Static strength and equation of state of rhenium at ultra-high 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 30-50 µm range. We present a 30 µm culet profile that reached a maximum pressure of 414(1) GPa based on a Pt scale. The 300 K 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.

Tensorial stress-plastic strain fields in α - ω Zr mixture, transformation kinetics, and friction in diamond-anvil cell

Various phenomena (phase transformations (PTs), chemical reactions, microstructure evolution, strength, and friction) under high pressures in diamond-anvil cell are strongly affected by fields of stress and plastic strain tensors. However, they could not be measured. Here, we suggest coupled experimental-analytical-computational approaches utilizing synchrotron X-ray diffraction, to solve an inverse problem and find fields of all components of stress and plastic strain tensors and friction rules before, during, and after α-ω PT in strongly plastically predeformed Zr. Results are in good correspondence with each other and experiments. Due to advanced characterization, the minimum pressure for the strain-induced α-ω PT is changed from 1.36 to 2.7 GPa. It is independent of the plastic strain before PT and compression-shear path. The theoretically predicted plastic strain-controlled kinetic equation is verified and quantified. Obtained results open opportunities for developing quantitative high-pressure/stress science, including mechanochemistry, synthesis of new nanostructured materials, geophysics, astrogeology, and tribology.

Revisiting the High-Pressure Behaviors of Zirconium: Nonhydrostaticity Promoting the Phase Transitions and Absence of the Isostructural Phase Transition in β-Zirconium

Zirconium (Zr) is an important industrial metal that is widely used in nuclear engineering, chemical engineering, and space and aeronautic engineering because of its unique properties. The high-pressure behaviors of Zr have been widely investigated in the past several decades. However, the controversies still remain in terms of the phase transition (PT) pressures and the isostructural PT in β-Zr: why the PT pressure in Zr is so scattered, and whether the β to β' PT exists. In the present study, to address these two issues, the Zr sample with ultra-high purity (>99.99%) was quasi-hydrostatically compressed up to ~70 GPa. We discovered that both the purity and the stress state of the sample (the grade of hydrostaticity/nonhydrosaticity) affect the PT pressure of Zr, while the stress state is the dominant factor, the nonhydrostaticity significantly promotes the PT of Zr. We also propose two reasons why the β-β' isostructural PT was absent in the subsequent and present experiments, which call for further investigation of Zr under quasi-compression up to 200 GPa or even higher pressures.

Oxidation of High Yield Strength Metals Tungsten and Rhenium in High-Pressure High-Temperature Experiments of Carbon Dioxide and Carbonates

The laser-heating diamond-anvil cell technique enables direct investigations of materials under high pressures and temperatures, usually confining the samples with high yield strength W and Re gaskets. This work presents experimental data that evidences the chemical reactivity between these refractory metals and CO2 or carbonates at temperatures above 1300 °Ϲ and pressures above 6 GPa. Metal oxides and diamond are identified as reaction products. Recommendations to minimize non-desired chemical reactions in high-pressure high-temperature experiments are given.

First principles calculation of the nonhydrostatic effects on structure and Raman frequency of 3C-SiC

For understanding the quantitative effect of nonhydrostatic stress on properties of material, the crystal structure and Raman spectra of 3C-SiC under hydrostatic and nonhydrostatic stress were calculated using a first-principles method. The results show that the lattice constants (a, b, and c) under nonhydrostatic stresses deviate those under hydrostatic stress. The differences of the lattice constants under hydrostatic stress from nonhydrostatic stresses with differential stress were fitted by linear equation. Nonhydrostatic stress has no effect on density of 3C-SiC at high pressure, namely the equations of state of 3C-SiC under hydrostatic stress are same as those under nonhydrostatic stress. The frequencies and pressure dependences of LO and TO modes of 3C-SiC Raman spectra under nonhydrostatic stress are just same as those under hydrostatic stress. Under nonhydrostatic stress, there are four new lines with 361, 620, 740, and 803 cm⁻¹ appeared in the Raman spectra except for the LO and TO lines because of the reduction of structure symmetry. However the frequencies and pressure dependences of the four Raman modes remain unchanged under different nonhydrostatic stresses. Appearance of new Raman modes under nonhydrostatic stress and the linear relationship of the differences of lattice constants under hydrostatic and nonhydrostatic stresses with differential stress can be used to indicate state of stress in high pressure experiments. The effect of nonhydrostatic stress on materials under high pressure is complicated and our calculation would help to understanding state of stress at high pressure experiments.

High pressure phase transformations revisited

High pressure phase transformations play an important role in the search for new materials and material synthesis, as well as in geophysics. However, they are poorly characterized, and phase transformation pressure and pressure hysteresis vary drastically in experiments of different researchers, with different pressure transmitting media, and with different material suppliers. Here we review the current state, challenges in studying phase transformations under high pressure, and the possible ways in overcoming the challenges. This field is critically compared with fields of phase transformations under normal pressure in steels and shape memory alloys, as well as plastic deformation of materials. The main reason for the above mentioned discrepancy is the lack of understanding that there is a fundamental difference between pressure-induced transformations under hydrostatic conditions, stress-induced transformations under nonhydrostatic conditions below yield, and strain-induced transformations during plastic flow. Each of these types of transformations has different mechanisms and requires a completely different thermodynamic and kinetic description and experimental characterization. In comparison with other fields the following challenges are indicated for high pressure phase transformation: (a) initial and evolving microstructure is not included in characterization of transformations; (b) continuum theory is poorly developed; (c) heterogeneous stress and strain fields in experiments are not determined, which leads to confusing material transformational properties with a system behavior. Some ways to advance the field of high pressure phase transformations are suggested. The key points are: (a) to take into account plastic deformations and microstructure evolution during transformations; (b) to formulate phase transformation criteria and kinetic equations in terms of stress and plastic strain tensors (instead of pressure alone); (c) to develop multiscale continuum theories, and (d) to couple experimental, theoretical, and computational studies of the behavior of a tested sample to extract information about fields of stress and strain tensors and concentration of high pressure phase, transformation criteria and kinetics. The ideal characterization should contain complete information which is required for simulation of the same experiments.

Pressure Self-focusing Effect and Novel Methods for Increasing the Maximum Pressure in Traditional and Rotational Diamond Anvil Cells

The main principles of producing a region near the center of a sample, compressed in a diamond anvil cell (DAC), with a very high pressure gradient and, consequently, with high pressure are predicted theoretically. The revealed phenomenon of generating extremely high pressure gradient is called the pressure self-focusing effect. Initial analytical predictions utilized generalization of a simplified equilibrium equation. Then, the results are refined using our recent advanced model for elastoplastic material under high pressures in finite element method (FEM) simulations. The main points in producing the pressure self-focusing effect are to use beveled anvils and reach a very thin sample thickness at the center. We find that the superposition of torsion in a rotational DAC (RDAC) offers drastic enhancement of the pressure self-focusing effect and allows one to reach the same pressure under a much lower force and deformation of anvils.

Exploring the Chemical Reactivity between Carbon Dioxide and Three Transition Metals (Au, Pt, and Re) at High-Pressure, High-Temperature Conditions

The role of carbon dioxide, CO₂, as oxidizing agent at high pressures and temperatures is evaluated by studying its chemical reactivity with three transition metals: Au, Pt, and Re. We report systematic X-ray diffraction measurements up to 48 GPa and 2400 K using synchrotron radiation and laser-heating diamond-anvil cells. No evidence of reaction was found in Au and Pt samples in this pressure-temperature range. In the Re + CO₂ system, however, a strongly-driven redox reaction occurs at P > 8 GPa and T > 1500 K, and orthorhombic β-ReO₂ is formed. This rhenium oxide phase is stable at least up to 48 GPa and 2400 K and was recovered at ambient conditions. Raman spectroscopy data confirm graphite as a reaction product. Ab-initio total-energy structural and compressibility data of the β-ReO₂ phase shows an excellent agreement with experiments, altogether accurately confirming CO₂ reduction P-T conditions in the presence of rhenium metal and the β-ReO₂ equation of state.

Evidence of scaling in the high pressure phonon dispersion relations of some elemental solids

First principles searches are carried out for the existence of an asymptotic scaling law for the zero temperature phonon dispersion relation of several elemental crystalline solids in the high pressure regime. The solids studied are Cu, Ni, Pd, Au, Al, and Ir in the face-centered-cubic (fcc) geometry and Fe, Re, and Os in the hexagonal-close-packed (hcp) geometry. At higher pressures, the dependence of the scale of frequency on pressure can be fitted well by a power law. Elements with a given crystalline geometry have values of the scaling exponent very close to each other (0.32 for fcc and 0.27 for hcp - with a scatter below five percent of the average).

Implementation of micro-ball nanodiamond anvils for high-pressure studies above 6 Mbar

Since invention of the diamond anvil cell technique in the late 1950s for studying materials at extreme conditions, the maximum static pressure generated so far at room temperature was reported to be about 400 GPa. Here we show that use of micro-semi-balls made of nanodiamond as second-stage anvils in conventional diamond anvil cells drastically extends the achievable pressure range in static compression experiments to above 600 GPa. Micro-anvils (10–50 μm in diameter) of superhard nanodiamond (with a grain size below ∼50 nm) were synthesized in a large volume press using a newly developed technique. In our pilot experiments on rhenium and gold we have studied the equation of state of rhenium at pressures up to 640 GPa and demonstrated the feasibility and crucial necessity of the in situ ultra high-pressure measurements for accurate determination of material properties at extreme conditions.

The study of materials at high pressure has been limited by the conditions achievable using single-crystal diamond anvils. The use of anvils that incorporate a second stage consisting of two hemispherical nanocrystalline diamond micro-balls, extends the range of static pressures that can be generated in the lab.

Reaction of rhenium and carbon at high pressures and temperatures

A study of the reaction of rhenium with carbon at high-(P, T) conditions up to P max = 67 GPa and T max = 3800 K is presented. A hexagonal ReC x was identified as the stable phase at high-(P, T) conditions. A composition of ReC0.5 is proposed. No evidence for a cubic ReC polymorph with rocksalt structure, as suggested in the literature, or for any other phase was found at the P-T conditions explored. A preliminary P-T rhenium-carbon phase diagram has been derived and properties such as bulk moduli and elastic stiffness coefficients were obtained.

Yield strength of molybdenum at high pressures

In the diamond anvil cell technology, the pressure gradient approach is one of the three major methods in determining the yield strength for various materials at high pressures. In the present work, by in situ measuring the thickness of the sample foil, we have improved the traditional technique in this method. Based on this modification, the yield strength of molybdenum at pressures has been measured. Our main experimental conclusions are as follows: (1) The measured yield strength data for three samples with different initial thickness (100, 250, and 500 microm) are in good agreement above a peak pressure of 10 GPa. (2) The measured yield strength can be fitted into a linear formula Y=0.48(+/-0.19)+0.14(+/-0.01)P (Y and P denote the yield strength and local pressure, respectively, both of them are in gigapascals) in the local pressure range of 8-21 GPa. This result is in good agreement with both Y=0.46+0.13P determined in the pressure range of 5-24 GPa measured by the radial x-ray diffraction technique and the previous shock wave data below 10 GPa. (3) The zero-pressure yield strength of Mo is 0.5 GPa when we extrapolate our experimental data into the ambient pressure. It is close to the tensile strength of 0.7 GPa determined by Bridgman [Phys. Rev. 48, 825 (1934)] previously. The modified method described in this article therefore provides the confidence in determination of the yield strength at high pressures.

Nonhydrostatic compression of gold powder to 60 GPa in a diamond anvil cell: estimation of compressive strength from x-ray diffraction data

Two gold powder samples, one with average crystallite size of ≈30 nm (n-Au) and another with ≈120 nm (c-Au), were compressed under nonhydrostatic conditions in a diamond anvil cell to different pressures up to ≈60 GPa and the x-ray diffraction patterns recorded. The difference between the axial and radial stress components (a measure of the compressive strength) was estimated from the shifts of the diffraction lines. The maximum micro-stress in the crystallites (another measure of the compressive strength) and grain size (crystallite size) were obtained from analysis of the line-width data. The strengths obtained by the two methods agreed well and increased with increasing pressure. Over the entire pressure range, the strength of n-Au was found to be significantly higher than that of c-Au. The grain sizes of both n-Au and c-Au decreased under pressure. This decrease was much larger than expected from the compressibility effect and was found to be reversible. An equation derived from the dislocation theory that predicts the dependence of strength on the grain size and the shear modulus was used to interpret the strength data. The strength derived from the published grain size versus hardness data agreed well with the present results.

Strength, anisotropy, and preferred orientation of solid argon at high pressures

The elasticity and plasticity of materials at high pressure are of great importance for the fundamental insight they provide on bonding properties in dense matter and for applications ranging from geophysics to materials technology. We studied pressure-solidified argon with a boron-epoxy-beryllium composite gasket in a diamond anvil cell (DAC). Employing monochromatic synchrotron x-radiation and imaging plates in a radial diffraction geometry (Singh et al 1998 Phys. Rev. Lett. 80 2157; Mao et al 1998 Nature 396 741), we observed low strength in solid argon below 20 GPa, but the strength increases drastically with applied pressure, such that at 55 GPa, the shear strength exceeded 2.7 GPa. The elastic anisotropy at 55 GPa was four times higher than the extrapolated value from 30 GPa. Extensive (111) slip develops under uniaxial compression, as manifested by the preferred crystallographic orientation of (220) in the compression direction. These macroscopic properties reflect basic changes in van der Waals bondings under ultrahigh pressures.

Osmium has the lowest experimentally determined compressibility

On the basis of high pressure diamond-anvil compression studies for the precious metals Ru, Ir, and Os we report the surprising discovery that metallic osmium has a lower compressibility than covalently bonded diamond. We also find that Ir and Ru are as incompressible as Re. In addition, we have performed first principles calculations that confirm the trend in the measured transition metal compressibilities.