishing it from proton-disordered phases that exhibit finite residual entropy due to multiple possible hydrogen configurations.Unlike Ice Ih, the common atmospheric ice phase, which maintains proton disorder at temperatures above approximately 72 K and undergoes a transition to the ordered Ice XI upon cooling, Ice II remains fully ordered throughout its thermodynamic stability range without requiring low temperatures for ordering. Similarly, Ice III exists as a proton-disordered phase at higher temperatures and orders to Ice IX below about 165 K, but Ice II has no such disordered high-temperature analog, a feature attributed to its unique rhombohedral lattice that inherently favors the ordered configuration.[27]The absence of a stable hydrogen-disordered counterpart for Ice II arises from thermodynamic considerations: computational analyses reveal that potential disordered variants satisfying the ice rules possess higher zero-point energies and pair interaction energies compared to the ordered Ice II structure, rendering them less favorable.[27] The residual entropy gain in disordered forms only compensates for this energy penalty at temperatures exceeding the melting point of Ice III (around 250 K at relevant pressures), preventing the disordered phase from manifesting under natural conditions.[27]Investigations into partially disordered configurations, generated by inverting select OH directions in the Ice II lattice, indicate that while one such variant exhibits a marginally lower potential energy, its overall Gibbs free energy remains slightly elevated due to unfavorable zero-point energy contributions, implying that real samples of Ice II are predominantly ordered with possible minor local disorder.[27] Experimental efforts have yet to identify a hydrogen-disordered pendant to Ice II, though theoretical models suggest it as a candidate for future high-pressure synthesis.
Applications and Significance
Planetary Interiors
Ice II, a high-pressure polymorph of water ice stable between approximately 0.2 and 2.1 GPa and temperatures below 250 K, was anticipated in older models (late 20th century) to occur in the interiors of large icy satellites of the outer solar system, such as Ganymede and Callisto, at moderate depths where self-gravitation generates pressures around 2 GPa in predominantly icy mantles.[28] These conditions were thought relevant for transitional zones between outer layers of low-pressure Ice Ih and deeper high-pressure ice phases like Ice III or V. In such environments, Ice II was proposed to contribute to the structural and dynamical evolution of these satellites by influencing mantle rheology.Experimental studies on the plastic deformation of Ice II suggest it exhibits high strength among high-pressure ice phases, with yield stresses around 10–20 MPa under confining pressures of 2–3 GPa at temperatures of 200–250 K. This rigidity could imply resistance to viscous flow, potentially affecting convection and heat transport in icy mantles, though applicability depends on specific P-T conditions.The phase transition from Ice Ih to Ice II, an exothermic process with a Clapeyron slope indicating volume decrease upon compression, can modulate convective dynamics within icy satellite mantles. This transition may distort phase boundaries, enhancing buoyancy-driven instabilities and promoting two-layer convection, as modeled for bodies like Ganymede.[29] In early evolutionary stages, such transitions may have coupled thermal and mechanical processes, aiding persistence of high-pressure ice layers.In Ganymede specifically, late 20th-century interior models positioned Ice II in the mid-mantle under pressures of 2–3 GPa, between an inner Ice VI layer and outer Ice Ih, influencing thermal evolution.[28] However, as of 2024, more recent geophysical interpretations favor higher-pressure phases like Ice V or VI in deeper layers due to updated phase diagrams, temperature profiles, and salinity effects in the ocean, excluding Ice II from current structural models.[30][31] Ice II remains a key reference for understanding rheology and convection in moderately pressurized icy interiors, informing missions like ESA's JUICE (launched 2023) aimed at probing these structures.
High-Pressure Research
Ice II's fully ordered hydrogen-bond network and open framework make it valuable for probing hydrogen ordering mechanisms under pressure and for studying clathrate formation. Its structure allows incorporation of guest molecules like H₂ or He in channels at pressures up to ~1 GPa, forming clathrate hydrates that inform models of hydrogen storage and planetary ices.[32][33]Modern studies, such as neutron diffraction in Paris-Edinburgh cells, have refined its equation of state. Fortes et al. (2005) measured properties of deuterated Ice II over 0.25–1.9 GPa and 4–270 K, yielding a zero-pressure bulk modulus of 12.1 GPa at 225 K and volumetric thermal expansion coefficient of 2.48 × 10^{-4} K^{-1}, with anisotropic expansion due to rigid frameworks.[1] These insights highlight Ice II's role in understanding water's anomalous behavior and materials under compression, including spectroscopic studies confirming long-range order via sharp O-H vibrational modes and an entropy drop of 3.22 J/mol·K upon transition from Ice Ih.[1]