Universal diamond edge Raman scale to 0.5 terapascal: The implication to metallization of hydrogen

The recent progress in generating static pressures up to terapascal values opens opportunities for studying novel materials with unusual properties, such as metallization of hydrogen and high-temperature superconductivity. However, an evaluation of pressure above ~0.3 terapascal is a challenge. We report a universal high-pressure scale up to ~0.5 terapascal, based on the shift of the Raman edge of stressed diamond anvils correlated with the equation of state of Au and does not require an additional pressure sensor. According to the new scale, the pressure values are substantially lower by 20% at ~0.5 terapascal compared to the extrapolation of the existing scales. We compared the available data of H2 at the highest static pressures. We showed that the onset of the proposed metallization of molecular hydrogen reported by different groups is consistent when corrected with the new scale and can be compared with various theoretical predictions.

The terapascal pressure range has recently been achieved in dynamic compression experiments at large facilities (1). Amazingly, similar pressures can be generated in static experiments using the incommensurably smaller and simpler device -a diamond anvil cell (DAC) (2,3), appropriate for many more diversified studies. Under such extreme pressure conditions, the structure and properties can change drastically even at ambient temperature because the work associated with the P-V compression is comparable to the energy of atomic bonds. For example, the "simple metal" sodium transforms to an insulator (electride)(4); conversely, oxygen and xenon transform to metals (5,6). Molecular nitrogen transforms into an atomic state with a diamond-like structure (7).
Motivation for generating multi-megabar static pressures is primarily driven by the pursuit of obtaining atomic metallic phase of hydrogen, which is predicted to be a room temperature superconductor at pressures of 500 GPa and may combine superconductivity and superfluidity (8). There has been substantial progress in the study of hydrogen, both theoretically and experimentally. Electrical conductivity studies showed that molecular hydrogen metalizes at 320 GPa through the closing of the indirect gap (9)(10)(11). At higher pressures, a direct bandgap likely closes according to the abrupt decrease in the infrared absorption at 427 GPa (12) and disappearance of the Raman modes at 450 GPa (10). The problem of metallic hydrogen, in turn, has stimulated the search for hightemperature superconductivity in hydrogen-rich compounds. Nearly room temperature superconductivity with a Tc  of 203 K in H3S (13) and Tc  250 K in LaH10 (14,15) was reached at pressures of 150-170 GPa. The latest theoretical calculations predict Tcs exceeding room temperature: Tc 330 K in CeH18 (16), and 470 K for Li2MgH16 (17) at higher pressures of 300-500 GPa.
Static pressures up to 1 TPa were gradually increased starting from the modest 10 GPa by improving the diamond anvil geometry and DAC design. A decisive step was the development of beveled anvils (18), which instantly opened the way for pressures beyond 100 GPa. With more complicated profiling of anvils, such as toroidal grooves, which surpass the plain Bridgeman anvils (19, necessity of comparison between experiments of different groups and theoretical predictions, which are becoming more and more precise. We prepared eight DACs with a gold sample as the X-ray pressure standard. The single-crystal diamond anvils had a culet plane normal to the [001] crystallographic direction. We created profiles of anvil tips of different shapes to achieve the highest pressure (Fig. S1). We established the correlation between the lattice parameters of a gold sample probed with X-ray diffraction and the high-wavenumber Raman edge of stressed diamond anvils from the same point of the sample (Fig. 1). The equation of state of gold was taken from the isotherm derived from the ramp data(23) (see Supplementary Materials for a detailed description of the experiment). We plotted this correlation over a wide pressure range for anvils of different shapes. The data are consistent with each other in different runs and with previously reported data obtained below 300 GPa (9,25,28) (Fig. 2). We fitted this combined data set over the entire pressure range of 0-477 GPa using equation (28) where ω is the shift of the diamond Raman edge of the stressed diamond anvil, ω0 = 1332.5 cm -1 is the initial position of the diamond Raman edge of unstressed diamond anvils at ambient pressure, and A and B are the fitting parameters. The refined universal parameters A = 517±5 and B = 764±14 fit the data well and apply for accurate pressure estimation from ambient pressure to 477 GPa.
The new diamond scale contradicts the currently used diamond scale(29) at pressures above 250 GPa, reaching a difference in pressure values over 100 GPa at approximately 500 GPa (Fig. 2). The highest pressure of 477 GPa based on a gold equation of state(23) measured in the present study corresponds to the record highest shift of the diamond Raman edge of stressed anvils of 2026 cm -1 (592 GPa according to the scale(29)). It was achieved in run 1 using toroidal diamond anvils with culets of diameter 10 µm. Note that a similar pressure of 446 GPa (the diamond Raman edge at 1996 cm -1 ) was reached in run 3 with traditional, not toroidal, but double-beveled diamond anvils (culet 12 µm).
The diamond edge Raman scale was robust to different load distribution patterns on the diamond tip. It works well for diamond anvils of different shapes (see Fig. S1 in Supplementary Materials). Notably, the refined diamond scale is valid for pressure estimation at the center of the diamond anvils and for a large area of 20-30 µm around the diamond tip (see Fig. 1D and Fig. S2-S4 in the Supplementary Materials).
The accuracy of the pressure evaluation from the X-ray diffraction data is affected by the deviatoric stress α(σ3 − σ1) (the difference between the maximal and minimal eigenvalues of the stress tensor) in the Au sample (Fig. 1F). The values of α(σ3 − σ1) reached 10-15 GPa at the highest pressures, which was lower than the reference data from the ramp experiments (23). The lattice volume of gold was determined from the X-ray diffraction data using the (111) diffraction peak position, which is the least affected by non-hydrostatic compression (2).
The universal scale for a sample pressure estimation is crucial for collating experimental results from different groups and comparison with theoretical predictions. Because of the inconsistency in the pressure scales used in the reported data, the intriguing observations of pressure-induced phase transitions in hydrogen and its metallization are difficult to compare in the multi-megabar pressure range. There is no consensus on which pressure scale should be used. The latest diamond edge Raman scale calibration up to 410 GPa (29) and more conservative scale(28) have both been used (12,31) to study hydrogen, but they differ dramatically above 300 GPa. This ambiguity raises the question of how suitable the diamond edge scale will be for hydrogen. The diamond scales are based on the equation of state of metals, but hydrogen is much softer. In addition, the compression of hydrogen is sensitive to the thickness and diameter of the sample and material of the gasket because a particular arrangement of experiments influences the stresses in the diamond anvils and the Raman spectrum. In particular, it develops in a pronounced sharp peak at the high-wavenumber Raman edge of diamond anvils recorded over the hydrogen sample (Fig.S5, run 7), whereas it manifests as a weak step in Raman spectra recorded over gold samples (Fig.S5).
We checked the validity of the diamond edge Raman scale by measuring the lattice volume of gold placed inside the hydrogen sample in run 7. Gold is the only metal that likely does not react with hydrogen. Theoretical works are contradictory: Kim et al.(32) predicted the formation of AuH above 220 GPa, whereas Gao et al. (33) demonstrated that AuH is thermodynamically unfavorable against elements. Experimentally, no hydrides of gold have been found at pressures up to 113 GPa and temperatures up to 600 K (34). In the present experiments performed at room temperature, gold did not form a hydride up to the highest pressure of 290 GPa, as both the face-centered cubic crystal structure and the lattice volume of the sample corresponded to pure gold (2,3). The pressure estimated from the gold sample surrounded by hydrogen in run 7 is in good agreement with the pressure value simultaneously estimated from the new diamond Raman edge scale, which strongly supports the application of the updated diamond edge Raman scale to hydrogen samples.
The position of the hydrogen vibron in the Raman spectra is sensitive to pressure. For example, one can observe a large scatter in the data of ~20 GPa from run to run on the plots of the pressure dependence of hydrogen vibron (9,35). The accuracy of the pressure determination can be significantly improved by using hydrogen itself as a pressure gauge by calibrating the pressure-induced shift of hydrogen vibron ω(P) against the gold chip placed in hydrogen. We found that hydrogen vibrons at 2990 cm -1 and 4085 cm -1 correspond to a pressure of 283 GPa, as determined from the gold chip ( Fig. 3A inset). At higher pressures, diamond anvils break during exposure to intense synchrotron Xrays; this premature failure is common (36). This calibration of the hydrogen vibron can serve as a reference, and the pressure correction can be performed by shifting the whole plot of ω(P) to the calibrated point at P=283 GPa, as shown in Fig. 3A.
The phase diagram of hydrogen was corrected according to the updated universal diamond scale (Fig. 3C), in particular, the metallization pressure was corrected to 300 GPa. Above this pressure, as follows from the electrical measurements(9-11), hydrogen transforms into a semimetal through a semiconducting state. This transformation is consistent with the current theoretical predictions of the metallization of hydrogen through the closing of the indirect gap (37)(38)(39). The direct gap is opened in the semi-metallic state, and hydrogen weakly absorbs light, allowing Raman(10) and IR (12) spectroscopy. At higher pressures, a sharp decrease in IR absorption was reported at 427 GPa (12), and the disappearance of the Raman signal at 450 GPa (10). According to the new scale, both observed transitions are, in fact, at close pressures of 400-410 GPa (Fig. 3B), indicating that both observations are likely related to the same transition. Experimentally, the nature of this transition is difficult to reveal because X-ray diffraction or spectroscopic data are not available above this pressure. Theoretically, a structural transformation from C2/c to Cmca-12 molecular phases was predicted at 423 GPa before the atomic Cs-IV phase at 447 GPa. In another scenario, the direct band of hydrogen closes at ∼450 GPa (37,38), or∼430 GPa(39) in the same molecular phase C2/c-24. Further studies are required to converge the experimental and theoretical data.
Correct pressure evaluation is crucial for the interplay between theory and experiment, which can be very fruitful, as illustrated by recent progress in near-room temperature superconductivity. The experiment, which is often guided by calculations, provides discrepancies that improve the computational models and fundamental understanding. Reliable predictions of crystal structures and properties of matter at high pressures, together with the development of the synthesis of new compounds, will advance science and technology.

Diamond anvil cell preparation.
High pressure was generated using DACs with a diameter of 25 mm and a length of 35 mm. The load is applied by pushing the piston, which is moved by screws at the top of the DAC. Anvils are made of synthetic or natural diamonds with culets that are normal to the [001] crystallographic direction. They were beveled at 8° to a diameter of ~250-400 µm. We used small culets of 10-20 µm with different shapes of the diamond tip to achieve the highest pressures (Fig. S1). The toroidal shape of the diamond anvils was made with the aid of a focused beam of xenon ions (FERA3, Tescan). The ion beam current was set between 1 and 10 nA under an accelerating voltage of 30 kV. The total duration of machining of the toroidal shape was approximately 1 hour per diamond anvil. The final profile of the diamond anvils was measured using a profilometer. For the sample loading, 250-µm-thick T301 stainless steel gaskets were preintended to a thickness of 5 µm, and a hole with a diameter of 20 mm was drilled by a laser. A piece of gold (SkySpring Nanomaterials, 99.99%) was placed in the prepared hole and clamped in the DACs. Gold was used as the standard for the pressure determination. In total, eight DACs were pressurized to 200-300 GPa in the home laboratory and transferred to synchrotron facilities, where the pressure was further increased.

X-ray diffraction and Raman measurements.
X-ray diffraction data were collected at the beamlines 13-IDD at GSECARS, Advanced Photon Source (λ = 0.2952 Å, a spot size of ~2.5×3.5 µm 2 , Pilatus 1M CdTe detector) and P02.2 at PETRA III, DESY (λ = 0.2910 Å, a spot size of ~3×3 µm 2 , LAMBDA GaAs detector). The typical exposure time was varied between 1s and 5s. Reference samples of LaB6 and CeO2 were used to calibrate the distance between the sample and detector. The X-ray beam was cleaned using a pinhole to remove the beam wings. The processing and integration of the data and background subtraction were performed using the Dioptas software(1).
The Raman spectra were recorded using an advanced Raman setup at GESECARS (2). The Raman signals of stressed diamond anvils in contact with gold samples were excited by lasers with two different wavelengths: λ1 = 660 nm and λ2 = 532 nm. The switching from red to green laser helped to reduce and shift the strong luminescence of the stressed diamond, which may appear in synthetic diamonds at pressures above 300 GPa and overlap the diamond Raman edge signal of stressed anvils. The laser power of the incident light coming from a 50 microscope objective (Mitutoyo) was reduced to 3-5 mW to protect the diamond anvils from failure because of the enhanced absorption of the highly stressed anvils. The typical exposure time was 60-120 s per Raman spectrum.
At each pressure point, the position of the X-ray beam was visualized with the X-ray-induced luminescence of the sample, and the spot was aligned relative to the center of a diamond culet, which was observed under illumination. For the Raman measurements, the focused laser beam was aligned relative to the image of the anvil. This alignment was reproducible at the same stage as the fixed DAC was placed in the Raman and X-ray setups with an accuracy of 1 µm. Thus, the X-ray and laser beams were aligned to probe the sample at the exact location. This is crucial because of the large pressure gradients over the diamond tip. The original X-ray powder diffraction patterns of gold and the corresponding Raman spectra of stressed diamond anvils measured at different pressures in different runs are illustrated in Fig. S5.
To measure the spatial pressure distribution at the diamond anvil tip, we performed X-ray diffraction and Raman mapping on an area of 20×20 µm 2 with a horizontal and vertical step of 2 µm. At certain highest pressure points, the grid step was reduced to 0.5-1 µm. In addition, at selected pressure points, diamond anvils were scanned horizontally and vertically up to 70 μm away from the center of the diamond culet (Fig. S2-S4 and S6).

Pressure determination
The diamond Raman edge was determined as a point at half the height of the step at the highwavenumber edge in the Raman spectra of the stressed diamond anvil (Fig. 1B). We assigned this wavenumber to the pressure value estimated from the X-ray diffraction measurements by referring the refined lattice volume of the gold sample to the reduced isotherm obtained from the ramp experiments (3).
We also estimated how the deviatoric stresses α(σ3 − σ1) (the difference between the maximal and minimal eigenvalues of the stress tensor) in our Au samples could influence the accuracy of the pressure determination. The deviatoric stress was estimated by applying the commonly used method (4)(5)(6). This method is based on the analysis of the positions of the diffraction peaks because different peaks shift differently under non-hydrostatic stress. In a cubic crystal lattice, all diffraction peaks yield identical lattice parameters. In contrast, in the strained crystal, they differ by a factor proportional to σ3 − σ1 and the elastic anisotropy of the crystal. The single-crystal elastic constants were taken from the low-pressure measurements in Ref. (7) and extrapolated to our high-pressure values. Five diffraction peaks of gold (111), (200), (220), (311), and (222), which were measured in most of our runs, were used for the analysis. We used an iso-stress assumption in our powder samples (α, which varies from 0.5 to 1, was set as 1), which provides minimum values of σ3 − σ1. The deviatoric stresses reach 10-15 GPa, i.e. 2-3% at 500 GPa (Fig. 1F), and are less than those sustained in the ramp experiments(3).

SUPPLEMENTARY FIGURES
Supplementary figure S1. Profiles of diamond anvil tips used in runs 1-7 of the present study. Insets illustrate the geometry of diamond culets. In run 8 we used anvils with culet of diameter 8 µm beveled at 7.5 to diameter 320 µm.   figure S4. Distribution of pressure on the diamond tip (culet 10 µm) in run 5. The plot is reconstructed from one-dimensional X-ray diffraction (black circles) and Raman (red circles) mappings. Pressure values were estimated using the equation of state of Au(3) (X-ray diffraction) and the universal diamond edge Raman scale. The difference in pressures values at distances farther 10 µm from the diamond culet center is naturally expected due to very ununiformed stresses distribution in the stressed anvil (8). Importantly that the pressure values well coincide within the diamond culet area. This fact supports the universality of the present pressure scale.