Hydrogen bond symmetrisation in D₂O ice observed by neutron diffraction

Water ice exhibits remarkable structural variety with at least 20 polymorphs. Above about 2 GPa, the phase diagram is dominated by body-centred cubic ices: hydrogen-disordered ice VII, ordered ice VIII, hydrogen-bond-symmetrised ice X, and recently discussed superionic ices. The concept of H-bond symmetrisation—hydrogen centred between donor and acceptor oxygens—was suggested soon after the discovery of ice VII. Experimental infrared and Raman studies in the 1990s reported symmetrisation around 60 GPa for H₂O and 70 GPa for D₂O, consistent with a strong isotope effect arising from nuclear quantum tunnelling. However, more recent ¹H-NMR and x-ray diffraction reports diverge widely (20–75 GPa). A key source of controversy is the presence of intermediate states between ice VII and X within the same space group (Pn3m) and the difficulty of locating hydrogen at megabar pressures. At lower pressures and longer O···O distances, hydrogen localises in one of two potential minima forming a covalent O–H bond and a weaker H-bond; in ice VII, these two equivalent sites are occupied in a disordered manner, seen as a bimodal distribution in diffraction. With pressure, O···O contracts and hydrogen/deuterium motion becomes more dynamic via thermal hopping or quantum tunnelling (ice VII′), which is difficult to distinguish by diffraction because Bragg intensities reflect time- and space-averaged structures. H-bond symmetrisation refers to localisation at the bond centre; when the double-well evolves toward single-well, the distribution initially elongates along O···O (often termed ice X′), and at higher pressure becomes perpendicular (ice X). First-principles molecular dynamics predicts a change from prolate (parallel) to oblate (perpendicular) distribution. Neutron diffraction is the most direct probe of hydrogen/deuterium distributions and, in principle, can distinguish ice VII and X(X′), but experiments above 30 GPa have been limited by source intensity. Advances in spallation sources, high-pressure cells, and neutron optics now extend neutron diffraction to ~100 GPa. The authors developed nano-polycrystalline diamond anvil cells (NPDACs), advantageous for hardness, toughness, and simpler attenuation corrections. Here, the atomic distribution of deuterium in D₂O ice above 100 GPa is measured by neutron diffraction to address the long-standing problem of H-bond symmetrisation.

Prior work established ice VII, VIII, and X as key high-pressure ice phases, with H-bond symmetrisation postulated decades ago and spectroscopic evidence reported around 60–70 GPa, showing strong isotope dependence due to nuclear quantum effects. Computational studies (DFT, path-integral MD) predict progressive evolution of the hydrogen potential from double- to single-well with increasing pressure, involving intermediate states (VII′ and X′) and changes in elasticity; tunnelling and zero-point motion play central roles with notable isotope effects. Experimental determinations of the symmetrisation pressure have been inconsistent (20–75 GPa) across techniques such as IR/Raman, NMR, and x-ray diffraction, complicated by the inability to directly resolve hydrogen positions at megabar pressures and potential influences of deviatoric stress and sample preparation. Neutron diffraction below ~60 GPa has provided structural parameters and indicated ring-like deuterium distributions linked to molecular rotation dynamics in ice VII, and anomalies near 10–15 GPa in various properties suggest a crossover in proton dynamics. Recent x-ray studies reported peak broadening/splitting and proposed symmetry lowering or phase coexistence, but interpretations may be confounded by stress states and instrumental factors. This study builds on these findings by directly probing deuterium distributions to >100 GPa with neutron diffraction to clarify the VII′–X′ transition.

Seven neutron diffraction runs (#1–#7) on D₂O (99.9%) at room temperature were performed at the PLANET beamline (MLF, J-PARC) using 25 Hz pulsed spallation neutrons with 500–800 kW accelerator power. Nano-polycrystalline diamond anvil cells (NPDACs) with varied culet sizes/shapes (cup-shaped in most runs to reduce diamond scattering and deviatoric stress; flat in run #2), gasket materials/thicknesses, diffraction geometries, and fine radial collimators (0.5–1.1 mm gauge) were employed. A focusing supermirror guide increased flux, and ³He detector banks at 2θ≈90° collected data. Most runs used through-anvil geometry (beam parallel to compression axis); run #6 used through-gasket geometry with a modified NPDAC. Sample preparation: runs #1–#3 used direct compression at room temperature yielding coarse grains; runs #4–#7 used a low-temperature path (load water, clamp near ambient, cool by dry ice or liquid N₂, compress at low T, reheat under pressure) to traverse phase boundaries and obtain fine powders suitable for Rietveld refinement. Pressures were determined from unit-cell volumes using a known ice VII equation of state (Hemley et al.). Rietveld analyses (GSAS with EXPGUI) refined mixed-phase patterns (ice sample, diamond anvils, iron gasket as needed). Structural refinement: oxygen fixed at 2a (1,1,1); deuterium at 8e (x,x,x). Runs #4 and #7 refined x(D) and isotropic atomic displacement parameters U(D) and U(O); multi-site oxygen disorder was neglected due to limited resolution and prior evidence supporting single-site modeling at comparable conditions. Runs #5 and #6 refined only x(D), with ADPs fixed via pressure-dependent extrapolation from runs #4 and #7 (empirical exponential fits). Anisotropic microstrain broadening (TOF profile function) was modeled to account for stress-induced peak broadening/splitting, improving fits especially near 20–30 GPa. Additional tests at 103 GPa explored anisotropic ADPs for D, finding nearly spherical or slightly prolate distributions along O···O. Diffraction quality varied by run: best up to 39.2 GPa (run #4); highest pressure reached 106 GPa (run #5).

- Direct neutron diffraction evidence shows the deuterium distribution transitions from bimodal (two-site) to unimodal (centred) at approximately 80 GPa in D₂O ice. This is established by the criterion where the intersite separation d(D···D) equals 2√U(D), with the observed crossing near 80 GPa. - Probability density maps of D positions versus pressure corroborate the change from bimodal to unimodal at ~80 GPa. - Refined ADPs U(D) and U(O) decrease up to ~15 GPa and plateau thereafter, consistent with earlier neutron studies, and with a ring-like D distribution at low pressure attributed to molecular rotation that diminishes with compression. - Derived bond lengths d(O–D) and d(D···O) agree with previous neutron data up to 62 GPa and with recent path-integral MD; they do not merge by 106 GPa. Extrapolation suggests merging around 120 GPa, consistent with a transition from prolate (X′) to oblate (X) distribution. - Peak width anomalies: Δd/d for 110 and 111 peaks broaden with pressure, with a maximum near ~20 GPa (linked to a proton dynamics crossover) and a pronounced reduction around ~80 GPa coincident with the VII′–X′ transition, indicating structural relaxation associated with changes in elastic properties. - Anisotropic broadening (especially in 110) is sensitive to external deviatoric stress and sample environment; observed variations between runs (e.g., culet shape effects) imply previous x-ray reports of tetragonal distortion or peak splitting may reflect stress-induced microstrain rather than intrinsic symmetry lowering. - At 103 GPa, anisotropic ADP refinement yields nearly spherical or slightly elongated D distribution (U≈0.021 and 0.017 Ų along principal axes), producing fits comparable to a two-site isotropic model, indicating limited sensitivity to small anisotropy at megabar pressures. - Experimental reach: high-quality Rietveld data to 39.2 GPa (run #4) and maximum pressure of 106 GPa (run #5).

The results pinpoint the pressure for hydrogen-bond symmetrisation (centred deuterium distribution) in D₂O ice at ~80 GPa, directly addressing longstanding discrepancies among spectroscopic, NMR, and x-ray studies. By quantifying when d(D···D) falls below 2√U(D), the work provides a clear, diffraction-based structural criterion for the VII′–X′ transition, consistent with theoretical predictions of a gradual evolution from a double- to single-well potential and with an isotope-dependent shift relative to H₂O. The observed sharp reduction in peak width (Δd/d) at ~80 GPa suggests structural relaxation linked to changes in bulk and shear moduli across the VII′–X′ transition, aligning with reports of elastic anomalies. The persistence of distinct d(O–D) and d(D···O) up to 106 GPa and their extrapolated merging near ~120 GPa support a subsequent X′→X change (from prolate to oblate hydrogen distributions), consistent with DFT and dynamic measurements. The study also clarifies that reported x-ray peak splittings and apparent symmetry lowering can arise from stress-induced anisotropic broadening, not necessarily intrinsic phase changes, and that coexistence interpretations should consider stress conditions. Overall, neutron diffraction directly locates deuterium and reconciles prior inconsistencies by distinguishing intrinsic hydrogen-centering from extrinsic stress effects and by connecting structural transitions to elastic property changes.

Neutron diffraction measurements on D₂O ice to 106 GPa directly reveal hydrogen-bond symmetrisation as deuterium centring at ~80 GPa (VII′→X′), accompanied by a sudden sharpening of diffraction peaks indicative of structural relaxation and elastic changes. Bond-length trends and probability density analyses, together with ADP behavior, align with prior neutron data and quantum simulations, and extrapolate an X′→X change near ~120 GPa. These findings refine the high-pressure ice phase diagram, highlight isotope effects, and call for reinterpretation of prior x-ray peak splitting as stress-related. Open questions remain regarding medium-dependent Bragg peak splitting and the persistence of tunnelling signatures up to ~97 GPa under a nominally single-well potential. Future work should probe stress conditions systematically, extend simultaneous neutron and complementary spectroscopic/elastic measurements to higher pressures, and compare H₂O vs D₂O to quantify isotope-dependent transition pressures and dynamics.

- Static vs dynamic disorder in ice VII/VII′ cannot be distinguished by diffraction; Bragg intensities reflect time- and space-averaged structures. - The criterion for VII′→X′ assumes near-isotropic deuterium distributions and uses extrapolated U(D) at the highest pressures; modest anisotropy or ADP extrapolation uncertainties may shift the inferred transition pressure slightly. - Oxygen multi-site disorder was neglected due to limited resolution; subtle oxygen displacements cannot be fully ruled out. - Some runs (#5, #6) fixed ADPs due to pattern quality; limited sensitivity to small U(D) variations may affect precision. - External deviatoric stress influences peak widths and apparent symmetry; stress heterogeneity and diamond peak overlaps (e.g., 110 with diamond 111 between 35–60 GPa) limit observable reflections and may bias line-shape analyses. - Transition pressures for VII→VII′ and X′→X remain approximate; merging of d(O–D) and d(D···O) is based on extrapolation beyond measured range. - The study focuses on D₂O; direct comparison to H₂O under identical conditions is needed to fully quantify isotope effects.