Diamond Anvil Cell Data Research Articles

Hugoniot, sound speed, and phase transitions of single-crystal sapphire for pressures 0.2–2.1 TPa

Sapphire (${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$) is a major constituent of the Earth's mantle and has significant contributions to the field of high-pressure physics. Constraining its Hugoniot over a wide pressure range and identifying the location of shock-driven phase transitions allows for development of a multiphase equation of state and enables its use as an impedance-matching standard in shock physics experiments. Here, we present measurements of the principal Hugoniot and sound velocity from direct impact experiments using magnetically launched flyers on the Z machine at Sandia National Laboratories. The Hugoniot was constrained for pressures from 0.2--2.1 TPa and a four-segment piecewise linear shock-velocity--particle-velocity fit was determined. First-principles molecular dynamics simulations were conducted and agree well with the experimental Hugoniot. Sound-speed measurements identified the onset of melt between 450 and 530 GPa, and the Hugoniot fit refined the onset to $525\ifmmode\pm\else\textpm\fi{}13$ GPa. A phase diagram which incorporates literature diamond-anvil cell data and melting measurements is presented.

Discovery of terrestrial allabogdanite (Fe,Ni)2P, and the effect of Ni and Mo substitution on the barringerite-allabogdanite high-pressure transition

Abstract Minerals formed at high pressures are sensitive indicators of extreme pressure-temperature conditions that occur in nature. The discovery of the high-pressure polymorph of (Fe,Ni)2P, allabogdanite in the surficial pyrometamorphic rocks of the Hatrurim Formation (the Mottled Zone) surrounding the Dead Sea basin in Israel is the first terrestrial occurrence of a mineral previously only found in iron meteorites. Stepwise annealing experiments demonstrate that allabogdanite is metastable at ambient pressure and that it irreversibly transforms into its low-pressure polymorph, barringerite, upon heating to 850 ± 50 °C. High-pressure, high-temperature diamond-anvil cell (DAC) experiments confirm the results of annealing experiments. The DAC data indicate that Hatrurim allabogdanite is metastable below 7.4 GPa, and the low-to high-pressure phase transition (barringerite → allabogdanite) occurs at 25 ± 3 GPa and 1400 ± 100 °C. The observed transition pressure of Hatrurim allabogdanite is significantly higher than that of pure synthetic Fe2P (8 GPa) due to partial substitution of Fe for Ni (4 wt%) and Mo (2.5 wt%). Because the influence of substituting impurities on the conditions of phase transitions can be unexpectedly strong, our findings confirm that caution should be exercised when extrapolating data from experiments on synthetic compounds to natural systems. Based on the discovery of terrestrial allabogdanite (Fe,Ni)2P coupled with experiments probing the phase transitions in this natural composition, we contend that terrestrial allabogdanite formed via transformation from barringerite and posit potential scenarios of its formation.

Dynamic experiments to study the α−ε phase transition in cerium

The ability to understand and predict the response of matter at extreme conditions requires knowledge of a material’s equation-of-state including the location of phase boundaries, transition kinetics, and the evolution of material strength. Cerium is a material with a complex phase diagram that continues to attract significant scientific interest. Recent dynamic experiments have provided information on the low-pressure γ–α phase transition, sound speed, and Hugoniot data for the higher-pressure α phase, as well as the incipient shock melt transition. Despite these efforts, there are still regions of the phase diagram that are largely unexplored dynamically, including the high-pressure region below the melt boundary. Along a room temperature isotherm, diamond anvil cell data report a transition to the ϵ phase between 13 and 17 GPa. At higher temperatures, similar diamond anvil cell data show significant disagreement regarding the existence, location, and slope of the ϵ-phase boundary. In this work, double-shock loading was used to access the α–ϵ region of the phase diagram to obtain equation-of-state information and to determine the location of the ϵ-phase boundary for shock loading.

Shock compression of niobium from first-principles

The equation of state (EOS) of bulk niobium (Nb) was investigated within the framework of density functional theory, with Mermin’s generalization to finite temperatures. The shock Hugoniot for fully-dense and porous Nb was obtained from canonical ab initio molecular dynamics simulations with Erpenbeck’s approach based on the Rankine-Hugoniot jump conditions. The phase space was sampled along isotherms between 300 and 4000 K, for densities ranging from ρ=5.5 to 12 g/cm3. Results from simulations compare favorably with room-temperature multianvil and diamond anvil cell data for fully-dense Nb samples and with a recent tabulated SESAME EOS. The results of this study indicate that, for the application of weak and intermediate shocks, the tabular EOS models are expected to give reliable predictions.

Systematics of the Third Row Transition Metal Melting: The HCP Metals Rhenium and Osmium

The melting curves of rhenium and osmium to megabar pressures are obtained from an extensive suite of ab initio quantum molecular dynamics (QMD) simulations using the Z method. In addition, for Re, we combine QMD simulations with total free energy calculations to obtain its phase diagram. Our results indicate that Re, which generally assumes a hexagonal close-packed (hcp) structure, melts from a face-centered cubic (fcc) structure in the pressure range 20–240 GPa. We conclude that the recent DAC data on Re to 50 GPa in fact encompass both the true melting curve and the low-slope hcp-fcc phase boundary above a triple point at (20 GPa, 4240 K). A linear fit to the Re diamond anvil cell (DAC) data then results in a slope that is 2.3 times smaller than that of the actual melting curve. The phase diagram of Re is topologically equivalent to that of Pt calculated by us earlier on. Regularities in the melting curves of Re, Os, and five other 3rd-row transition metals (Ta, W, Ir, Pt, Au) form the 3rd-row transition metal melting systematics. We demonstrate how this systematics can be used to estimate the currently unknown melting curve of the eighth 3rd-row transition metal Hf.

Stress induced phase transitions in silicon

Silicon has a tremendous importance as an electronic, structural and optical material. Modeling the interaction of a silicon surface with a pointed asperity at room temperature is a major step towards the understanding of various phenomena related to brittle as well as ductile regime machining of this semiconductor. If subjected to pressure or contact loading, silicon undergoes a series of stress-driven phase transitions accompanied by large volume changes. In order to understand the material's response for complex non-hydrostatic loading situations, dedicated constitutive models are required. While a significant body of literature exists for the dislocation dominated high-temperature deformation regime, the constitutive laws used for the technologically relevant rapid low-temperature loading have severe limitations, as they do not account for the relevant phase transitions. We developed a novel finite deformation constitutive model set within the framework of thermodynamics with internal variables that captures the stress induced semiconductor-to-metal (cd-Si→β-Si), metal-to-amorphous (β-Si→a-Si) as well as amorphous-to-amorphous (a-Si→hda-Si, hda-Si→a-Si) transitions. The model parameters were identified in part directly from diamond anvil cell data and in part from instrumented indentation by the solution of an inverse problem. The constitutive model was verified by successfully predicting the transformation stress under uniaxial compression and load–displacement curves for different indenters for single loading–unloading cycles as well as repeated indentation. To the authors' knowledge this is the first constitutive model that is able to adequately describe cyclic indentation in silicon.

Three-dimensional X-ray diffraction in the diamond anvil cell: application to stishovite

Three-dimensional X-ray diffraction can be used for characterizing the orientation, position, and strain tensor of single grains in a polycrystalline aggregate. Here, we show how the method is well suited for diamond anvil cell data with heterogeneous grain sizes, with an application to two samples of stishovite at 15 and 26 GPa. For each grain, we obtain a well-defined orientation matrix and cell parameters. Center of mass position can also be adjusted to the experimental data, with errors in the present experiment. Finally, strain tensors are adjusted for the individual grains. The stress distribution obtained is in agreement with expectations from the diamond anvil cell geometry and previous measurements of stishovite strength. Advantages and potential for improvement of the method are then discussed.

Improving the understanding of the melting curve of tantalum at extreme pressures through the pressure dependence of fusion volume and entropy

Molecular dynamics simulations of the melting curve of tantalum for the pressure range 0–300GPa are reported. The calculated melting curve agrees well with shock wave measurements and other calculations, but disagrees strongly with the diamond anvil cell data at high pressure. Calculated results for the pressure dependence of the fusion volume and entropy show that the pressure dependence of melting temperature approximately followed the Clausius–Clapeyron relation, and the slope of melting curve is mainly due to the variation of fusion volume. Entropy change due to latent volume change in melting, ΔSV and change in the configuration, ΔSD were evaluated. It is found that they have similar trend as the overall entropy change in melting, and ΔSD is more dominant. Furthermore, the value of ΔSD at ambient pressure is close to Rln2 per mole, which is the specific value of ΔSD predicted by the Rln2 rule, while it decreases when pressure goes from 50 to 300GPa. The analysis of the pair distribution function at extreme pressure shows that the change of configuration on melting decreases with increasing pressure, which supports the pressure dependence of ΔSD.

High-pressure melting curve of hydrogen

The melting curve of hydrogen was computed for pressures up to 200 GPa, using molecular dynamics. The inter- and intramolecular interactions were described by the reactive force field (ReaxFF) model. The model describes the pressure-volume equation of state solid hydrogen in good agreement with experiment up to pressures over 150 GPa, however the corresponding equation of state for liquid deviates considerably from density functional theory calculations. Due to this, the computed melting curve, although shares most of the known features, yields considerably lower melting temperatures compared to extrapolations of the available diamond anvil cell data. This failure of the ReaxFF model, which can reproduce many physical and chemical properties (including chemical reactions in hydrocarbons) of solid hydrogen, hints at an important change in the mechanism of interaction of hydrogen molecules in the liquid state.

Improving the quality of diamond anvil cell data collected on an area detector by shading individual diamond overlaps

Crystallographic data collected on a CCD using a diamond anvil cell may present overlapping diamond and sample reflections. These false intensities may not be rejected by common data processing programs and may affect the finalhkllist. A utility was developed that shades these reflections during the integration, enabling their elimination before the solution or refinement. Moreover, this procedure avoids the error propagation to other reflections, caused by overlapping spots, through the profile fitting procedure of an integration run.

First-principles equations of state and elastic properties of seven metals

We present a systematic comparison of first-principles zero-temperature equations of state and elastic constants of seven metals (aluminum, titanium, copper, tantalum, tungsten, platinum, and gold) with the most recent diamond-anvil-cell (DAC) experimental data, for pressures up to 150 GPa. Our calculations were performed within density functional theory, testing both the local density approximation (LDA) and the generalized gradient approximation (GGA) to the exchange-correlation term, and using several types of pseudopotentials. The obtained pressure-volume relationships show good agreement with DAC data: the difference between ab initio pressure and experiment is at most 5 GPa at 100--150 GPa except for Au and Pt. The equilibrium volumes ${V}_{0}$ and bulk moduli ${K}_{0}$ are determined within 1.5% and 6% of DAC data respectively. Experimental results are better reproduced with GGA for Al, Ti, Cu, Ta and W, but with LDA for Pt and Au, in agreement with previous theoretical studies. The predicted elastic constants are within 10% of experiment. For tantalum we have also calculated phonon spectra under pressure. They are in excellent agreement with experimental data: especially they accurately reproduced the inflexion on the longitudinal branch in the $\ensuremath{\Gamma}$-H direction, which is typical of the VB column (V, Nb, Ta).

High-pressure thermoelasticity of body-centered-cubic tantalum

We have investigated the thermoelasticity of body-centered cubic (bcc) tantalum from first principles by using the linearized augmented plane wave (LAPW) and mixed--basis pseudopotential methods for pressures up to 400 GPa and temperatures up to 10000 K. Electronic excitation contributions to the free energy were included from the band structures, and phonon contributions were included using the particle-in-a-cell (PIC) model. The computed elastic constants agree well with available ultrasonic and diamond anvil cell data at low pressures, and shock data at high pressures. The shear modulus $c_{44}$ and the anisotropy change behavior with increasing pressure around 150 GPa because of an electronic topological transition. We find that the main contribution of temperature to the elastic constants is from the thermal expansivity. The PIC model in conjunction with fast self-consistent techniques is shown to be a tractable approach to studying thermoelasticity.

Equation of state for tantalum from relativistic linear combinations of Gaussian-type orbitals calculations

The zero-temperature equation of state (EOS) for tantalum (Ta) is calculated to 2.5 Mbar with the relativistic linear combinations of Gaussian type orbital--fitting-function (LCGTO-FF) method, for two density functional models: the local density approximation (LDA) and the generalized gradient approximation (GGA). The EOS is determined both with and without spin-orbit coupling included. The effect of spin-orbit coupling is found to be nearly negligible over the compression range considered, in sharp disagreement with a previous calculation using the full-potential linear muffin-tin orbital method. A serious discrepancy between 300 K diamond anvil cell data and reduced shock data for Ta is shown to result from an underestimate of the Grueneisen parameter during the reduction of the shock data. The GGA model reproduces the zero-pressure properties of Ta quite well, while the high-pressure EOS data is in better accord with the LDA calculations. Neither model provides an adequate representation for the EOS over the full range of the data.

All-electron full-potential calculation of the electronic band structure, elastic constants, and equation of state for graphite

The all-electron full-potential linear combinations of Gaussian-type orbitals---fitting-function technique has been used to calculate the electronic structure, equation of state (EOS), and elastic constants for crystalline graphite. An analysis of the zero-pressure band structure is used to resolve inconsistencies between previous local-density-approximation (LDA) calculations. The calculated band structure is consistent with experimental data to the extent expected given the known limits of LDA one-electron energies. The in-plane lattice constant found here exhibits the usual LDA-induced contraction, whereas the interlayer separation and the unit-cell volume exhibit an anomalous expansion due to a LDA underestimate of the weak interlayer bonding. The calculated values of ${\mathrm{C}}_{11}$+${\mathrm{C}}_{12}$ and ${\mathrm{C}}_{33}$ are in good agreement with ultrasound measurements, while the value of ${\mathrm{C}}_{13}$ (\ensuremath{\approx}0) is much smaller than the ultrasound value. The bulk modulus and pressure derivatives of the lattice constants derived from the theoretical elastic constants are in very good agreement with diamond anvil cell (DAC) data, suggesting that the theoretical value for ${\mathrm{C}}_{13}$ is more reliable than the ultrasound measurement. An analytical EOS has been determined for pressures up to 50 GPa, well beyond the range of stability for the graphite structure. The EOS and the pressure dependencies of c/a and the optical transition energies (${\mathrm{A}}_{1}$ and ${\mathrm{A}}_{2}$) are in reasonable agreement with DAC data up to 14 GPa.

High-precision, all-electron, full-potential calculation of the equation of state and elastic constants of corundum

The all-electron, full-potential linear combinations of Gaussian type orbitals{endash}fitting function technique has been used to perform high-precision total-energy calculations on {alpha}-alumina (corundum). The calculations yield zero-pressure lattice parameters that are in 0.3{percent} agreement with experiment and symmetry-preserving elastic constants that agree with experiment to within 5{percent}. The bulk modulus and pressure derivatives of the lattice parameters are also in good agreement with existing data. The calculated energies have been used to generate an analytical equation of state (EOS) for corundum that should be valid up to at least 250 GPa. The fitted EOS agrees with room temperature diamond anvil cell data up to 175 GPa to within the known limitations of the experimental data. The c/a ratio, band gap, and tetragonal shear modulus have been determined for pressures up to 250 GPa. The c/a ratio varies by less than 3{percent} over the entire pressure range. For pressures above 150 GPa, the band gap changes from direct to indirect and the tetragonal shear modulus softens. The linear pressure coefficient of the band gap is estimated to be 5.1 meV/kbar at zero pressure. {copyright} {ital 1997} {ital The American Physical Society}

Shock temperature and melting in iron sulfides at core pressures

The temperatures of shock‐compressed FeS and FeS2 in the pressure ranges 125–170 GPa and 100–244 GPa, respectively, are reported and used to constrain the melting curves and thermodynamic properties to core pressures. A fit of the Lindemann law parameters corresponding to the usual functional form for the lattice Grüneisen parameter gives γL = 1.17 ± 0.13 and nL = 0.5 ± 0.5 for the high‐pressure phase of FeS at ρ = 5340 kg/m3 and γL = 2.18 ± 0.32 and nL = 1.6 ± 0.7 for FeS2 at ρ = 5011 kg/m3. The entropies of fusion are ∼203 J kg−1 K−1 for FeS at 120 GPa and ∼180 J kg−1 K−1 for FeS2 at 220 GPa. We find that the melting temperature of FeS is 3240±200 K, 4210 ± 700 K, and 4310 ± 750 K at 136 GPa, 330 GPa, and 360 GPa, respectively. For FeS2, the melting temperatures are 3990 ± 300 K, 5310 ± 700 K, and 5440 ± 750 K, respectively, for the same pressures. The electronic specific heat for FeS is given by Ce = β0 (ρ0/ρ)γe with β0 = 0.25 ± 0.10 J kg−1 K−2 and γe = 1.34 for ρ0 = 5340 kg/m3 for the high‐pressure solid phase and β0 ≈ 0.05 J kg−1 K−2 and γe = 1.34 for ρ0 = 5150 kg/m3 for the liquid phase. For FeS2, there is no detectable electronic contribution, and the lattice specific heat is only 67% of the Dulong‐Petit limit, possibly implying tight S‐S binding in S2 units. A reexamination of all shock wave melting data for Fe indicates these approximately agree, but they do not resolve the disagreement between the extrapolated static diamond anvil cell data sets. Fe should melt at ∼6600 K at 243 GPa and 6900 ± 750 K at 330 GPa (the pressure of the inner core‐outer core boundary). Because the FeS melting curve falls well below that of FeS2, FeS may eventually undergo peritectic melting at high pressures, while FeS2 melts congruently.