Multimegabar Pressures Research Articles

Design of a Three-Layer Impactor for Material Strength Measurements at Multi-Megabar Pressures

Design of a Three-Layer Impactor for Material Strength Measurements at Multi-Megabar Pressures

Exploring toroidal anvil profiles for larger sample volumes above 4 Mbar.

With the advent of toroidal and double-stage diamond anvil cells (DACs), pressures between 4 and 10 Mbar can be achieved under static compression, however, the ability to explore diverse sample assemblies is limited on these micron-scale anvils. Adapting the toroidal DAC to support larger sample volumes offers expanded capabilities in physics, chemistry, and planetary science: including, characterizing materials in soft pressure media to multi-megabar pressures, synthesizing novel phases, and probing planetary assemblages at the interior pressures and temperatures of super-Earths and sub-Neptunes. Here we have continued the exploration of larger toroidal DAC profiles by iteratively testing various torus and shoulder depths with central culet diameters in the 30-50µm range. We present a 30µm culet profile that reached a maximum pressure of 414(1) GPa based on a Pt scale. The 300K equations of state fit to our P-V data collected on gold and rhenium are compatible with extrapolated hydrostatic equations of state within 1% up to 4 Mbar. This work validates the performance of these large-culet toroidal anvils to > 4 Mbar and provides a promising foundation to develop toroidal DACs for diverse sample loading and laser heating.

Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. I. Inverse Lagrangian analysis

Absolute measurements of solid-material compressibility by magnetically driven shockless dynamic compression experiments to multi-megabar pressures have the potential to greatly improve the accuracy and precision of pressure calibration standards for use in diamond anvil cell experiments. To this end, we apply characteristics-based inverse Lagrangian analysis (ILA) to 11 sets of ramp-compression data on pure platinum (Pt) metal and then reduce the resulting weighted-mean stress–strain curve to the principal isentrope and room-temperature isotherm using simple models for yield stress and Grüneisen parameter. We introduce several improvements to methods for ILA and quasi-isentrope reduction, the latter including calculation of corrections in wave speed instead of stress and pressure to render results largely independent of initial yield stress while enforcing thermodynamic consistency near zero pressure. More importantly, we quantify in detail the propagation of experimental uncertainty through ILA and model uncertainty through quasi-isentrope reduction, considering all potential sources of error except the electrode and window material models used in ILA. Compared to previous approaches, we find larger uncertainty in longitudinal stress. Monte Carlo analysis demonstrates that uncertainty in the yield-stress model constitutes by far the largest contribution to uncertainty in quasi-isentrope reduction corrections. We present a new room-temperature isotherm for Pt up to 444 GPa, with 1-sigma uncertainty at that pressure of just under ±1.2%; the latter is about a factor of three smaller than uncertainty previously reported for multi-megabar ramp-compression experiments on Pt. The result is well represented by a Vinet-form compression curve with (isothermal) bulk modulus K0=270.3±3.8 GPa, pressure derivative K0′=5.66±0.10, and correlation coefficient RK0,K0′=−0.843.

Density deficit of Earth's core revealed by a multimegabar primary pressure scale.

An accurate pressure scale is a fundamental requirement to understand planetary interiors. Here, we establish a primary pressure scale extending to the multimegabar pressures of Earth's core, by combined measurement of the acoustic velocities and the density from a rhenium sample in a diamond anvil cell using inelastic x-ray scattering and x-ray diffraction. Our scale agrees well with previous primary scales and shock Hugoniots in each experimental pressure range and reveals that previous scales have overestimated laboratory pressures by at least 20% at 230 gigapascals. It suggests that the light element content in Earth's inner core (the density deficit relative to iron) is likely to be double what was previously estimated, or Earth's inner core temperature is much higher than expected, or some combination thereof.

The stress state in bismuth to 298 GPa and its use as a pressure transmitting medium and pressure marker at multi-megabar pressures

We have conducted diffraction studies of bismuth (Bi) to 298 GPa using both conventional and toroidal diamond anvil cells (DACs) to investigate its suitability as a pressure-transmitting medium (PTM) to such pressures. Using microfocused x-ray beams, we have determined the pressure dependence of the uniaxial stress component (t) in cubic Bi-V from 7 to 298 GPa and find that at 298 GPa, t<0.5 GPa. Bi-V, therefore, cannot support significant shear stresses, making it an excellent PTM. We have also measured the compressibility of Bi-V against that of copper (Cu) and gold (Au), allowing it to be used as a pressure marker as well as a PTM.

Hellmann–Feynman theorem and internal pressure for atoms, molecules and plasmas under pressure

Since the beginning of the twentieth century, confinement of atoms, molecules and plasma inside impenetrable sharp (hard) and smooth (soft) cavities has been studied with utmost interest. Physically, such situations introduce the trapping of a quantum system under high pressure. The internal pressure () of the system under multi-megabar external pressure has not yet been explored. Also, there is a lack of Hellmann–Feynman theorem (HFT) in such a scenario, which is essential to derive a concrete analytical expression of under stressed condition. Here using a scaling concept we provide a general HFT in terms of expectation values of total energy, potential and kinetic energy of a given confined system. A change in boundary condition (from smooth to sharp and vice versa) does not affect this. Applying this proposed HFT, a closed-form expression of and has been obtained for confined and shell-confined quantum systems. Based on this , several virial-like equations are also modeled. This HFT and are demonstrated for one- and many-electron atoms, plasmas and molecules using both analytical and numerical methods. Their applicability in several other confined systems is discussed from simple arguments.

Metallization in hydrogenlike systems under high pressure

Almost a century ago, it was proposed that solid hydrogen could become metallic at sufficiently high pressure. Five years back, scientists observed an insulator to metal transition in liquid deuterium experimentally, at around 300 $\mathrm{GPa}$. The present work discusses and demonstrates the metal-like behavior in elemental hydrogen under various plasma environments. At the onset, the Herzfeld criterion is invoked to examine such characteristics in such plasmas under multimegabar pressure. However, a thorough study using this condition can only explain the metal-like pattern in $s$-wave states under a shell-confined condition (the system is trapped inside two concentric spheres with inner and outer radii ${R}_{a},{R}_{b}$). Moreover, using this criterion, it is not possible to explain such phenomena in (i) confined systems (involving all $\ensuremath{\ell}$) and (ii) for $\ensuremath{\ell}\ensuremath{\ne}0$ states in a shell-confined environment. Here this criterion is modified to incorporate the environmental conditions (nuclear charge, screening constant, boundary conditions) by utilizing several independent and generalized scaling concepts. The present condition can interpret a metallic pattern in confined and shell-confined plasmas connecting $\ensuremath{\ell}\ensuremath{\ge}0$ states. Further, a different descriptor is proposed therefrom. The role of pressure in defining such a descriptor is also examined. Pilot calculations are performed using Debye H\"uckel, exponential screen Coulomb potential, and ion-sphere plasmas. The relevance of the shell-confined model in the context of plasmas is elaborated. Additionally, an attempt is made to investigate the metallic character in H-like systems embedded in fullerene under high pressure.

Stress-induced high-Tc superconductivity in solid molecular hydrogen

Solid molecular hydrogen has been predicted to be metallic and high-temperature superconducting at ultrahigh hydrostatic pressures that push current experimental limits. Meanwhile, little is known about the influence of nonhydrostatic conditions on its electronic properties at extreme pressures where anisotropic stresses are inevitably present and may also be intentionally introduced. Here we show by first-principles calculations that solid molecular hydrogen compressed to multimegabar pressures can sustain large anisotropic compressive or shear stresses that, in turn, cause major crystal symmetry reduction and charge redistribution that accelerate bandgap closure and promote superconductivity relative to pure hydrostatic compression. Our findings highlight a hitherto largely unexplored mechanism for creating superconducting dense hydrogen, with implications for exploring similar phenomena in hydrogen-rich compounds and other molecular crystals.

Sub-micrometer focusing setup for high-pressure crystallography at the Extreme Conditions beamline at PETRA III.

Scientific tasks aimed at decoding and characterizing complex systems and processes at high pressures set new challenges for modern X-ray diffraction instrumentation in terms of X-ray flux, focal spot size and sample positioning. Presented here are new developments at the Extreme Conditions beamline (P02.2, PETRA III, DESY, Germany) that enable considerable improvements in data collection at very high pressures and small scattering volumes. In particular, the focusing of the X-ray beam to the sub-micrometer level is described, and control of the aberrations of the focusing compound refractive lenses is made possible with the implementation of a correcting phase plate. This device provides a significant enhancement of the signal-to-noise ratio by conditioning the beam shape profile at the focal spot. A new sample alignment system with a small sphere of confusion enables single-crystal data collection from grains of micrometer to sub-micrometer dimensions subjected to pressures as high as 200 GPa. The combination of the technical development of the optical path and the sample alignment system contributes to research and gives benefits on various levels, including rapid and accurate diffraction mapping of samples with sub-micrometer resolution at multimegabar pressures.

Melting of Tantalum at Multimegabar Pressures on the Nanosecond Timescale

Tantalum was once thought to be the canonical bcc metal, but is now predicted to transition to the Pnma phase at the high pressures and temperatures expected along the principal Hugoniot. Furthermore, there remains a significant discrepancy between a number of static diamond anvil cell experiments and gas gun experiments in the measured melt temperatures at high pressures. Our insitu x-ray diffraction experiments on shock compressed tantalum show that it does not transition to the Pnma phase or other candidate phases at high pressure. We observe incipient melting at approximately 254±15 GPa and complete melting by 317±10 GPa. These transition pressures from the nanosecond experiments presented here are consistent with what can be inferred from microsecond gas gun sound velocity measurements. Furthermore, the observation of a coexistence region on the Hugoniot implies the lack of significant kinetically controlled deviation from equilibrium behavior. Consequently, we find that kinetics of phase transitions cannot be used to explain the discrepancy between static and dynamic measurements of the tantalum melt curve. Using available high pressure thermodynamic data for tantalum and our measurements of the incipient and complete melting transition pressures, we are able to infer a melting temperature 8070_{-750}^{+1250} K at 254±15 GPa, which is consistent with ambient and a recent static high pressure melt curve measurement.

Spectral proxies for bonding transitions in SiO2 and MgSiO3 polymorphs at high pressure up to 270 GPa by O K -edge x-ray Raman scattering

Advances in synchrotron x-ray Raman scattering (XRS) techniques enable probing of pressure-induced element-specific bonding transitions in diverse oxides beyond megabar pressures. Evolution of the electronic structures under extreme pressure involves an emergence of additional oxygen $1s$ electron excitation pattern and shifts in the electronic states toward high-energy ranges in an XRS spectrum. Structural origins of such changes and proper spectral proxy for the corresponding evolution in electronic density of states remain to be established. Here, we calculated the O $K$-edge features in the XRS spectrum for diverse crystalline ${\mathrm{SiO}}_{2}$ polymorphs, from \ensuremath{\alpha}-quartz (1 atm) to a pyrite-type structure (at \ensuremath{\sim}271 GPa), beyond the current experimental pressure limit (\ensuremath{\sim}160 GPa). The ab initio results unravel the electronic origins of the evolution in the XRS patterns, such as the emergence of the bimodal feature with decreasing oxygen-oxygen distance $({d}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{O}}) <\ensuremath{\sim}2.5 \AA{}$ and a subsequent merging of the doublet patterns with a further decrease in ${d}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{O}}$ down to $\ensuremath{\sim}2.3--2.4 \AA{}$. Ab initio simulations of the XRS spectrum of pyrite-type ${\mathrm{SiO}}_{2}$ phase at $\ensuremath{\sim}271 \mathrm{GPa}$ revealed the significant electron dispersion in $2{p}^{*}$ states and the pronounced electron density between edge-sharing oxygen atoms with ${d}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{O}}$ of \ensuremath{\sim}2.1 \AA{}, in contrast to an earlier prediction with a negligible electron density between those oxygen atoms. The pressure-induced increase in electron interactions leads to a systematic change in the edge energy at half of the spectrum area $({E}_{M})$ and the edge energy at the center of mass of the spectrum $({E}_{C})$ of XRS patterns beyond multimegabar pressures. Particularly, the ${E}_{M}$ and ${E}_{C}$ increase linearly with decreasing oxygen proximity $({d}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{O}})$ and bulk density up to 270 GPa. The ${E}_{M}$ and ${E}_{C}$ for ${\mathrm{MgSiO}}_{3}$ phases show larger changes with varying ${d}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{O}}$ than those in ${\mathrm{SiO}}_{2}$ phases, demonstrating the effect of the electronic hybridization between Mg and O on the evolution of the XRS patterns. The strong linear correlation among ${E}_{M}$, ${E}_{C}$, and ${d}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{O}}$ (and density) up to \ensuremath{\sim}270 GPa confirms that the ${E}_{M}$ and ${E}_{C}$ can be effective spectral proxies to quantify the densification of crystalline and noncrystalline oxides. The results with the statistical evaluations of the electronic density of states provide improved prospects for the prediction of the evolution in core-level excitation features of diverse complex, multicomponent oxides under multimegabar pressure conditions toward the deep lower mantle of Earth and other super-Earth bodies.

Novel Rhenium Carbides at 200 GPa

Laser heating of rhenium in a diamond anvil cell to 3000±300 K at about 200 GPa results in formation of two previously unknown rhenium carbides, hexagonal WC‐type structured ReC and orthorhombic TiSi2‐type structured ReC2. The shortest C–C distances [1.758(3) Å at 219(5) GPa and 1.850(4) Å at 180(7) GPa] found in honeycomb‐like carbon nets in the structure of ReC2 are quite unusual. The Re–C solid solution formed at multimegabar pressure has the carbon content of ≈ 20 at%.

Crystallography of low Z material at ultrahigh pressure: Case study on solid hydrogen

Diamond anvil cell techniques have been improved to allow access to the multimegabar ultrahigh-pressure region for exploring novel phenomena in condensed matter. However, the only way to determine crystal structures of materials above 100 GPa, namely, X-ray diffraction (XRD), especially for low Z materials, remains nontrivial in the ultrahigh-pressure region, even with the availability of brilliant synchrotron X-ray sources. In this work, we perform a systematic study, choosing hydrogen (the lowest X-ray scatterer) as the subject, to understand how to better perform XRD measurements of low Z materials at multimegabar pressures. The techniques that we have developed have been proved to be effective in measuring the crystal structure of solid hydrogen up to 254 GPa at room temperature [C. Ji et al., Nature 573, 558–562 (2019)]. We present our discoveries and experiences with regard to several aspects of this work, namely, diamond anvil selection, sample configuration for ultrahigh-pressure XRD studies, XRD diagnostics for low Z materials, and related issues in data interpretation and pressure calibration. We believe that these methods can be readily extended to other low Z materials and can pave the way for studying the crystal structure of hydrogen at higher pressures, eventually testing structural models of metallic hydrogen.

New aluminium hydroxide at multimegabar pressures: Implications for water reservoirs in deep planetary interiors

Hydrogen is the most abundant element in the universe and has played an important role in the structure, dynamics, and evolution of the planets. In the Earth, hydrogen is transported into deep mantle regions in the form of hydrous minerals via the subduction of oceanic plates. However, in contrast to the extensive studies on the behaviours of hydrous phases in the deep interior of the Earth, little is known about those in larger planets, such as ice giants and super-Earths. Based on in-situ X-ray diffraction experiments in a laser-heated diamond anvil cell as well as first principles calculations, we found that δ-AlOOH transforms into a new phase with orthorhombic symmetry, named ε-AlOOH, at ~190 GPa. We also found that FeOOH and AlOOH form solid solutions with a pyrite-type structure at ~150 GPa. These findings clarified that some hydrous phases remain stable beyond pressures found in the Earth's core-mantle boundary. Hydrogen may thus be stored in these hydroxides or their potential high-pressure forms in the deep interiors of terrestrial super-Earths, and the rocky cores of some ice giants.

Static compression of B2 KCl to 230 GPa and its P-V-T equation of state

The pressure-volume-temperature (P-V-T) measurements of the B2 (CsCl-type) phase of KCl were performed at 9–61 GPa/1500–2600 K and up to 229 GPa at room temperature, based on synchrotron X‑ray diffraction measurements in a laser-heated diamond-anvil cell (DAC). The nonhydrostatic stress conditions inside the sample chamber were critically evaluated based on the platinum pressure marker. With thermal annealing by laser after each pressure increment, the deviatoric stress was reduced to less than 1% of the sample pressure even at the multi-megabar pressure range. The obtained P-V-T data were fitted to the Vinet equation of state with the Mie-Grüneisen-Debye model for thermal pressure. The thermal pressure of KCl was found to be as small as ~10 GPa even at 3000 K at any given volume, which is only half of that of common pressure markers (i.e. Pt, Au, or MgO). Such a low-thermal pressure validates the use of a KCl pressure medium as a pressure marker at high temperatures.

Characterizing equation of state and optical properties of dynamically pre-compressed materials

Characterising materials at pressures of several megabar and temperatures of a few thousand Kelvin is critical for the understanding of the Warm Dense Matter regime and to improve planetary models as these conditions are typical of planets' interiors. Today, laser-driven shock compression is the only technique to achieve multimegabar pressures, but the associated temperatures are too high to be representative of planetary states. Double-shock compression represents an alternative to explore lower temperatures. Here we present a method to create well-controlled double-shocked states and measure their thermodynamic state and optical reflectivity using standard optical diagnostics (Doppler velocimetry and optical pyrometry) in a laser-driven shock experiment. This method, which does not require the support of hydrodynamical simulations, is based on the application of generalised Rankine-Hugoniot relations together with a self impedance mismatch technique. A validation experiment has been performed at the LULI2000 facility (\'Ecole Polytechnique, France) on a sample of $\alpha$-quartz. A temperature $60 \%$ lower than along the principal Hugoniot has been obtained at 7.5 Mbar.

Diamond anvil cell behavior up to 4 Mbar

The diamond anvil cell (DAC) is considered one of the dominant devices to generate ultrahigh static pressure. The development of the DAC technique has enabled researchers to explore rich high-pressure science in the multimegabar pressure range. Here, we investigated the behavior of the DAC up to 400 GPa, which is the accepted pressure limit of a conventional DAC. By using a submicrometer synchrotron X-ray beam, double cuppings of the beveled diamond anvils were observed experimentally. Details of pressure loading, distribution, gasket-thickness variation, and diamond anvil deformation were studied to understand the generation of ultrahigh pressures, which may improve the conventional DAC techniques.

Equations of state of minerals at multi-megabar pressure

Equations of state of minerals at multi-megabar pressure

Structural, magnetic and electronic properties of CrO2 at multimegabar pressures.

As the only half-metallic ferromagnetic material in 3d transition metal dioxides, CrO2 has attracted great scientific interest from materials science to physical chemistry. Here, an investigation into the structural, magnetic and electronic properties of CrO2 under high pressure has been conducted by first-principles calculations based on density functional theory. Static calculations have predicted that CrO2 undergoes structural transitions with the sequence of rutile-type → CaCl2-type → pyrite-type → Pnma → (Fe2P-type→) I4/mmm at high pressures. In addition, a transition from the ferromagnetic state to the non-magnetic state with the magnetic collapse of Cr is observed in CrO2 at the pyrite–Pnma transition. This transition also delocalizes the 3d electrons of Cr and leads to a metallic character of CrO2. The equation of state, elasticity and band gap for each energetically favorable phase of CrO2 are determined. Our results not only bridge the gap about the high-pressure behavior of CrO2 in previous studies but also extend our understanding of its properties up to multimegabar conditions. According to previous data and present results, we further discuss and summarize the high-pressure behavior of various AO2 compounds. This can contribute to investigating properties of other AO2 compounds or exploring novel materials at high pressures.

Absolute measurement of the Hugoniot and sound velocity of liquid copper at multimegabar pressures

Measurement of the Hugoniot and sound velocity provides information on the bulk modulus and Gr\uneisen parameter of a material at extreme conditions. The capability to launch multilayered (copper/aluminum) flyer plates at velocities in excess of 20 km/s with the Sandia Z accelerator has enabled high-precision sound-velocity measurements at previously inaccessible pressures. For these experiments, the sound velocity of the copper flyer must be accurately known in the multi-Mbar regime. Here we describe the development of copper as an absolutely calibrated sound-velocity standard for high-precision measurements at pressures in excess of 400 GPa. Using multilayered flyer plates, we performed absolute measurements of the Hugoniot and sound velocity of copper for pressures from 500 to 1200 GPa. These measurements enabled the determination of the Gr\uneisen parameter for dense liquid copper, clearly showing a density dependence above the melt transition. Combined with earlier data at lower pressures, these results constrain the sound velocity as a function of pressure, enabling the use of copper as a Hugoniot and sound-velocity standard for pressures up to 1200 GPa.