Primary Pressure Scale Research Articles

Primary Pressure Scale of KCl B2 Phase to the Core‐Mantle Boundary

Primary Pressure Scale of KCl B2 Phase to the Core‐Mantle Boundary

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.

Ultrasound elasticity of diamond at gigapascal pressures

Diamond is the hardest known material in nature and features a wide spectrum of industrial and scientific applications. The key to diamond's outstanding properties is its elasticity, which is associated with its exceptional hardness, shear strength, and incompressibility. Despite many theoretical works, direct measurements of elastic properties are limited to only ∼1.4 kilobar (kb) pressure. Here, we report ultrasonic interferometry measurements of elasticity of void-free diamond powder in a multianvil press from 1 atmosphere up to 12.1 gigapascal (GPa). We obtained high-accuracy bulk modulus of diamond as K0 = 439.2(9) GPa, K0' = 3.6(1), and shear modulus as G0 = 533(3) GPa, G0' = 2.3(3), which are consistent with our first-principles simulation. In contrast to the previous experiment of isothermal equation of state, the K0' obtained in this work is evidently greater, indicating that the diamond is not fully described by the "n-m" Mie-Grüneisen model. The structural and elastic properties measured in this work may provide a robust primary pressure scale in extensive pressure ranges.

Analytical solutions of some model cases of piston-cylinder assemblies

Pressure balances are an important part of the sets of primary pressure standards in many national metrology institutes. The most critical factor determining their accuracy is the effective area of their piston-cylinder assemblies (PCAs). This can be determined (for PCAs with undistorted pressure) by applying a numerical procedure based on a theory by Dadson while knowing a gapprofile (of an axisymmetric PCA approximation). The pressure balances are also a basis for the primary pressure scale of the Czech Metrology Institute. Hence, we wanted to test our programme by computing the effective area from the geometrical data. Therefore, we solved the analytical formulae of Dadson et al (1982) The Pressure Balance—Theory and Practice (London: Her Majesty’s Stationery Office) for several simple geometries with a constant gap width, which are easy to calculate analytically. It is shown that the analytical results always agreed perfectly with the results of our programme. This success confirmed the correctness of our programme. However, it also pointed out a problem of discretization which can be non-negligible, even in the case of relatively simple geometries. We assume that the analytical formulae obtained can be of practical use for any other pressure metrology laboratory requiring an independent way to confirm their own PCA-modelling software.

Born’s valence force-field model for diamond at terapascals: Validity and implications for the primary pressure scale

Born’s valence force-field model (VFM) established a theoretical scheme for calculating the elasticity, zero-point optical mode, and lattice dynamics of diamond and diamond-structured solids. In particular, the model enabled the derivation of a numerical relation between the elastic moduli and the Raman-active F2g mode for diamond. Here, we establish a relation between the diamond Raman frequency ω and the bulk modulus K through first-principles calculation, rather than extrapolation. The calculated K exhibits a combined uncertainty of less than 5.4% compared with the results obtained from the analytical equation of the VFM. The results not only validate Born’s classic model but also provide a robust K–ω functional relation extending to megabar pressures, which we use to construct a primary pressure scale through Raman spectroscopy and the crystal structure of diamond. Our computations also suggest that currently used pressure gauges may seriously overestimate pressures in the multi-megabar regime. A revised primary scale is urgently needed for such ultrahigh pressure experiments, with possible implications for hot superconductors, ultra-dense hydrogen, and the structure of the Earth’s core.

Absolute Primary Pressure Scale to 120 GPa: Toward a Pressure Benchmark for Earth's Lower Mantle

AbstractSelf‐consistent absolute primary pressure scale available to whole Earth's lower mantle pressure regime was established by the simultaneous measurement of densities and acoustic wave velocities of NaCl‐B2 phase up to ~120 GPa without any use of prior pressure standards. While our pressure scale shows excellent agreement with the theoretical predictions, some of the previous secondary pressure scales constructed based on the prior pressure standard by the shock wave data significantly deviate from our primary scale reaching around 10 GPa at most within lower mantle pressure regime, which corresponds to ~170‐km difference in depth. Our newly established pressure scale would thus be a new benchmark to deal with the controversy on the depth of the boundaries of Earth's layered structure, such as magnesium‐silicate postperovskite phase transition boundary at the bottom of the Earth's mantle which might represent the D″ seismic discontinuity.

Elastic constants of single-crystal Pt measured up to 20 GPa based on inelastic X-ray scattering: Implication for the establishment of an equation of state

Phonon velocities and densities for Pt were measured based on inelastic X-ray scattering from ambient pressure to 20GPa in order to independently determine its equation of state (EOS). Phonon velocities were determined with sine dispersion relations. Cij values were obtained by fitting phonon velocities and densities to the Christoffel equation. We found that the obtained Cijs were in good agreement with previously reported Cijs at ambient condition. Based on the Cij values in various conditions, experimental pressures were calculated. The EOS of Pt as a primary pressure scale was determined based on the experimental pressures. We report K’=5.17 with fixed KT=274.1GPa and V0=60.360 Å3 for Vinet EOS. Our scale is in good agreement with several previously published scales based on shock experiments and XRD.

Single crystal elasticity of gold up to ∼20 GPa: Bulk modulus anomaly and implication for a primary pressure scale

We measured the elasticity of single crystal gold (Au) and its lattice parameters under high pressure using inelastic X-ray scattering (IXS). The elastic moduli were obtained at five pressure points between 0 and 20 GPa. The pressure variation of the bulk modulus displays anomalous behavior, being nearly constant up to ∼5 GPa, and then steeply increasing at higher pressure. A similar anomaly is observed in first-principles calculations. An absolute pressure scale was derived by direct numerical integration of the bulk modulus over volume change. This yields a scale that gives slightly lower pressure values than those of previous work, about 5–10% lower at ∼20 GPa.

Revised calibration of the Sm:SrB4O7 pressure sensor using the Sm-doped yttrium-aluminum garnet primary pressure scale

The pressure-induced shift of Sm:SrB4O7 fluorescence was calibrated in a quasi-hydrostatic helium medium up to 60 GPa using the recent Sm-doped yttrium-aluminum garnet primary pressure scale as a reference. The resulting calibration can be written as P = −2836/14.3 [(1 + Δλ/685.51)−14.3 − 1]. Previous calibrations based on the internally inconsistent primary scales are revised, and, after appropriate correction, found to agree with the proposed one. The calibration extended to 120 GPa was also performed using corrected previous data and can be written as P = 4.20 Δλ (1 + 0.020 Δλ)/(1 + 0.036 Δλ).

一次圧力標準物質としてのNaClの温度－圧力－体積状態方程式

一次圧力標準物質としてのNaClの温度－圧力－体積状態方程式

The Sm:YAG primary fluorescence pressure scale

AbstractPrimary pressure determinations involve the measurement of pressure without recourse to secondary standard materials. These measurements are essential for ensuring the accuracy of pressures measured in gasketed high‐pressure devices. In this study, the wavelength of optical fluorescence bands and the density of single crystal Sm‐doped yttrium aluminum garnet Y3Al5O12 (Sm:YAG) have been calibrated as a primary pressure scale up to 58 GPa. Absolute pressures were obtained by integrating the bulk modulus determined via Brillouin spectroscopy with respect to volumes measured simultaneously by X‐ray diffraction. A third‐order Birch‐Murnaghan equation of state of Sm:YAG yields V0 = 1735.15(26) Å3, KT0 = 185(1.5) GPa, and K` = 4.18(5). The accompanied pressure‐induced shifts of the fluorescence lines Y1 and Y2 of Sm:YAG were calibrated to the primary pressure, thus creating a highly accurate fluorescence pressure scale. These shifts are described as P = (A/B) * {[1 + (Δλ/λ0)]B − 1} with A = 2089.91(23.04), B = −4.43(1.07) for Y1, and A = 2578.22(48.70), B = −15.38(1.62) for Y2 bands, where ∆λ = λ − λ0, λ and λ0 are wavelengths in nanometer at pressure and ambient conditions. The sensitivity in the pressure determination of the Sm:YAG fluorescence shift is 0.32 nm/GPa, which is identical to that of the ruby scale. Sm:YAG can be considered elastically isotropic up to 58 GPa, implying insensitivity of the determined pressure to the crystallographic orientation under nonhydrostatic or quasi‐hydrostatic conditions. The Sm:YAG fluorescence shift is apparently also independent of crystallographic orientation, in contrast to that of ruby. Since the Y fluorescence band of Sm:YAG is insensitive to temperature changes, this material is highly suitable for the measurement of pressure at elevated temperatures.

Vibrational, elastic, and structural properties of cubic silicon carbide under pressure up to 75 GPa: Implication for a primary pressure scale

We present results of concomitant measurements of synchrotron x-ray diffraction (XRD), Brillouin, and Raman spectroscopy on the single crystal samples of cubic silicon carbide (3C-SiC) under quasi-hydrostatic pressures up to 65 GPa, as well as x-ray diffraction and Raman spectroscopy up to 75 GPa. We determined the equation of state of 3C-SiC and pressure dependencies of the zone-center phonon, elastic tensor, and mode Gruneisen parameters. Cubic SiC lattice was found to be stable up to 75 GPa, but there is a tendency for destabilization above 40 GPa, based on softening of a transverse sound velocity. By applying the concomitant density and elasticity measurements, we determined the pressure on the SiC sample without referring to any other pressure scale thus establishing a new primary pressure scale with a 2%–4% precision up to 65 GPa. We proposed corrections to the existing ruby and neon pressure scales, and also calibrated cubic SiC as a pressure marker for the x-ray diffraction and Raman experiments.

Tactics and Strategy Toward a Construction of Primary Pressure Scale

An accurate pressure scale is essential for conducting high-pressure experiments. Simultaneous measurements of elasticity and density enable us to construct a primary pressure scale, which can independently determine the pressure, but this has been so far limited to low pressures and at ambient temperature due to the experimental difficulties. Recent development of Brillouin scattering and synchrotron X-ray diffraction techniques have proven to be highly suitable for exploring the sound velocities and lattice parameters under high-pressure and high temperature conditions. Here I describe the strategy, challenges and current status toward an establishment of primary pressure scale applicable to Mbar pressure using both Brillouin scattering and synchrotron X-ray diffraction techniques.

Elasticity of MgO and a primary pressure scale to 55 GPa.

We have studied the elasticity and pressure-density equation of state of MgO in diamond cells to 55 GPa and have doubled the previous pressure limit of accurate elasticity determinations for crystals. Integrating single-crystal velocity data from Brillouin scattering measurements and density data from polycrystalline x-ray diffraction, we obtained the three principal elastic tensor elements (C(11), C(12), and C(44)) and various secondary elasticity parameters, including single-crystal elastic anisotropy, Cauchy relation, aggregate sound velocities, and Poisson's ratio, as functions of pressure. The present study also provides a direct determination of pressure without recourse to any prior pressure standard, thus creating a primary pressure scale. The commonly used ruby fluorescence pressure scale has thus been improved to 1% accuracy by the new MgO scale.

New diamond anvil cells for gigahertz ultrasonic interferometry and X-ray diffraction

Two new diamond anvil cells have been designed for ultrasonic and X-ray diffraction measurements on a single crystal sample up to 6 GPa and 250 °C. Advances in the generation and transmission of coherent GHz ultrasonic signals with wavelengths of the order of micrometers now make it practical to measure elastic properties of samples small enough to be subjected to pressure and temperature in diamond anvil cells. The signal is carried from a thin transducer through a sapphire buffer rod coupled to one of the diamond anvils by means of force. The signal traverses the diamond anvil and enters the single crystal sample which is coupled to the anvil face by cement, adhesion, or by a normal force. Interference of superimposed waves reflected from the near and far faces of the single crystal is used to measure travel time of the sound waves in the sample. One of the diamond anvil cells employs the conventional geometry in which access for the X-rays is through the diamond anvils. The other provides access for X-rays at high angles to the load axis so that they do not need to pass through the diamond anvils and can therefore have access to the sample while the buffer rod is in place. Both diamond anvil cells make it possible to measure d-spacings at several different orientations using a four-circle goniometer. This capability is used for detecting and correcting displacement of the sample from the center of the goniometer. Measurement of travel times and lattice parameters at the same pressure-temperature conditions allows conversion of travel times to velocities and can provide simultaneous equations of state, which EOS can then be used to make an independent determination of pressure vs. lattice parameter. This provides a primary pressure scale

Simultaneous Gigahertz Ultrasonic Interferometry and X-ray Diffraction in a New Diamond Anvil Cell.

Advances in the generation and transmission of very high frequency ultrasonic signals make it practical to measure elastic properties in single crystals small enough to be subjected to high pressures and temperatures in a new diamond anvil cell designed for simultaneous ultrasonic and x-ray diffraction measurements up to 5 GPa and 400°C. In addition to providing a new accurate method for measuring elastic properties this technique can provide simultaneous equations of state which can be used to produce a new primary pressure scale. Preliminary measurements on MgO show the feasibility of this new technique.

High-Pressure Calibration: A Critical Review

A critical review of experimental technique for measuring high pressures has been made. The broad coverage includes discussions relating to (a) the establishment of a primary pressure scale using the free-piston gage, (b) the selection and precise measurement of identifiable phase changes as fixed pressure points, and (c) the use of interpolation and extrapolation techniques such as resistance gages, equations of state, and optical changes. The emphasis is on static pressure measurements above 10 kbar, but shock measurements are also considered for completeness. The pressure values to be associated with the fixed points have been analyzed in detail. Temperature measurement in the high pressure environment is also reviewed. The accuracy with which pressures can be measured has been carefully considered; the maximum accuracies now obtainable are considered to be of the order of 0.02 percent at 8 kbar, 0.25 percent at 25 kbar, 2 percent at 50 kbar, and 4 percent at 100 kbar.