Introduction

Familiar concepts of chemical bonding and interactions in molecular systems can change dramatically upon compression and new concepts can be revealed. At gigapascal pressures the atomic rare gases (e.g., He, Ar, Xe), diatomic molecules (e.g., H2, N2, O2) and even full-shell molecules (e.g., CH4, SiH4) can interact with each other and form compounds. The first reported, pressure-stabilized, stoichiometric van der Waals (vdW) solid was reported in the He-N2 system, He(N2)111. Since then a variety of stoichiometric vdW compounds have been synthesised under pressure for example, in the systems He-Ne2, Ar-H23, CH4-H24 and most recently Xe-H25,6. The study of hydrogen-rich binary mixtures has attracted particular attention because they are of interest to planetary science and astronomy, are potentially relevant technologically for hydrogen storage7, and, last but not least, offer the tantalising prospect to promote the pressure-induced insulator-metal transition in hydrogen at a lower pressure than required for pure hydrogen (e.g., 3, 8).

Two hydrogen-rich rare gas RG binary mixtures have been investigated so far: Ar-H2 and Xe-H2; and two vdW compounds have been discovered and characterised in detail: Ar(H2)2 and Xe(H2)8. Ar(H2)2 forms at 4.3 GPa and X-ray diffraction data showed Ar(H2)2 to be isostructural with the MgZn2 Laves phase to at least 27 GPa3. The observation of a Raman active H2 vibron confirmed the presence of molecular H2 in the structure and its disappearance around 175 GPa indicated the possibility of a pressure-induced molecular dissociation followed by metallization3. The prospect of metallic hydrogen stimulated extensive experimental and theoretical investigation of this molecular compound (e.g., 9,10,11,12) with the latest study in fact predicting a much higher metallization pressure for hydrogen mixed with argon than for pure hydrogen12. Stability of Ar(H2)2 to at least 220 GPa is supported by IR spectroscopic measurements13.

Xe(H2)8 was found to be stable above 5.4 GPa with a hexagonal crystal structure5. The Xe sublattice, as determined by X-ray diffraction, consists of Xe-Xe pairs oriented along the c axis of the unit cell. Raman and IR spectra composed of multiple H2 vibrons confirmed the presence of molecular hydrogen in Xe(H2)8 and support that its structure can be viewed as a tripled, solid H2 hcp lattice modulated by layers consisting of Xe dimers5. IR spectra showed the Xe(H2)8 compound to remain an insulator to at least 255 GPa5 while its calculated metallization pressure is around 250 GPa14.

The Kr-H2 binary system has not been investigated under compression experimentally and so the possible vdW compounds are unknown. A recent first-principles study suggested that Kr(H2)2 was a possible candidate for observing the pressure-induced metallization of hydrogen based on the similarities of RG(H2)2 to RG(He)2 systems15. Here we present the first high-pressure single-crystal X-ray diffraction study of a Kr-H2 solid synthesised at pressures ≥5.3 GPa in the diamond-anvil cell from a mixture of 8 vol% Kr and balance H2 (Fig. 1). Complementary Raman spectroscopic measurements were performed to verify the structural environments of the hydrogen molecules determined from single-crystal X-ray diffraction data and to characterize the evolution of the H2 molecular bond under pressure.

Figure 1
figure 1

Optical microscope photographs showing a Kr(H2)4 single-crystal in solid hydrogen in the diamond-anvil cell under pressure at 298 K.

There is a striking visible difference in shape between the crystal of experiment 1 (a) and experiment 2 (b) (squared, sharp edges versus rounded shape). Except for a difference in their crystallographic orientation with respect to the X-ray beam the X-ray diffraction and Raman spectroscopic data match showing both crystals as well crystalline.

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Results

The structure of Kr(H2)4 and its evolution under pressure

The structure of the Kr-H2 compound was solved from a single-crystal data set collected at 11.24 GPa (Tab. 1, Supplementary Fig. S1 and Tab. S2). The Kr sublattice is face-centred cubic (fcc), space group Fm-3m and characterised by isolated Kr octahedra occupying the fcc sites (Fig. 2). Interestingly the intra-octahedral Kr-Kr bond distances (3.35 Å at 11.24 GPa) are comparable to the Kr bond distance in the pure krypton solid at the same pressure. The inter-octahedral distances are comparably long with the shortest inter-octahedral Kr-Kr distance being 4.89 Å at 11.24 GPa. Under pressure the volume of Kr(H2)4 compresses continuously to at least 51 GPa with the longer inter-octahedral Kr-Kr distance decreasing faster than the shorter intra-octahedral distance (Fig. 3). Compression of the intra-octahedral distance follows the compressional behaviour of the Kr-Kr distance in solid krypton. Above 15 GPa the fcc Kr sublattice indicates a small tetragonal distortion (space group I4/mmm) deviating form the cubic unit cell by about 1% based on ctet/a√2 = 1.01. Cubic and tetragonal refinements of the Kr(H2)4 structure are of comparable quality to 51 GPa and for the purpose of volume determination we have refined the Kr substructure with cubic symmetry.

Table 1 Details of the structural refinement of Kr(H2)4 at 11.24 GPa and 298 K
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Figure 2
figure 2

Face-centered cubic structure of Kr(H2)4 at 11.24 GPa.

Isolated krypton octahedra (green) are located at each lattice point. Grey spheres represent rotationally disordered hydrogen molecules.

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Figure 3
figure 3

Compressional behaviour of the Kr(H2)4 structure.

(a) Pressure-volume data. A Vinet equation of state (EoS) fitted to the data with V0 = 5237.952 Å3 gives B0 = 0.18(3) GPa and B′ = 7.7(2). The fixed V0 value is based on the equivalent volumes of pure, solid krypton and hydrogen. (b) Intra- and shortest inter-octahedral Kr-Kr distances as function of pressure. For comparison Kr-Kr distances in the pure krypton solid (16) are given in the inset. Solid lines are guides to the eye.

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The low X-ray scattering cross-section of hydrogen, the contrast with heavier elements and the micron-sized sample in the diamond-anvil cell pose a major challenge in high-pressure X-ray diffraction experiments on hydrogen-rich samples for the determination of H2 positions. In addition, single-crystals become increasingly strained under pressure and the reflection rocking curve deteriorates. Our structural model of Kr(H2)4 could be completed by locating the hydrogen molecules using difference-Fourier maps. The H2 positions were identified at four different interstitial sites (Tab. 2) appearing with peak scattering densities from 0.9 to 1.23 eÅ−3 in the Fcalc-Fobs difference electron density maps. Including the H2 molecules in the refinement improved the refinement quality factor R1 by 1.2% compared to a model with Kr atoms only. Further, the number of H2 molecules refined confirms the stoichiometry Kr(H2)4 which was initially (with only the Kr substructure established) derived from volume considerations based on the separate equation of states of pure krypton16 and hydrogen17.

Table 2 Refined atomic coordinates and displacement parameters for Kr(H2)4 at 11.24 GPa and 298 K
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High-pressure Raman spectra and the H2 sublattice of Kr(H2)4

The Raman spectra of Kr(H2)4 are characterised by roton peaks between 200–1200 cm−1 and by a maximum of four H2 vibrons between 4200–4500 cm−1 confirming the presence of molecular hydrogen in the structure (Fig. 4, 5). The roton frequencies cannot be distinguished from those of pure hydrogen at the same pressure indicating rotational disorder of the H2 molecules. The four H2 vibrons are observed at higher frequencies than the Q1(1) vibron of solid H2 at the same pressure. Attributing these vibrons to H2 molecules in four different crystallographic sites is consistent with the four H2 sites determined from the difference-Fourier maps.

Figure 4
figure 4

Raman spectrum of Kr(H2)4 at a selected pressure of 19.6 GPa; background has not been subtracted.

Roton peaks are observed in the low frequency range and two vibrons, ν1 and ν2, in the high-frequency range. The other two, much weaker vibrons, ν3 and ν4, are not observed at this pressure. The rotons and Q1(1) vibron frequency of solid H2 at the same pressure are indicated by cyan, dotted lines.

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Figure 5
figure 5

Raman spectra of Kr(H2)4 (black) and the surrounding, solid H2 (cyan) as a function of pressure at 298 K.

Spectra are normalised to the most intense vibron and offset for clarity.Background due to fluorescence of the diamond anvils has been subtracted.

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Under compression the vibrons shift continuously to higher frequencies (Fig. 6) confirming the persistence of molecular H2 and the absence of a major structural change in Kr(H2)4 to at least 51 GPa in agreement with the continuous volume compression. The two lower frequency vibrons (ν1, ν2) remain intense to the highest pressure, the higher frequency vibron ν3 weakens significantly and the fourth vibron, ν4, is very weak and not uniformly observed across the pressure range studied. Interestingly, the two H2 vibrons, ν1 and ν2, show a striking reversal in their relative intensities under pressure: ν1 looses intensity while ν2 gains intensity. Around 15 GPa ν1 and ν2 are of equal intensity and above about 30 GPa their intensity ratio is constant. The changeover in dominant intensity from ν1 to ν2 occurs at the pressure above which a tetragonal distortion is detectable in the fcc Kr sublattice. Such coincidence suggests that the change in relative intensity of the H2 vibrons can be associated with a change in the H2 sublattice which in turn subtly affects the Kr sublattice at pressures >15 GPa. We can exclude a re-distribution of H2 molecules between two different crystallographic sites because all four hydrogen sites are fully occupied.

Figure 6
figure 6

Pressure dependence of the H2 vibrons of Kr(H2)4 and surrounding solid H2 (cyan).

Errors in frequency and pressure are within the size of the symbol. The data is well represented with 2nd and 3rd order polynomials (Supplementary Tab. S3). The pressure dependence of the vibron of solid hydrogen agrees well with literature values (dotted grey line22; solid grey line23). The pressure dependence of the vibron of Ar(H2)210 and the most intense vibron of Xe(H2)8 are given for comparison. The latter matches the data by Somayazulu et al. (2010). The inset shows the pressure dependence of the most intense Xe(H2)8 vibron and the Q1(1) vibron from the surrounding, bulk H2 zoomed out to 142 GPa.

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Discussion

In order to provide additional insight and to enable a more systematic understanding of weakly-bonded systems under pressure we compare Kr(H2)4 with the two, other known RG-H2 compounds, Xe(H2)8 and Ar(H2)2.

From the RG sublattice point of view a common characteristic of Kr(H2)4, Xe(H2)8 and Ar(H2)2 is that the smallest RG-RG distance is comparable to the next nearest-neighbour distances in the pure RG solid at the same pressure. While Ar(H2)2 features only Ar-Ar distances close to those in solid Ar at the same pressure, Kr(H2)4 and Xe(H2)8 show a striking difference: Two different sets of atomic distances occur: intra- and inter-atomic RG-RG distances with the intra-atomic distances being comparable to the next nearest-neighbour distances in the pure RG solid at the same pressure. For Kr(H2)4 the intra-octahedral Kr-Kr distances are comparable to the Kr-Kr distances in solid krypton and for Xe(H2)8 the Xe-Xe dimer separation was reported to match the Xe-Xe distance in solid xenon5.

Further, the pressure dependence of the intra-octahedral Kr-Kr distance follows closely that of the Kr-Kr distance in solid krypton making the Kr-octahedra appear as detached units, neither interacting with each other nor with the H2 sublattice. A similar observation applied to the Xe-dimers in Xe(H2)85. However, clearly compound formation and stability is a complex process dominated by a subtle interplay of van der Waals and weak covalent forces or possibly charge transfer interactions as argued for in Xe(H2)85,14.

The hydrogen-lattice vibrational properties of Kr(H2)4, Xe(H2)8 and Ar(H2)2 show strong similarities to solid H2. The rotational vibrations of all compounds are reported as indistinguishable from those of solid hydrogen indicating freely rotating H2 molecules. The observation of multiple vibrons for Xe(H2)8 and Kr(H2)4 contrasts with solid H2. The origin of the vibron multiplet structure for Xe(H2)8 has been explained with H2 forming a sublattice that is a 3 × 3 × 3 superstructure of the hcp lattice of solid hydrogen5. The Raman spectrum of Kr(H2)4 reveals four H2 vibrons that can be attributed to hydrogen molecules in four different crystallographic sites. Three H2 vibrons are expected for Ar(H2)2 based on group theoretical arguments10 but only a single vibron has been measured with the other two being thought to be too weak to be observed.

The H2 vibrons in the RG-H2 compounds increase under compression as is expected from increasing repulsion between molecules. An interesting, well studied characteristic of the vibron in solid hydrogen is its turnover around 35 GPa above which its frequency decreases monotonically. This behaviour has been attributed to vibrational coupling between H2 molecules; pressure-induced bond weakening does not occur until over 145 GPa18. We observe that the intense H2 Raman vibron of Xe(H2)8 mirrors the behaviour of the vibron in solid hydrogen turning over around 40 GPa (inset Fig. 6). Starting from a lower frequency, it crosses the pressure-frequency trajectory of the pure hydrogen vibron at about 50 GPa and remains at a higher frequency to at least 142 GPa. The intense H2 vibron we observe in Xe(H2)8 is the only vibron of the RG-H2 compounds reported so far that on compound formation and at pressures <50 GPa exhibits a frequency lower than the vibron of pure hydrogen at the same pressure.

The H2 vibrons of Kr(H2)4 and the single vibron of Ar(H2)2 are initially higher than the vibron of pure H2 and harden continuously under compression over the investigated pressure range with the ν1 vibron of Kr(H2)4 appearing to flatten around 40–50 GPa so likely turning over at higher pressures. Continuously increasing H2 Raman vibron frequencies have also been observed for H2 dissolved in rare-gas matrices where there is no possibility of vibrational coupling due to mismatch of vibrational frequencies between matrix and H2 molecules19. The RG-H2 compounds appear therefore to show “composite” behaviour, with some of the H2 vibrational properties dominated by H2-H2 intermolecular interactions of near by H2 and some more strongly modified by nearby RG structural units.

Details of the electronic band structure of Kr(H2)4 and the possibility of metallization present a challenge for future experimental and theoretical studies; experimental IR data in the megabar range would be particularly valuable. Furthermore, the low-pressure phase diagram of the Kr-H2 binary system is unexplored and there may be other stoichiometries stabilized for different starting mixtures.

Methods

Diamond-anvil cell sample loading and crystal synthesis

In two separate experiments a single-crystal of Kr(H2)4 was grown in a diamond-anvil cell (DAC) from a pre-mixed gas of composition 8 vol% Kr and 92 vol% H2 (certified accuracy ±2% from Air Liquide). In both runs a DAC equipped with 0.3 mm culet diamonds and an opening angle of 76 deg (Betsa, France) was used. A Re gasket pre-indented to 25 μm thickness with a hole of 120 μm diameter formed the sample chamber and a ruby sphere served as pressure calibrant20. The pre-mixed Kr-H2 gas was loaded in the DAC at 0.2 GPa21. Kr and H2 are miscible in the liquid phase. By increasing the pressure delicately a crystal was grown from the mixture at a pressure ≥5.3 GPa. At slightly higher-pressure, ~5.5 GPa, solidification of the excess liquid was observed. 5.5 GPa is the known solidification pressure for pure hydrogen (e.g., 22, 23) and Raman spectroscopic measurements confirmed the solidified excess liquid as solid hydrogen. For the high-pressure experiment hydrogen acts as a pressure-transmitting medium and ensures quasi-hydrostatic conditions up to the highest pressures reached in these experiments; 26.7 GPa in experiment 1 and 50.9 GPa in experiment 2. We cannot exclude the possibility that the starting stoichiometry was changed due to hydrogen dissolving into the gasket material under compression24. A possible loss of H2 to the Re gasket would affect the total amount of pure hydrogen in the sample chamber but not the formation of the observed Kr-H2 compound because this compound was grown in the presence of excess hydrogen and is in equilibrium with pure, solid H2 at pressures ≥5.5 GPa.

Single-crystal X-ray diffraction

Single-crystal diffraction data have been collected on beamline I15 at Diamond Light Source (UK). The diffraction experiments were performed with a monochromatic beam (λ = 0.3647 Å) collimated by a tungsten pinhole down to 20 μm in diameter. A MAR345 image plate (MarResearch) was used as a detector with sample-to-detector distances between 250 and 270 mm. The DAC, positioned on a 6-circle Newport diffractometer with kappa geometry, could be rotated around the φ-axis and data sets were collected using φ-scans over 60 and 73 deg, step sizes between 0.5 and 2 deg and exposure times of 0.25 to 4.0 sec per step. The data were processed using CrysAlisPro software (Agilent Technologies) and the WinGX version of SHELXS and SHELXL25.

Raman spectroscopy

Unpolarized Raman spectra have been recorded from the Kr-H2 single-crystal and the excess, solid H2 in 180° back-scattering geometry over the range 3800–4800 cm−1 (region of the H2 vibron) with spot tests in the range 200–1200 cm−1 (region of the H2 rotons). The instrument used was the Labram HR800 (Horiba Jobin Yvon) at beamline I15, Diamond Light Source (UK). It was equipped with 1200 g grating and an air cooled CCD detector. The spectra were excited by the 473 nm line of a 50 mW Cobalt Blues TM laser focused down to a 10 μm spot on the sample and collected through a 50 μm confocal aperture. The intrinsic resolution of the spectrometer is <1.0 cm−1 and calibrations are accurate to ±1 cm−1. The frequency of each Raman band was obtained by Voigtian curve fitting using a least-squares algorithm. In experiment 1 some spectra collected on the Kr(H2)4 and H2 crystal each contained weak contributions from the other solid phase due to the small sample size but deconvolution was readily done.

The Raman spectroscopic data of Xe(H2)8 to 142 GPa were measured in 135 deg scattering geometry with a SPEX Triplemate equipped with a back-illuminated liquid-N2-cooled CCD detector at the Department of Earth Sciences, University of Oxford, UK. The spectra were excited by the 514.5 or 488-nm line of an argon-ion laser focused to a ≤ 10 μm spot on the sample and collected through an adjustable confocal aperture closed down to about 10 μm in diameter >90 GPa. The intrinsic resolution of the spectrometer is 1.5 cm−1 and calibrations are accurate to ±1 cm−1.