# X-ray signature of the superionic transition in warm dense fcc water ice

Alexis Forestier, Gunnar Weck, Frédéric Datchi, Sandra Ninet, Gaston Garbarino, Mohamed Mezouar, Paul Loubeyre

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Alexis Forestier, Gunnar Weck, Frédéric Datchi, Sandra Ninet, Gaston Garbarino, et al. X-ray signature of the superionic transition in warm dense fcc water ice. Physical Review Letters, 2025, 134 (7), pp.076102. 10.1103/PhysRevLett.134.076102. hal-04975705

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Distributed under a Creative Commons Attribution 4.0 International License
X-Ray Signature of the Superionic Transition in Warm Dense fcc Water Ice

Alexis Forestier,¹,²,* Gunnar Weck,¹,²,† Frédéric Datchi,³ Sandra Ninet,³

Gaston Garbarino,⁴ Mohamed Mezouar,⁴ and Paul Loubeyre¹,²

¹CEA DAM DIF, F-91297 Arpajon, France

²Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, F-91680 Bruyères-le-Châtel, France

³Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC),
Sorbonne Université, CNRS UMR 7590, MNHN, 4 place Jussieu, F-75005 Paris, France

⁴European Synchrotron Radiation Facility, Boîte Postale 220, F-38043 Grenoble, France

The fcc superionic phase of ice is a key component of the warm dense water phase diagram. While a few X-ray diffraction studies, under dynamic and static compressions, have reported the stability of the fcc structure, the transition to the superionic state has not been investigated in detail. Here, a remarkable thermal volume expansion is disclosed, which is interpreted as being directly related to the superionic transition. This could be achieved by implementing a heating capsule geometry within the laser-heated diamond anvil cell. Fcc ice is recovered metastable at ambient temperature, allowing to observe that superionicity in the fcc phase emerges at a slightly lower temperature than for the bcc-fcc structural transition. The crossover in volume thermal expansion at the superionic transition agrees with recent ab-initio calculations; however, its magnitude is larger than predicted.

*Introduction* Ice VII exhibits the simplest high density packing among the diverse forms of hydrogen-bonded ice, featuring a body-centered cubic oxygen (bcc) sublattice [1]. The proton-disordered arrangement forming hydrogen bonds is constrained by the O–O double-minimum potential. Around 50 GPa, the O–O potential evolves into a single well, with the H atom settling symmetrically between the oxygen atoms, forming ice X. Initially, ice X was indirectly identified through optical spectroscopy data [2, 3], and subsequently, single-crystal X-ray and neutron diffraction confirmed the symmetrization of H-bonds [4, 5]. It has been conjectured that, as pressure escalates, ice X might transform into an ionic crystal exhibiting an anti-fluorite structure [6]. This hypothetical structure would have oxygen ions occupying the regular positions of a face-centered cubic (fcc) lattice, with H ions residing in tetrahedral interstitial sites. Given the known propensity of such ionic anti-fluorite lattice to exhibit fast-ion conduction [7–9], fcc ice was predicted to show high proton diffusivity at high temperature and become a superionic (SI) conductor [6, 10]. Yet, ice X was observed remarkably stable at room temperature up to at least 200 GPa [3, 4] and calculations indicate the symmetric H-bond is maintained up to the TPa range [11, 12].

Several theoretical works indicated that extensive protonic diffusion is likely to occur at high temperature, either within the bcc oxygen sublattice of ices VII and X or through the adoption of oxygen sublattice close-packed structures [13–21]. Warm dense water ice holds great significance as a fundamental component of icy planets and of water worlds within and beyond our solar system. The superionic properties of ice could strongly impact planetary interior modeling [22, 23]. The high protonic conduction has been proposed as an explanation for the multipolar, non-axisymmetric magnetic field of Uranus and Neptune [24, 25].

Recently, several experimental studies have reported observations of superionic ice. Millot et al. first inferred the superionic nature of ice at megabar pressures [26], by comparing optical reflectivity and absorption measurements in laser-driven shocks with earlier gas-gun conductivity data [27, 28]. Soon after, by coupling reverberating shocks with X-ray diffraction (XRD), ice was observed to adopt an fcc oxygen sub-lattice in that superionic state, referred to as ice XVIII [29]. Using static compression, Queyroux et al. identified a first-order isostructural transition keeping bcc oxygen sublattice with a significant jump in volume in the range of 15-20 GPa near the melting line, indicative of a type-I superionic transition [30]. Subsequently, two static studies reaching megabar pressures confirmed the transition to the fcc oxygen sublattice using in situ XRD in laser-heated diamond anvil cells (DACs) [31, 32]. However, the nature of the superionic transition and its structural effects have remained unclear. Additionally, significant variability exists in the stability ranges of these two superionic phases, both calculated and observed. Here, we demonstrate an anomalous thermal expansion of fcc ice that is typical of a type-II superionic transition [7–9]. The stability field of fcc-SI ice is also determined.

*A new way of heating ice for precise control of sample P-T conditions.* Warm dense water ice samples were compressed in membrane DACs and laser-heated using opaque absorbers. As shown in Fig. 1(a), the ice sample was encapsulated between two boron-doped diamond (BdD) disks facing each other. These disks had a central recess to accommodate a larger volume of hot ice. They were positioned in pits on each anvil culet, allowing for increased sample thickness and secure placement. A 2.5 µm layer of Al₂O₃ was deposited in pits for thermal insulation. The high thermal conductivity of BdD absorbers and their wavelength-independent emissivity ensured efficient and homogeneous heating and a ther-
<figure><img src="image_2.png" /><figcaption>FIG. 1. Synchrotron XRD of H₂O ice at extreme pressures and temperatures. (a) Sketch of the DAC experimental chamber, approximately to scale at 191 GPa: the ice sample is confined in the laser-heated capsule made of two facing cupped BdD disks. (b) Temperature determination by fitting Planck's function to the absorber thermal emission, and sliding two-color pyrometry (left and right panels, respectively). The used temperature is 2370 ± 200 K. (c) XRD patterns collected at P = 191 GPa, T = 1650 K and 2370 K (bottom and top patterns respectively). Diffraction peaks from Al₂O₃ (corundum), rhenium gasket and BdD disks are indicated by ticks, as well as the bcc and fcc ice signatures. The small peak labeled with an asterisk is a non-indexed peak that may originate from another high P-T phase of Al₂O₃ or an impurity.</figcaption></figure>

mal Planck emission. Temperatures on both absorbers were monitored and equilibrated by carefully adjusting laser powers. In total, four different samples were examined using DACs with culet diameters ranging from 300 µm to 75 µm, spanning pressure range from 25 to ~200 GPa. Temperature was gauged by analyzing the emitted thermal spectra collected between 500 and 800 nm using reflective optics on both sides of the sample. Fig. 1(b) displays how a gray body model matches the collected spectra. A sliding two-color analysis was used to evaluate the temperature uncertainty [33]. The heating capsule design ensures that a substantial portion of the ice sample is heated at the absorber's temperature, while part of the sample is at a lower temperature. Heating of the sample remained far below the melting line, minimizing the risks of chemical reactions and uncontrolled heating.

Angular dispersive XRD measurements were conducted at the ID27 beamline of the European Synchrotron Radiation Facility (ESRF) [34]. The 0.3738 Å x-ray beam was focused to a 0.6 × 0.6 µm² FWHM spot, and the diffraction signal was collected on an Eiger 9M CdTe detector. Fig. 1(c) shows the XRD pattern at the highest pressure investigated, revealing peaks from various sample assembly components. The BdD diffraction peaks were used to monitor the volume of the diamond absorber in contact with the ice sample, enabling

the pressure to be calculated using the equation of state (EOS) for diamond [35]. Additionally, a small gold piece positioned adjacent to the BdD disk was employed to determine pressure at 300 K, utilizing the gold EOS [36]. The resulting estimate closely aligns with the determination obtained through BdD disk diffraction, showing agreement within 5% or better [see table S3 in the Supplementary Material (SM)]. The pressure uncertainty was ±10 GPa at 191 GPa. At 1650 K, the diffraction peaks from bcc ice are predominant, whereas at 2370 K, the intensity of the bcc peaks decreases significantly while four diffraction peaks from the fcc structure become dominant. In the sample geometry used, the heating of the sample is homogeneous radially over the diameter of the BdD heater, but an axial temperature gradient remains due to the colder ice layer not embedded in the BdD heaters. This explains why bcc peaks are still observed at 2370 K, as bcc ice persists in the 5 µm thick central ice layer, away from both BdD couplers. This is schematically represented in Fig. 1(a) as a color gradient in the ice sample. The presence of fcc peaks at 1650 K is due to metastability (see below).

*An intriguing thermal expansion is observed in fcc ice.* For all runs, XRD and temperature measurements were conducted during quasi-isobaric temperature ramps using YLF lasers in continuous mode. For each temperature value, XRD data acquisition was performed for 30
or 60 seconds while the laser power was maintained constant. Temperature stability during XRD data acquisition was monitored by repeating simultaneous temperature measurements. Data were collected during ascending and descending temperature ramps to investigate the hysteresis of the bcc-fcc transition. Notably, the metastability of fcc ice was observed, persisting down to ambient temperature at pressures of 75, 133 and 191 GPa (see SM). This hysteresis effect made it impossible to locate the bcc-fcc thermodynamic transition temperature in some heating ramps. Recrystallization of both fcc and bcc crystals was frequent upon heating, whereas the patterns exhibited less change during temperature decrease. The hysteresis phenomenon was exploited to measure, by decreasing temperature, the thermal expansion of fcc ice across a broad temperature range.

In Fig. 2, a representative dataset at 191 GPa is displayed. Data for other pressures are available in the SM. Integrated diffraction patterns, focusing on the 111 and 200 fcc peaks, are presented in a two-dimensional plot in Fig. 2(a). The 111 diffraction peak from the BdD disks shows a slight variation essentially due to thermal expansion, hence showing a quasi-isobaric heating ramp (Fig. 2(b) bottom panel). The 110 peak of bcc ice shows a slight positive thermal shift with respect to temperature. In contrast, a large thermal expansion of fcc ice, as evidenced by the evolution of its 111 and 200 peaks, is observed. For a more precise analysis of fcc ice volume expansion, the d-spacings corresponding to the larger unit cell volume, hence associated to the hottest crystals in contact to the absorber were selected (see SM for details).

In Fig. 2(b), the volume expansion of the bcc and fcc ices at 191 GPa are presented. The measured bcc ice volume below ~1700 K agrees with ab-initio calculations [21, 37]. Beyond this temperature, the bcc ice signal remains observable but corresponds to a colder region due to the axial thermal gradient in the DAC cavity, and so a volume plateau is observed. The latter is usually attributed to the end of stability of the low-temperature phase (see e.g. Ref. 38). On the other hand, the measured fcc ice volume is notably lower than predicted by ab-initio calculations [18, 21], particularly in the metastable region below 2000 K.

The volume of fcc ice versus temperature shows three different regimes: below 1700 K, volume expansion resembles that of the bcc phase; between 1700 K and 2500 K, significant volume expansion occurs; above 2500 K, the volume increases with a slower rate. This unusual volume behavior is reproducible and has also been observed at 5 lower pressure values, see SM.

The thermal expansion behavior indicates the superionic transition of fcc ice. Analyzing the volume change of fcc ice at 191 GPa in Fig. 3, a crossover between two states, marked by an approximately 6% volume change, is observed. That evolution is compared to ab-initio calculations at about the same pressure [18, 21]. Both calculations, using the same exchange-correlation functional, agree above 2000 K in the fcc superionic phase. Only Cheng et al.'s calculations, covering both insulating and superionic fcc ice regimes, predict a jump in volume expansion, though it is smaller than that observed experimentally [21].

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>FIG. 2. Temperature evolution of fcc and bcc ice volumes at 191 ± 10 GPa. (a) XRD patterns collected during temperature decrease: the diffracted intensity is coded using a grayscale. Diffraction peaks from ice phases and sample assembly components are indicated with ticks. (b) Extracted fcc (black dots and red diamonds corresponding to decreasing and increasing temperature ramps, respectively) and bcc ice volumes (blue dots) as function of temperature. Open blue symbols correspond to the bcc volume observed from colder regions of the sample (see text). BdD volume evolutions are shown in the bottom panel (black triangles and red squares correspond to ramp 1 and 2, respectively) along with diamond isobars using the EOS from Ref. 35. In (b), ab-initio EOS for bcc and fcc ices at 200 GPa are included [18, 21, 37].</figcaption></figure>

To understand the observed crossover, we employed an interstitial formation model that describes the free energy of the system as depending on the fraction $x$ of the conducting hydrogen cations thermally promoted to interstitial sites, as described in Ref. 39. It considers the parameters $\epsilon_0$ (interstitial defect formation energy), $\lambda$ (defect interaction energy with the crystal strain) and $g$ (number of interstitial sites available, assuming $g = 12$).
The minimization of the free energy can then allow to evaluate $x$ ($0 \le x \le 1$) as the solution of

$$ \varepsilon_0 - \lambda x = k_B T \ln[g(1-x)/x] \quad (1) $$

with $k_B$ the Boltzmann constant. The volume increase due to the fraction of mobile hydrogen is then given by $\Delta V = xv_0$, where $v_0$ is the volume of defect formation. The fit of this phenomenological model to the measured fcc ice volume change versus temperature of Fig. 3(a), gives $\varepsilon_0 \approx 0.63$ eV, $\lambda \approx 0.44$ eV and $v_0 \approx 0.49$ cm³/mol. Note that the thermal expansion below the superionic transition is neglected, possibly giving a slight overestimation of $v_0$.

<figure><img src="image_5.png" /><figcaption>FIG. 3. Fcc ice volume, thermal expansion and interstitial hydrogen concentration as function of temperature at 191 GPa. (a) Fcc ice volume from the 111 reflection of a single crystallite (black circles). The interstitial cations model fit is plotted as a black solid line. The ab-initio EOS from Refs. 21 and 18, plotted for P = 200 GPa, are represented by gray squares and the solid gray line respectively. (b) Volumetric thermal expansion $\alpha = (1/V)\partial V/\partial T$ derived from the fit, and from smoothed ab-initio data of Ref. 21, are shown as solid black and dashed gray curves respectively. (c) Interstitial hydrogen concentration $x(T)$ deduced from the phenomenological model based fit (solid black line) compared with ab-initio data [21] at 200 GPa (gray dashed curve).</figcaption></figure>

The volumetric thermal coefficient, $\alpha$, is derived from the fit and plotted in Fig. 3(b). It exhibits a Λ-shaped bump that is a characteristic of the superionic transition. Similar behavior has been observed at the superionic transition of well-known fast-ion conductors, by

macroscopic dilatometry [40, 41] and in neutrons scattering measurements [42–44]. The plotted $\alpha$ for Cheng et al.’s simulations exhibits the bump behavior, but with a smaller magnitude [21]. Fig. 3(c) indicates that the fraction $x$ of mobile hydrogen derived from the fit closely resembles the $x(T)$ curve from simulations at 200 GPa [21]. The gradual transition of fcc ice observed here is typical of type-II superionic conductors [8, 9], contrasting with the discontinuous volume jump at the isostructural insulator-superionic transition of bcc ice [30].

When $x$ approaches 1, ab-initio calculations still overestimate the experimental fcc volume, similar to the case of bcc ice [21]. This discrepancy may arise from approximations made in density functional theory, specifically the selection of the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. The significant decrease of the volume of cold metastable fcc ice, when H cations are expected to be ordered is intriguing. This may result from the zero-point energy of hydrogen, causing an O–O distance contraction, akin to the Ubbelohde effect observed in strongly H-bonded systems [45]. Further research is necessary to provide a convincing interpretation and similar measurements performed on D₂O could shed light on that matter.

Another question arises why the fcc structure is observed at 300 K while simulations indicate an enthalpy excess of 0.3 eV (at 0 K) compared to ice X below 200 GPa [21]. However, Cheng et al. noted that the fcc and hcp structures are the lowest enthalpy metastable forms at 0 K [21]. Simulations suggest that the fcc volume is 2.1% smaller than the bcc one at 500 K [21], whereas our measurement is ~6% smaller. The significantly smaller fcc volume observed in the metastable regime compared to calculations by Cheng et al. [21] suggests that the calculated metastable fcc enthalpy may be overestimated. This supports our observation of a quenched fcc phase at 300 K.

The superionic regime stabilizes the fcc sublattice. The present dataset, which pertains to structural changes in warm dense ice, is summarized in Fig. 4. Measurements performed across different pressures and temperatures has unveiled the onset of superionicity in fcc ice, along with the structural transition from bcc ices to fcc-SI ice. These data points are represented as green squares and red dots in Fig. 4, respectively. The superionicity onset is assigned to the temperature at which the volume begins to increase sharply, evidencing interstitial defects formation. To report the transition from bcc to fcc structure, we selected heating ramps free of any metastable fcc peaks, to observe the appearance of fcc diffraction lines with temperature (at 49, 75 and above 171 GPa, traces of metastable fcc ice remained). Notably, the superionicity in fcc ice emerges at a slightly lower temperature than the bcc-fcc structural transition at a given pressure. Although the denser close-packed fcc structure is expected to be more stable at high pressure [11], we show here
<figure><img src="image_6.png" /><figcaption>FIG. 4. Phase diagram of H₂O. The onset of superionic state in fcc ice in its metastable domain, deduced from the thermal expansion bump, is shown as green squares. The calculated onset of superionicity is shown as a green dashed line [21]. Red dots indicates the structural bcc-fcc transition. The large red line shows our guess for the bcc-fcc phase boundary, which brings together the concordant experimental observations. Previous experimental data from static and dynamic studies are included [29–32], as well as calculated phase boundaries [18, 21, 24].</figcaption></figure>

that the excess entropy from hydrogen disorder is crucial for stabilizing fcc-SI ice, as suggested by Millot et al. [29]. This entropy helps to relax the tetrahedral coordination constraints of ice H-bonds. The transition lines show good agreement with recent calculations by Cheng et al., albeit diverging below 70 GPa where the calculated superionic transition undergoes a change of slope [21].

The bcc-fcc transition line is consistent with prior determinations using laser-heated DACs by Weck et al. [32], except that the fcc phase was not detected below 57 GPa in that previous work. However, that experiment was optimized for melting detection using a multichannel collimator which may have masked fcc single crystal diffraction peaks [46]. In contrast, our determined bcc-fcc transition line is in disagreement with the work of Prakapenka et al. [31] who reported much higher transition temperatures. This discrepancy has been conjectured to originate from flawed temperature measurements [46]. Shock compression data of Millot et al. [29] are in good agreement with the present phase diagram whereas Gleason et al. [47] did not observe microscopic

evidence for the fcc phase and it is not clear why.

In summary, accurate volume measurements under controlled P-T conditions provide a distinctive indicator of the superionic transition in the fcc ice phase, in agreement with large-scale machine learning ab-initio simulations [21]. However, the discrepancy between calculated and experimental volume expansions associated with the superionic state warrants further investigation. A novel phase diagram of dense ice, outlining the boundary lines between bcc, fcc, and fcc-SI phases, is presented here.

We thank Olivier Marie (CEA) for performing the FIB machining, and Grégory Geneste (CEA) for discussions. We acknowledge the ESRF for provision of synchrotron beamtime at beamline ID27 under proposal numbers HC4677 and HC5078. The authors acknowledge the Agence Nationale de la Recherche (ANR) for financial support under Grant No. ANR-21-CE30-0032-01 (LILI).

<footnote>* alexis.forestier@cea.fr</footnote>

<footnote>† gunnar.weck@cea.fr</footnote>

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