Spectroscopic limits of diamond anvils to 520 GPa and projected bandgap closure

Domain: physics
Published: 2026-02-12
Editorial outcome: major_revision

Abstract
Diamond anvils serve as optical windows in static ultrahigh-pressure experiments, now reaching the terapascal regime. However, they exhibit poorly understood changes in their optical properties under multimegabar pressure. Here, we present broadband absorption measurements (ultraviolet to infrared wavelengths) up to 520 GPa, revealing a pronounced loss of transparency with pressure. Diamond Raman scattering is used to infer the stress profile along the anvils’ axis under the assumption of tetragonal distortion, and crucially at the sample interface. This enables a quantitative analysis of absorption spectra, showing an indirect bandgap narrowing towards the infrared, with metallization projected near 560 GPa sample pressure within our stress model. A universal optical behavior is observed across different anvil geometries, which is consistent with the universality of the Raman edge pressure scale, here refined. These findings help define the spectroscopic operational limits of diamond anvil cells under extreme pressure with important implications for recent claims of hydrogen metallization.

Introduction
The Diamond Anvil Cell (DAC) is a workhorse of static high-pressure physics. It fully exploits the exceptional mechanical properties of diamond—namely its record-breaking hardness, ability to undergo significant elastic deformation, and remarkable optical transparency due to a wide indirect bandgap. A wide range of spectroscopic techniques have been adapted to probe the properties of materials under high pressure1, with one of the latest developments being magnetic measurements using NV quantum sensors (ref. 2 and references therein). A wealth of data on material properties at high pressures have been obtained up to the conventional DAC limit of about 400 GPa3.

Currently, the frontier of extreme pressure research lies in the terapascal (TPa) regime. This range is readily accessible through shockless dynamic compression techniques available at large laser facilities4,5; however, microscopic diagnostics under such approach are typically limited to X-ray diffraction. Static compression into the TPa regime has been made possible by two novel anvil designs: toroidal anvils and the double-stage anvil, which have reached pressures close to 600 GPa6 and 1000 GPa7, respectively. The toroidal DAC, in particular, offers advantages in terms of sample volume and optical access, enabling continued use of spectroscopy probes up to ultrahigh pressures.

Among the key motivations for reaching pressures in the 0.5–1 TPa range is the quest to reach the atomic metallic state of hydrogen. This phase is predicted to exhibit many intriguing quantum phenomena, such as room-temperature superconductivity8, supersolidity9, or a combined superfluid-superconducting state10. Various claims of observation have been made regarding metallic hydrogen, including a semi-metallic state near 350 GPa11, molecular metallic hydrogen at around 425 GPa for H2 12 and 460 GPa for D2 13, and atomic metallic hydrogen near 500 GPa14. However, these findings are not fully consistent, and the claim of atomic metallic hydrogen has faced serious criticism15. Central to the debate are two key issues: the differences in the diamond Raman edge-based pressure scales used16,17, and the pressure-induced changes in the optical properties of stressed diamond. Recently, the Raman pressure scale has been recalibrated up to 0.5 TPa, demonstrating its robustness across different anvil geometries. Using only this refined pressure scale has helped to improve consistency in literature hydrogen Raman data18. Yet, the effect of diamond transparency remains to be studied to critically evaluate the metallization claims.

Since the 1990’s, it has been recognized that deviatoric stresses at the anvil tip significantly affect the optical properties of the diamond window19,20. Specifically, the absorption edge of diamond has been observed to shift to lower energies with increasing pressure. Ab initio calculations suggested that diamond’s minimum bandgap is highly sensitive to anisotropic stress, and that beyond a certain level of tetragonal distortion, the bandgap decreases with pressure—opposite to what occurs under hydrostatic compression21–23. However, this loss of transparency under extreme pressure has remained a qualitative observation. Progress toward a quantitative understanding demands to consider several issues: the non-uniform stress distribution within the anvil, evolution of deviatoric stress with pressure, dependence on anvil geometry and difficulty to reach pressures in excess of 300 GPa. This is tackled here below using optical absorption spectroscopy experiments performed in DACs, allowing for the quantitative extraction of the pressure evolution of the indirect bandgap in diamond under proposed tetragonal distortion, corresponding to the maximally stressed layer of diamond at the sample interface. Based on these findings, the pressure limits for various spectroscopic techniques, commonly used to characterize samples under very high pressure in a DAC, are discussed.

Results
Marked visual changes in diamond anvils above 300 GPa
The main effect is illustrated in Fig. 1A, which shows a complete loss of transparency in the visible range around 500 GPa. We have measured the optical transmission spectra of diamond anvils from the UV to near-infrared (220–950 nm) range with increasing pressure. Two complementary setups were used: one using the SOLEIL synchrotron as a UV source, and the other one using a supercontinuum laser (see Supplementary Fig. 2). Experiments were performed using different anvil shapes oriented with the [100] diamond axis on the compression direction, beveled and toroidal geometries, and all diamond anvils were electronic-grade type IIas, so as to minimize any influence of impurities. All DACs were loaded with a neon sample, as solid neon remains a wide bandgap insulator into the TPa range24 so any absorption from the Ne sample could be neglected. The evolution of the observed diamond absorption edge from ambient pressure to over 500 GPa is shown in Fig. 1B–D, corresponding to three independent runs, each targeting a different pressure range with specific anvils. A continuous redshift of the absorption edge is observed. This shift is quantified in Fig. 1E, which reports optical density thresholds of 1 and 2 under pressure. This evolution was found reversible with pressure cycling and reproducible across different runs (see Supplementary Fig. 11). While absorption spectroscopy is a well-established technique for determining the bandgap of a semiconductor, its use in the present case is more complex. The absorption of light is not measured through a homogeneous sample, but rather along the entire axis of the diamond anvils, where the tensorial stress continuously evolves from ambient hydrostatic pressure to the maximum pressure at the sample interface, accompanied by a large elastic tetragonal distortion of the diamond lattice. Understanding this internal stress distribution is therefore essential for accurately interpreting the absorption data.

Stress state in the diamond anvil tip inferred from Raman measurements
Under [100] axial pressure loading, only the diamond Raman singlet LO mode is observed in back-scattering geometry. The shift of this phonon mode, derived from the Raman edge spectra, has been calibrated as a pressure gauge for multi-megabar pressures16. Above 300 GPa, the calibration validity could be questioned, as it relies on an inaccurate equation of state (EOS) of platinum17. A recent calibration resolved this issue and aligns well with the extrapolation of the calibration made up to 300 GPa18. Also, a key finding of that study is the robustness of the diamond edge scale to variation in the load distribution and to operation with diamond anvils of different shapes. In the present work, we conducted a similar calibration using gold samples as the X-ray pressure standard. Measurements of the phonon edge frequency versus pressure, conducted with both toroidal and beveled anvils, follow a single curve (Fig. 2), confirming the universal applicability of the Raman diamond edge scale. Furthermore, the fit shows excellent agreement with the recent calibration. Minor discrepancies are attributed to differences in the gold EOS since we updated the gold EOS to align with the IPPS-Ruby2020 scale25 (see Supplementary Fig. 7). The Raman phonon was also measured under hydrostatic compression of diamond, in which case the triply degenerate LO-TO mode is observed, there by extending previous data to 200 GPa. The difference in Raman frequency between the hydrostatic and the anvil-tip cases arises from anisotropic stress in the latter. Stress normal to the diamond surface at the anvil culet center can be taken as the sample pressure, Ps, and the stress tensor assumed to have axial symmetry with a perpendicular proportional component δPs. Raman data were used to reconstruct the stress state at diamond tip using recent ab initio calculations of the diamond Raman frequencies under non-hydrostatic stress26. Notably, it is found that the deviatoric stress parameter δ remains nearly constant under pressure, around 0.68. Linear elasticity calculations predicts δ = 0.6127, while NV centers measurements determined δ = 0.57 to be constant up to at least 70 GPa2. In the case of [111]-oriented anvils, the splitting of LO/TO phonon modes can be measured by Raman spectroscopy and the deviatoric ratio can be estimated, as reported up to 220 GPa28. In this configuration, the deviatoric ratio was found to remain constant at 0.56 up to about 100 GPa, in very good agreement with NV measurements under [100] loading. Above 100 GPa, it may gradually increase with a weak pressure dependence, reaching only 0.63 at 220 GPa. These independent estimates, summarized in Fig. 2B, give further confidence that δ can be considered constant with sample pressure, about 0.6 ± 0.05 in our analysis. The axial pressure distribution along the diamond anvil axis was mapped using confocal Raman spectroscopy. As shown in Fig. 2C, the observed pressure evolution along the compression axis is well reproduced by a simplified elasticity model of a semi-infinite anvil with uniform pressure applied to a circular flat face29. A notable feature of this pressure evolution is the presence of a region with nearly constant pressure extending a few microns below the culet surface, followed by a quasi-exponential pressure decrease with increasing depth. The thickness of this uniform slab is mostly determined by the diameter of the loaded region, i.e., the anvil culet (see “Methods”). Recently, the pressure distribution within a diamond anvil was studied using spatially-resolved inelastic X-ray scattering, however only a monotonous pressure decay was observed, and the constant stress layer could not be resolved30. Still, this study confirmed the fast pressure decay within the anvil thickness, supporting the idea that the absorption edge of stressed anvils along their axis should be dominated by the high pressure layer close to the tips.

Our Raman study thus supports the existence of a homogeneous, tetragonally distorted diamond slab—several microns thick—located at the center of the anvil tip/sample interface, where the axial pressure distribution within the anvil reaches its maximum and the deviatoric stress parameter remains constant up to the highest pressures reached. This configuration is favorable for extracting the pressure dependence of the bandgap in the tetragonally distorted diamond from absorption data.

Determination of the indirect bandgap energy from absorption data
One of the most fundamental properties affecting the optical behavior of diamond is the bandgap describing the energy barrier between conduction and valence bands. Absorption measurements were first used in the 1960’s to determine the energy value of the indirect bandgap in diamond, found to be 5.47 eV under ambient conditions31. Redshift and blueshift of this bandgap were also measured by absorption, under increasing temperature32 and pressure22,23,33. For diamond, optical absorption spectroscopy primarily probes the indirect bandgap, with indirect inter-band transitions assisted by phonons dominating the absorption process near the threshold. As a result, the absorption coefficient above the absorption threshold is described as being proportional to (hν ± Eph − Eg)2, where hν is the photon energy, Eph is the phonon energy and Eg is the indirect bandgap energy. The ± Eph accounts for phonon absorption and emission processes, both of which occur at 300 K. Using the LO phonon energy as given in Fig. 2, the phonon contribution is estimated to be at most 0.25 eV in the 300 GPa range. In our analysis, we neglect this contribution, as the induced error falls within the uncertainty of the current bandgap determination. In Fig. 3A, we apply the standard method for extracting the indirect bandgap value from the absorption threshold by plotting A1/2 versus hν, where A is the absorbance defined as −log(I/I0). A clear linear region at the threshold is observed, consistent with previous absorption studies, and the indirect bandgap Eg is thus determined from the x-intercept of this linear region. These results can be explained within our stress model by the presence of a homogeneous diamond slab—located at the diamond–sample interface—that dominates the absorption threshold. Indeed, the measured absorption spectra are well reproduced by the model (discussed further in “Methods”) that incorporates the stress distribution in the diamond anvil tip, consistent with Raman measurements. This agreement is illustrated in Fig. 3B, where the absorbance spectra calculated at 80 GPa and 328 GPa closely match observations.

This analysis proves effective for beveled anvils, while in the case of toroidal anvils the absorption threshold appears more broadened in energy. This likely indicates that the homogeneous layer at maximum pressure at the sample interface is not sufficiently thick to dominate the absorption threshold in this geometry. Nevertheless, the evolution of the OD=1 threshold with pressure—which tracks the minimum bandgap, albeit shifted in pressure—agrees between beveled and toroidal anvils (see Fig. 3C). This consistency supports a universal evolution of diamond anvil minimal bandgap, that is independent of tip geometry similarly to the behavior observed for the diamond Raman edge scale.

At the diamond anvil’s tip, the bandgap decreases with pressure, as expected for diamond subjected to tetragonal distortion under anisotropic stress. Considering that this evolution occurs under a quasi-constant deviatoric stress parameter δ = 0.6 ± 0.05, the average pressure in the maximally distorted diamond slab is given by P = Ps(1 + 2δ)/3, Ps being the quasi-hydrostatic sample pressure in contact with the diamond anvil. The measured evolution of the indirect bandgap is converted to a density dependence, within our anisotropic stress model, using diamond’s EOS (IPPS-Ruby202025 recommended values, see “Methods”) and the mean pressure, as shown in Fig. 3C. A linear relationship between the indirect bandgap and density is observed. Extrapolation of this trend suggests that the indirect bandgap would close at an estimated density of 5.41 ± 0.05 g/cm3, corresponding to a sample pressure of about 555 ± 6 GPa. Sample pressures about 600 GPa have been reported using toroidal anvils6 and diamond was not observed to lose its strength, even though metallization may have occurred in the thin diamond layer in contact with the sample.

Spectroscopic limitations illustrated in the search for metallic hydrogen
Up to now, only light absorption and scattering techniques have been implemented to probe the properties of matter in the DAC above 400 GPa. The primary diagnostics rely on high-brilliance hard X-ray beams (>15 keV) produced at large-scale facilities34. The X-ray transparency of the diamond anvils is not affected by the closure of their indirect bandgap, and measurements in the TPa range should be performed similarly to those at a few GPa, especially since X-ray beams can now be focused to sub-micron spots. In our case, X-ray diffraction of the Ne sample and the Re gasket was used on our highest pressure run to determine the sample pressure at 523 ± 13 GPa (Supplementary Fig. 12), at which point Raman edge determination was no longer possible due to diamond absorption. This pressure measurement aligns well with the evolution of sample pressure versus applied force on the piston (Supplementary Fig. 9). Additionally, X-ray absorption mapping across the sample clearly reveals the positions of the gasket and Ne sample (Fig. 4) and enables measurement of the thickness profile across the sample chamber. Unfortunately, X-ray diffraction on hydrogen samples remains extremely challenging, and the maximum achieved pressure—about 250 GPa—is still well below the predicted metallization pressure35.

In laboratory high-pressure experiments, Raman scattering and optical absorption are the two most widely used optical spectroscopy techniques. Both are affected by pressure-evolution of the indirect bandgap, which governs the transparency of diamond. The measured changes in diamond anvil transparency with pressure define three pressure-energy regimes (as shown in Fig. 4): one in which optical measurements are unaffected, one where they are partially perturbed between the indirect bandgap and an optical density threshold of 2, and one where measurements become impossible. This evolution of transparency with pressure applies similarly to measurements in reflection, due to the dual light path through one anvil in this configuration. This classification is exemplified in the present Ne measurements. Above 480 GPa, the Ne sample becomes completely obscured by the anvils (Fig. 4C), marking the onset of the opaque-anvil regime in the visible spectrum. However, the sample remains observable in the infrared using wavelengths around 1900 nm, which is only slightly absorbed even at 520 GPa. Conversely, Raman diamond edge measurements become infeasible above 480 GPa (Supplementary Fig. 10), as the 660 nm excitation line we used reaches the OD=2 threshold. Pressures beyond this point were extrapolated from the pressure vs load curve (Supplementary Fig. 9) and subsequently validated by X-ray diffraction, as mentioned previously.

The observation of metallic hydrogen has recently been reported by two groups. Both used the Raman pressure scale of ref. 16, which differs only slightly from the present updated calibration, thereby supporting the accuracy of their reported pressures. The first group employed infrared absorption and reported a probable transition to the molecular metallic state at 425 GPa for hydrogen12 and 460 GPa for deuterium13. As shown in Fig. 4, these infrared measurements fall within the transparent diamond anvil regime and thus do not require reevaluation. The second group claimed the observation of atomic metallic hydrogen at 495 GPa14, based on visual inspection in the visible range and reflectance measurements at four wavelengths (three visible and one near-infrared). However, as shown in Fig. 4, both visual observation and reflectance in the visible fall deep within the opaque anvil regime at this claimed pressure. Only the near-infrared reflectance point could remain accessible, though still significantly affected by anvil absorption. This inconsistency with the now well-established pressure-dependent transparency of diamond anvils raises serious doubts about the validity of the claim and quantitatively reinforces earlier criticisms36,37. As such, the observation of atomic metallic hydrogen remains an open and unresolved challenge.

Methods
DAC sample preparation
High pressure was generated using Le Toullec-type membrane DACs equipped with Boehler-Almax type IIas synthetic diamond anvils obtained from Almax easyLab. Beveled and toroidal anvil shapes were used, as indicated in Supplementary Information Tables 1 and 2. The toroidal shape was machined by focused ion beam machining. The central flat diameter, groove and depth are 24 μm, 80 μm and 4.6 μm, respectively. Rhenium gaskets were used. The neon sample was loaded in the DACs under a pressure of 140 MPa. The sample pressure versus the membrane pressure follows the typical S curve, as illustrated for the highest pressure run in Supplementary Fig. 9. The conversion between the membrane pressure, Pm, and the force on the piston, F, amounts to F [kN] = 0.05 × Pm [bar].

Effective diamond anvil EOS
Quantitative analysis of the optical behavior of diamond anvils with increasing pressure seems to be well linearized by expressing quantities relative to diamond density. However, the non-hydrostatic nature of the stress field at the diamond anvil tip implies that the relationship between DAC sample pressure and the relevant diamond density is not simply the hydrostatic diamond EOS. To account for this effect, we derived an effective EOS for the diamond at the tip of the diamond anvil from the community-standard IPPS-Ruby2020 hydrostatic diamond EOS25 combined with a our model of stress anisotropy. This modified EOS, illustrated in Supplementary Fig. 5, is computed from the 25 Vinet EOS with parameters V0 = 3.4178 cm3/mol, K0 = 443.3 GPa, K0' = 3.7, corrected considering that the actual average pressure on the anvil tip is P = Ps(1 + 2δ)/3 with δ = 0.6, Ps being the sample pressure. The resulting effective EOS can also be fitted to a Vinet form with parameters K0 = 604.5 GPa, K0' = 3.7.

Anvil absorption model
The intrinsic absorption of the diamond anvils can be approached by a simple model combining different parts of the known behavior of stressed diamond. Qualitatively, the optical path through a loaded diamond anvil is a straight line through a diamond single crystal under a complex stress field. This stress is maximum at the anvil culet, where the normal stress is assumed to be equal to the quasi-hydrostatic pressure within the sample Ps, by continuity. Then it decays through the thickness of the anvil towards its back-face, where the stress is minimal and very close to zero. Along this optical path, light traverses compressed diamond with a pressure gradient, and is progressively absorbed in a spectrally non-uniform way.

To model this effect, we need to combine estimates for three parameters. First, the stress tensor as a function of depth within the stressed anvil σ(z). Then, an estimate of the local bandgap evolution with said stress Eg(σ). Finally, we need a simple model of the spectral shape of the absorption profile of diamond for a given bandgap value α(E, Eg). These estimates are visually shown in Supplementary Fig. 6. Putting together all of these parameters will confirm that in the case of stressed diamond anvils, the resulting absorption edge at the lowest energy is dominated by the behavior of the thin surface layer at the anvil tip that is submitted to the highest stress, acting like a quasi-uniform slab with an indirect bandgap varying with pressure.

Regarding the stress tensor evolution within the depth of the loaded anvil, this is a complex problem that has been approached many times in past studies. However, we believe that for the purpose of this work, we can apply a simple elasticity model from ref. 29, which has also previously been used in the work of ref. 27. Considering a semi-infinite anvil with applied load q on a disk of radius a, the normal stress field as a function of depth z can be derived as:
σ(z) = q [1 − z3 / (a2 + z2)3/2] (1)
In our case, we will consider that load is equal to the hydrostatic pressure at the sample interface q = Ps, applied over the area of the disk formed by the culet of the anvil. This gives rise to a stress profile that decays with depth z relative to the the anvil surface, after a small slab of quasi-uniform stress. Notably, this profile does not depend on the elastic properties of the material considered, and the characteristic dimensions of the resulting profile are determined by the disk radius, or culet size in our case. This model may at first seem like an oversimplification, but comparison to our spatially resolved diamond Raman measurements show that it allow a very satisfactory description of physical reality when combined to the usual description of Raman frequency with normal stress16 (see Fig. 2C), while introducing a minimal number of parameters. The question of transverse stress is much more complex, as it more heavily relies on the elastic properties of diamond, and on the particular massive support geometry of the anvil-gasket assembly. However, following the successful reproduction of the maximum-Raman-signal frequency with anvil depth that we obtained when using 16, we will assume for simplicity that the deviatoric fraction of stress within the anvil is constant, taken as the value measured at the anvil tip.

For the spectral shape of the local absorption edge at a given depth (and thus local stress value), we will simply assume a standard indirect bandgap energy dependence of the absorption coefficient α(E, Eg), of the form:
α(E, Eg) = { 0 for E < Eg
{ C(E − Eg)2 for E ≥ Eg (2)
where E is the photon energy, and C is a constant giving the steepness of the absorption edge. Note that we only consider here the absorption due to the diamond’s indirect bandgap (no higher energy contribution from the direct gap), and that absorption coefficient values will be limited to a saturation maximum value αmax to avoid nonphysical divergences of the quadratic edge (this value only matters for the description of the high energy-high absorbance regime that we are not considering here for the determination of the lowest bandgap).

The bandgap evolution with normal stress will be adjusted to our experimental observation, and taken to be linear in diamond density. Note that the conclusion that the shape of the total absorption edge is consistent with a simple indirect bandgap is essentially independent of the exact shape of Eg(σ), as long as it is monotonously decreasing.

Bringing all of these assumptions together, one can estimate the total anvil absorption profile from the following reasoning. At a given sample pressure, we estimate the stress profile within the anvil from Ps and culet radius a. At each depth, we estimate the local absorption coefficient as a function of local gap value, and photon energy. Finally, we numerically sum the contribution throughout the anvil thickness to get an integrated absorbance profile A(Ps, E, a) = ∫ α(z, Ps, a, E) dz. Results of this procedure are shown in Supplementary Fig. 6.

Applying parameters relevant to our experimental conditions, the resulting profiles do confirm our observations. In spite of the significant pressure gradient within the bulk of the anvil, the behavior of the absorption profile at low energy is dominated by the absorption of a slab of quasi-uniformly stressed diamond.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Dear Editor,\nThe authors present a challenging absorption spectroscopy investigation of the optical band-gap of diamond anvils as a function of pressure, up to 520 GPa and in the IR-UV spectral range. It is shown a pronounced loss of transparency upon increasing pressure with an inferred metallization (band-gap closure) at about 560 GPa. Very importantly, this behaviour is shown to be dominated by the fact that a micron-size slab of the anvil at the sample interface is tetragonally distorted, and it is so for different anvil geometries: beveled and toroidal. The authors also refine the Raman edge pressure scale and show that it too is universal, i.e. independent of the anvil geometry. The study is of crucial importance for the spectroscopic investigation of metallization of materials in the multi-Mbar regime and, particularly, for hydrogen. To my opinion the study is compelling, timing, and robust and I recommend its publication on Nature Communications after some minor issues are resolved.\n1. On page 4 and figure 2, the authors discuss Raman phonon measurements of diamond under hydrostatic compression. The figure shows pressure shift of the diamond phonon frequency. Could the authors also provide some spectra for these measurements and specify the compression medium?\n2. At page 7: “In our case,…the sample pressure at 523 ± 13 GPa (Fig. 2),…”. I do not see data at this pressure in figure 2.\n3. In figure 1, there is a data gap between approximately 160 GPa and 280 GPa. What is the reason? Please comment on the article.\n4. In figure 1, panel B, I see absorbance peaks at wavelengths below 250 nm, for the lowest pressures. Similar peaks at high photon energies also appear in Extended Data, figures 1 and 2. I presume these peaks are artifacts related to absorption saturation rather than true maxima. Isn’t that the case?\n5. In the caption of figure 2, could the authors specify also “ 0” in the P-   relationship for the diamond Raman edge?\n6. There are some inconsistencies between the absorbance A reported in figure 1 and square root of A seen in figure 3. For instance, the maximum value of sqrtA at 146 GPa is equal to about 1.9 (fig. 3, panel A), which leads to a maximum in A of 3.6, whereas all absorbance values are cut well below 3.0 in figure 1, panel B.\n7. In figure 3, it would be good to specify which data are measured using beveled or toroidal diamonds, either in the caption or through labels.\n8. In figure 4, panel A, I presume “m” for m-H and so on means metallic. Please, specify.\n9. In the methods, I think it would be helpful to show a schematic cross-sectional figure of toroidal diamonds, for the benefit of the reader.\n10. Equation 1 for the normal stress. I think a minus sign should be applied to the right-hand side to be consistent with Extended Data figure 4, panel A.\n11. In the caption of Extended Data Fig. 6: “Coupled Raman spectroscopy…”, the second “(B)” should be a “(C)”.", "reviewer_2": "This paper reports on the diamond band gap closure under non-hydrostatic stresses up to pressures of 520 GPa that has implications for researchers performing spectroscopic measurements at high pressures including claims of metallic hydrogen that have appeared periodically in the literature. The paper reports on absorption studies on a variety of diamond geometrical configurations under high pressures including beveled anvils as well as recently developed toroidal diamonds. The studies reported are exhaustive and have some technical relevance. However, scientific impact of this study is debatable as it has been known since the 1990s that diamonds do change colors under non-hydrostatic stresses and appear dark red in reflection around 300-400 GPa through a metallic gasket indicating bandgap approaching infrared frequencies (Ref.19-20).\nThere are several additional comments regarding this submission that need attention.\n(1) Fig. 1 A needs a scale to indicate dimensions of the sample assembly, and it is not clear what the dark region near the middle of the cell in the neon medium. Is that a pressure marker, toroidal culet outline, or some other sample that needs to be clarified. Also, the orange/dark region at 307 GPa appears to at the edge of the sample hole. It should be pointed out that the biaxial state of stress with a fixed delta = 0.6 assumed throughout this paper is true only near the center of diamond anvil and that could complicate the interpretation of the absorption spectra presented in this work.\n(2) It appears that “diamond edge pressure calibration” in Figure 2 A has been carried out to 420 GPa. This is likely due to the absorption by diamond of the 600 nm laser used for Raman excitation. Any claims of pressures higher than 420 should be substantiated with x-ray diffraction included of the appropriate pressure standards.\n(3) The experimental data in Figure 4 suggests band gap closure to near 600 GPa. In the introduction, it is stated that diamond anvils have reached pressures of 1000 GPa (Ref.7). These two statements are in contradiction as it is highly unlikely that metallic diamond would be able to support largely shear stresses as is known for its covalently bonded state. Therefore, claims of 1000 GPa are questionable and have not been reproduced by other researchers in the field. It is important to present a realistic assessment of what is possible in future studies for a broad audience of Nature communications.\n(4) The idea of infrared reflectivity for future experiments on hydrogen is interesting. It may be worthwhile also providing an analysis of extensive cupping of the diamond anvil and what effect that may have on the reflectivity measurements.", "reviewer_3": "The manuscript describes the results of broadband absorption measurements over a wide range of electromagnetic radiation (from ultraviolet to infrared wavelengths) in diamond anvils at pressures exceeding 500 GPa, which reveal a pronounced loss of transparency with pressure. At pressures up to ~200 GPa, beveled anvils were employed, and above that — toroidal ones. The authors claim that they have documented the closing of the band gap in diamond under uniaxial stress, quantified the effect, and expect metallization of the anvils above ~560 GPa. The experiments appear carefully performed, the reproducibility of the results is well demonstrated, and the text is clearly written.\nHowever, there are several major problems with accepting the authors’ results and conclusions. The most important points are outlined below.\n1. Effect of compressed medium (Ne):\nIn all experiments, neon was used as the pressure-transmitting medium. While both theoretical and experimental works (including those considered here) suggest that diamond under stress changes its structural, vibrational, and electronic properties, an appropriate discussion of similar effects in neon is missing. One cannot a priori be sure that the enormous uniaxial stresses in the TPa pressure range do not affect the absorption of Ne. If comparable experiments using He or Ar, for example, resulted in the same absorption effects as those observed with Ne, the influence of the compressed medium could be excluded.\n2. Anvil deformation and optical effects:\nEven at moderate pressures, diamond anvil tips are known to deform (“cupping”), forming a concave lens. Above ~300 GPa, such shape changes become severe: light may refract, reflect, and scatter within the tip and surrounding diamond. These effects are not considered by the authors at all, and therefore it is unclear whether the observed loss of transparency is caused by changes in the electronic structure of the stressed anvil or by its mechanical deformation. In fact, there is a clear indication that the authors’ interpretation is not correct, or at least not complete. In Figure 1a changes in anvil transparency are visible not only at the point of maximum pressure (in the middle), but also over a much larger area at moderate pressures. It is well known that in toroidal anvils, pressure typically drops by a factor of 2–3 away from the central region, and at pressures of 2–2.5 Mbar rhenium behaves as a normal metal, reflecting light strongly. Where Re had to be observed, we do not see it. Thus, what is shown in Fig. 1a is not related to changes in electronic properties of diamond.\n3. Incorrect assumption of tetragonal distortion:\nThe assumption that anvil distortion is simply tetragonal is not correct even at moderate pressures, and certainly invalid at multi-megabar pressures. Even if one assumes purely elastic deformation and stress along the [100] direction, additional stresses from the gasket acting on the bevel and pavilion reduce the symmetry below tetragonal. In the toroidal case, the situation is even more complex. At sufficiently high pressures —above several hundred GPa certainly — the anvil undergoes plastic deformation, so purely elastic considerations no longer apply. If certain observations of anvil behavior (for example, Fig. 2c) can be described under the assumption of tetragonal stress, this means either (i) the stress/pressure is not sufficiently high (in Fig. 2c it is ~76 GPa, that is incomparable with ~500 GPa of interest here), (ii) the methodology is not sensitive to the symmetry and type of distortion, or (iii) the agreement between observation and model is coincidental.\n4. Figure 1a and presentation issues:\nAs the manuscript is, in my opinion, not ready for publication and must be substantially revised before further consideration, a detailed analysis of technical deficiencies would be premature. However, I would like to comment on Figure 1a, which is crucial for the entire presentation. It is not clear what is shown in this figure. What are the darker areas within the transparent toroidal part? Why is one circular and another irregular in shape? Where is the scale for these photos? How are the photographs related to the spectra shown in the same figure?\nTo summarize:\nThe amount of work performed by the authors and the complexity of the experiments are impressive. The implications for attempts to “see” hydrogen metallization using beveled, toroidal, and probably double-stage anvils are obvious — and the prospects, unfortunately, appear grim. This outcome is important for the high-pressure and, to some extent, solid-state physics communities, and should be published in a specialized physics journal. Metallization of diamond due to deformation requires real experimental investigation, probably accompanied by careful theoretical analysis."}, "author_response": "Response to referees\nThis document provides point-by-point responses to the comments from the reviewers. Initial\ncomments are reported verbatim in blue color, our responses in black. Red text is added to specify\nmodifications made tothe revisedsubmittedmanuscript.\nPlease find attached a revised version of our manuscript, together with a version explicitly showing\nthe modifications made.\nReviewer#1(Remarks tothe Author):\nDearEditor,\nThe authors present a challenging absorption spectroscopy investigation of the optical band-gap of\ndiamond anvils as a function of pressure, up to 520 GPa and in the IR-UV spectral range. It is\nshown a pronounced loss of transparency upon increasing pressure with an inferred metallization\n(band-gap closure) at about 560 GPa. Very importantly, this behaviour is shown to be dominated by\nthe fact that a micron-size slab of the anvil at the sample interface is tetragonally distorted, and it\nis so for different anvil geometries: beveled and toroidal. The authors also refine the Raman edge\npressure scale and show that it too is universal, i.e. independent of the anvil geometry. The study is\nof crucial importance for the spectroscopic investigation of metallization of materials in the multi-\nMbar regime and, particularly, for hydrogen. To my opinion the study is compelling, timing, and\nrobust and I recommend its publication on Nature Communications after some minor issues are\nresolved.\nWe thankthe referee forhis accurate summaryofourworkandhis positive assessment ofits\npotential impact.\n1. On page 4 and figure 2, the authors discuss Raman phonon measurements of diamond under\nhydrostatic compression. The figure shows pressure shift of the diamond phonon frequency. Could\nthe authors also provide some spectra for these measurements and specify the compression\nmedium?\nThese measurements were performed using Ne as a pressure transmitting medium. Typical Raman\nspectra recorded have been added to the supplementary material, together with a photograph of the\nsample.\n2. At page 7: “In our case,…the sample pressure at 523 ± 13 GPa (Fig. 2),…”. I do not see data at this pressure infigure 2.\nAs stated in the text, diamond Raman edge measurements cannot be performed at this pressure\nbecause the signal is obstructed by the diamond’s opacity. However, at 523 GPa, the DAC was\nbrought to ESRF and the pressure measured by the XRD volume of Ne and Re. The reference to\nFig. 2 is here a mistake. The correct reference is to Ext. Data Fig. 10, which shows XRD data\njustifyingthe claimedachievedpressure of523GPa. This has beencorrectedinthe manuscript.\n3. In figure 1, there is a data gap between approximately 160 GPa and 280 GPa. What is the reason?\nPlease comment onthe article.\nThis apparent gap in the probed experimental pressures is due to experimental constraints. First,\n70µm diamond culets were used in front of the synchrotron beamline UV light source to ensure the\nsample had a sufficient diameter. (Note that the coupling of the DAC to this UV beamline still\nrequires optimization in order to measure samples with smaller diameters.) The maximum pressure\nreachedinthese experiments was 160GPa.\nFor experiments at higher pressures, a supercontinuum laser light source, providing visible to near-\nIR spectroscopy, was used in our laboratory. This source offers a significant light output across the\n450nm to 1000nm wavelength range, as shown in Extended Data Fig. 1, panels B and C. Within\nthis wavelength range, no diamond absorption significant enough for a proper fit of the bandgap\nedge was observedforpressures below 280GPa.\nThe data gap between 160 GPa and 280 GPa is thus due to the difference between the highest\npressure achieved in our UV experiment, and the lowest pressure at which absorbance could be\ndetected on our setup for the visible experiments. A sentence relative to this point has been added in\nthe legendoffigure 1.\n4. In figure 1, panel B, I see absorbance peaks at wavelengths below 250 nm, for the lowest\npressures. Similar peaks at high photon energies also appear in Extended Data, figures 1 and 2. I\npresume these peaks are artifacts related to absorption saturation rather than true maxima. Isn’t that\nthe case?\nThis analysis is correct. The apparent absorbance maxima observed, particularly at low wavelengths\n(high energies), are artifacts resulting from absorbance saturation. This occurs because the input\nspectrum used for absorbance measurements through the DAC is not perfectly flat. As the light\nintensity decreases toward the edges of the available spectrum, the maximum detectable absorbance\nalso decreases, creating an apparent saturation envelope in the absorbance curves. However, this\neffect does not interfere with our estimations of the diamond anvils' bandgap, as these estimations\nare basedonfits tothe low-absorbance/low frequencyregionofeachcurve.\n5. In the caption of figure 2, could the authors specify also “nu0” in the P relationship for the\ndiamondRamanedge?\nThis omissionhas beenfixedinthe captionofFig.2.\n6. There are some inconsistencies between the absorbance A reported in figure 1 and square root of\nA seen in figure 3. For instance, the maximum value of sqrtA at 146 GPa is equal to about 1.9 (fig.\n3, panel A), which leads to a maximum in A of 3.6, whereas all absorbance values are cut well\nbelow 3.0infigure 1,panel B.\nAs shown in the uncropped absorbance data in Extended Data Fig. 1A, this apparent inconsistency\narises solely from the way the data were cropped for clarity in Fig. 1. The uncropped absorbance\nmeasured at 146 GPa indeed reaches a maximum value of approximately 3.6, consistent with the\nreported value of 1.9 for √A. We cropped the absorbance curves in Fig. 1 to avoid confusion caused\nby the saturation effect discussed earlier (point 4). However, the raw data are correctly presented in\nExtended Data Fig. 1. We apologize for this minor misunderstanding and have adjusted the\ncroppingofthe absorbance curves inFig.1tominimize anypotential confusion.\n7. In figure 3, it would be good to specify which data are measured using beveled or toroidal\ndiamonds,eitherinthe captionorthroughlabels.\nIndeed, we distinguished between beveled and toroidal anvils in Fig. 3C, following the same\nconvention used in the other figures: circular symbols for beveled anvils and triangular symbols for\ntoroidal ones. We have addedthis clarificationtothe captionofFig.3forimprovedclarity.\n8.Infigure 4,panel A,Ipresume “m” form-H andsoonmeans metallic.Please,specify.\nWe confirm “m” here stands for metallic as a short-hand to prevent clutter in the figure legend. We\nhave addedthis clarificationinthe captionofthis figure.\n9. In the methods, I think it would be helpful to show a schematic cross-sectional figure of toroidal\ndiamonds,forthe benefit ofthe reader.\nThis is an excellent suggestion. However, we believe the Methods section cannot contain figures\nandhave thus addedsucha figure tothe SupplementaryInformationsection.\n10. Equation 1 for the normal stress. I think a minus sign should be applied to the right-hand side to\nbe consistent withExtendedData figure 4,panel A.\nWe thankthe referee forpointingout this mistake. We have correctedEquation1accordingly.\n11. In the caption of Extended Data Fig. 6: “Coupled Raman spectroscopy…”, the second “(B)”\nshouldbe a “(C)”.\nWe again thank the referee for his/her careful examination of the manuscript. This correction was\nmade tothe captionofExtendedData Fig.6.\nReviewer#2(Remarks tothe Author):\nThis paper reports on the diamond band gap closure under non-hydrostatic stresses up to pressures\nof 520 GPa that has implications for researchers performing spectroscopic measurements at high\npressures including claims of metallic hydrogen that have appeared periodically in the literature.\nThe paper reports on absorption studies on a variety of diamond geometrical configurations under\nhigh pressures including beveled anvils as well as recently developed toroidal diamonds. The\nstudies reported are exhaustive and have some technical relevance. However, scientific impact of\nthis study is debatable as it has been known since the 1990s that diamonds do change colors under\nnon-hydrostatic stresses and appear dark red in reflection around 300-400 GPa through a metallic\ngasket indicatingbandgapapproachinginfraredfrequencies (Ref.19-20).\nWe agree with the referee that changes in the optical properties of diamond anvils under pressure in\nDAC experiments have been qualitatively known within the ultra-high-pressure community for\nmore than 30 years. Since then, this issue has been repeatedly highlighted as a concern for correctly\ninterpretingspectroscopic measurements inthe multi-megabarpressure range.\nIn the seminal studies cited (Refs. 19 and 20), a red shift of the absorption edge was already\ndiscussed in terms of the gradual closing of the indirect bandgap of the stressed diamond anvil tip.\nHowever, in those earlier works, a strong stress-induced photoluminescence was also observed,\nmaking it difficult to disentangle the intrinsic effects of diamond bandgap absorption. This strong\nfluorescence signal was attributed to the use of type Ia diamonds containing color-center impurities,\nas well as to color changes arising from possible plastic deformation of the anvil tip when pushed\nclose to its pressure limit. Such plastic deformation was, for example, clearly reported by M.\nEremets in AppliedPhysics Letters 87,141902(2005).\nOur study fully acknowledges the contributions of these earlier works. However, we believe that we\nhave achieved a significant advance. We have eliminated these parasitic effects by using ultra-pure\nsynthetic diamonds and by ensuring that the anvils operate strictly within their elastic deformation\nrange, thus avoiding plasticity-induced fluorescence. This has been made possible by employing\nultra-pure HPHT synthetic diamonds, as well as beveled and toroidal anvil designs that maintain\npurely elastic deformation under extreme load. The toroidal geometry, in particular, enables such\nelastic behaviorevenat the highest pressures.\nImportantly, the toroidal anvils are recovered at ambient pressure without any change in their\noptical properties, as clearly demonstrated by the recovered anvil after compression to 530 GPa (see\nSEM image below). The reversibility of the optical measurements upon compression and\ndecompression,showninExtendedData Fig.9,furtherconfirms the absence ofplastic deformation.\nWe feel that Reviewer 2 may have underestimated the scientific impact of our measurements and\nanalysis. Here, we present an unprecedented quantitative investigation of this phenomenon under\nideal conditions, reaching the highest pressures ever reported for optical spectroscopy in DACs. We\nreveal the evolution of the optimum transparency of diamond under the anvil-tip pressure\nconfiguration, demonstrating that it follows a universal behavior along the compression axis. The\nabsorption data are shown to follow the expected characteristics of an indirect bandgap,\ncorresponding to that of the diamond layer at the sample interface, subjected to a deviatoric stress\nwitha constant anisotropyof0.6.\nThis has allowed us, for the first time, to quantitatively, reproducibly, and reversibly measure the\nclosure of the diamond anvil bandgap under non-hydrostatic stress. We believe this represents an\nunprecedented and intrinsic characterization of the limit optical properties of diamond anvils under\nextreme conditions.\nSEM image ofthe diamondanvil recoveredfrom 520GPa.The FIB-machinedtoroidal shape is\nfullypreserved.\nThere are several additional comments regarding this submission that need attention.\n(1) Fig. 1 A needs a scale to indicate dimensions of the sample assembly, and it is not clear what the\ndark region near the middle of the cell in the neon medium. Is that a pressure marker, toroidal culet\noutline, or some other sample that needs to be clarified. Also, the orange/dark region at 307 GPa\nappears to at the edge of the sample hole. It should be pointed out that the biaxial state of stress with\na fixed delta = 0.6 assumed throughout this paper is true only near the center of diamond anvil and\nthat couldcomplicate the interpretationofthe absorptionspectra presentedinthis work.\nIt seems there has been a misunderstanding in the referee’s interpretation of the sample\nphotographs. The toroidal shape of the diamond tip modifies the usual appearance of a standard\nDAC sample. What the referee has identified as the neon sample is, in fact, the culet. The central\nbright area corresponds to the 24 µm culet of the toroidal diamond anvil, while the small grey circle\nnear its center is the gasket hole (approximately 4 µm in diameter) that contains the neon sample.\nThe dark spots on the upper-right edge of the culet correspond to Sm:SrB₄O₄ fluorescence pressure\ngauge particles, which were used as pressure markers during pre-indentation of the gasket. Since\nthese particles lie on the culet edge between the diamond and the gasket—clearly outside the\nsample hole—they did not affect the transmission measurements. The dark region surrounding the\nculet is causedbythe toroidal groove.\nWe acknowledge that the microphotographs shown in Fig. 1 may require additional explanation. To\nclarify the sample geometry, we provide below an explanatory figure, also now provided in the\nSupplementaryInformationofthe paper.\nWe fully agree that the fixed δ = 0.6 stress state assumed in our analysis is only valid at the center\nof the diamond culet. However, this is precisely where the gasket sample hole is located in our\nexperiment. Because our optical transmission measurements were performed through the sample\nhole at the anvil center, we are confident that the detected light rays predominantly traversed the\nanvils along the DAC’s central symmetry axis, where this assumption holds. We do not claim that\nour simplified model describes the optical properties of the entire anvil, where a more complex\nstress distribution must be considered. Rather, our measurements and modeling are restricted to the\nabsorptionbehavioralongthe anvils’central axis ofsymmetry.\n(2) It appears that “diamond edge pressure calibration” in Figure 2 A has been carried out to 420\nGPa. This is likely due to the absorption by diamond of the 600 nm laser used for Raman excitation.\nAny claims of pressures higher than 420 should be substantiated with x-ray diffraction included of\nthe appropriate pressure standards.\nThe 420 GPa limit in our Raman scale calibration arises solely from anvil failure in our dedicated\ncoupled Raman/XRD measurements. However, we have performed diamond Raman measurements\nup to approximately 480 GPa, beyond which we observed the clear disappearance of the high-\npressure diamond Raman edge due to increasing anvil absorbance (see Extended Data Fig. 8 for\nrepresentative data). We believe that the physically justified fit applied to our Raman calibration\ndata allows for an accurate extrapolation of pressure up to the highest value at which the diamond\nRaman edge could still be recorded—around 480 GPa in our case. As clarified in Extended Data\nFig. 7, pressures reported above this limit were linearly extrapolated from the load–pressure curve\nof this experiment, with final verification by X-ray diffraction (as suggested by the referee),\nconfirming the terminal pressure of 520 GPa within experimental uncertainty (see Extended Data\nFig.10).Hence validatingourdiamondedge pressure calibrationuptoits maximum pressure.\n(3) The experimental data in Figure 4 suggests band gap closure to near 600 GPa. In the\nintroduction, it is stated that diamond anvils have reached pressures of 1000 GPa (Ref.7). These two\nstatements are in contradiction as it is highly unlikely that metallic diamond would be able to\nsupport largely shear stresses as is known for its covalently bonded state. Therefore, claims of 1000\nGPa are questionable and have not been reproduced by other researchers in the field. It is important\nto present a realistic assessment of what is possible in future studies for a broad audience of Nature\ncommunications.\nThe point raised by the referee is not entirely correct. The only comparable ultra-high-pressure\nDAC experiments using toroidal-shaped diamond anvils that have reported pressures higher than\nthose presented here are the previous results from our group in Dewaele et al. (2018, Ref. 6). A\npressure of 600 GPa has been reported on gold, and this may correspond to the upper limit of what\nconventional anvils with a toroidal-shaped tip can withstand once surface metallization occurs.\nHowever,we cannot rule out at this stage that evenmore extreme pressures couldstill be achieved.\nIt is important to note that the significant stress gradient within the anvils implies that the region of\ndiamond experiencing the highest pressure is extremely thin. Consequently, catastrophic failure due\nto changes in diamond’s mechanical properties at metallization may not occur until much higher\nsample pressures, at which point a sufficient thickness of the diamond tip would be affected by\nmetallization,leadingtoa change inmechanical behavior.\nIt is important to note that claims of pressures exceeding 1000 GPa obtained in DACs (Ref. 7) were\nachieved using nano-polycrystalline diamond secondary anvils. Such anvils may exhibit both\ndistinct electronic behavior under stress and markedly different stress-anisotropy distributions\ncompared to those in our experiments. Therefore, we do not believe that our work should be used to\nassess the validityofthose claims.\n(4) The idea of infrared reflectivity for future experiments on hydrogen is interesting. It may be\nworthwhile also providing an analysis of extensive cupping of the diamond anvil and what effect that mayhave onthe reflectivitymeasurements.\nWe agree that IR reflectivity measurements must be performed with careful consideration of\npotential detrimental effects of cupping. This is a well-known issue for reflectivity measurements in\nDACs and has significantly hindered the development of high-pressure reflection spectroscopy\ndespite its strongscientific potential.\nWe have performed X-ray absorption measurements on the sample presented here, which reached\n520GPa, allowing us to estimate gasket-thickness profiles across the anvil culet and thus the\ncorresponding anvil surface deformation profiles. Such a profile is provided in Supplementary\nInformation Fig. 2B. As expected from the very small anvil-culet diameter and very thin gasket, the\nanvil surface cupping is relatively small for this type of anvil. Moreover, results from Dewaele et al.\n(2018) showed, based on similar measurements performed at multiple pressures during\ncompression, that culet cupping already occurs at pressures well below 3 Mbar and remains\nessentiallystable at higherpressures.\nWe therefore believe that, even if cupping might affect the absolute value of a reflectivity\nmeasurement in these extreme regimes, a relative reflectivity jump associated with hydrogen\nmetallization in the infrared (a jump from 0.5 to 0.9) should still significantly exceed uncertainties\narising from cupping changes across the transition. The reflectivity measurements will also be\ncalibrated on a Ne sample, which remains a large-bandgap insulator and whose refractive index\nshould reasonably follow a Gladstone–Dale relation up to very high pressure. Furthermore, the\ninfrared photograph of the culet at 520 GPa presented in Fig. 4D demonstrates that the cupping is\nsmall enough to yield a clear image of the culet, with a bright gasket and a much less reflecting Ne\nsample inthe IR.\nReviewer#3(Remarks tothe Author):\nThe manuscript describes the results of broadband absorption measurements over a wide range of\nelectromagnetic radiation (from ultraviolet to infrared wavelengths) in diamond anvils at pressures\nexceeding 500 GPa, which reveal a pronounced loss of transparency with pressure. At pressures up\nto ~200 GPa, beveled anvils were employed, and above that — toroidal ones. The authors claim\nthat they have documented the closing of the band gap in diamond under uniaxial stress, quantified\nthe effect, and expect metallization of the anvils above ~560 GPa. The experiments appear carefully\nperformed, the reproducibility of the results is well demonstrated, and the text is clearly written.\nHowever, there are several major problems with accepting the authors’ results and conclusions. The\nmost important points are outlinedbelow.\n1.Effect ofcompressedmedium (Ne):\nIn all experiments, neon was used as the pressure-transmitting medium. While both theoretical and\nexperimental works (including those considered here) suggest that diamond under stress changes its\nstructural, vibrational, and electronic properties, an appropriate discussion of similar effects in neon\nis missing. One cannot a priori be sure that the enormous uniaxial stresses in the TPa pressure range\ndo not affect the absorption of Ne. If comparable experiments using He or Ar, for example, resulted\nin the same absorption effects as those observed with Ne, the influence of the compressed medium\ncouldbe excluded.\nWe disagree. Changing to another rare-gas medium would be less satisfactory and would not\nprovide additional insight. Our choice of neon as the pressure-transmitting medium was primarily\nmotivated by its exceptionally large bandgap, which is expected to remain high even under extreme\ncompression (metallization has repeatedly been computed to occur only near 200 TPa under\nhydrostatic stress). Neon’s experimental bandgap is 21 eV at ambient pressure, and solid Ne is even\ncalculated to exhibit an unusual positive pressure dependence of the bandgap up to 1 TPa [Tang et\nal.,J.Chem.Phys.150,111103(2019)].\nWe also emphasize that neon is very likely the best pressure-transmitting medium in terms of\nhydrostaticity at multi-megabar pressures, as recently shown, for example, by Liang et al. [J. Phys.\nChem. C 128, 4839 (2024)]. Our own XRD measurements confirm that the deviatoric component of\nthe stress exerted on neon samples at ~500 GPa in the rhenium gasket hole was very small (example\ndata is provided in Extended Data Fig. 10). From the two detectable diffraction peaks—\ncorresponding to the (111) and (200) planes—the difference in observed d-spacing relative to an\nideal fcc structure was only 0.6%, corresponding to a lattice tetragonal distortion of merely ~2%.\nThis demonstrates that even under the extreme stress conditions of our experiments, compression of\nthe neon sample in the toroidal DAC remains quasi-hydrostatic, and its electronic properties should\ndeviate from theoretical predictions onlymarginally.\nTherefore, we consider it reasonable to attribute the absorption behavior observed in our loaded\nDACs with pure neon samples solely to anvil opacification under stress. For these reasons—\nnamely, its superior hydrostatic performance and its exceptionally large electronic bandgap—neon\nis indeedthe optimal medium forthese absorptionmeasurements.\n2.Anvil deformationandoptical effects:\nEven at moderate pressures, diamond anvil tips are known to deform (“cupping”), forming a\nconcave lens. Above ~300 GPa, such shape changes become severe: light may refract, reflect, and\nscatter within the tip and surrounding diamond. These effects are not considered by the authors at\nall, and therefore it is unclear whether the observed loss of transparency is caused by changes in the\nelectronic structure of the stressed anvil or by its mechanical deformation. In fact, there is a clear\nindication that the authors’ interpretation is not correct, or at least not complete. In Figure 1a\nchanges in anvil transparency are visible not only at the point of maximum pressure (in the middle),\nbut also over a much larger area at moderate pressures. It is well known that in toroidal anvils,\npressure typically drops by a factor of 2–3 away from the central region, and at pressures of 2–2.5\nMbar rhenium behaves as a normal metal, reflecting light strongly. Where Re had to be observed,\nwe do not see it. Thus, what is shown in Fig. 1a is not related to changes in electronic properties of\ndiamond.\nThe toroidal shape of the diamond tip modifies the usual appearance of a standard DAC sample. We\nbelieve that the referee’s interpretation of the visual changes to the anvil culets shown in Fig. 1\nlikelyresults from a misunderstandingofthe image due tothe use oftoroidal anvils.\nAs illustrated in the explanatory figure below, the central bright circular region in the images is\nindeed the entire culet of the toroidal anvil, which is in contact with the highly reflecting rhenium\ngasket. The apparent dark ring surrounding it arises from the slope of the toroidal groove on the\nFIB-machined anvil, where light is not reflected toward the objective. Pressure across the 24µm\ncentral culet is actually remarkably uniform, even at the highest pressures achieved, as shown in\nSupplementaryInformationFig.2A.\nCupping of this 24 µm culet does occur and was measured at the maximum pressure of 520 GPa by\nX-ray absorption (Supplementary Information Fig. 2B). However, the cupping angle is less than\n3.5 , which is not sufficient to cause significant distortion of the culet image. This explains why\nprogressive opacification occurs across the entire culet as pressure increases in the reflection\nimages. We therefore observe high reflectivity of the rhenium metal everywhere it is close to\nnormal incidence with respect to our visualization optics. In these regions, the appearance of\nprogressive coloration indicates that the diamond between the microscope objective and the\nrhenium gasket is undergoingchanges toits electronic/optical properties.\nThe discussion of changes in anvil transparency in reflection should thus focus solely on this nearly\nflat, 24 µm-diameter central culet region. The Ne sample itself is about 4 µm in diameter at the\ncenterofthe culet, as this is now indicatedinSupplementaryInformationFig.4.\nWe acknowledge that the microphotographs in Fig. 1 may require additional explanation. To clarify\nthe sample geometry, we included an explanatory figure in the Supplementary Information of the\npaper.\nRegarding the quantitative absorption measurements we present, these were performed in\ntransmission geometry along the DAC axis through the small central gasket hole containing the\nneon sample. This corresponds to the axis of revolution symmetry of the DAC, where the effects of\nanvil cupping and changes in the diamond refractive index are negligible for paraxial light rays.\nWhile cupping may indeed need to be considered for reflectivity measurements, it is clearly\nnegligible inourtransmissionmeasurements.\n3.Incorrect assumptionoftetragonal distortion:\nThe assumption that anvil distortion is simply tetragonal is not correct even at moderate pressures,\nand certainly invalid at multi-megabar pressures. Even if one assumes purely elastic deformation\nand stress along the [100] direction, additional stresses from the gasket acting on the bevel and\npavilion reduce the symmetry below tetragonal. In the toroidal case, the situation is even more\ncomplex. At sufficiently high pressures —above several hundred GPa certainly — the anvil\nundergoes plastic deformation, so purely elastic considerations no longer apply. If certain\nobservations of anvil behavior (for example, Fig. 2c) can be described under the assumption of\ntetragonal stress, this means either (i) the stress/pressure is not sufficiently high (in Fig. 2c it is ~76\nGPa, that is incomparable with ~500 GPa of interest here), (ii) the methodology is not sensitive to\nthe symmetry and type of distortion, or (iii) the agreement between observation and model is\ncoincidental.\nAgain, we have to disagree. The reviewer is correct in noting that the exact nature of anvil\ndistortion may not be purely tetragonal across the entire tip. However, our measurements are\nextracted at the center of the culet, where the paraxial approximation should hold. Symmetry\nconsiderations along the central axis of the revolution-symmetric DAC imply that distortion cannot\ntake on a more complex form along this particular line. For this reason, we limit our analysis to the\nbehaviorofthe diamondalongthis central axis,where suchsimplifyingassumptions are justified.\nFurthermore, we have strong evidence that the observed optical changes arise from modifications to\nthe electronic properties of the diamond anvils under elastic deformation, even at multi-megabar\npressures. First, we determined that the pressure-induced absorbance shift is not due to irreversible\nplastic deformation, as it is fully reversible upon decompression (see Extended Data Fig. 9). In\naddition, extensive evidence indicates that deformation of toroidal diamond anvils remains purely\nelastic: SEM imaging of recovered anvils after multi-megabar experiments shows that the FIB-\nmachined region of the anvil tip returns to its exact original shape and properties after unloading.\nThis is illustrated in the SEM image below of the recovered anvil from the 520 GPa experiment.\nAcross the dozens of runs performed by our group over the past ten years, we consistently observe\nthat—even in cases of apparent catastrophic anvil failure—the failure occurs tens or hundreds of\nmicrons awayfrom the culet center,outside the central FIB-machinedregiononthe bevel.\nSEM photoofa recoveredtoroidal anvil after520GPa compression.\n4.Figure 1a andpresentationissues:\nAs the manuscript is, in my opinion, not ready for publication and must be substantially revised\nbefore further consideration, a detailed analysis of technical deficiencies would be premature.\nHowever, I would like to comment on Figure 1a, which is crucial for the entire presentation. It is\nnot clear what is shown in this figure. What are the darker areas within the transparent toroidal part?\nWhy is one circular and another irregular in shape? Where is the scale for these photos? How are\nthe photographs relatedtothe spectra showninthe same figure?\nWe apologies if the content of Fig. 1a appears to be misleading. We realize that the observation of\nthe sample through a toroidal anvil can be somewhat misleading because few examples up to now\nhave been published in the literature. Fig.1A shows the microphotographs of the sample through the\ntoroidal diamond anvil culet in visible light reflection, in the experiment where optical absorbance\nmeasurements through a neon sample were measured up to about 520 GPa and are presented in Fig.\n1D. A more detailed description of microphotograph is now given in the Fig 1 caption: “The\ntoroidal shape of the diamond tip modifies the usual appearance of a standard DAC sample. The\ncentral bright area corresponds to the 24 µm culet of the toroidal diamond anvil, while the small\ngrey circle near its center is the gasket hole (approximately 4 µm in diameter) that contains the neon\nsample. The dark spots on the upper-right edge of the culet correspond to Sm:SrB₄O₄ fluorescence\npressure gauge particles, which were used as pressure markers during pre-indentation of the gasket.\nThe darkregionsurroundingthe culet is causedbythe toroidal groove.”\nAlso, a scale has been added to the photos of Fig. 1 for easier comprehension, together with a\nschematic of the sample assembly in the Supplementary Information section as suggested by\nanotherreferee.The Ne sample is clearlyindicated.\nTosummarize:\nThe amount of work performed by the authors and the complexity of the experiments are\nimpressive. The implications for attempts to “see” hydrogen metallization using beveled, toroidal,\nand probably double-stage anvils are obvious — and the prospects, unfortunately, appear grim. This\noutcome is important for the high-pressure and, to some extent, solid-state physics communities,\nand should be published in a specialized physics journal. Metallization of diamond due to\ndeformation requires real experimental investigation, probably accompanied by careful theoretical\nanalysis.\nWe thank the referee for his/her appreciation of our work and for recognizing the forefront\ncomplexity of the experiments. We hope that, in the above responses, we have satisfactorily\naddressedthe referee’s concerns regardingthe “technical deficiencies” ofthe present study.\nWe believe that clearly identifying the intrinsic limits of optical spectroscopy in DACs, as well as\ntheir implications for the possible observation of hydrogen metallization—and more broadly for the\nspectroscopic investigation of molecular systems and other compounds above 400 GPa—is an\nimportant contribution to the solid-state physics community. We also believe that this paper will\nserve as a reference for the interpretation of future extreme static-pressure studies. Finally, we are\nconfident in the correctness of our quantitative determination of the bandgap closing in diamond\nunder tetragonal distortion, up to almost its metallic state, and note that reporting the metallization\nofsimple molecularsystems has longbeenofgreat interest.\nFor these reasons, we respectfully disagree with the referee and believe that the present work\nwarrants publicationina broad,reputable journal suchas Nature Communications."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Dear Editor,\nthe authors have convincingly replied all my criticisms and have revised the paper accordingly. I think that referee’s #3 concerns on the possible role of Ne and of diamond cupping and structural distortions on the optical absorption were reasonable, in principle. On the other hand, in my opinion the authors have extensively and convincingly replied also to these criticisms. Shortly, they show that: (i) the Ne band-gap is very far from the investigated spectral region and so it is irrelevant, (ii) Ne is the best pressure-transmitting medium in terms of quasi-hydrostaticity, (iii) cupping and potential sub-tetragonal distortions within the diameter of the gasket hole (4 micron) are both negligible. In conclusions, I recommend publication of the revised manuscript on Nature Communications as is.", "reviewer_2": "The authors have made substantial efforts to improve the technical presentation of results and included optical micrographs to clarify the description of sample geometry. The claim of bandgap closure in diamond at 560 GPa is valid for a specific assumption of biaxial stress with a deviatoric stress parameter delta value of 0.6. I still have concerns about the universality of results reported in this manuscript as different diamond geometries with different stress state (non-biaxial stress state) will likely result in a different metallization condition for diamond. Therefore, the broader impact of this study in high pressure science may be limited.", "reviewer_3": "I am somewhat disappointed by the authors’ response to my questions and criticisms. I find their answers to be sophistic and lacking solid scientific arguments.\nMy first question concerned the possible effects of large stresses on the optical properties of Ne. Instead of engaging with my arguments, the authors simply state that Ne is the best pressure medium and support this claim by citing literature on compressed cubic Ne. However, if the authors argue (correctly) that stresses fundamentally alter the optical properties of diamond, it is unclear how they can exclude analogous effects in Ne.\nMy second question addressed anvil deformation and its optical consequences. First, the authors are fundamentally mistaken in discussing effects limited only to the tip of the toroidal anvil. Deformations propagate through the entire anvil and may be not strongest at the tip, and the light passes through the whole anvil. Second, Supplementary Information Figure 2B does not provide any direct measure of capping, and my own attempt to estimate anvil deformation from this figure yields a value of at least ~20°, in contrast to the 3.5° claimed by the authors. Third, Supplementary Information Figure 2B appears highly manipulative, as the region corresponding to Ne absorption is obscured by a green rectangular overlay.\nIn their response to my third question, the authors state: “Across the dozens of runs performed by our group over the past ten years, we consistently observe that—even in cases of apparent catastrophic anvil failure—the failure occurs tens or hundreds of microns away from the culet center.” This statement reinforces my concern: the main mechanical (and probably structural) changes occur not at the anvil tip but beneath the surface. These changes lead to elastic/plastic deformation, breaking the symmetry of the material and causing variations in optical properties. Consequently, optical measurements reflect the overall (“integrated”) properties of the anvil rather than those of a localized region.\nIn summary, I am convinced that the authors’ observations are real, but I have fundamental reservations about their interpretation and conclusions. It is up to the Editor to decide whether the empirical part of the work is sufficient for publication in Nature Communications. In the event of publication, I hope that my review will help readers adopt a more critical and sober view of the results."}, "author_response": "Response to referees\n1st revision\nThis document provides point-by-point responses to the comments from the reviewers. Initial\ncomments are reported verbatim in blue color, our responses in black. Red text is added to specify\nmodifications made tothe revisedsubmittedmanuscript.\nPlease find attached a revised version of our manuscript, together with a version explicitly showing\nthe modifications made.\nReviewer#1(Remarks tothe Author):\nThe authors have convincingly replied all my criticisms and have revised the paper accordingly. I\nthink that referee’s #3 concerns on the possible role of Ne and of diamond cupping and structural\ndistortions on the optical absorption were reasonable, in principle. On the other hand, in my opinion\nthe authors have extensively and convincingly replied also to these criticisms. Shortly, they show\nthat: (i) the Ne band-gap is very far from the investigated spectral region and so it is irrelevant, (ii)\nNe is the best pressure-transmitting medium in terms of quasi-hydrostaticity, (iii) cupping and\npotential sub-tetragonal distortions within the diameter of the gasket hole (4 micron) are both\nnegligible. In conclusions, I recommend publication of the revised manuscript on Nature\nCommunications as is.\nWe thankthe referee againforhis thoroughassessment ofourworkandsubsequent reply.\nReviewer#2(Remarks tothe Author):\nThe authors have made substantial efforts to improve the technical presentation of results and\nincluded optical micrographs to clarify the description of sample geometry. The claim of bandgap\nclosure in diamond at 560 GPa is valid for a specific assumption of biaxial stress with a deviatoric\nstress parameter delta value of 0.6. I still have concerns about the universality of results reported in\nthis manuscript as different diamond geometries with different stress state (non-biaxial stress state)\nwill likely result in a different metallization condition for diamond. Therefore, the broader impact of\nthis studyinhighpressure science maybe limited.\nWe thankthe referee forhis/heruseful suggestions,whichimprovedthe clarityofthe manuscript.\nOur claim of a universal behavior would indeed not extend to completely arbitrary anvil geometries\n(secondary spherical anvil stages, for example, are obviously very different). The validity of our\nwork applies to beveled and toroidal anvils, which are those most commonly used. We have also\nspecified the high purity of the anvils studied, since it is well known that impurities can alter\nabsorptionproperties.\nFurthermore, we believe that the universal diamond Raman scale—previously established and here\nconfirmed—for both beveled and toroidal diamond anvils with culet diameters ranging from several\nhundred microns down to about 20 µm, provides strong additional evidence that the stress\ndistribution at the anvil–sample interface along the anvil axis depends primarily on the sample\npressure rather than on the anvil geometry. Independent estimates of the pressure gradient within\nthe anvils, obtained via Raman spectroscopy (e.g., Hanfland and Syassen, Journal of Applied\nPhysics 57, no. 8 (1985), and our own work) or inelastic X-ray scattering (Lee et al., Science\nAdvances 9 (20), 2023), all agree that the maximum stress along the anvil central axis (which\ncorresponds toouroptical path)likelyoccurs close tothe diamondtip–sample interface.\nIn conclusion, we assert that our measurements and analysis are of broad impact since valid for\nbeveled and toroidal anvils, in the region near the anvil tip along the anvil axis, where the\nspectroscopic measurements are performed.\nReviewer#3(Remarks tothe Author):\nI am somewhat disappointed by the authors’ response to my questions and criticisms. I find their\nanswers tobe sophistic andlackingsolidscientific arguments.\nWe regret that our initial responses did not fully meet the referee’s expectations. We have carefully\nreformulatedthem andbelieve theynow address the concerns more satisfactorily.\nMy first question concerned the possible effects of large stresses on the optical properties of Ne.\nInstead of engaging with my arguments, the authors simply state that Ne is the best pressure\nmedium and support this claim by citing literature on compressed cubic Ne. However, if the authors\nargue (correctly) that stresses fundamentally alter the optical properties of diamond, it is unclear\nhow theycanexclude analogous effects inNe.\nOur statement regarding the optical properties of neon was not that stress has no effect.\nCompression—and even more so possible anisotropic stress—does affect optical properties. Our\npoint was instead to justify our choice of neon as a sample material because of its extremely large\nbandgap, which has been both computed and experimentally measured to be around 21 eV at low\npressure. An initial bandgap of such magnitude would require stresses orders of magnitude larger\nthan those considered in our study to produce any effect at the energy scales relevant to our work\n(below 6 eV). This is why we considered, as rightly remarked by Reviewer #1, that this issue is\nessentiallyirrelevant toouranalysis ofdiamondoptical properties.\nIn his initial comments, Reviewer #3 stated that “one cannot a priori be sure that the enormous\nuniaxial stresses in the TPa pressure range do not affect the absorption of Ne”. However, we have\nquantitatively shown by XRD that, even in our highest-pressure sample, neon does not exhibit\nsignatures of strong uniaxial stress, as explained in our initial round of replies. For a neon sample\ncompressed in a DAC, we have experimentally confirmed that the stress state is predominantly\nhydrostatic.\nTo further strengthen our claim that the optical properties of neon are not significantly modified by\nthe minor deviatoric stress we measured, we have now performed DFT calculations on solid fcc\nneon, as well as on a tetragonally distorted derivative lattice with c/a=0.98, consistent with our\nexperimental results. Calculations performed using the GGA-PBE functional within the ABINIT\npackage yielded the electronic band structures shown below. Our results confirm the positive\npressure dependence of the bandgap reported in the literature (see Tang et al., J. Chem. Phys. 150,\n111103 (2019)) and indicate a large bandgap of 24.62 eV at 520 GPa (noting that the GGA-PBE\nfunctional typically underestimates bandgaps). Applying the distortion corresponding to our\nmeasured XRD values leads to only a very small reduction of the bandgap, to 24.39 eV in the\nresulting I4/mmm cell, confirming that deviatoric stress has a negligible effect on this rare-gas\natomic solid.\nThese results further reinforce our confidence that the optical properties of solid neon compressed\nin a DAC in the 500 GPa pressure range cannot influence the present optical measurements, and\nthat the observed evolution of transparency is solely attributable to changes in the optical properties\nofdiamond.\nFigure: Electronic bandstructures calculatedforfcc neonat 520GPa,(a)underhydrostatic stress\nand(b)withlattice distortionmeasuredbyXRD.The minimal bangapenergyE is betweenthe G\ng\nandX point forthe cubic cell,andbetweenthe G andM point inthe distortedtetragonal structure.\nNonhydrostatic strainhas onlya verysmall effect,reducingthe bandgapfrom 24.62eV to\n24.39eV.\nMy second question addressed anvil deformation and its optical consequences. First, the authors are\nfundamentally mistaken in discussing effects limited only to the tip of the toroidal anvil.\nDeformations propagate through the entire anvil and may be not strongest at the tip, and the light\npasses throughthe whole anvil.\nWe must disagree. While the dominant contribution to the absorption edge indeed arises from the\nregion close to the tip of the toroidal anvil, in both the manuscript and our responses to the\nreviewer’s comments we have explicitly considered the behavior of the entire anvil along the\noptical light path. The question of optical behavior deeper within the anvil is entirely legitimate and\nhas in fact been a central part of our reasoning in claiming that we can accurately determine the\nminimum bandgapofthe stressedanvils,whichis the mainresult ofthis work.\nWe developed a detailed model of optical absorption along the full stressed central axis of the anvil,\nwithin clearly stated approximations. This model is described in the Methods section, illustrated in\nExtended Data Fig. 4, and its results are used in Fig. 3. The main conclusion of this model—\nsupported by Raman measurements as well as by inelastic X-ray scattering data (Lee et al., Science\nAdvances 9 (20), 2023)—is that the stress distribution along the central axis of the anvil is\ncharacterized by a very steep pressure gradient. As a result, the anvil regions that most strongly\naffect the absorptionedge are those locatedclose tothe anvil tip.\nIn addition, our elastic deformation model predicts the presence of a thin layer of nearly\nhomogeneous stress close to the anvil surface. The Raman measurements shown in Fig. 2C appear\nto corroborate this effect, at least at the pressure where this hypothesis was tested. This feature also\nprovides a physically motivated explanation for our observation that the lowest-energy absorbance\nprofiles are consistent with those expected for a uniform slab of material characterized by a single\nindirect bandgapvalue.\nSecond, Supplementary Information Figure 2B does not provide any direct measure of capping, and\nmy own attempt to estimate anvil deformation from this figure yields a value of at least ~20 , in\ncontrast tothe 3.5 claimedbythe authors.\nWe provide a more explicit determination of the cupping. Supplementary Information Fig. 2B\nprovides a direct measurement of the rhenium gasket thickness compressed between the two\nstressed anvils at a sample pressure of 523 GPa and therefore directly reflects the deformation\nprofile of the anvil tips. This is a well-established and commonly used experimental method to\ndemonstrate diamond anvil cupping (see, for example, Li et al., “Diamond Anvil Cell Behavior up\nto4Mbar,” Proceedings of the National Academy of Sciences 115,no.8(2018)).\nIn the figure below, we have taken the radial derivative of the rhenium thickness in order to extract\nthe cupping angle as a function of radius. The resulting angular profile is consistent with a\nspheroidal shape, with a maximum angle close to the edge and a minimum at the center, where the\nneon sample is located and where the optical absorption measurements are performed. We therefore\nmaintain that this cupping effect, which certainly remains below 5° in the middle, is entirely\nnegligible at the culet center,where the ~4µm neonsample resides.\nFigure: Plot ofthe computedabsolute value ofthe anvil surface angle across the 24µm culet ofa\nd𝑒\ntoroidal anvil at 523GPa sample pressure.The surface angle is derivedas 𝜃(𝑥) = 𝑎𝑟𝑐𝑡𝑎𝑛( ) where\nd𝑥\ne(x)is the gasket thickness profile as measuredbyx-rayabsorption.The blackdashedlines\nmaterialize the edges ofthe anvil central culet.The central greenshadedregionindicates the neon\nsample inthe gasket hole where computationresult is irrelevant.The sharpangularrises oneach\nside ofthis area are due tothe edges ofthe gasket hole.The reddashedline is a guide tothe eye\nshowingthe expectedsignal fora cuppeddiamondanvil ifnogasket hole was perturbingthe\nmeasurement inthe center,reflectingthe real shape ofthe elasticallydeformeddiamond.\nThird, Supplementary Information Figure 2B appears highly manipulative, as the region\ncorrespondingtoNe absorptionis obscuredbya greenrectangularoverlay.\nThere is no manipulation here. The green overlay displayed in Supplementary Information Figure\n2B was meant to indicate the region of the scan where the X-ray beam was going through the neon\nsample. In this region the beam undergoes no absorption from the rhenium gasket, and the\ncomputation of gasket thickness is thus physically irrelevant (no gasket there). The data logically\nshows a steep vanishing of the gasket thickness at the central hole walls, convoluted by the X-ray\nbeam lateral extension (~1 µm). We have modified the figure to include the data in this region to\nclarify.\nIn their response to my third question, the authors state: “Across the dozens of runs performed by\nour group over the past ten years, we consistently observe that—even in cases of apparent\ncatastrophic anvil failure—the failure occurs tens or hundreds of microns away from the culet\ncenter.” This statement reinforces my concern: the main mechanical (and probably structural)\nchanges occur not at the anvil tip but beneath the surface. These changes lead to elastic/plastic\ndeformation, breaking the symmetry of the material and causing variations in optical properties.\nConsequently, optical measurements reflect the overall (“integrated”) properties of the anvil rather\nthanthose ofa localizedregion.\nWhen we previously stated that “failure occurs tens or hundreds of microns away from the culet\ncenter,” we meant that fractures occurs on the beveled slope of the anvil, away from the anvil tip.\nThis is illustrated in the photograph of a recovered anvil from 520 GPa shown in our previous reply.\nThe recovered anvil retains its integrity along the anvil axis, and no plastic deformation is observed\nthere.\nOur point is that the mechanical response along the anvil central axis, and within a significant\nsurrounding radius, remains elastic. We agree that, when considering the anvil as a whole, regions\nof maximal relative deviatoric stress may be located away from the culet. However, this is not\nrelevant to our discussion, which concerns effects along the optical light path traversing the anvils\nthroughtheircenters.We believe that ourstatement mayhave beenmisinterpretedbythe reviewer.\nIn summary, I am convinced that the authors’ observations are real, but I have fundamental\nreservations about their interpretation and conclusions. It is up to the Editor to decide whether the\nempirical part of the work is sufficient for publication in Nature Communications. In the event of\npublication, I hope that my review will help readers adopt a more critical and sober view of the\nresults.\nWe thank the referee for the time devoted to evaluating our work. We hope that the responses\nprovided here satisfactorily address his/her concerns. We have amended the manuscript in multiple\nplaces (as indicated in the differential document provided) to clarify the dependence of our claims\nonthe underlyingmodel andassumptions."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The manuscript is much improved after multiple revisions. I do not have any additional concerns or comments. I support publication of the manuscript in the current form even though have some reservations on the broader impact of this study (true nature of diamond strain field under extreme conditions varies a lot depending on diamond geometry, sample strength, and sample geometry). Nevertheless, these results will be of interest to select groups of researchers worldwide interested in extending the limit of static high pressures.", "reviewer_3": "I appreciate the authors’ efforts to address the concerns that were raised. The responses demonstrate a strong command of the subject and have substantially clarified the issues. While further discussion could be pursued and additional questions could be raised, I believe that in its present form the paper is suitable for publication in Nature Communications."}, "author_response": ""}]

Decision letter