Exploring High-Pressure Transformations in Low-Z (H 2 , Ne) Hydrates at Low Temperatures

: The high pressure structural behavior of H 2 and Ne clathrate hydrates with approximate composition H 2 /Ne · ~4H 2 O and featuring cubic structure II (CS-II) was investigated by neutron powder diffraction using the deuterated analogues at ~95 K. CS-II hydrogen hydrate transforms gradually to isocompositional C 1 phase (ﬁlled ice II) at around 1.1 GPa but may be metastably retained up to 2.2 GPa. Above 3 GPa a gradual decomposition into C 2 phase (H 2 · H 2 O, ﬁlled ice I c ) and ice VIII’ takes place. Upon heating to 200 K the CS-II to C 1 transition completes instantly whereas C 1 decomposition appears sluggish also at 200 K. C 1 was observed metastably up to 8 GPa. At 95 K C 1 and C 2 hydrogen hydrate can be retained below 1 GPa and yield ice II and ice I c , respectively, upon complete release of pressure. In contrast, CS-II neon hydrate undergoes pressure-induced amorphization at 1.9 GPa, thus following the general trend for noble gas clathrate hydrates. Upon heating to 200 K amorphous Ne hydrate crystallizes as a mixture of previously unreported C 2 hydrate and ice VIII’.


Introduction
Clathrate hydrates are crystalline inclusion compounds in which a guest species (i.e., small molecules or monoatomic noble gases) occupy the polyhedral cages formed by a hydrogen-bonded water network [1]. These materials form when guest-water solutions freeze, or when gaseous guest interacts with hexagonal ice, I h , at elevated pressure (above 50 bar) [2]. Clathrate hydrates occur abundantly in nature, storing natural gas, and are of interest for e.g., CO 2 sequestration and H 2 storage [3]. Clathrate hydrates with the low Z guests Ne and H 2 are distinguished because of the rather extreme pressure conditions (>2 kbar at 280 K) that have to be applied for their synthesis [4]. Both Ne and H 2 clathrate hydrate have been reported to form the so-called clathrate structure II (CS-II) which possesses hexakaidecahedral 5 12 6 4 cages (consisting of 5-and 6-membered rings, in the following abbreviated as "L"-cages) and dodecahedral 5 12 cages (exclusively built from 5-membered rings, in the following abbreviated as "S"-cages). The cubic CS-II unit cell contains 136 water molecules and 16 S and 8 L cages. At pressurized synthesis conditions the large L cages can be occupied by up to four H 2 molecules (whereas the smaller S cages are occupied by one), yielding an extremely high H-storage capacity (H 2 ·3H 2 O) [5]. At ambient pressure conditions the L occupancy is reduced to two [6]. The composition for Ne clathrate hydrate appears to be less established (or contradictorily reported) [7,8]. Furthermore, unique for low Z clathrate hydrate is the high mobility of the guest species, based on defect-free diffusion through 6-membered rings [9][10][11]. This is manifested by the discovery of empty CS-II (ice XVI) from pumping Ne and H 2 clathrate hydrate between 110 and 145 K [7].
Interestingly a He clathrate hydrate does not form from ice I h -gas interaction (but may be obtained by filling ice XVI at around 100 K [12]). Instead, at comparable conditions leading to H 2 and Ne clathrate hydrate a different, denser, hydrate is obtained which is based on rhombohedral ice II (filled ice II hydrate, typically abbreviated as C 1 ) and which possesses a guest:water ratio 1:~6 [13,14]. The C 1 hydrate has been found also for the Ne-H 2 O and H 2 -H 2 O systems at pressures above 5 kbar (0.5 GPa) and temperatures 250-280 K [4,15,16]. The high pressure behavior of the H 2 -H 2 O system has been recently well investigated. The highest pressure phase known is based on cubic ice, I c (filled cubic ice, typically abbreviated as C 2 ) with a guest:water composition 1:1 and found to be stable above 3 GPa up to at least 20 GPa [17]. The C 2 phase has not yet been reported for the Ne-H 2 O system. In addition to the CS-II, C 1 , and C 2 phases, hydrogen hydrate also exists as C 0 phase (in the pressure range 0.2-0.5 GPa) with a composition 1H 2 :2H 2 O. Note that these phase relations between hydrates of variable guest:water compositions have been established for a rather narrow temperature range,~220-270 K, and in the presence of a reservoir of H 2 and Ne (either using diamond anvil cell or gas pressure vessel equipment).
In this paper we want to address specifically the high pressure behavior of the low Z CS-II hydrates, i.e., employing ex-situ synthesized starting materials with a specific composition and no reservoir of H 2 and Ne, at low temperatures (below 200 K). It has been shown that CS-II hydrates with high Z guests (e.g., Ar, THF) undergo transitions to more dense, exotic, clathrate structures and/or breakdown reactions into filled forms of ice (accepting larger concentrations of guest species) and ice when compressed to 2-3 GPa at 260-280 K [3]. At lower temperatures (<130 K) CS-II hydrates would instead exhibit a sharp, first-order-like transition to an amorphous state at 1.2-2 GPa [18,19], similar to the behavior of pure water ice I h which undergoes pressure-induced amorphization to "high density amorphous" (HDA) ice when compressed to around 1 GPa at temperatures below 130 K [20]. Since the low Z CS-II hydrates appear distinguished, it was deemed important to establish their high pressure behavior at low temperatures.

Experimental Details and Methods of Analysis
Fully deuterated CS-II hydrogen hydrate (HH) and neon hydrate (NeH) samples (H 2 O and H 2 99.9 atom % deuterated, Sigma Aldrich, Saint Louis, MO, USA; Ne ≥ 99.99% purity, Sigma Aldrich, Saint Louis, MO, USA) were synthesized following the procedure by Lokshin et al. [5]. A high-pressure rated vessel compatible for hydrogen gas was filled with finely ground ice and loaded with pressurized hydrogen/neon at 200 MPa using a gaspressure intensifier. Both ice and gas transfers were done in a eutectic ethanol-water bath at freezing temperature (~278 K). The pressurized vessels were then kept at 253 K for one week in a freezer. The fully converted CS-II samples were recovered at LN 2 temperature on the day of the experiments. The complete conversion of ice I h to the CS-II clathrate was confirmed by X-ray powder diffraction on a Panalytical X'Pert Pro (Almelo, Overijssel, The Netherlands) diffractometer using the Anton Paar TTK 450 Low Temperature Chamber, and all samples were verified to be initially ice-free. A total of three CS-II HH sample batches were prepared (A, B, and C) and we report on four HH experiments (a1, a2, a3, b) based on samples A and B (C was only used for structure/composition characterization of CS-II HH). One CS-II NeH sample was prepared and one Ne experiment (c) was run. Details of the experimental pathways and compositions throughout each experiment can be found in the Supplementary Materials.
In situ high pressure neutron diffraction experiments were conducted on the SNAP high-pressure diffractometer at the Spallation Neutron Source in the Oak Ridge National Laboratory, Oak Ridge, TN, USA, using the Paris-Edinburgh (PE) VX5 press [21]. Samples were handled at LN 2 temperature, loaded into a null-scattering Ti-Zr alloy encapsulated gasket and set into the pre-cooled anvils. The gaskets were slightly pressurized upon loading for sealing and stabilizing the samples, which warmed up to about 170 K during transferring the pressure cell to the cryostat where they were cooled to 90-95 K. Pressurization was done in steps of 0.1-0.2 GPa, followed by data collection during 15 min to up to several hours. (Note that data collection is quantified by proton charge accumulated, but usually referred to by time of irradiation for simplicity.) Compression rates were averaged over time taking into account loading and collection periods. Pressure was estimated using a Birch-Murnaghan equation of state for lead [22], which was added to all samples. Data reduction was performed using the Mantid package (Workbench version 6.2) [23], and Rietveld refinements were conducted using GSAS-II version 5113 [24]. Refined parameters for the hydrate and ice phases consisted of phase fractions, lattices, positional and thermal parameters, atomic fractions (for guest atoms) and peak profile parameters. In addition, silicon powder, vanadium powder and an empty gasket were measured for calibration, intensity normalization and background correction, respectively.
Molecular dynamics (MD) simulations were performed at 95 K, with pressure increase in steps of 0.1 GPa. The simulation cells for CS-II HH and NeH corresponded to 2 × 2 × 2 unit cells and were created with GenIce [25]. We considered a guest:water ratio 1:4 which was obtained by occupying some of the L cages triply. Simulations were done at similar conditions to those proposed by Alavi et al. [26]. Two different software were used for calculations, GROMACS (version 2021.3) [27] and LAMMPS (release 29 September 2021) [28]. GROMACS was used for the CS-II HH system where pressure was controlled by the isotropic Parrinello-Rahman barostat [29] and temperature by the velocity-rescaling thermostat [30]. The Van der Waals and Coulomb interactions were set to a cutoff radius of 0.85 nm and the long-range part of the electrostatic interactions was treated by the Particle Mesh Ewald (PME) method [31]. Hydrogen molecules were modelled as a rigid diatomic molecule with bond constrained to 0.7414 Å and a massless center of mass where the LINCS algorithm was adopted to constrain molecular bonds [32]. The force-field parameters for H 2 were set as those determined by Harada et al. [33]. CS-II NeH was simulated with LAMMPS. The Nose-Hoover barostat with the Melchionna modification was employed to control the temperature and pressure of the systems [34]. The UFF [35] force field was used to describe the interatomic interactions of Ne. The Van der Waals and Coulomb interactions were set to a cutoff radius of 1.25 nm and the long-range part of the electrostatic interactions was treated by the Particle-Particle Particle Mesh (PPPM) method [36]. In both systems the water molecules were described by the TIP4P/ice force field model [37] and the Lorentz-Berthelot mixing rules were applied [38]. At each pressure step the system was first incremented gradually over 2 ns, the system was then equilibrated for 5 ns followed by a further 1 ns simulation during which statistics for analyses were collected. The simulation time step was 1.0 fs and barostat relaxation time was set to 2000 time steps.

CS-II HH and NeH Starting Materials
The various pathways and the phase diagrams of hydrogen-water system [39] and pure water [40] are shown in Figure 1. In the Supplementary Materials there are more details, together with a thorough description of phase changes on each experiment. Diffraction data of the crystalline CS-II hydrates of hydrogen (HH) and neon (NeH) (space group Fd3m) at the initial stage of the experiments (near ambient pressure (<0.1 GPa) and 90-95 K) are shown in Figure 2. For the refinement of CS-II HH, the structure model for the ambient pressure recovered material at 100 K according to Ranieri et al. was applied [41]. This model describes the orientationally disordered H 2 molecule in S cages with a 96g Wyckoff position (0, 0,~0.022), accounting for three orientations of a H 2 molecule around the S cage center at 16c (0, 0, 0). The positionally and orientationally disordered H 2 molecules in L cages are also modeled with a 96g position (~0.43,~0.43,~0.4) which yields a distribution of 12 H atoms around the center at 8b (3/8, 3/8, 3/8) at a distance~1.45 Å from the center.
In our refinements the parameters of the 96g positions were restrained to the values of Ranieri et al. [41] and only thermal parameters (B iso ) and occupancies were refined. An occupancy of 1/6 would correspond to one and two H 2 molecules in S and L, respectively. Rietveld refinement of the CS-II HH data showed that all samples were pure CS-II with an (inverse-variance weighted over 3 sample batches A, B, C) average unit cell lattice parameter a = 17.095(3) Å. Refinement of the S and L cage occupancies yielded 0.99(4) and 2.1(4) H 2 molecules, respectively (1H 2 :~4.2H 2 O), which is in good agreement with the composition reported by Ranieri et al. [41]. Also the NeH sample was pure CS-II phase. For its refinement Ne atoms were positioned at the center of the L and S cages (i.e., the Wyckoff sites 8b and 16c), and B iso values and occupancies were refined. The refinement of CS-II NeH yielded a lattice parameter a = 17.1161(8) Å (at 0.09(5) GPa), and 0.98(9) and 2.3(3) Ne atoms in S cages and L cages, respectively (1Ne:~4H 2 O), which is a similar guest:water composition as for CS-II HH. We note that the value of the lattice parameter is close to that reported by Falenty et al. (17.1028 Å at ambient pressure and 5 K) [7]. However, the refined composition deviates. Falenty et al. reported contradictory values for the L cage occupancy (either 4.7 or 0.85 Ne atoms) for CS-II NeH at 5 K, which appears either too high or too low. The reason for the discrepancy is not clear. Subsequently the CS-II samples were compressed at 90-95 K to pressures between 1 and 5 GPa and then heated to 200 K, followed by either further compression or decompression.

Compression of CS-II HH and NeH at~95 K
CS-II HH was initially compressed at 95 K to 1.3(2) GPa (experiment a1) upon which a gradual transformation into C 1 phase was observed at 1.1(2) GPa. The CS-II to C 1 transition was identified from the growth of the two strongest C 1 reflections (311 and 212) over the CS-II reflections (cf. Figure 3a). Upon recovery to ambient pressure (at 95 K), C 1 transformed back to CS-II. No other phases (i.e., ices) were observed, suggesting that the composition 1H 2 :4.2H 2 O was kept constant throughout. A new sample was then loaded (experiment a2) and the compression was repeated. This time gradual transition into C 1 phase was observed at 1.12(5) GPa. The compression rates in experiments a1 and a2 were about 90 bar/h and 50 bar/h. Loading CS-II HH from a different sample batch (experiment b), we repeated the compression at a slower rate (~12.5 bar/h). In this experiment the CS-II phase was retained to 2.2(1) GPa. Although highly strained, the diffraction patterns above 1.5 GPa show clear remnant features of the CS-II phase alongside growing reflections of the C 1 phase (Figure 3a).
CS-II NeH was compressed at~90 K (experiment c). Its pressure-induced amorphization (PIA) was indicated by the loss of Bragg peak intensity and the evolution of diffuse scattering at 1.86(3) GPa. Figure 3b shows the evolution of the diffraction patterns of CS-II NeH up to 3.0(1) GPa. The PIA behavior follows the established trend of noble gas clathrate hydrates which has been earlier investigated by MD simulations [19]. The collapse for CS-II NeH with doubly and singly occupied L and S cages, respectively, was predicted at 1.65 GPa, which is close to the here reported experimental finding.  the volume at zero pressure, the bulk modulus, and its first pressure derivative, respectively [42]. According to Manakov et al. [43] the compressibility of CS-II hydrates is rather similar, irrespective the kind of guest species and cage filling, thus essentially being determined by the H-bond structure. The universal bulk modulus for the pressure range up to 1.5 GPa was specified as (9 ± 2) GPa [43]. Our V(p) data appear somewhat scattered, which is mostly attributed to the rapidly degrading quality of the CS-II patterns above 0.3 GPa. The extracted bulk moduli for HH and NeH are 10.9(6) and 12 (2)GPa, respectively (with B' fixed at 4.0), which would follow the general trend. We also include the V-p relation from MD simulations (which for (heavier) noble gas clathrate hydrates follow well the experiment [19]). For CS-II HH and NeH deviations from experiment are certainly due to the limited data quality, but in addition it appears that MD underestimates the volume of CS-II HH (at least for the case with doubly and singly occupied L and S cages, respectively). We note that also the simulation results by Katsumasa et al. show a systematic volume underestimation [44]. As mentioned above, MD simulations of CS-II NeH show PIA at around 1.65 GPa. Also CS-II HH collapses according to MD (at~0.8 GPa) indicating its instability at somewhat lower pressures than the experimentally observed crystal-crystal transition to C 1 (which is not possible to simulate in MD).

Formation, Compressibility and Decompression Behavior of C 1 and C 2 HH Phases
As described above, in experiments a1 and a2 gradual CS-II to C 1 transition was observed at 1.1 GPa. The C 1 phase has an ideal crystallographic composition 1:6 [16], but is known to accept hydrogen contents up to 1:~4 [45], which is the expected composition in our experiments. Experiment a2 proceeded by further compressing the sample up to 4.8(4) GPa. At 3.5(2) GPa the sample constituted about 50% C 1 and about 50% a mixture of C 2 and ice VIII' (apostrophe designates unspecified proton-ordering). This indicates that at 95 K and above 3 GPa C 1 HH sluggishly decomposes according to C 1 (H 2 ·(H 2 O) 4 In Rietveld refinements, C 1 was modeled as H-filled high-pressure ice II with a rhombohedral R3h structure based on Londono et al.'s C 1 He hydrate [13]. The C 1 unit cell closely resembles that of ice II. The c/a ratio of He hydrate (0.481) is smaller than that of pure ice II (0.483) [46], and was predicted to decrease with pressure reaching 0.473 at 1.1 GPa [13]. This prediction agrees well with our observation, a = 12.8025(8) Å and c = 6.0673(4) Å and c/a = 0.474 at 1.1 GPa. H 2 molecules were described as a single D position (Wyckoff position 6c) at the center of six-membered water rings. Thermal parameters and occupancy were refined and resulted in a composition of 1:~4.5. C 2 HH was modeled according to Komatsu et al. [47] as a twice-as-large ice I c unit cell (a ≈ 6.5 Å, space group Fd3m) where randomly oriented D 2 molecules are described by a Wyckoff position 48f (0.064, 1/8, 1/8). Only the lattice parameters were refined and the composition was assumed to be 1:1 (i.e., the 48f occupancy was constrained to 1/3), since the C 2 phase is considered only stable at maximum filling of ice I c by hydrogen [8]. Figure 5 shows selected diffractograms and Rietveld fits for C 1 and C 2 HH.
In experiment a3 an alternative route was taken and CS-II HH was heated from 95 K just before the phase transition seen in a1 and a2 (~1 GPa). During this non-isobaric step diffraction patterns were collected for 1h at each temperature, at 10 K intervals. At 165 K and 1.19(4) GPa, CS-II HH fully transformed into C 1 . At 200 K, the sample was continuously compressed to 7.8(2) GPa. During this compression C 1 transformed/decomposed into C 2 + ice VIII' above 3 GPa, similar to experiment a2 at 95 K, but C 1 phase was partially maintained up to the highest pressures. (Due to the low quality of the data C 1 /C 2 phase fractions could not be refined). The compressibility of C 1 HH was followed and the EoS was extracted, which is shown in Figure 6. The bulk modulus of C 1 HH (16.3(5) GPa) is very close to that reported for ice II (12.13(7) GPa) [48]. Experiment a3 was concluded by decompressing the sample upon which C 1 reformed from C 2 + ice VIII'. Between 4.6(1) and 1.90(4) GPa the sample developed into single phase C 1 which at atmospheric pressure turned into pure ice II (empty C 1 ). Ice II is known to be recoverable at LN 2 temperature and is metastable at 200 K due to its low entropy (H-ordering) [49,50].  In experiment b CS-II HH was observed metastably up to 2.2(1) GPa (at 95 K). At this stage, the sample was heated to 200 K and immediately transformed into C 1 . After further compressing at 200 K to 5.0(2) GPa (and after about 18 h), the sample constituted 20% C 1 and 20% C 2 /60% ice VIII'. Considering C 1 and C 2 as 1:4 and 1:1 hydrates, respectively, the overall composition would be maintained at 1:~4.2. The sample was then cooled back to 95 K and decompressed in small steps (Figure 7). After complete removal of the load from the PE press the residual pressure remained at 0.1(2) GPa. At this pressure, crystalline C 1 HH could be still noticed in the diffraction pattern whereas reflections from C 2 HH appeared absent. Komatsu et al. reported that C 2 HH undergoes amorphization below 0.5 GPa on decompression at 100 K [47]. Interestingly, from this amorphous form the authors could obtain stacking-disorder free ice I c upon ambient pressure recovery. Thus, possibly the absence of C 2 reflections relates to amorphization since also diffuse features grew in the diffractogram. Experiment b was completed by recovering the sample to ambient pressure at 95 K (by opening the PE press breech). As in experiment a3 hydrogen escaped and the recovered sample constituted ice II (which should correlate to C 1 HH present in the pressurized sample) and either ice stacking-disordered ice (I sd ) or a mixture of ice I h and ice I c . Against the background Komatsu et al.'s [47] finding, we assumed the presence of ice I c (which should correlated to C 2 HH in the pressurized sample) and I h (from the fraction of ice VIII').

Synthesis of C 2 NeH
As described above (experiment c), the CS-II NeH sample became fully amorphous when compressed to 1.86(3) GPa at 90 K. Experiment c proceeded with heating the sample at 3.0(1) GPa to 170 K. The heavier noble gas CS-II Ar clathrate hydrate amorphizes at around 1.4 GPa at the same temperature. Heating amorphous Ar hydrate to 170 K and annealing at this temperature then creates a second amorphous form, which is more dense [51]. However, in contrast with amorphous Ar hydrate, amorphous NeH recrystallized as a mixture of C 2 , ice VIII' and a small fraction of (metastable) ice I c during heating to 170 K. C 2 NeH has not been observed before experimentally although it was predicted to be more stable than C 1 above 0.85 GPa (at 273 K) in a grand-canonical Monte Carlo simulation [52]. This is the first report, to our knowledge, of the synthesis of C 2 NeH. The diffraction pattern, shown in Figure 8, was modeled with a C 2 NeH phase based on C 2 HH, together with ice VIII [53] and ice I c [47]. The refinement (presented in more details in the Supplementary Materials) resulted in 27.5% C 2 , 40.7% ice VII' and 4.2% ice I c , which again maintains the overall composition 1:~4.  . Rietveld refinement and modelled C 2 neutron diffraction pattern obtained for Ne hydrate at 3.6(1) GPa and 90 K. The observed intensities are shown as blue crosses, and calculated patterns as solid lines (total calculated in black, C 2 NH phase in red). The difference curve is shown below in cyan. Fitted phases include ices VIII', ice I c , lead (pressure marker) and parasite peaks from the anvil (steel and c-BN).

Discussion
The high pressure behavior of CS-II HH (H 2 :4.2H 2 O) at low temperatures (~95 K) deviates from the established phase relations of HH at higher temperatures (220-270 K). A gradual transition into C 1 phase with the same or similar H 2 content is seen at 1.1-1.2 GPa. The instability of crystalline CS-II HH above 0.8 GPa as revealed in MD simulations may indicate that a mixture of H 2 fluid and C 0 phase with 1:6 composition is more stable in the narrow range 0.8-1.1 GPa but is not observed for kinetic reasons. The transition to C 2 phase (1H 2 :1H 2 O) is seen above 3 GPa and inevitably leads to a phase mixture C 2 HH and ice VIII' because of the higher H 2 content of the C 2 phase (the ideal ratio of this mixture is 1:3). The decomposition of C 1 HH into C 2 HH and ice VIII' appears to be very sluggish. C 1 can be observed (metastably) at very high pressures, up to 8 GPa even at 200 K. In contrast, the transition of CS-II to C 1 HH completes readily at 1.1-1.2 GPa when rising the temperature from 95 to 200 K.
Once completely transformed, reformation of CS-II HH upon decompression has not been observed. Instead C 1 and C 2 HH can be retained to very low pressures and recovered as empty ice II and I c /I sd , respectively, at ambient pressure. Backformation of C 1 from C 2 /ice VIII' can be observed at 200 K, whereas at 95 K it seems to be suppressed. Similarly, Komatsu et al. [47] could retain a pure C 2 HH sample (which was produced at 3 GPa and 300 K in the presence of a reservoir of H 2 ) to below 0.5 GPa on decompression at 100 K.
Different to CS-II HH, CS-II NeH undergoes PIA at low temperature high pressure conditions, thus following the trend of the heavier noble gas clathrate hydrates. However, different to these, pressure-amorphized CS-II NeH cannot be annealed to produce a densified and (potentially) recoverable amorphous state, but undergoes recrystallization to C 2 NeH and ice VIII' when heating from 90 to 170 K at 2.65 GPa. The existence of C 2 NeH has been predicted at this pressure but has not yet been reported.
In summary, the high pressure behavior of CS-II hydrates with the low Z guests H 2 and Ne is distinguished from high Z analogues. CS-II HH undergoes transitions/decompositions to crystalline high pressure hydrates even at low temperatures where high Z analogues undergo PIA. CS-II NeH undergoes PIA but the amorphous form readily forms the high pressure hydrate C 2 NeH at slightly elevated temperatures instead of a densified polyamorph.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/cryst12010009/s1, experimental details of high pressure neutron diffraction data collected at the high-pressure diffractometer SNAP (beamline 3) at the Spallation Neutron Source, USA; Table S1. Refinement details from neutron powder diffraction data for C2 neon hydrate.

Conflicts of Interest:
The authors declare no conflict of interest.