Ice XXI: High-Pressure Water Phase

• Ice XXI is a metastable crystalline phase of water defined by its high-pressure formation and distinctive tetragonal structure.
• Advanced x-ray and neutron diffraction techniques, alongside MD simulations and DFT calculations, have elucidated its unique hydrogen-bond networks and complex unit cell.
• Its discovery bridges gaps in water’s phase diagram, offering critical insights for planetary science and condensed matter physics, including potential metallic transitions.

Ice XXI is a crystalline phase of water that occupies a central position at the intersection of metastable and high-pressure ice polymorphism. Identified both experimentally and theoretically, Ice XXI displays a unique structural, thermodynamic, and dynamic profile. Critical advances have been achieved through integration of high-precision x-ray and neutron diffraction data, molecular dynamics (MD) simulations, and density functional calculations. Ice XXI is now recognized as a key metastable phase reachable through isothermal compression of supercooled emulsified water at gigapascal pressures, and, under even more extreme pressures, as part of an insulating-to-metallic transition sequence theorized at megabar scales. These discoveries bridge longstanding gaps in the phase diagram of water and have significant implications for condensed matter physics, planetary science, and our understanding of complex hydrogen-bonded systems.

1. Experimental Discovery and Formation

Ice XXI was first isolated experimentally via isothermal compression of deeply supercooled emulsified water within diamond anvil cells under high pressures, typically in the range of 2.41–3.2 GPa and temperatures between 210 K and 295 K (Kobayashi et al., 18 Jul 2025). Crystallization of Ice XXI was facilitated either directly from emulsified water or from high-density amorphous ice (HDA). Optimized protocols involved powder x-ray and neutron diffraction, which enabled discrimination against coexisting phases (notably, ice VII). Key procedures for structural determination included indexing of powder diffraction patterns, whole-pattern fitting using Le Bail and Pawley methods, and density estimation through sequential maximum entropy calculations and charge flipping. Clean samples allowed assignment of the unit cell without interference from other ices in select experiments, thus providing precise structural models.

2. Structural Elucidation and Crystallography

The atomic structure of Ice XXI is distinguished by both its oxygen sublattice and the nature of its hydrogen bonding (Kobayashi et al., 18 Jul 2025). The oxygen framework was established through the extraction of Bragg peak intensities and computation of the Patterson function,

$$\mathcal{P}(u,v,w)=\sum_{h,k,l} |F_{hkl}|^2 \exp\left[-2\pi i\,(hu+kv+lw)\right],$$

enabling electron density map recovery by charge-flipping algorithms. This approach, combined with maximum entropy progressions, revealed the oxygen array to adopt the high-symmetry, tetragonal space group I={4}2d with a significantly large unit cell ($Z=152$).

Hydrogen positions were resolved by superimposing MD simulation predictions on experimental data. Two principal hydrogen-bond networks were considered: a “4-site” model aligned with the TIP4P/Ice force field, and a “6-site” disordered model from the TIP5P potential. Rietveld analysis of diffraction data decidedly favored the 4-site hydrogen network, confirming a quasi-tetrahedral, partially disordered arrangement. This model specifies a hydrogen network structurally homologous to the computationally predicted ‘ice T2’, validating earlier simulation work and providing a quantitative benchmark for force field development.

3. Dynamic Disorder and Local Structure

Analysis of both simulation and experimental data highlights substantial disorder localized around a specific subset of water molecules, denoted as the W6 environment (Kobayashi et al., 18 Jul 2025). Dynamic and static disorder are quantified via the root-mean-square displacement (RMSD): $$\rho^{\mathrm{RMSD}}(W_k)= \sqrt{\frac{1}{N_{W_k}} \sum_{i\in W_k} \Delta r_i^2},$$ where

$$\Delta r_i^2=\frac{1}{N_t}\sum_t \lVert \mathbf{r}_i(t)-\bar{\mathbf{r}}_i\rVert^2.$$

Molecules in the W6-type sites display elevated $U_{iso}$ parameters and RMSD values, reflecting an environment with pronounced local fluctuations. This structural motif is postulated to underpin the especially high “structural complexity” of Ice XXI compared with other ice polymorphs.

4. Theoretical Predictions and High-Pressure Variants

Independent first-principles density functional calculations predict Ice XXI as a sequence of high-pressure phases with distinct symmetries and electronic properties (1009.4722). At 7.6 Mbar, Ice XXI is predicted to adopt a Pbca symmetry, consisting of two interpenetrating hydrogen-bonded networks. In this regime, hydrogen atoms deviate from ideal tetrahedral midpoints but maintain a configuration near their tetrahedral sites. The result is alternating distortion and doubling of the unit cell along the $a$ axis. At even higher pressures (15.5 Mbar), a transformation to the Cmcm symmetry occurs, marking the emergence of a metallic phase wherein hydrogen atoms occupy octahedral positions between next-nearest oxygen atoms. This Cmcm structure comprises corrugated sheets of hydrogen and oxygen, with metallic character inferred from electronic band structure—specifically, the crossing of bands at the Fermi level.

The structural parameters for the Pbca and Cmcm phases at megabar pressures are summarized below:

Symmetry	a (Å)	b (Å)	c (Å)
Pbca	3.117	3.762	3.295
Cmcm	1.869	2.841	2.778

Density functional theory (DFT) calculations, utilizing VASP with projector-augmented wave pseudopotentials, and vibrational plus band structure analyses were pivotal in uncovering these transitions and their implications.

5. Phase Relations, Metastability, and Thermodynamics

Ice XXI occupies a distinct position on the water phase diagram as a metastable phase, with a density intermediate between ices VI and VII (Kobayashi et al., 18 Jul 2025). The high-pressure, low-temperature conditions necessary for its formation make it directly relevant for models of planetary interiors and for the paper of deep Earth ice chemistries. Its metastability and ability to crystallize from highly supercooled water illuminate previously “hidden” branches in the phase diagram, revealing complex phase relations otherwise inaccessible under equilibrium conditions.

Thermodynamic stability assessment involves the computation of the Gibbs free energy: $G=H-TS,$ and pressure-volume-temperature relations,

$P = \rho R T,$

are significant for modeling clathrate stabilization and phase transitions at high pressures (Bartels-Rausch et al., 2012).

6. Implications for Planetary Science and Astrophysics

The stability domains of Ice XXI and its high-pressure relatives directly influence hypotheses about the composition and dynamics within planetary and satellite interiors (Bartels-Rausch et al., 2012). The presence or detection of Ice XXI in subsurface environments of large icy moons or exoplanets with substantial overburden pressures could enable unique forms of gas storage or alter models of planetary differentiation. Metallic variants (Cmcm symmetry) also suggest reflectivity signatures potentially observable in high-pressure laboratory or in situ planetary conditions, providing diagnostic markers for remote sensing and deep probe analysis.

7. Methodological Advances and Future Directions

The methodical integration of high-pressure experimental techniques (diamond anvil cell, synchrotron x-ray and neutron diffraction), advanced computational mapping (charge-flipping, maximum entropy procedures), and molecular dynamics simulations sets a new standard for resolving complex, disordered ice structures (Kobayashi et al., 18 Jul 2025). The demonstration that MD simulations using the TIP4P/Ice potential accurately predicted the experimentally observed hydrogen network, while TIP5P did not, underscores the importance of force field choice.

Future research will likely explore:

• The rotational and translational dynamics of highly disordered local environments such as W6.
• The evolution of hydrogen bonding and geometrical deviations from ideal tetrahedrality.
• The prospect of superionic or plastic phases arising from further increases in pressure.
• The role of clathrate-forming Ice XXI analogs in extraterrestrial ices.

Continued efforts at combining experimental and computational strategies are essential for elucidating the metastable phase relations and structural subtleties that persist across the diverse landscape of water’s crystalline forms.