Sapphire (Al2O3) 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. In this paper 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 ± 13 GPa. A phase diagram which incorporates literature diamond-anvil cell data and melting measurements is presented.
Sapphire (Al2O3) 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±13 GPa. A phase diagram which incorporates literature diamond-anvil cell data and melting measurements is presented.
The high-pressure dynamic response of titanium dioxide (TiO 2) is not only of interest because of its numerous industrial applications but also because of its structural similarities to silica (SiO 2). We performed plate impact experiments in a two-stage light gas gun, at peak stresses from 64 to 221 GPa to determine the TiO 2 response along the Hugoniot. The lower stress experiment at 64 GPa shows an elastic behavior followed by an elastic-plastic transition, whereas the high stress experiments above 64 GPa show a single wave structure. Previous shock studies have shown the presence of high-pressure phases (HPP) I (26 GPa) and HPP II (100 GPa); however, our data suggest that the HPP I phase is stable up to 150 GPa. Using a combination of data from our current study and our previous Z-data, we determine that TiO 2 likely melts on the Hugoniot at 157 GPa. Furthermore, our data confirm that TiO 2 is not highly incompressible as shown by a previous study.
Shock compression experiments on natural compositions are imperative to accurately model planetary accretion and the interior dynamics of planets. Combining shock compression experiments from the Sandia Z Machine and the OMEGA EP laser facility with density functional theory-based molecular dynamics calculations, we report the first pressure-density-temperature (P-ρ-T) relationship of natural iron (Fe)-bearing olivine ((Mg0.91Fe0.09)2SiO4) on the principal Hugoniot between 166 and 1,465 GPa. Additionally, we report the first reflectivities of natural olivine liquid in this pressure range. Compared to the magnesium-endmember forsterite (Mg2SiO4), the presence of Fe in typical mantle abundance (∼9 wt% FeO) alters the US-uP relation of olivine. On the other hand, the shock temperature and reflectivity of olivine are indistinguishable from forsterite where experimental conditions overlap. Both forsterite and olivine increase in reflectivity (and hence optical conductivity) with increasing temperature, with a maximum reflectivity of ∼31% at shock velocities greater than 22 km/s (∼800 GPa).
The physical processes during planet formation span a large range of pressures and temperatures. Giant impacts, such as the one that formed the Moon, achieve peak pressures of 100s of GPa. The peak shock states generate sufficient entropy such that subsequent decompression to low pressures intersects the liquid-vapor phase boundary. The entire shock-and-release thermodynamic path must be calculated accurately in order to predict the post-impact structures of planetary bodies. Forsterite (Mg2SiO4) is a commonly used mineral to represent the mantles of differentiated bodies in hydrocode models of planetary collisions. Here, we performed shock experiments on the Sandia Z Machine to obtain the density and temperature of the liquid branch of the liquid-vapor phase boundary of forsterite. This work is combined with previous work constraining pressure, density, temperature, and entropy of the forsterite principal Hugoniot. We find that the vapor curves in previous forsterite equation of state models used in giant impacts vary substantially from our experimental results, and we compare our results to a recently updated equation of state. We have also found that due to under-predicted entropy production on the principal Hugoniot and elevated temperatures of the liquid vapor phase boundary of these past models, past impact studies may have underestimated vapor production. Furthermore, our results provide experimental support to the idea that giant impacts can transform much of the mantles of rocky planets into supercritical fluids.
The strength of brittle porous media is of concern in numerous applications, for example, earth penetration, crater formation, and blast loading. Thus, it is of importance to possess techniques that allow for constitutive model calibration within the laboratory setting. The goal of the current work is to demonstrate an experimental technique allowing for strength assessment of porous media subjected to shock loading, which can be implemented into pressure-dependent yield surfaces within numerical simulation schemes. As a case study, the deviatoric response of distended α-SiO2 has been captured in a tamped Richtmyer–Meshkov instability (RMI) environment at a pressure regime of 4–10 GPa. Hydrocode simulations were used to interpret RMI experimental data, and a resulting pressure-dependent yield surface akin to the often employed modified Drucker–Prager model was calibrated. Simulations indicate that the resulting jet length generated by the RMI is sensitive to the porous media strength, thereby providing a feasible experimental platform capable of capturing the pressurized granular deviatoric response. Furthermore, in efforts to validate the RMI-calibrated strength model, a set of Mach-lens experiments was performed and simulated with the calibrated pressure-dependent yield surface. Excellent agreement between the resulting Mach-lens length in experiment and simulation provides additional confidence to the RMI yield-surface calibration scheme.
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.
We discuss major challenges in modeling giant impacts between planetary bodies, focusing on the equations of state (EOS). During the giant impact stage of planet formation, rocky planets are melted and partially vaporized. However, most EOS models fail to reproduce experimental constraints on the thermodynamic properties of the major minerals over the required phase space. Here, we present an updated version of the widely-used ANEOS model that includes a user-defined heat capacity limit in the thermal free energy term. Our revised model for forsterite (Mg2SiO4), a common proxy for the mantles of rocky planets, provides a better fit to material data over most of the phase space of giant impacts. We discuss the limitations of this model and the Tillotson equation of state, a commonly used alternative model.
We report the atomic- and nanosecond-scale quantification of kinetics of a shock-driven phase transition in Zr metal. We uniquely make use of a multiple shock-and-release loading pathway to shock Zr into the β phase and to create a quasisteady pressure and temperature state shortly after. Coupling shock loading with in situ time-resolved synchrotron x-ray diffraction, we probe the structural transformation of Zr in the steady state. Our results provide a quantified expression of kinetics of formation of β-Zr phase under shock loading: transition incubation time, completion time, and crystallization rate.
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.
In this work we provide direct evidence of shock-induced melting and associated kinetics in a porous solid (aluminum powder) using time-resolved x-ray diffraction. Unambiguous evidence of melting in 50% porous aluminum (Al) powder samples, shocked to peak pressures between ∼13-19GPa, was provided by the broadening of the Debye-Scherrer ring corresponding to the (111) peak. Shocked Al powder did not melt completely in any of our experiments within the durations of measurement. Incomplete (partial) melting of the powder, even after several hundreds of nanoseconds of shock loading, provides insights into thermal transport with Al powder particles under high-pressure dynamic loading. Such insights are quite valuable for developing well-constrained melting models and thermodynamic equations of state for porous Al and other porous solids relevant to planetary and materials science.
Collisions that induce melting and vaporization can have a substantial effect on the thermal and geochemical evolution of planets. However, the thermodynamics of major minerals are not well known at the extreme conditions attained during planet formation. We obtained new data at the Sandia Z Machine and use published thermodynamic data for the major mineral forsterite (Mg2SiO4) to calculate the specific entropy in the liquid region of the principal Hugoniot. We use our calculated specific entropy of shocked forsterite, and revised entropies for shocked silica, to determine the critical impact velocities for melting or vaporization upon decompression from the shocked state to 1 bar and the triple points, which are near the pressures of the solar nebula. We also demonstrate the importance of the initial temperature on the criteria for vaporization. Applying these results to N-body simulations of terrestrial planet formation, we find that up to 20% to 40% of the total system mass is processed through collisions with velocities that exceed the criteria for incipient vaporization at the triple point. Vaporizing collisions between small bodies are an important component of terrestrial planet formation.