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.