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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Effect of Pressure and Oxidation State on Pnictogen Metal-Silicate Partitioning

The partitioning of trace elements between metal and silicate melts serves as the foundation for understanding the differentiation of a planetary body into a metallic core and silicate mantle. Element activity influences metal-silicate partitioning behavior. Activity coefficients are directly dependent on composition and temperature, and can be indirectly dependent on oxygen fugacity and pressure. Distinguishing the effect of pressure from other variables on the activity coefficients and partitioning is important for understanding the chemical evolution of different planetary bodies during differentiation. In this study, we investigated the influence of pressure on the activity coefficients of Cu, Mo, Pd, Pt, As, Sb, and Bi in Fe-Si metallic liquids. All of these elements exhibit moderate to high activity coefficients in Fe-Si liquids at low pressure, which significantly controls their metal-silicate partitioning behavior. Identifying whether this strong dependence persists at higher pressures is critical to modeling and understanding the chemical consequences of core formation. New experiments at 10 GPa were used to derive activity coefficients for these metals which can be compared to activity coefficients determined at 1 GPa. Experiments were conducted at 10 GPa and 2373K using a 10/5 assembly in the 880-ton multi anvil press at NASA Johnson Space Center. The standard 10/5 COMPRES assembly was slightly modified to accommodate a sample capsule machined from single-crystal MgO that minimizes melt percolation out of the sample volume during the experiment. Experiment starting materials were comprised of 70 wt.% Knippa basalt and 30 wt.% metal. The metal mixture (~85 wt.% Fe) was created by adding the elements of interest (Cu, Mo, Pd, Pt, As, Sb, Bi) to Fe metal powder. Varied amounts of Si metal (0-10 wt.% Si) were added to the metal-silicate mixtures to generate a systematic series of starting materials. For each element, an epsilon interaction parameter in Fe-Si liquid was derived from the results of our 0-10 wt.% Si metal series. To investigate whether pressure influences the trace element activity coefficients in the 1-10 GPa pressure range, we compared our results at 10 GPa to those at 1-4 GPa [1-3]. Our results can also be directly compared to interaction parameters for Au, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb previously determined at 10 GPa and 2373K following the same methods [4]. Combined, this suite of interaction parameters will directly inform metal- silicate partitioning between 1 and 10 GPa, and assess whether these values can be extrapolated to modeling differentiation processes at pressures >10 GPa. [1] Righter et al. (2018) GCA 232, 101-123 [2] Righter et al. (2019) MaPS 54, 1379-1394 [3] Steenstra et al. (2020) Icarus, 335, 113391 [4] Righter et al. (2020) Geochem. Persp. Let. 15, 44-49

Kelsey Prissel↗
NASA NTRSDate not supplied

Effect of Pressure on Trace Element Activity Coefficients in Metal-Silicate Systems

The partitioning of trace elements between metal and silicate melts serves as the foundation for understanding the differentiation of a planetary body into a metallic core and silicate mantle. Element activity influences metal-silicate partitioning behavior. Activity coefficients are directly dependent on composition and temperature, and can be indirectly dependent on oxygen fugacity and pressure. Distinguishing the effect of pressure from other variables on the activity coefficients and partitioning is important for understanding the chemical evolution of different planetary bodies during differentiation. In this study, we investigated the influence of pressure on the activity coefficients of Cu, Mo, Pd, Pt, As, Sb, and Bi in Fe-Si metallic liquids. All of these elements exhibit moderate to high activity coefficients in Fe-Si liquids at low pressure, which significantly controls their metal-silicate partitioning behavior. Identifying whether this strong dependence persists at higher pressures is critical to modeling and understanding the chemical consequences of core formation. New experiments at 10 GPa were used to derive activity coefficients for these metals which can be compared to activity coefficients determined at 1 GPa. Experiments were conducted at 10 GPa and 2373K using a 10/5 assembly in the 880-ton multi-anvil press at NASA Johnson Space Center. The standard 10/5 COMPRES assembly was slightly modified to accommodate a sample capsule machined from single-crystal MgO that minimizes melt percolation out of the sample volume during the experiment. Experiment starting materials were comprised of 70 wt.% Knippa basalt and 30 wt.% metal. The metal mixture (~85 wt.% Fe) was created by adding the elements of interest (Cu, Mo, Pd, Pt, As, Sb, Bi) to Fe metal powder. Varied amounts of Si metal (0-10 wt.% Si) were added to the metal-silicate mixtures to generate a systematic series of starting materials. For each element, an epsilon interaction parameter in Fe-Si liquid was derived from the results of our 0-10 wt.% Si metal series. To investigate whether pressure influences the trace element activity coefficients in the 1-10 GPa pressure range, we compared our results at 10 GPa to those at 1-4 GPa [1-3]. Our results can also be directly compared to interaction parameters for Au, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb previously determined at 10 GPa and 2373K following the same methods [4]. Combined, this suite of interaction parameters will directly inform metal-silicate partitioning between 1 and 10 GPa, and assess whether these values can be extrapolated to modeling differentiation processes at pressures >10 GPa.

Kelsey Prissel↗
NASA NTRS1978

Implications of liquid-liquid distribution coefficients to mineral-liquid partitioning

In order to evaluate the influence of a silicate liquid structure on mineral-liquid partitioning, element partitioning data is obtained for coexisting anhydrous immiscible granitic and ferrobasaltic magmas. It is found that: (1) mineral-liquid distribution coefficients indicate the competition of crystal and liquid for cation incorporation, (2) increased polymerization of the residual liquid during crystal-liquid fractionation increases the mineral-liquid distribution coefficients for high-charge-density cations, (3) incompatible element ratios of low- and high-charge-density cations may vary during crystal-liquid fractionation because of changes in the melt composition and structure, (4) relative solubilities of REE's in melts do not vary with melt polymerization, (5) the changes of Sm/Eu ratios during crystal-liquid fractionation depend on the melt composition, and (6) minor components and volatiles can significantly influence the silicate melt structure and the mineral-liquid distribution coefficients.

Ryerson, F. J.↗
NASA NTRS1989

Efficient estimation of diffusion during dendritic solidification

A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing the computed results with the results of an analytical solution derived by Kobayashi (1988) for the assumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a parabolic rate of the advancement of the solid/liquid interface. The flexibility of the method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy.

Yeum, K. S.↗
NASA NTRS1994

Improved image decompression for reduced transform coding artifacts

The perceived quality of images reconstructed from low bit rate compression is severely degraded by the appearance of transform coding artifacts. This paper proposes a method for producing higher quality reconstructed images based on a stochastic model for the image data. Quantization (scalar or vector) partitions the transform coefficient space and maps all points in a partition cell to a representative reconstruction point, usually taken as the centroid of the cell. The proposed image estimation technique selects the reconstruction point within the quantization partition cell which results in a reconstructed image which best fits a non-Gaussian Markov random field (MRF) image model. This approach results in a convex constrained optimization problem which can be solved iteratively. At each iteration, the gradient projection method is used to update the estimate based on the image model. In the transform domain, the resulting coefficient reconstruction points are projected to the particular quantization partition cells defined by the compressed image. Experimental results will be shown for images compressed using scalar quantization of block DCT and using vector quantization of subband wavelet transform. The proposed image decompression provides a reconstructed image with reduced visibility of transform coding artifacts and superior perceived quality.

Orourke, Thomas P.↗
NASA NTRS2001

CAP: A Computer Code for Generating Tabular Thermodynamic Functions from NASA Lewis Coefficients

For several decades the NASA Glenn Research Center has been providing a file of thermodynamic data for use in several computer programs. These data are in the form of least-squares coefficients that have been calculated from tabular thermodynamic data by means of the NASA Properties and Coefficients (PAC) program. The source thermodynamic data are obtained from the literature or from standard compilations. Most gas-phase thermodynamic functions are calculated by the authors from molecular constant data using ideal gas partition functions. The Coefficients and Properties (CAP) program described in this report permits the generation of tabulated thermodynamic functions from the NASA least-squares coefficients. CAP provides considerable flexibility in the output format, the number of temperatures to be tabulated, and the energy units of the calculated properties. This report provides a detailed description of input preparation, examples of input and output for several species, and a listing of all species in the current NASA Glenn thermodynamic data file.

Zehe, Michael J.↗
NASA NTRS2002

CAP: A Computer Code for Generating Tabular Thermodynamic Functions from NASA Lewis Coefficients

For several decades the NASA Glenn Research Center has been providing a file of thermodynamic data for use in several computer programs. These data are in the form of least-squares coefficients that have been calculated from tabular thermodynamic data by means of the NASA Properties and Coefficients (PAC) program. The source thermodynamic data are obtained from the literature or from standard compilations. Most gas-phase thermodynamic functions are calculated by the authors from molecular constant data using ideal gas partition functions. The Coefficients and Properties (CAP) program described in this report permits the generation of tabulated thermodynamic functions from the NASA least-squares coefficients. CAP provides considerable flexibility in the output format, the number of temperatures to be tabulated, and the energy units of the calculated properties. This report provides a detailed description of input preparation, examples of input and output for several species, and a listing of all species in the current NASA Glenn thermodynamic data file.

Zehe, Michael J.↗
NASA NTRS1978

Partitioning of transition metals between diopside and coexisting silicate liquids. I - Nickel, cobalt, and manganese

Distribution coefficients have been found for the partitioning of Ni, Co, and Mn between calcium-rich clinopyroxenes and coexisting silicate liquids. Values are found for the 1110-1360 C temperature range. The breakdown of Henry's Law was not observed. The measured clinopyroxene/liquid distribution coefficients ranged from 1.5-14.0 for Ni, 0.5-2.0 for Co, and 0.3-1.2 for Mn. Analyses of pyroxenes grown from charges differing in the amounts of transition metals indicate that Ni and Co occupy the M1 site of diopside and that Mn occupies the M1 and M2 sites. Equilibrium constants were found in terms of the activities of the components in the liquid and solid phases. These activities are based on the mole fractions. An activity/concentration model was used for the liquid phase in order to explain the variations in the clinopyroxene/liquid coefficients due to bulk composition.

Lindstrom, D. J.↗
NASA NTRS2013

The W-W02 Oxygen Fugacity Buffer at High Pressures and Temperatures: Implications for f02 Buffering and Metal-silicate Partitioning

Oxygen fugacity (fO2) controls multivalent phase equilibria and partitioning of redox-sensitive elements, and it is important to understand this thermodynamic parameter in experimental and natural systems. The coexistence of a metal and its oxide at equilibrium constitutes an oxygen buffer which can be used to control or calculate fO2 in high pressure experiments. Application of 1-bar buffers to high pressure conditions can lead to inaccuracies in fO2 calculations because of unconstrained pressure dependencies. Extending fO2 buffers to pressures and temperatures corresponding to the Earth's deep interior requires precise determinations of the difference in volume (Delta) V) between the buffer phases. Synchrotron x-ray diffraction data were obtained using diamond anvil cells (DAC) and a multi anvil press (MAP) to measure unit cell volumes of W and WO2 at pressures and temperatures up to 70 GPa and 2300 K. These data were fitted to Birch-Murnaghan 3rd-order thermal equations of state using a thermal pressure approach; parameters for W are KT = 306 GPa, KT' = 4.06, and αKT = 0.00417 GPa K-1. Two structural phase transitions were observed for WO2 at 4 and 32 GPa with structures in P21/c, Pnma and C2/c space groups. Equations of state were fitted for these phases over their respective pressure ranges yielding the parameters KT = 190, 213, 300 GPa, KT' = 4.24, 5.17, 4 (fixed), and αKT = 0.00506, 0.00419, 0.00467 GPa K-1 for the P21/c, Pnma and C2/c phases, respectively. The W-WO2 buffer (WWO) was extended to high pressure by inverting the W and WO2 equations of state to obtain phase volumes at discrete pressures (1-bar to 100 GPa, 1 GPa increments) along isotherms (300 to 3000K, 100 K increments). The slope of the absolute fO2 of the WWO buffer is positive with increasing temperature up to approximately 70 GPa and is negative above this pressure. The slope is positive along isotherms from 1000 to 3000K with increasing pressure up to at least 100 GPa. The WWO buffer is at a higher fO2 than the IW buffer at pressures lower than 40 GPa, and the magnitude of this difference decreases at higher pressures. This qualitatively indicates an increasingly lithophile character for W at higher pressures. The WWO buffer was quantitatively applied to W metal-silicate partitioning by using the WWO-IW buffer difference in combination with literature data on W metal-silicate partitioning to model the exchange coefficient (KD) for the Fe-W exchange reaction. This approach captures the pressure dependence of W metal-silicate partitioning using the WWO-IW buffer difference and models the activities of the components in the silicate and metallic phases using an expression of the Gibbs excess energy of mixing. Calculation of KD along a peridotite liquidus predicts a decrease in W siderophility at higher pressures that supports the qualitative behavior predicted by the WWO-IW buffer difference, and agrees with findings of others. Comparing the competing effects of temperature and pressure on W metal-silicate partitioning, our results indicate that pressure exerts a greater effect.

Shofner, G. A.↗
NASA NTRS2011

Molybdenum Valence in Basaltic Silicate Melts: Effects of Temperature and Pressure

The metal-silicate partitioning behavior of molybdenum has been used as a test for equilibrium core formation hypotheses [for example, 1-6]. However, current models that apply experimental data to equilibrium core-mantle differentiation infer the oxidation state of molybdenum from solubility data or from multivariable coefficients from metal-silicate partitioning data [1,3,7]. Molybdenum, a multi-valent element with a valence transition near the fO2 of interest for core formation (approx.IW-2) will be sensitive to changes in fO2 of the system and silicate melt structure. In a silicate melt, Mo can occur in either 4+ or 6+ valence state, and Mo(6+) can be either octahedrally or tetrahedrally coordinated. Here we present X-ray absorption near edge structure (XANES) measurements of Mo valence in basaltic run products at a range of P, T, and fO2 and further quantify the valence transition of Mo.

Danielson, L. R.↗
DOE OSTI2024

Improving modular bootstrap bounds with integrality

We propose methods that efficiently impose integrality — i.e., the condition that the coefficients of characters in the partition function must be integers — into numerical modular bootstrap. We demonstrate the method with a number of examples where it can be used to strengthen modular bootstrap results. First, we show that, with a mild extra assumption, imposing integrality improves the bound on the maximal allowed gap in dimensions of operators in theories with a U(1) c symmetry at c = 3, and reduces it to the value saturated by the SU(4) 1 WZW model point of c = 3 Narain lattices moduli space. Second, we show that our method can be used to eliminate all but a discrete set of points saturating the bound from previous Virasoro modular bootstrap results. Finally, when central charge is close to 1, we can slightly improve the upper bound on the scaling dimension gap.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1976

Compositional interrelationships of mare basalts from bulk chemical and melt inclusion studies

Petrographic and electron microprobe data (355 new analyses) are presented on melt inclusions and their host phases found in a reexamination of the Apollo thin section collection. In addition, occurrences of early armalcolite and ilmenite are described and new data are presented on quench-pyroxene compositions and melt inclusions in chromian ulvospinel. Compositional differences between mare basalt types and their melt inclusions are illustrated with plots of compositions normalized to a terrestrial lava composition, that of the 1965 Makaopuhi lava lake. The plots emphasize the fact that mare basalts are not significantly differentiated relative to the compositions that are possible as defined by the melt inclusion data. Distribution coefficients for Fe and Mg partitioning between trapped melt and host olivine and ilmenite are calculated and show a range about probable equilibrium values. It is suggested that the crystallization sequence olivine-ilmenite-plagioclase-pyroxene defined by the melt inclusion data may be the actual sequence which obtained generally for Apollo 11 and 17 mare basalts just prior to eruption.

Weiblen, P. W.↗
NASA NTRS1985

Multiple-scale turbulence closure modeling of confined recirculating flows

A multiple-scale turbulence closure scheme is developed for the numerical predictions of confined recirculating flows. This model is based on the multiple-time-scale concepts of Hanjalic et al. (1980) and takes into account the non-equilibrium spectra energy transfer mechanism. Problems concerning new formulation of energy transfer rate equations and subsequent model coefficient redefinition and energy spectrum partition are discussed. Comparisons are made with several experiments of internal recirculating flows for the purpose of model validation. Numerical results using the present model show significant improvement of predictive capability over that obtained with the single-scale k-epsilon model and show promising potential for complex turbulent flow predictions.

Chen, C. P.↗
NASA NTRS2010

Molybdenum Valence in Basaltic Silicate Melts

The moderately siderophile element molybdenum has been used as an indicator in planetary differentiation processes, and is particularly relevant to core formation [for example, 1-6]. However, models that apply experimental data to an equilibrium differentiation scenario infer the oxidation state of molybdenum from solubility data or from multivariable coefficients from metal-silicate partitioning data [1,3,7]. Partitioning behavior of molybdenum, a multivalent element with a transition near the J02 of interest for core formation (~IW-2) will be sensitive to changes in JO2 of the system and silicate melt structure. In a silicate melt, Mo can occur in either 4+ or 6+ valence state, and Mo6+ can be either octahedrally or tetrahedrally coordinated. Here we present first XANES measurements of Mo valence in basaltic run products at a range of P, T, and JO2 and further quantify the valence transition of Mo.

Danielson, L. R.↗
NASA NTRS1981

Solute partitioning under continuous cooling conditions as a cooling rate indicator

A model of solute partitioning in a finite body under conditions of continuous cooling is developed for the determination of cooling rates from concentration profile data, and applied to the partitioning of zirconium between ilmenite and ulvospinel in the Apollo 15 Elbow Crater rocks. Partitioning in a layered composite solid is described numerically in terms of concentration profiles and diffusion coefficients which are functions of time and temperature, respectively; a program based on the model can be used to calculate concentration profiles for various assumed cooling rates given the diffusion coefficients in the two phases and the equilibrium partitioning ratio over a range of temperatures. In the case of the Elbow Rock gabbros, the cooling rates are calculated from measured concentration ratios 10 microns from the interphase boundaries under the assumptions of uniform and equilibrium initial conditions at various starting temperatures. It is shown that the specimens could not have had uniform concentrations profiles at the previously suggested initial temperature of 1350 K. It is concluded that even under conditions where the initial temperature, grain sizes and solute diffusion coefficients are not well characterized, the model can be used to estimate the cooling rate of a grain assemblage to within an order of magnitude.

Onorato, P. I. K.↗
DOE OSTI2025

Global Simulations of Phase State and Equilibration Time Scales of Secondary Organic Aerosols with GEOS-Chem

The phase state of secondary organic aerosols (SOA) can range from liquid through amorphous semisolid to glassy solid, which is important to consider as it influences various multiphase processes including SOA formation and partitioning, multiphase chemistry, and cloud activation. In this study, we simulate the glass transition temperature and viscosity of SOA over the globe using the global chemical transport model, GEOS-Chem. The simulated spatial distributions show that SOA at the surface exist as liquid over equatorial regions and oceans, semisolid in the midlatitude continental regions, and glassy solid over lands with low relative humidity. The predicted SOA viscosities are mostly consistent with the available measurements. In the free troposphere, SOA particles are mostly predicted to be semisolid at 850 hPa and glassy solid at 500 hPa, except over tropical regions including Amazonia, where SOA are predicted to be low viscous. Phase state also exhibits seasonal variation with a higher frequency of semisolid and solid particles in winter compared to warmer seasons. We calculate equilibration time scales of SOA partitioning (τ eq ) and effective mass accommodation coefficient (α eff ), indicating that τ eq is shorter than the chemical time step of GEOS-Chem of 20 min and αeff is close to unity for most locations at the surface level, supporting the application of equilibrium SOA partitioning. However, τ eq is prolonged and α eff is lowered over drylands and most regions in the upper troposphere, suggesting that kinetically limited growth would need to be considered for these regions in future large-scale model studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2020

Effect of Pressure on the Activity Coefficients of Au and Other Siderophile Elements in Liquid Fe-Si Alloys

Light elements can alloy into the iron cores of terrestrial planetary bodies. It is estimated that the Earth’s core contains ~10% of a light element, most likely a combination of S, C, Si, and O with Si probably being the most abundant. Si dissolved into Fe metal liquids can have a significant influence on the activity coefficients of siderophile elements, and thus the partitioning behavior of those elements between the core and mantle. Many of these elements have been investigated extensively at ambient pressure, and studies up to 1 GPa are becoming more common, but few have been studied at pressures above this. The formation of the Earth’s core has been estimated to have formed at pressures between 40-60 GPa, so investigating the effect pressure has on Si’s influence on siderophile element partitioning is important for modeling core formation in the Earth and smaller planets. Pressure is well known to influence volumetric properties of metallic and silicate liquids, and oxygen fugacity (e.g., [10,11]), but less is known about its effect on activity coefficients (e.g., [12]). Some activity coefficients depend strongly upon the Si content of Fe liquids, and the concentration of siderophile elements such as P, Sb, and As in the terrestrial mantle is easily influenced by dissolved Si in the core. Thus, isolating the effect of pressure on activity coefficients in general is critical in quantitative analysis of core formation models. In this work, we investigate the effect variable Si content has on the partitioning of Au between Fe metal and silicate melt at 10 GPa and 2373 K, with the intention of comparing the behavior to that already investigated at lower pressures. In addition, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb were also measured and could thus be included in the assessment of potential pressure effects.

Righter, K.↗