Simple method to determine equations of state of liquids in the 0–10 GPa range

X-ray and optical studies of GaAsx- P1-x crystals : S.A. Abagyan, S.M. Goridetsky and T.B. Jukova (Vol. 7, No. 1, pp. 200–206.

Hydrostaticity of poly(methyl methacrylate) loaded in a diamond anvil cell for high-pressure study

4:1 methanol-ethanol (ME) mixture and silicone oil are common, important pressure transmitting media used in high pressure diamond anvil cell (DAC) experiments. Their thermal conductivities and elastic properties are critical for modeling heat conduction in the DAC experiments and for determining thermal conductivity of measurement samples under extreme conditions. We used time-domain thermoreflectance and picosecond interferometry combined with the DAC to study the thermal conductivities and elastic constants C11 of the ME mixture and silicone oil at room temperature and to pressures as high as ≈23 GPa. We found that pressure dependence of the thermal conductivity of ME and silicone oil are both well described by the prediction of the minimum thermal conductivity model, confirming the diffusion of thermal energy between nonpropagating molecular vibrational modes is the dominant heat transport mechanism in a liquid and amorphous polymer. Our results not only provide new insights into the physics of thermal transport in these common pressure media for high pressure thermal measurements, but will also significantly extend the feasibility of using silicone fluid medium to much higher pressure and moderately high temperature conditions with higher measurement accuracy than other pressure media.

To understand the practical effects of pressure-transmitting media (PTM) on neutron diffraction using Paris–Edinburgh presses, diffraction patterns of MgO were collected to approximately 20 GPa using PTMs of Pb, AgCl, 4:1 methanol–ethanol (ME) mixture with and without heating, N2, and Ar. Hydrostaticity in the sample chamber estimated from the MgO 220 peak width improves in the order of Pb, AgCl, Ar, ME mixture, N2, and the heated ME mixture. Unlike previous results using diamond anvil cells, the unheated ME mixture is superior to Ar even after freezing, probably due to the cup on the anvil face. Considering these results and the sizable coherent scattering of Ne, which would show good hydrostaticity, we conclude that the ME mixture (preferably the heated one) is the best PTM in neutron experiments up to 20 GPa, while Ar can be substituted when a sample is reactive to alcohols.

Despite the widespread use of the 4:1 methanol–ethanol mixture as a hydrostatic medium by the high-pressure community, its equation of state (EOS) is usually substituted by that of pure methanol. Here we report accurate direct volumetric measurements of the room temperature EOS for this mixture up to 5 GPa. A brief description of the optical technique (imaging+interferometric) specifically developed for this purpose is given, as well as the general characteristics of the required miniature diamond anvil cell. Our results are compared with the available data of similar pure fluids’ EOS in the same pressure range. We find that there exist noticeable differences between the EOS of the mixture and that of pure methanol in terms of molar quantities.

The core of the Earth is predominately iron alloyed with approximately 5 wt% nickel along with some amount of light elements, e.g., Si, O, S, C, H, Mg. Mineral physics studies, in conjunction with seismological and cosmochemical observations, provide an opportunity to improve constraints on the composition of the core. In this thesis, we investigate the thermoelastic and vibrational properties of bcc- and hcp-structured Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 (atomic percent) at high pressures. We present powder x-ray diffraction data on bcc- and hcp-structured Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 at 300 K up to 167 GPa and 175 GPa, respectively. The alloys were compressed in diamond anvil cells, and their equations of state and axial ratios were measured with high statistical quality. These equations of state are combined with thermal parameters from previous reports to improve the extrapolation of the density, adiabatic bulk modulus, and bulk sound speed to the pressures and temperatures of Earth’s inner core. We place constraints on the composition of Earth’s inner core by combining these results with seismic observations and available data on other light-element alloys of iron. We find the addition of 4.3 to 5.3 wt% silicon to Fe0.95Ni0.05 alone can explain geophysical observations of density, adiabatic bulk modulus, and bulk sound speed at the inner core boundary, as can up to 7.5 wt% sulfur with negligible amounts of silicon and oxygen. Our findings favor an inner core with less than ∼2 wt% oxygen and less than ∼1 wt% carbon, although uncertainties in electronic and anharmonic contributions to the equations of state may shift these values. Seismic studies provide evidence for an anisotropic inner core, which is suggested to be related to the ratio of the c- to a-unit cell parameters of hcp-structured materials. We demonstrate hcp-Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 have measurably greater c/a axial ratios than those of hcp-Fe over the measured pressure range. We further investigate the relationship between the axial ratios, their pressure derivatives, and elastic anisotropy of hcp-structured materials. Next, we present high pressure NRIXS data on bcc- and hcp-Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 at 300 K with in situ x-ray diffraction. From these data, we determine the partial phonon density of states for each composition, and we systematically compare our results to iron. We constrain the Debye sound velocity from the low energy region of the phonon density of states. Using our previously determined equations of state for the same compositions, we constrain the compressional and shear sound velocities and shear moduli. At 300 K, we find that 9 at% nickel decreases the shear velocity of hcp-iron by ∼6% and that silicon has a minimal effect on the shear velocity of hcp-Fe0.91Ni0.09. Thermal effects likely play a large role in the sound velocities of iron alloys at core conditions, so constraining these effects is critical to further constrain the composition of the core. From the volume scaling of the phonon DOS, we find the 300 K vibrational components of the Gruneisen parameter for hcp-Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 are very similar to that of hcp-Fe within uncertainties. We also constrain vibrational thermal pressure from the volume dependence of vibrational free energy, and we find negligible differences within uncertainty between the vibrational thermal pressures of hcp-Fe, Fe0.91Ni0.09, and Fe0.8Ni0.1Si0.1. By combining the vibrational component of thermal pressure with theoretical estimates of the anharmonic and electronic contributions, we provide an estimate for the total thermal pressure. We constrain a variety of additional parameters from the NRIXS data and phonon density of states, including the vibrational component of entropy, the vibrational thermal expansion, the vibrational kinetic energy, the Lamb-Mossbauer factor, and the vibrational specific heat.

In situ high-pressure diffraction experiments on single-crystal α-quartz under quasi-hydrostatic conditions up to 19 GPa were performed with diamond-anvil cells. Isotropic pressures were calibrated through the ruby-luminescence technique. A 4:1 methanol–ethanol mixture and the densified noble gases helium and neon were used as pressure media. The compression data revealed no significant influence of the pressure medium at room temperature on the high-pressure behavior of α-quartz. In order to describe its compressibility for use as a pressure standard, a fourth-order Birch–Murnaghan equation of state (EoS) with parameters K T0 = 37.0 (3) GPa, K T0′ = 6.7 (2) and K T0′′ = −0.73 (8) GPa−1 was applied to fit the data set of 99 individual data points. The fit of the axial compressibilities yields M T0 = 104.5 (8) GPa, M T0′ = 13.7 (4), M T0′′ = −1.04 (11) GPa−1 (a axis) and M T0 = 141 (3) GPa, M T0′ = 21 (2), M T0′′ = 8.4 (6) GPa−1 (c axis), confirming the previously reported anisotropy. Assuming an estimated standard deviation of 0.0001% in the quartz volume, an uncertainty of 0.013 GPa can be expected using the new set of EoS parameters to determine the pressure.

The Liquid density predicted by the Peng-Robinson (P-R) equation of state is often off by 10% or more at temperature and pressure conditions encountered in most reservoirs. To improve the density predictions, two new density correlations have been developed. The first correlation is based on the chain-of-rotators (COR) equation of state and the second is based on the three-parameter Peng-Robinson (PR3) equation of state. The COR correlation is applicable to wider pressure and temperature ranges, but is computationally expensive. It is suited for interpreting fluid-analysis data, where no extensive phase-behavior calculations are needed. On the other hand, the PR3 correlation is more limited in its application range, but is computationally more efficient. It is particularly suited for compositional reservoir simulation where many density calculations are repeatedly carried out. In general, both correlations are comparable to the Standing-Katz correlation for liquid-density calculation and comparable to the P-R equation of state for vapor-density calculation. However, they are superior to the Standing-Katz correlation for liquid mixtures near critical points or liquid mixtures at high pressures. Overall, the COR equation of state gives an average prediction error of 1.9% for liquid densities and 2.7% for vapor densities, and the PR3 gives an average prediction error of less than 2% for both liquid and vapor densities. The required inputs are any two of the following properties for each pseudocomponent: molecular weight, specific gravity, and normal boiling point. This easy input requirement makes the correlations very attractive for engineering uses.

Results of theoretical calculations and experimental measurements of the equation of state (EOS) at extreme conditions are discussed and applied to aluminum. It is pointed out that the available high pressure and temperature information covers a broad range of the phase diagram, but only irregularly and, as a rule, is not thermodynamically complete; its generalization can be done only in the form of a thermodynamically complete EOS. A multi-phase EOS model is presented, accounting for solid, liquid, gas, and plasma states, as well as two-phase regions of melting and evaporation. The thermodynamic properties of aluminum and its phase diagram are calculated with the use of this model. Theoretical calculations of thermodynamic properties of the solid, liquid, and plasma phases, and of the critical point, are compared with results of static and dynamic experiments. The analysis deals with thermodynamic properties of solid aluminum at T = 0 and 298 K from different band-structure theories, static compression experiments in diamond anvil cells, and the information obtained in isentropic-compression and shock-wave experiments. Thermodynamic data in the liquid state, resulting from traditional thermophysical measurements, “exploding wire” experiments, and evaluations of the critical point are presented. Numerous shock-wave experiments for aluminum have been done to measure shock adiabats of crystal and porous samples, release isentropes, and sound speed in shocked metal. These data are analyzed in a self-consistent manner together with all other available data at high pressure.The model's results are shown for the principal shock adiabat, the high-pressure melting and evaporation regions and the critical point of aluminum. New experimental and theoretical data helped to improve the description of the high-pressure, high-temperature aluminum liquid. The present EOS describes with high accuracy and reliability the complete set of available information.

New Cage-Like Cerium Trihydride Stabilized at Ambient Conditions

A thermodynamically consistent Equation Of State (EOS) was developed to predict and analyse the behaviour of multiphase metals under shock wave loading. Assuming the Mie-Gruneisen hypothesis together with the Birch (for example) formulation, the EOS gives the relation between pressure P, temperature T and atomic volume V. Experimental data (P,V,T) for each phase are provided mainly by X-ray diffraction measurements with diamond anvil cells. In this work, mathematical tools are designed to optimize the determination of the EOS parameters and evaluate uncertainty. The general EOS form is y = f ϑ (x ) where y = P, x = (V,T) and ϑ is the parameter vector to calibrate. Using experimental data (x i ,y i ), the least square (non-linear) regression provides an optimal value ϑ∗ for the fit parameters. The measurement errors on y and x give biased estimation of ϑ∗ with the standard method. Assuming centered and known variance laws for the errors, a statistical procedure is proposed to estimate ϑ∗ and determine confidence intervals. Thanks to a Bayesian approach it is possible to introduce physical interval knowledge of the parameters in this procedure. Moreover, various EOS f ϑ∗ formulations are evaluated with a chi-squared type statistical test. The present method is applied on experimental data for multi phase tin (β and γ phases and liquid state) in order to provide an optimized multi-phase model. Furthermore, the method is used to design further experimental campaign and to evaluate the gain of new experimental data with the corresponding estimated errors.

A 4:1 (volume ratio) methanol–ethanol (ME) mixture and silicone oil are two of the most widely used liquid pressure-transmitting media (PTM) in high-pressure studies. Their hydrostatic limits have been extensively studied using various methods; however, the evolution of the atomic structures associated with their emerging nonhydrostaticity remains unclear. Here, we monitor their structures as functions of pressure up to ∼30 GPa at room temperature using in situ high-pressure synchrotron x-ray diffraction (XRD), optical micro-Raman spectroscopy, and ruby fluorescence spectroscopy in a diamond anvil cell. No crystallization is observed for either PTM. The pressure dependence of the principal diffraction peak position and width indicates the existence of a glass transition in the 4:1 ME mixture at ∼12 GPa and in the silicone oil at ∼3 GPa, beyond which a pressure gradient emerges and grows quickly with pressure. There may be another liquid-to-liquid transition in the 4:1 ME mixture at ∼5 GPa and two more glass-to-glass transitions in the silicone oil at ∼10 GPa and ∼16 GPa. By contrast, Raman signals only show peak weakening and broadening for typical structural disordering, and Raman spectroscopy seems to be less sensitive than XRD in catching these structural transitions related to hydrostaticity variations in both PTM. These results uncover rich pressure-induced transitions in the two PTM and clarify their effects on hydrostaticity with direct structural evidence. The high-pressure XRD and Raman data on the two PTM obtained in this work could also be helpful in distinguishing between signals from samples and those from PTM in future high-pressure experiments.

We report an updated isothermal equation of state (EoS) of molybdenum (Mo) obtained by compression in beveled and toroidal diamond-anvil cells (DACs). For an improved compression environment, we developed a copper (Cu) pressure-transmitting medium (PTM) for the toroidal diamond-anvil cell samples, as it is a soft metal compared to Mo with a well calibrated EoS. A Ne PTM was used for the conventional beveled DAC samples. The unit-cell volumes of Mo were measured to 336(1) GPa in the Cu PTM and 231.2(6) GPa in the Ne PTM at room temperature. We additionally calculated elastic stiffness and compliance constants and evaluated the uniaxial stress of Mo and Cu with pressure. A new EoS for Mo is presented from data collected in all sample environments and compared to our theoretical predictions as well as previous compression studies of Mo. The (200) lattice plane of Mo produced the lowest volumes across the pressure range of this study for all compression environments, suggesting that it is less affected by nonhydrostatic stresses in the DAC compared to the other observed diffraction planes. The presented Mo EoS is compatible with extrapolations of EoS fits of Mo in helium (He) within ∼1% at 330 GPa. Results from this work demonstrate that compressing a sample in a softer metal in the toroidal DAC can improve the compression environment and result in measured sample volumes comparable to those collected in noble-gas media at multi-megabar conditions.

Transformation pathways and isothermal compressibility of a MTN-type clathrasil using penetrating and non-penetrating fluids

The behavior of a number of commonly used pressure media, including nitrogen, argon, 2-propanol, a 4:1 methanol–ethanol mixture, glycerol and various grades of silicone oil, has been examined by measuring the X-ray diffraction maxima from quartz single crystals loaded in a diamond-anvil cell with each of these pressure media in turn. In all cases, the onset of non-hydrostatic stresses within the medium is detectable as the broadening of the rocking curves of X-ray diffraction peaks from the single crystals. The onset of broadening of the rocking curves of quartz is detected at ∼9.8 GPa in a 4:1 mixture of methanol and ethanol and at ∼4.2 GPa in 2-propanol, essentially at the same pressures as the previously reported hydrostatic limits determined by other techniques. Gigahertz ultrasonic interferometry was also used to detect the onset of the glass transition in 4:1 methanol–ethanol and 16:3:1 methanol–ethanol–water, which were observed to support shear waves above ∼9.2 and ∼10.5 GPa, respectively, at 0.8–1.2 GHz. By contrast, peak broadening is first detected at ∼3 GPa in nitrogen, ∼1.9 GPa in argon, ∼1.4 GPa in glycerol and ∼0.9 GPa in various grades of silicone oil. These pressures, which are significantly lower than hydrostatic limits quoted in the literature, should be considered as the practical maximum limits to the hydrostatic behavior of these pressure media at room temperature.