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DOE OSTI2024

Viscosity Measurements at High Pressures: A Critical Appraisal of Corrections to Stokes' Law

Abstract Fluids and melts in planetary interiors significantly influence geodynamic processes from volcanism to global‐scale differentiation. The roles of these geofluids depend on their viscosities ( η ). Constraining geofluid η at relevant pressures and temperatures relies on laboratory‐based measurements and is most widely done using Stokes' Law viscometry with falling spheres. Yet small sample chambers required by high‐pressure experiments introduce significant drag on the spheres. Several correction schemes are available for Stokes' Law but there is no consensus on the best scheme(s) for high‐pressure experiments. We completed high‐pressure experiments to test the effects of (a) the relative size of the sphere diameter to the chamber diameter and (b) the top and bottom of the chamber, that is, the ends, on the sphere velocities. We examined the influence of current correction schemes on the estimated viscosity using Monte Carlo simulations. We also compared previous viscometry work on various geofluids in different experimental setups/geometries. We find the common schemes for Stokes' Law produce statistically distinct values of η . When inertia of the sphere is negligible, the most appropriate scheme may be the Faxén correction for the chamber walls. Correction for drag due to the chamber ends depends on the precision in the sinking distance and may be ineffective with decreasing sphere size. Combining the wall and end corrections may overcorrect η . We also suggest the uncertainty in η is best captured by the correction rather than propagated errors from experimental parameters. We develop an overlying view of Stokes' Law viscometry at high pressures.

Geochemistry & Geophysics↗

DOE OSTI2025

The structure of liquid carbon elucidated by in situ X-ray diffraction

Carbon has a central role in biology and organic chemistry, and its solid allotropes provide the basis of much of our modern technology. However, the liquid form of carbon remains nearly uncharted, and the structure of liquid carbon and most of its physical properties are essentially unknown. But liquid carbon is relevant for modelling planetary interiors and the atmospheres of white dwarfs, as an intermediate state for the synthesis of advanced carbon materials, inertial confinement fusion implosions, hypervelocity impact events on carbon materials and our general understanding of structured fluids at extreme conditions. Here we present a precise structure measurement of liquid carbon at pressures of around 1 million atmospheres obtained by in situ X-ray diffraction at an X-ray free-electron laser. Our results show a complex fluid with transient bonding and approximately four nearest neighbours on average, in agreement with quantum molecular dynamics simulations. The obtained data substantiate the understanding of the liquid state of one of the most abundant elements in the universe and can test models of the melting line. The demonstrated experimental abilities open the path to performing similar studies of the structure of liquids composed of light elements at extreme conditions.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Building wet planets through high-pressure magma–hydrogen reactions

Close-in transiting sub-Neptunes are abundant in our Galaxy. Planetary interior models based on their observed radius–mass relationship suggest that sub-Neptunes contain a discernible amount of either hydrogen (dry planets) or water (wet planets) blanketing a core composed of rocks and metal. Water-rich sub-Neptunes have been believed to form farther from the star and then migrate inwards to their present orbits. Here we report experimental evidence of reactions between warm, dense hydrogen fluid and silicate melt that release silicon from the magma to form alloys and hydrides at high pressures. We found that oxygen liberated from the silicate melt reacts with hydrogen, producing an appreciable amount of water up to a few tens of weight per cent, which is much greater than previously predicted based on low-pressure ideal gas extrapolation. Consequently, these reactions can generate a spectrum of water contents in hydrogen-rich planets, with the potential to reach water-rich compositions for some sub-Neptunes, implying an evolutionary relationship between hydrogen-rich and water-rich planets. Therefore, detection of a large amount of water in exoplanet atmospheres may not be the optimal evidence for planet migration in the protoplanetary disk, calling into question the assumed link between composition and planet formation location.

Horn, H. W. [Arizona State University, Tempe, AZ (↗

DOE OSTI2026

Equilibrium and non-equilibrium effects in high pressure phase transformations of carbon

The behavior of carbon in the range 1–100 GPa and 1–10 kK is central to problems in planetary interiors, inertial confinement fusion targets, and high-pressure synthesis of carbon-based materials, but experiments in this regime are difficult and often provide only indirect constraints on phase behavior. As a result, phase boundary loci, structure, and limits of metastability at high pressure remain uncertain. In this work, machine-learning enhanced atomistic simulations are used to address this knowledge gap. We determine the melt line up to 100 GPa, the graphite-diamond phase boundary up to the melt line, and analyze structure of the coexisting phases. We show that the coexisting liquid evolves smoothly with pressure without evidence for a first-order liquid–liquid transition. Orientation-resolved graphite melting simulations indicate that basal-plane interfaces develop a dewetting layer and undergo layer-by-layer melting, producing kinetic hysteresis and an apparent orientation dependence of the melt line. Non-equilibrium quenches from the melt are used to construct a kinetically limiting graphite–diamond phase boundary for rapid quenches from above the melt line, and show that graphite is metastable at pressures of up to ≈ 25 GPa. These results provide bounds on equilibrium and metastable behavior in carbon relevant for interpreting high-pressure experiments and for designing synthesis pathways to specific carbon microstructures.

Lyu, Yanjun [Department of Materials Science and E↗

DOE OSTI2024

Multimessenger measurements of the static structure of shock-compressed liquid silicon at 100 GPa

The ionic structure of high-pressure, high-temperature fluids is a challenging theoretical problem with applications to planetary interiors and fusion capsules. Here we report a multimessenger platform using velocimetry and angularly and spectrally resolved x-ray scattering to measure the thermodynamic conditions and ion structure factor of materials at extreme pressures. We document the pressure, density, and temperature of shocked silicon near 100 GPa with uncertainties of 6%, 2%, and 20%, respectively. The measurements are sufficient to distinguish between and rule out some ion screening models. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Modeling the Interaction of Laser-Produced Proton Beams with Matter

A major goal of this project is to significantly increase our understanding of isochoric heating of matter using laser produced proton beams, and the associated high energy density (HED) and warm dense matter (WDM) regimes generated. This will benefit research fields such as planetary science, fusion energy, plasma physics, and material science. For example, it will enhance our understanding of WDM properties of iron and silica under conditions encountered in planetary interiors and diagnostic components in fusion devices exposed to high fluxes of energetic plasma ions. The project is motivated by recent experiments that irradiated Si targets with proton beams generated by the 20 TW-laser at the SLAC MEC end-station. The HED/WDM states are probed using the 50 fs hard X-rays available in the 3rd harmonic of the LCLS. As part of this project, results from the phase contrast X-ray imaging, which shows the generation of compression waves that produces rear surface spallation, are compared with results from the 3D multi-physics multi- material code, PISALE, that combines Arbitrary Lagrangian-Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR). This comparison required modifications to several physics models in the PISALE (Pacific Island Structured-AMR with ALE) code. An important aspect of this project is the continued training of graduate students in HED physics and in conducting complex multiphysics simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1973

Phase equilibria in molecular hydrogen-helium mixtures at high pressures

Experiments on phase behavior in hydrogen-helium mixtures have been carried out at pressures up to 9.3 kilobars, at temperatures from 26 to 100 K. Two distinct fluid phases are shown to exist at supercritical temperatures and high pressures. Both the trend of the experimental results and an analysis based on the van der Waals theory of mixtures suggest that this fluid-fluid phase separation persists at temperatures and pressures beyond the range of these experiments, perhaps even to the limits of stability of the molecular phases. The results confirm earlier predictions concerning the form of the hydrogen-helium phase diagram in the region of pressure-induced solidification of the molecular phases at supercritical temperatures. The implications of this phase diagram for planetary interiors are discussed.

Streett, W. B.↗

NASA NTRS1975

The magnetic field of Mercury. I

An updated analysis and interpretation are presented of the magnetic field observations obtained during the Mariner 10 encounter with the planet Mercury on March 29, 1974. The combination of data relating to position of the detached bow shock wave and magnetopause and the geometry and magnitude of the magnetic field within the magnetosphere-like region surrounding Mercury lead to the conclusion that an internal planetary field exists with dipole moment approximately 5.1 times 10 to the 22nd G per cu cm. The dipole axis has a polarity sense similar to that of earth and is tilted 7 deg from the normal to Mercury's orbital plane. The magnetic field observations reveal a significant distortion of the modest Hermean field by the solar wind flow and the formation of a magnetic tail and neutral sheet which begins close to the planet on the night side. Presently, an active dynamo mechanism in the planetary interior appears to be favored in the interpretation of the field origin.

Ness, N. F.↗

NASA NTRS1976

Interaction of solar wind with Mercury and its magnetic field

A brief review is presented of magnetic field and solar wind electron observations by Mariner 10 spacecraft. The intrinsic magnetic field of the planet Mercury and the implications of such a field for the planetary interior are also discussed.

Ness, N. F.↗

NASA NTRS1976

Observations of Mercury's magnetic field

Magnetic-field observations made during the third encounter of Mariner 10 with Mercury are discussed along with implications of an intrinsic field for the planetary interior. The data obtained confirm the presence of characteristic bow-shock, magnetosheath, and magnetosphere regions surrounding the planet and also indicate that Mercury occupies a much larger portion of its magnetosphere than does earth. Combined plasma, charged-particle, and magnetic-field data establish that the origin of the field is intrinsic to the planet rather than associated with an induction process due to solar-wind flow. Spherical harmonic analysis of the field data shows that the internal field of the planet is well described by a centered dipole with a moment of 5.0 by 10 to the 22nd power gauss-cu cm and oriented within 12 deg of the normal to the orbital plane in the same sense as earth. Surface intensities are deduced to be between about 300 and 800 gammas. It is concluded that an active dynamo is a more likely candidate than fossil magnetization for the origin of the field.

Ness, N. F.↗

NASA NTRS1978

The redox state of planetary basalts

Redox variations of terrestrial and lunar basalts and the redox variations in single cooling units (e.g., lava flows and lava lakes) are reviewed. Estimates for the redox states of inner solar system planetary basalts are presented; these estimates are based on consideration of a number of cosmogenic properties, models for planetary interiors, and the sequence of condensation with heliocentric distance from the protosun. It is suggested that basalts on Mercury and the Moon crystallized below the iron-wustite buffer curve; Venusian basalts are more oxidized than those on Mercury, less oxidized than those on earth, and crystallization within the field of wustite stability is thought likely; basalts on earth are dominantly in the field of magnetite stability; Martian basalts are estimated to crystallize in the upper regions of magnetite stability and well into the hematite field of stability expressed in terms of temperature and oxygen fugacity.

Haggerty, S. E.↗

NASA NTRS1979

Venus lower atmospheric composition - Analysis by gas chromatography

The first gas chromatographic analysis of the lower atmosphere of Venus is reported. Three atmospheric samples were analyzed. The third of these samples showed carbon dioxide (96.4 percent), molecular nitrogen (3.41 percent), water vapor (0.135 percent), molecular oxygen (69.3 ppm), argon (18.6 ppm), neon (4.31 ppm), and sulfur dioxide (186 ppm). The amounts of water vapor and sulfur dioxide detected are roughly compatible with the requirements of greenhouse models of the high surface temperature of Venus. The large positive gradient of sulfur dioxide, molecular oxygen, and water vapor from the cloud tops to their bottoms, as implied by Earth-based observations and these results, gives added support for the presence of major quantities of aqueous sulfuric acid in the clouds. A comparison of the inventory of inert gases found in the atmospheres of Venus, Earth, and Mars suggests that these components are due to outgassing from the planetary interiors.

Oyama, V. I.↗

NASA NTRS1979

The solubility of carbon monoxide in silicate melts at high pressures and its effect on silicate phase relations

Autoradiographic analysis and gas chromatography were used to measure the solubility in silicate melts of CO-CO2 vapors (30 to 40% CO by thermodynamic calculation) in equilibrium with graphite at temperatures up to 1700 deg C and pressures to 30 kbar. At near-liquidus temperatures CO-CO2 vapors were found to be slightly more soluble than CO2 alone. As a result of the apparently negative temperature dependence of CO solubility, the solubility of CO-CO2 at superliquidus temperatures is less than that of CO2. Melting points of two silicates were depressed more by CO than by CO2. Phase boundary orientations suggest that CO/CO + CO2 is greater in the liquid than in the vapor. The effect of the presence of CO on periodotite phase relations was investigated, and it was found that melts containing both CO and CO2 are nearly as polymerized as those containing only CO2. These results suggest that crystallization processes in planetary interiors can be expected to be about the same, whether the melts contain CO2 alone or CO2 and CO.

Eggler, D. H.↗

NASA NTRS1981

The magnetic fields of Jupiter and Saturn

The magnetic fields of Jupiter and Saturn and the characteristics of their magnetospheres, formed by interaction with the solar wind, are discussed. The origins of both magnetic fields are associated with a dynamo process deep in the planetary interior. The Jovian magnetosphere is analogous to that of a pulsar magnetosphere: a massive central body with a rapid rotation and an associated intense magnetic field. Its most distinctive feature is its magnetodisk of concentrated plasma and particle flux, and reduced magnetic field intensity. The magnetopause near the subsolar point has been observed at radial distances ranging over 50 to 100 Jovian radii, implying a relatively compressible obstacle to solar wind flow. The composition of an embedded current sheet within the magnetic tail is believed to be influenced by volcanic eruptions and emissions from Io. Spectral troughs of the Jovian radiation belts have been interpreted as possible ring particles. The Saturnian magnetosphere appears to be more like the earth in its topology. It is mainly characterized by a dipole axis parallel to the rotational axis of the planet and a magnetic field intensity much less than expected.

Ness, N. F.↗

NASA NTRS1982

A possible link between the rotation of Saturn and its ring structure

Evidence is presented that two previously unidentified, yet conspicuous gaps in Saturn's rings lie at distances corresponding to 2/3 and 4/3 of the planet's rotation period. Gaps such as these can be produced in a ring of large bodies or small uncharged particles by a nonaxisymmetric gravitational field (both of the above can be associated with the l = m = 3 harmonic), a fact that is relevant to models of planetary interiors.

Franklin, F. A.↗

NASA NTRS1983

Character and stability of axisymmetric thermal convection in spheres and spherical shells

The influence of shell size and mode of heating on the behavior and stability of axisymmetric, infinite Prandtl number convection in a spherical geometry is studied. Heating from within and below features convection onset governed by a self-adjoint system of equations and boundary conditions. For heating only from within or from below, linearized equations and boundary conditions are non-self-adjoint. Identification of the parameter which initiates the departure from self-adjointness, together with the properties of the self-adjoint solution, provide a basis for calculating the heat transfer characteristics of the non-self-adjoint situations. The investigations are an effort to develop a model for heat transfer in planetary interiors. Further development of the technique by modifying the Galerkin method by the introduction of diagonal mode truncation is suggested to permit the consideration of higher values of the Rayleigh numbers, i.e., those more commensurate with terrestrial planet mantles.

Zebib, A.↗

NASA NTRS1983

A comparison of volcanic eruption processes on earth, moon, Mars, Io and Venus

The physical, chemical, and atmospheric characteristics of the silicate planets and satellites are surveyed in terms of their effects on the volcanic evolution of the surfaces of these bodies. The equations relating the parameters affecting magma ascent through the crust and eruption are analyzed, and three major types of eruption are characterized: effusive, steady explosive, and unsteady explosive. This analytical framework is then used to predict the nature of volcanic activity on each of the planets and satellites, and the predictions are compared with actual observations. Outstanding problems are discussed, with emphasis on the need for a general model of planetary interior dynamics applicable to bodies with varying degrees of interior viscosity, mantle activity, and lithospheric plate tectonics.

Wilson, L.↗

NASA NTRS1983

Origin of the atmospheres of the terrestrial planets

The monotonic decrease in the atmospheric abundance of per gram of planet in the sequence, Venus, earth, and Mars has been assumed to reflect some conditions in the primitive solar nebula at the time of formation of the planetary atmospheres, having to do either with the composition of the nebula itself or the composition of the trapped gases in small solid bodies in the nebula. Behind such hypotheses lies the assumption that planetary atmospheres steadily gain components. However, not only can gases enter atmospheres; they may also be lost from atmospheres both by adsorption into the planetary interior and by loss into space as a result of collisions with minor and major planetesimals. In this paper a necessarily qualitative discussion is given of the problem of collisions with minor planetesimals, a process called atmospheric cratering or atmospheric erosion, and a discussion is given of atmospheric loss accompanying collision of a planet with a major planetesimal, such as may have produced the earth's moon.

Cameron, A. G. W.↗