Ice Ic without stacking disorder by evacuating hydrogen from hydrogen hydrate

Water freezes below 0 °C at ambient pressure ordinarily to ice Ih, with hexagonal stacking sequence. Under certain conditions, ice with a cubic stacking sequence can also be formed, but ideal ice Ic without stacking-disorder has never been formed until recently. Here we demonstrate a route to obtain ice Ic without stacking-disorder by degassing hydrogen from the high-pressure form of hydrogen hydrate, C2, which has a host framework isostructural with ice Ic. The stacking-disorder free ice Ic is formed from C2 via an intermediate amorphous or nano-crystalline form under decompression, unlike the direct transformations occurring in ice XVI from neon hydrate, or ice XVII from hydrogen hydrate. The obtained ice Ic shows remarkable thermal stability, until the phase transition to ice Ih at 250 K, originating from the lack of dislocations. This discovery of ideal ice Ic will promote understanding of the role of stacking-disorder on the physical properties of ice as a counter end-member of ice Ih.

W ater freezes below 0°C at ambient pressure, ordinarily to ice I h with a hexagonal stacking sequence. However, it is also known to produce "ice I c " nominally with a cubic stacking sequence under certain conditions 1 , and its existence in Earth's atmosphere [2][3][4] , or in comets 5,6 is debated. "Ice I c ", or called as cubic ice, was first identified in 1943 by König 7 , who used electron microscopy to study the condensation of ice from water vapor to a cold substrate. Subsequently, many different routes to "ice I c " have been established, such as the dissociation of gas hydrates, warming amorphous ices or annealing high-pressure ices recovered at ambient pressure, freezing of μor nano-confined water (see ref. 1 ). Despite the numerous studies on "ice I c ", its structure has not been fully verified, because the diffraction patterns of "ice I c " show signatures of stacking disorder 1,8,9 , and ideal ice I c without stacking disorder had not been formed until very recently 10 . This is the reason why "ice I c " is double-quoted 1 , and it is recently proposed that the stackingdisordered ice should not be termed as ice I c , but as ice I sd 8 .
"Ice I c " (ice I sd ) is known as a metastable form of ice at atmospheric pressure. But, recent computer simulations suggest that even ice I sd could be the stable phase for crystallites up to sizes of at least 100,000 molecules 11 . The stability of stackingdisordered ices is extremely important because of the ubiquitous nature of ice. Stacking-disordered ice can be characterized by the degree of ice cubicity, χ, which is defined as the fraction of cubic stacking 1,8,9,12,13 . Until very recently, the highest cubicity was limited to~80% 8,14 , but it has been reported that ideal ice I c with 100% cubicity has been obtained by annealing ice XVII 10 .
Recently new ice polymorphs, ice XVI 15 and ice XVII 16,17 are obtained by degassing gas molecules from neon and hydrogen hydrates, respectively. From these findings, we hypothesized that ideal ice I c could be obtained by degassing hydrogen from hydrogen hydrate, C 2 . Five different phases in the H 2 -H 2 O system have been reported to date (see ref. 18 ): Among them, neutron diffraction experiments have never been conducted for the higher-pressure phases, C 1 and C 2 , probably due to the technical difficulty in loading hydrogen into a pressure vessel, or compressing it to pressures in the giga-pascal range. To synthesize ideal ice I c , decompression under low-temperature conditions for degassing is necessary, which is also not straight-forward using conventional pressure-temperature controlling systems. We have developed a Mito system 19 , and have overcome these technical difficulties (see details in Methods).
Here we present the neutron and X-ray diffraction results showing ice I c without stacking disorder, obtained from degassing hydrogen hydrate C 2 . We also report an unexpected amorphouslike state in the transformation from C 2 to ice I c , and the thermal stability of ice I c .

Results
The route to obtain ice I c . We started by using a mixture of D 2 O and MgD 2 , which is an internal deuterium source, to synthesize hydrogen hydrate, C 2 . After loading the mixture into a pressuretemperature controlling system, MgD 2 was decomposed by heating at 403 K and at ca. 0 GPa for 1 h through a nominal reaction of MgD 2 + 3D 2 O → Mg(OD) 2 + 2D 2 + D 2 O (at b in Fig. 1, the observed neutron diffraction patterns are shown in Supplementary Fig. 1). Then, the samples were cooled to room temperature (at c in Fig. 1) and typically compressed up tõ 3 GPa until a C 2 phase was observed (at d in Fig. 1). The neutron diffraction pattern for the C 2 phase obtained at 3.3 GPa and 300 K (at d in Fig. 1) was analyzed by the Rietveld method. We adopted a splitting site model for guest D atoms located at the 48f site (x, 1/8, 1/8), and the host structure was identical to ice I c 9 (Fd 3m, O at the 8b site (3/8, 3/8, 3/8), D at the 32e site (x, x, x)). The calculated diffraction pattern was in good agreement with the observed one, as shown in Fig. 2a. The refined structural parameters are listed in Supplementary Table 1.
The sample was then cooled from 300 K to 100 K at around 3 GPa (path d → e). In the diffraction pattern taken at e in Fig. 1, peaks from solid deuterium (phase I) appeared at around 200 K ( Supplementary Fig. 2), which is consistent with the known melting curve of hydrogen 20 . This observation indicates that fluid deuterium coexisted with C 2 through the path from b to d.
The C 2 phase persisted at pressures at least as low as 0.5 GPa on decompression at 100 K (path e → f). However, surprisingly, the Bragg peaks of C 2 mostly disappeared at 0.2 GPa (Fig. 3). This phenomenon is totally unexpected, because the host structure of gas hydrates retains its framework in the previous cases with ice XVI 15 and XVII 16 . The sample was further decompressed to 0 GPa and evacuated using a turbo-molecular-pump. The broad peaks corresponding to ice I c appeared at this stage. The peak disappearance of C 2 before the appearance of ice I c was reproducibly observed in at least two separate neutron runs and one X-ray diffraction run for a hydrogenated sample (Supplementary Fig. 3). In the neutron diffraction pattern at 0.2 GPa, except for the Bragg peaks from Mg(OD) 2 , only a broad peak was observed at around d = 3.75 Å, which was between the peak positions of 111 of C 2 and that of Ice I c (Fig. 3). This fact implies that this state does not have long-range periodicity like a normal crystal, but has only local-ordering like an amorphous or nanocrystal. Considering the observed d-spacing, this amorphous-like form would be an intermediate transition state from C 2 to ice I c , which forms while hydrogen molecules are partially degassed. It is highly likely that this apparent amorphization is derived from the Phase boundaries for hydrogen hydrates and ices are drawn using thick blue lines and thin black lines, respectively. Experimental p-T paths are shown as black arrows in alphabetical sequence from a to g. The structural models for a high-pressure form of hydrogen hydrate, C 2 , and ice I c are schematically drawn with a newly found amorphous-like state as an intermediate transitional state from C 2 to ice I c . Red, white, and light blue balls in the structure model depict oxygen, hydrogen in water molecules, and hydrogen in guest molecules, respectively. Note that hydrogens in water molecules are disordered, so that two of four possible sites surrounding one oxygen are actually occupied.
lattice mismatch between C 2 and ice I c , originating from the relatively small cage in the host framework of the ice I c structure.
From the X-ray diffraction run, ice I c , which may partially include molecular hydrogen, even appeared at 0.1 GPa through the transition from the C 2 phase to the amorphous-like state, even under pressure ( Supplementary Fig. 3). This also represents a difference from the previous cases of ice XVI and XVII; ice XVI is formed under evacuation 15 , and hydrogen molecules can be refilled into ice XVII at an order of 10 bar of pressure 16 . It is worth noting that the partially degassed states are allowed in the cases of both ice XVI and XVII, so that the guest molecules can be continuously degassed from a fully occupied state to an empty state. The observed phase-separation behavior even under pressure in the ice H 2 -H 2 O system indicates that the partially degassed C 2 phase would be unstable compared to the fully occupied or emptied phases, probably due to their latticemismatch.
The Bragg peaks in the neutron diffraction pattern for ice I c obtained at 100 K were still broad, probably due to the small crystallite size and/or the remaining guest hydrogen molecules. The peaks of ice I c sharpened with increasing temperature. This sharpening is dependent not only on temperature but also on time, which indicates that it is kinetic behavior.
Structure refinement for ice I c . We conducted a separate run in order to obtain a neutron diffraction pattern for the structure refinement of the ice I c . In this run, the neutron diffraction pattern was obtained at 130 K, which is well below the temperature at which the nucleation of ice I h occurs 21 . We confirmed that the peak width did not change in the temperature region from 130 K to 180 K, such that the peak sharpening was almost complete, even at 130 K. The obtained neutron diffraction pattern was well fitted using the ice I c structure model 9 , as shown in Fig. 2b and Supplementary Table 1. We also conducted the Rietveld analysis using C 2 structure model, and found that the occupancy of the D2 site is zero, within experimental error (occ (D2) = −0.001 (1)). This shows that the guest hydrogen molecules are below the detectable limit at 130 K under evacuation. The peak profile around 111 peak of ice I c has neither the feature of stacking disorder nor the peaks from ice I h , as shown in the diffraction pattern in the region at around d = 3.9 Å, where the strongest 100 reflection of ice I h is expected (see inset in Fig. 2b, and more detailed discussion for the peak broadening for ice I c is described in Supplementary Note, Supplementary Table 2 and Supplementary Fig. 4). This should be a clear indication of the presence of ideal ice I c without stacking disorder (χ = 100%) 13 , as clear as the recent discovery of ideal ice I c by annealing ice XVII 10 .
Thermal stability of ice I c . It is also noteworthy that the ice I c surprisingly persists up to at least 240 K until ice I h started to appear at 250 K (Fig. 3). The temperature of 240 K corresponds to the upper limit of the reported metastable region of "ice I c " (ice I sd ) 1 . However, in stacking-disordered ice, the cubic stacking sequence starts to change into a hexagonal stacking sequence at a much lower temperature, and the phase transition to ice I h is completed at 240 K. The notable stability of the ice I c would be derived from the lack of stacking disorder. The stackingdisordered ice has more dislocations, which promote the phase transformation from ice I sd to ice I h by reducing the activation energy required to change the stacking sequence 22 . This is also supported by a recent mesoscopic-size calculation 23 . Note here that the critical temperature of 240 K has been identified as the temperature above which ice I h without cubic stacking faults   forms spontaneously, which is the reason for the anomalous selfpreservation regime of natural gas hydrates 24 . The diffraction pattern observed at 250 K looks a mixture of bulk ice I c and I h , rather than stacking-disordered ice with many stacking faults, judging from "stackogram" reported in the literatures 8,13 . At 250 K, crystal growth would be dominant, rather than crystal nucleation. Therefore, once a crystallite nucleates, it quickly grows before other crystallites nucleate, resulting in the mixture of ice I c and I h , rather than stackingdisordered ice. This observation also suggests a smaller number of dislocations in the ice I c observed in this study. On the contrary, the remarkable stability of the ice I c and the bulk mixture of ice I c and I h at 250 K strongly support the conclusion that the obtained ice is not stacking-disordered, and it can therefore be called ice I c without the need for quotation marks.
The discovery of ideal ice I c will allow us to research the real physical properties of ice I c without stacking disorder. For example, accurate heat capacity or vapor pressure measurements from low temperature will provide the free energy of ice I c , which settle the long-standing argument for the thermodynamic stability of ice I c compared to ice I h . The physical properties of the ideal ice I c are also important to understand how stacking disorder plays a role in the physical properties of ice I sd . For instance, since the thermal conductivity of ice I sd is significantly smaller than ice I h 25 , the difference of thermal conductivities between ices I h and I c will emboss the effect of stacking disorder. It is also interesting what will be happened when ice I c is compressed under low temperature; whichever ice I c will be transformed into HDA (High Density Amorphous ice 26 ) or not? In any case, it is worth conducting what we previously did for ice I h , to this ideal ice I c as well.

Methods
Synthesis of MgD 2 . MgD 2 , used as the starting material in this study, was synthesized from reagent-grade MgH 2 as follows. MgH 2 powder (Wako pure chemical industries, Ltd.) was purchased and further ground in an agate motor to increase the surface area, after which it was placed in a copper tube with a diameter of 4 mm and a length of 40 mm. The tube was mechanically sealed and but not welded, allowing the transfer of hydrogen gas. The copper tube was inserted into a 1/4" Inconel tube and connected in parallel to a deuterium gas cylinder and a turbomolecular pump (TMP) with 1/16" stainless tubes and stop bulbs. The Inconel tube, including the sample copper tube, was heated to 773 K for 1 h using a tube furnace under evacuation using the TMP. Under these conditions, MgH 2 completely decomposed to Mg and H 2 27 , and the degassed H 2 was evacuated. Then, the D 2 gas was introduced up to 4 MPa, and the temperature was cycled at the rate of 1 K/min between 673 K and 773 K while keeping the pressure at 4 MPa, which represents stable and unstable conditions for MgH 2 27 , and this temperature cycle was repeated for 20 times. This activation process is necessary for the reaction Mg + D 2 → MgD 2 . Finally, the p-T conditions were maintained at 673 K and 4 MPa for 3 days to complete the reaction. The recovered sample was analyzed by powder X-ray diffraction (MiniFlex-II, Rigaku) and identified to be MgD 2 with a trace amount of MgO. Both MgD 2 and MgO react with D 2 O and produce Mg (OD) 2 , so this small amount of MgO does not affect the conclusion of this study.
Neutron diffraction and p-T control. Neutron powder diffraction experiments were conducted at the beamline PLANET 28 in the Material and Life Science Experiment Facility (MLF) of J-PARC, Ibaraki, Japan. The incident beam consists of 25 Hz pulsed spallation neutrons produced from a liquid Hg target via a decoupled moderator and traveled through collimators, choppers and supermirror guides to the sample positioned at 25.0 m from the moderator 28 . Approx. 20 mg of MgD 2 , synthesized as described above, was filled into TiZr null scattering gaskets, and D 2 O water (99.9%, Wako pure chemical industries, Ltd.) was dropped on the MgD 2 powder, resulting in the molar ratio of MgD 2 :D 2 O~1:3. The gaskets were sandwiched between a pair of tungsten carbide anvils, and loaded by using a hybrid Mito system, which is a modified version of an original pressure-temperature variable Mito system 19 . The hybrid Mito system uses both flowing liquid nitrogen and a 4 K cryostat (RDK-415D, Sumitomo Heavy Industries, Ltd.), which allows us to control temperature rapidly, owing to the large latent heat of liquid nitrogen and efficient thermal insulation by zirconia and GFRP seats. The hybrid Mito system also allows us to achieve temperatures below 77 K, and reach a minimum temperature of~35 K, owing to the cryostat. Another remarkable feature of the hybrid Mito system is that it affords pressure control, even at low temperature, as well as the original Mito system, which is indispensable for this study. Flexible copper cloths were attached on the support rings of the anvils, and the cloths were placed in contact with the cold head of the cryostat for thermal conduction. The accessible minimum temperature of the hybrid Mito system is~35 K, which may be the current technical limitation due to an unavoidable influx of heat from the surrounding cell. The sample pressure was estimated from the observed lattice parameter of Mg(OD) 2 brucite using the equation of states 29 and the observed unit cell volume of brucite at 0 GPa, assuming the temperature derivative of the bulk modulus of brucite, dK/dT, was~0. Although this assumption may cause some error in the pressure estimated at low temperature, we placed emphasis on avoiding unwanted Bragg peaks from additional sources of pressure marker. Moreover, the error would be too small to affect the conclusion. The sample position was aligned by scanning to maximize the sample scattering intensity. The obtained intensities from the sample in the cell was subtracted by the intensity of the empty cell, and subsequently normalized by the attenuation corrected intensity of vanadium pellet in the cell, which was also subtracted by the intensity of the empty cell 30 . The Rietveld analyses were performed using the GSAS 31 with EXPGUI 32 , and the crystal structure was drawn with the VESTA program 33 . The GSAS TOF profile function 3 31 is used as the profile function in the Rietveld analyses.
X-ray diffraction. Powder X-ray diffraction measurements using a H 2 O (Milli-Q) and MgH 2 (Wako pure chemical industries, Ltd.) mixture as starting materials were performed at the beamline BL-18C in the Photon Factory (KEK, Tsukuba, Japan). Samples were exposed to 0.6134 Å monochromatized synchrotron radiation, and the diffracted scattering was detected by an imaging plate (IP). The pressure was generated using CuBe alloy diamond-anvil cells and the temperature was controlled using a 4 K GM cryostat (MiniStat, Iwatani Co.) equipped with a temperature controller (Model 335, Lakeshore). Sample pressure was estimated from the difference in the R1 line wavelengths of rubies inside and outside the sample chamber 34 . The temperature was monitored using a Si-diode sensor inserted in the cold head edge. We confirmed that the measured temperature was almost the same as that of the diamond anvils after temperature stabilization. The experimental p-T path was basically identical to the case of neutron diffraction, as shown in Fig. 1, while the achieved pressure at path d was 4.1 GPa.
One conically shaped Boehler-Almax type diamond-anvil 35 with a 0.6 mm culet was placed in the direction of the detector with an opening angle of 2θ < 40°, whereas a conventional anvil with a 0.8 mm culet was positioned in the direction of the X-ray source. A CuBe plate with a hole of diameter 0.3 mm and an initial thickness of 0.2 mm was used as a gasket. This gasket was not subjected to preindentation. The load was applied by driving the piston by bellows using a He gas cylinder. The bellows allow us to control pressure at a few kbar more precisely than conventionally used membranes.
DFT calculations. Quantum Espresso 36 was used for the DFT calculations 37,38 . We used Perdew-Burke-Ernzerhof (so-called PBE) type nonempirical exchangecorrelation functions 39 for this study. The pseudopotentials were derived using projector augmented-wave approximation 40 . The dispersion effects were taken into account using the exchange-hole dipole moment method (XDM), which calculates coefficients for polynomial of DFT-D dispersion energy 41 from the exchange-hole dipole moment calculated from simulated electron wave function 42,43 . XDM damping function parameters are taken from 44 . The enthalpies of four possible configurations for the ordered form of ice I c were calculated within a unit cell with a kinetic energy cutoff of 70 Ry and a Brillouin zone k mesh of 8 × 8 × 8. The cell parameters and atomic coordinates were optimized using BFGS quasi-Newtonian methods at atmospheric pressure.

Data availability
The primary data that support the plots within this paper and other finding of this study are available from the corresponding author on reasonable request. The neutron crystallographic coordinates for structures reported in this study have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under deposition numbers