The outer core of the Earth is composed primarily of liquid iron, and the inner core boundary is governed by the intersection of the melt line and the geotherm. While there are many studies on the thermodynamic equation of state for solid iron, the equation of state of liquid iron is relatively unexplored. In this work, we use dynamic compression to diagnose the high-pressure liquid equation of state of iron by utilizing the shock-ramp capability at Sandia National Laboratories’ Z-Machine. This technique enables measurements of material states off the Hugoniot by initially shocking samples and subsequently driving a further, shockless compression. Planetary studies benefit greatly from isentropic, off-Hugoniot experiments since they can cover pressure-temperature (P-T) conditions that are close to adiabatic profiles found in planetary interiors. We used this method to drive iron to P-T conditions similar to those of the Earth’s outer-inner core boundary, along an elevated-temperature isentrope in the liquid from 275 GPa to 400 GPa. We derive the equation of state using a hybrid backward integration – forward Lagrangian technique on particle velocity traces to determine the pressure-density history of the sample. Our results are in excellent agreement with SESAME 92141, a previously published equation of state table. With our data and previous experimental data on liquid iron we provide new information on the iron melting line and derive new parameters for a Vinet-based equation of state. The table and our parameterized equation of state are applied to provide an updated means of modeling the pressure, mass, and density of liquid iron cores in exoplanetary interiors.
Elucidating the mechanisms responsible for sub-microsecond desorption of water and other impurities from electrode surfaces at high heating rates is crucial for understanding pulsed power behavior. Ionization of desorbed impurities in the vacuum regions causes power or current loss; devising methods to limit such desorption during the short time scale of pulsed power is needed to improve corresponding applications. Previous molecular modeling studies have strongly suggested that, under high vacuum conditions, the amount of water impurity desorbing from oxide surfaces on metal electrodes is at a sub-monolayer level at room temperature, which appears insufficient to explain observed pulsed power energy losses at high current densities. In this work, we apply Density Functional Theory (DFT) techniques to show that hydrogen trapped inside iron metal can diffuse into hematite (α-Fe2O3) on the metal surface, ultimately reacting with the oxide to form Fe(II) and H2O. The latter desorbs at elevated temperature and may explain the anomalous amount of desorbed impurity inferred from pulsed-power experiments. We also apply a suite of characterization techniques to demonstrate that when iron metal is heated to 650 °C, the dominant surface oxide component becomes α-Fe2O3. The oxide facets exposed are found to be a mixture of (0001), (10-10), and others, in agreement with the DFT models used.
This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.
The equation of state (EOS) and shock compression of bulk vanadium were investigated using canonical ab initio molecular dynamic simulations, with experimental validation to 865 GPa from shock data collected at Sandia's Z Pulsed Power Facility. In simulations the phase space was sampled along isotherms ranging from 3000 K to 50000 K, for densities between -ü=3 and 15g/cm3, with a focus on the liquid regime and the body-centered-cubic phase in the vicinity of the melting limit. The principal Hugoniot predicted from first principles is overall consistent with shock data, while it showed that current multiphase SESAME-type EOS for vanadium needed revision in the liquid regime. A more accurate SESAME EOS was developed using constraints from experiments and simulations. This work emphasizes the need to use a combined theoretical and experimental approach to develop high-fidelity EOS models for extreme conditions.
Hypervelocity impact-driven vaporization is characteristic of late-stage planet formation. Yet the behavior and properties of liquid-vapor mixtures of planetary materials of interest are typically unknown. Multiphase equations of state used in hydrodynamic simulations of planet impacts therefore lack reliable data for this important phenomenon. Here, we present the first constraints on the liquid-vapor critical point and coexistence phase boundary of Mg2SiO4 computed from ab initio molecular dynamics simulations. We found that the vapor is depleted in magnesium and enriched in silica and oxygen, while the coexisting liquid is enriched in magnesium and depleted in oxygen, from which we infer vaporization is incongruent. The critical point was estimated from an equation of state fit to the data. The results are in line with recent calculations of MgSiO3 and together confirm that extant multiphase equation of state (EOS) models used in planetary accretion modeling significantly underestimate the amount of supercritical material postimpact.
The high-pressure response of titanium dioxide (TiO2) is of interest because of its numerous industrial applications and its structural similarities to silica (SiO2). We used three platforms - Sandia's Z machine, Omega Laser Facility, and density-functional theory-based quantum molecular dynamics (QMD) simulations - to study the equation of state (EOS) of TiO2 at extreme conditions. We used magnetically accelerated flyer plates at Sandia to measure Hugoniot of TiO2 up to pressures of 855 GPa. We used a laser-driven shock wave at Omega to measure the shock temperature in TiO2. Our Z data show that rutile TiO2 reaches 2.2-fold compression at a pressure of 855 GPa and Omega data show that TiO2 is a reflecting liquid above 230 GPa. The QMD simulations are in excellent agreement with the experimental Hugoniot in both pressure and temperature. A melt curve for TiO2 is also proposed based on the QMD simulations. The combined experimental results show TiO2 is in a liquid at these explored pressure ranges and is not highly incompressible as suggested by a previous study.
The high-pressure response of titanium dioxide (TiO2) is of interest because of its numerous industrial applications and its structural similarities to silica (SiO2). We used three platforms - Sandia's Z machine, Omega Laser Facility, and density-functional theory-based quantum molecular dynamics (QMD) simulations - to study the equation of state (EOS) of TiO2 at extreme conditions. We used magnetically accelerated flyer plates at Sandia to measure Hugoniot of TiO2 up to pressures of 855 GPa. We used a laser-driven shock wave at Omega to measure the shock temperature in TiO2. Our Z data show that rutile TiO2 reaches 2.2-fold compression at a pressure of 855 GPa and Omega data show that TiO2 is a reflecting liquid above 230 GPa. The QMD simulations are in excellent agreement with the experimental Hugoniot in both pressure and temperature. A melt curve for TiO2 is also proposed based on the QMD simulations. The combined experimental results show TiO2 is in a liquid at these explored pressure ranges and is not highly incompressible as suggested by a previous study.
Using the analogy between hydrodynamic and electrical current flow, we study how electrical current density j redistributes and amplifies due to two commonly encountered inhomogeneities in metals. First, we consider flow around a spherical resistive inclusion and find significant j amplification, independent of inclusion size. Hence, even μm-scale inclusions can affect performance in applications by creating localized regions of enhanced Joule heating. Next, we investigate j redistribution due to surface roughness, idealized as a sinusoidal perturbation with amplitude A and wavelength λ. Theory predicts that j amplification is determined by the ratio A/λ, so that even "smooth"surface finishes (i.e., small A) can generate significant amplification, if λ is correspondingly small. We compare theory with magnetohydrodynamic simulation to illustrate both the utility and limitations of the steady-state theory.
Mixing of cold, higher-Z elements into the fuel region of an inertial confinement fusion target spoils the fusion burn efficiency. This mixing process is driven by both "turbulent" and "atomic" mixing processes, the latter being modeled through transport corrections to the basic hydrodynamic models. Recently, there has been a surge in the development of dense plasma transport modeling and the associated transport coefficients; however, experimental validation remains in its infancy.
The shock Hugoniot for full-density and porous CeO2 was investigated in the liquid regime using ab initio molecular dynamics (AIMD) simulations with Erpenbeck's approach based on the Rankine-Hugoniot jump conditions. The phase space was sampled by carrying out NVT simulations for isotherms between 6000 and 100 000 K and densities ranging from ρ=2.5 to 20g/cm3. The impact of on-site Coulomb interaction corrections +U on the equation of state (EOS) obtained from AIMD simulations was assessed by direct comparison with results from standard density functional theory simulations. Classical molecular dynamics (CMD) simulations were also performed to model atomic-scale shock compression of larger porous CeO2 models. Results from AIMD and CMD compression simulations compare favorably with Z-machine shock data to 525 GPa and gas-gun data to 109 GPa for porous CeO2 samples. Using results from AIMD simulations, an accurate liquid-regime Mie-Grüneisen EOS was built for CeO2. In addition, a revised multiphase SESAME-Type EOS was constrained using AIMD results and experimental data generated in this work. This study demonstrates the necessity of acquiring data in the porous regime to increase the reliability of existing analytical EOS models.
Absolute Hugoniot measurements for empty plastic foams at ∼10% of solid polystyrene density and supporting rad-hydro simulation results are reported. Planar foam slabs, ∼400 μm thick and ∼500 μm wide, some of which were covered with a 10 μm solid plastic ablator, were directly driven by 4 ns long Nike krypton-fluoride 248 nm wavelength laser pulses that produced strong shock waves in the foam. The shock and mass velocities in our experiments were up to 104 km/s and 84 km/s, respectively, and the shock pressures up to ∼9 Mbar. The motion of the shock and ablation fronts was recorded using side-on monochromatic x-ray imaging radiography. The steadiness of the observed shock and ablation fronts within ∼1% has been verified. The Hugoniot data inferred from our velocity measurements agree with the predictions of the SESAME and CALEOS equation-of-state models near the highest pressure ∼9 Mbar and density compression ratio ∼5. In the lower pressure range 2-5 Mbar, a lower shock density compression is observed than that predicted by the models. Possible causes for this discrepancy are discussed.
Presented are the results from the liner ablation experiments conducted at 550 kA on the Michigan Accelerator for Inductive Z-Pinch Experiments. These experiments were performed to evaluate a hypothesis that the electrothermal instability (ETI) is responsible for the seeding of magnetohydrodynamic instabilities and that the cumulative growth of ETI is primarily dependent on the material-specific ratio of critical temperature to melting temperature. This ratio is lower in refractory metals (e.g., tantalum) than in non-refractory metals (e.g., aluminum or titanium). The experimental observations presented herein reveal that the plasma-vacuum interface is remarkably stable in tantalum liner ablations. This stability is particularly evident when contrasted with the observations from aluminum and titanium experiments. These results are important to various programs in pulsed-power-driven plasma physics that depend on liner implosion stability. Examples include the magnetized liner inertial fusion (MagLIF) program and the cylindrical dynamic material properties program at Sandia National Laboratories, where liner experiments are conducted on the 27-MA Z facility.
In recent years, α-quartz has been used prolifically as an impedance matching standard in shock wave experiments in the multi-Mbar regime (1 Mbar = 100 GPa = 0.1 TPa). This is due to the fact that above ∼90-100 GPa along the principal Hugoniot α-quartz becomes reflective, and thus, shock velocities can be measured to high precision using velocity interferometry. The Hugoniot and release of α-quartz have been studied extensively, enabling the development of an analytical release model for use in impedance matching. However, this analytical release model has only been validated over a range of 300-1200 GPa (0.3-1.2 TPa). Here, we extend this analytical model to 200-3000 GPa (0.2-3 TPa) through additional α-quartz Hugoniot and release measurements, as well as first-principles molecular dynamics calculations.
Included in this memo are the final values for the BSE and SiO2 critical points. VASP 5.3.3 was used to calculate the values in each table. Standard methodology is to continue equilibrating the simulation until the block averaged standard deviation is less than 1%. However, due to the simulation sizes in these simulations, the average standard deviation of the BSE pressure is 5% (ranging between 2% and 7%, which is much higher than the usual under 1% considered acceptable) and the SiO2 pressure is 6% with the lower density error bars being significantly larger than the highest density. The critical point is chosen where the dP/dρ >= 0 for an entire isotherm but is often difficult to distinguish because of the noise along each isotherm. As such, the actual values of the critical points are found by “best guess”. Further computer simulations creating a more pressure values along each isotherm would help but time constraints preclude this. Similarly, the ability to calculate pressures at lower densities that are currently feasible with VASP would also make determination of the critical point easier.
The electrical conductivity of materials under extremes of temperature and pressure is of crucial importance for a wide variety of phenomena, including planetary modeling, inertial confinement fusion, and pulsed power based dynamic materials experiments. There is a dearth of experimental techniques and data for highly compressed materials, even at known states such as along the principal isentrope and Hugoniot, where many pulsed power experiments occur. We present a method for developing, calibrating, and validating material conductivity models as used in magnetohydrodynamic (MHD) simulations. The difficulty in calibrating a conductivity model is in knowing where the model should be modified. Our method isolates those regions that will have an impact. It also quantitatively prioritizes which regions will have the most beneficial impact. Finally, it tracks the quantitative improvements to the conductivity model during each incremental adjustment. In this paper, we use an experiment on Sandia National Laboratories Z-machine to isentropically launch multiple flyer plates and, with the MHD code ALEGRA and the optimization code DAKOTA, calibrated the conductivity such that we matched an experimental figure of merit to +/-1%.