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At least 109 records · Page 6

Crystal-chemistry and partitioning of REE in whitlockite

Partitioning of Rare Earth Elements (REE) in whitlockite is complicated by the fact that two or more charge-balancing substitutions are involved and by the fact that concentrations of REE in natural whitlockites are sufficiently high such that simple partition coefficients are not expected to be constant even if mixing in the system is completely ideal. The present study combines preexisting REE partitioning data in whitlockites with new experiments in the same compositional system and at the same temperature (approximately 1030 C) to place additional constraints on the complex variations of REE partition coefficients and to test theoretical models for how REE partitioning should vary with REE concentration and other compositional variables. With this data set, and by combining crystallographic and thermochemical constraints with a SAS simultaneous-equation best-fitting routine, it is possible to infer answers to the following questions: what is the speciation on the individual sites Ca(B), Mg, and Ca(IIA) (where the ideal structural formula is Ca(B)18 Mg2Ca(IIA)2P14O56); how are REE's charge-balanced in the crystal; and is mixing of REE in whitlockite ideal or non-ideal. This understanding is necessary in order to extrapolate derived partition coefficients to other compositional systems and provides a broadened understanding of the crystal chemistry of whitlockite.

Colson, R. O.↗

The Parameterization of Solid Metal-Liquid Metal Partitioning of Siderophile Elements

The composition of a metallic liquid can significantly affect the partitioning behavior of elements. For example, some experimental solid metal-liquid metal partition coefficients have been shown to increase by three orders of magnitude with increasing S-content of the metallic liquid. Along with S, the presence of other light elements, such as P and C, has also been demonstrated to affect trace element partitioning behavior. Understanding the effects of metallic composition on partitioning behavior is important for modeling the crystallization of magmatic iron meteorites and the chemical effects of planetary differentiation. It is thus useful to have a mathematical expression that parameterizes the partition coefficient as a function of the composition of the metal. Here we present a revised parameterization method, which builds on the theory of the current parameterization of Jones and Malvin and which better handles partitioning in multi-light-element systems.

Chabot, N. L.↗

Solid Metal-Liquid Metal Partitioning of Pt, Re, and Os: The Effect of Carbon

If the measured Os isotopic ratios are a signature from the Earth's outer core, understanding them is a unique opportunity to understand more about the Earth's core. The distribution of elements between the Earth's solid inner core and the liquid outer core will depend on their solid metal-liquid metal partition coefficients (D). Solid metal-liquid metal partitioning data are loosely consistent with the needed fractionations between Re-Os and Pt-Os to account for the Os isotopic signature; D(Os) is greater than both D(Re) and D(Pt), and the magnitude of the partition coefficients are similar to those needed [e.g. 7, 8]. The pressure in the core, the composition of the core, and the crystal structure of the solid Fe alloy in the inner core may influence the specific values of the partition coefficients. It may thus be possible to use these sensitivities of the partition coefficients to gain insight into the conditions within the Earth's core. In this abstract, we focus on the compositional influence of C, a potential component of the light element in the Earth's core [9], on the partitioning behaviors of Pt, Re, and Os.

Chabot, N. L.↗

Influence of Silicate Melt Composition on Metal/Silicate Partitioning of W, Ge, Ga and Ni

The depletion of the siderophile elements in the Earth's upper mantle relative to the chondritic meteorites is a geochemical imprint of core segregation. Therefore, metal/silicate partition coefficients (Dm/s) for siderophile elements are essential to investigations of core formation when used in conjunction with the pattern of elemental abundances in the Earth's mantle. The partitioning of siderophile elements is controlled by temperature, pressure, oxygen fugacity, and by the compositions of the metal and silicate phases. Several recent studies have shown the importance of silicate melt composition on the partitioning of siderophile elements between silicate and metallic liquids. It has been demonstrated that many elements display increased solubility in less polymerized (mafic) melts. However, the importance of silicate melt composition was believed to be minor compared to the influence of oxygen fugacity until studies showed that melt composition is an important factor at high pressures and temperatures. It was found that melt composition is also important for partitioning of high valency siderophile elements. Atmospheric experiments were conducted, varying only silicate melt composition, to assess the importance of silicate melt composition for the partitioning of W, Co and Ga and found that the valence of the dissolving species plays an important role in determining the effect of composition on solubility. In this study, we extend the data set to higher pressures and investigate the role of silicate melt composition on the partitioning of the siderophile elements W, Ge, Ga and Ni between metallic and silicate liquid.

Singletary, S. J.↗

High Pressure/Temperature Metal Silicate Partitioning of Tungsten

The behavior of chemical elements during metal/silicate segregation and their resulting distribution in Earth's mantle and core provide insight into core formation processes. Experimental determination of partition coefficients allows calculations of element distributions that can be compared to accepted values of element abundances in the silicate (mantle) and metallic (core) portions of the Earth. Tungsten (W) is a moderately siderophile element and thus preferentially partitions into metal versus silicate under many planetary conditions. The partitioning behavior has been shown to vary with temperature, silicate composition, oxygen fugacity, and pressure. Most of the previous work on W partitioning has been conducted at 1-bar conditions or at relatively low pressures, i.e. <10 GPa, and in two cases at or near 20 GPa. According to those data, the stronger influences on the distribution coefficient of W are temperature, composition, and oxygen fugacity with a relatively slight influence in pressure. Predictions based on extrapolation of existing data and parameterizations suggest an increased pressured dependence on metal/ silicate partitioning of W at higher pressures 5. However, the dependence on pressure is not as well constrained as T, fO2, and silicate composition. This poses a problem because proposed equilibration pressures for core formation range from 27 to 50 GPa, falling well outside the experimental range, therefore requiring exptrapolation of a parametereized model. Higher pressure data are needed to improve our understanding of W partitioning at these more extreme conditions.

Shofner, G. A.↗

Anionic Pt in Silicate Melts at Low Oxygen Fugacity: Speciation, Partitioning and Implications for Core Formation Processes on Asteroids

Most siderophile element concentrations in planetary mantles can be explained by metal/ silicate equilibration at high temperature and pressure during core formation. Highly siderophile elements (HSE = Au, Re, and the Pt-group elements), however, usually have higher mantle abundances than predicted by partitioning models, suggesting that their concentrations have been set by late accretion of material that did not equilibrate with the core. The partitioning of HSE at the low oxygen fugacities relevant for core formation is however poorly constrained due to the lack of sufficient experimental constraints to describe the variations of partitioning with key variables like temperature, pressure, and oxygen fugacity. To better understand the relative roles of metal/silicate partitioning and late accretion, we performed a self-consistent set of experiments that parameterizes the influence of oxygen fugacity, temperature and melt composition on the partitioning of Pt, one of the HSE, between metal and silicate melts. The major outcome of this project is the fact that Pt dissolves in an anionic form in silicate melts, causing a dependence of partitioning on oxygen fugacity opposite to that reported in previous studies.

Medard, E.↗

Understanding the Impact of Unobservable Variables on the Performance of Predictive Models: The Need for Feature Space Partitioning and Fusion

When developing predictive models over a dataset, the model is globally optimized across the entire feature space to learn a decision boundary. However, when unobservable variables—which cannot be measured or estimated—interact with the observable variables, this can negatively impact the optimization applied to the decision boundary since the data samples introduced by unobservable variables may have little to no association with the applied global optimization. This, consequently, penalizes the entire decision boundary and model performance. This paper examines some of the detrimental effects of unobservable variables, particularly their role in creating new modes in the distribution of observable variables and reducing the separability of class distributions. Such challenges result in skewed or warped decision boundaries and decreased accuracy of model predictions, particularly for interpretable models like logistic regression and decision trees. Through two illustrative case examples, we highlight the need to address the challenges imposed by unobservable variables. We propose a strategy to mitigate these challenges by creating local regions within the feature space through partitioning. This enables the optimization of local models within the regions to overcome the impact of unobservability in different feature space localities. Research into a more sophisticated partitioning strategy and where the partition should be relative to the sample of interest is left as future work. Through the analysis of the impact of unobservability and the development of a partitioning method, we demonstrate the clear need for a partitioning strategy that integrates knowledge from multiple local models to estimate risk factors using information fusion. Thus, we establish the foundation and motivation for using partitioning and information fusion to overcome the effects of unobservability in predictive models. Formal fusion methods, such as Dempster-Shafer theory, can better leverage the information from local regions to improve the performance of interpretable predictive models in the presence of unobservable variables.

Time Series Data↗

Nanoscale Solute Partitioning and Carbide Precipitation in a Multiphase TRIP Steel Analyzed by Atom Probe Tomography

Nanoscale solute partitioning across multiple constituent phases in a 980-grade quenched and partitioned (Q&P) steel was analyzed using atom probe tomography (APT). The Q&P process was used to increase the C content in the retained austenite phase thereby improving its stability under plastic straining. Significant carbon enrichment of austenite was measured with decreased levels of C in martensite and almost depleted C content in ferrite, supporting the C partitioning mechanism in the literature. The APT analysis of retained austenite surrounded by martensite demonstrated a higher amount of C content compared with retained austenite surrounded by the ferrite phase. Lath and discrete carbide particle precipitation was also observed inside martensite colonies, tying up C and reducing the total amount of C available for austenite stabilization. In addition, the partitioning of Mn and other minor elements was quantitatively investigated by correlating APT and SEM-EBSD. Furthermore, these techniques provide a robust methodology for analyzing nanoscale compositional partitioning in multiphase steels, TRIP steels in particular, which can be used to better explain their microstructure-mechanical property relationships.

36 MATERIALS SCIENCE↗

Thermal and dynamic partition of dumbbell interstitials in complex concentrated alloys

Complex concentrated alloys (CCAs) are promising candidates for applications in extreme conditions, such as irradiation where interstitial mediated diffusion is important. In CCAs with N principal elements, $\frac{N(N+1)}{2}$ types of dumbbell interstitials exist. Currently, there is no way to predict the thermal partition (fractional concentration at equilibrium) and the dynamic partition (fractional time an interstitial spends during diffusion) of each type of dumbbell interstitial. To mitigate this issue, this work proposes a theoretical model for computing the equilibrium concentrations and thermal partition of dumbbell interstitials in CCAs and validates the model using grand canonical Monte Carlo simulations. Lattice kinetic Monte Carlo simulations show that the thermal partition is equivalent to the dynamic partition, and both are governed by composition and formation energies of dumbbells. As a result, the model proposed provides a foundation for understanding radiation enhanced diffusion and induced segregation in CCAs under irradiation.

36 MATERIALS SCIENCE↗

Effects of Inclusion Precipitation, Partition Coefficient, and Phase Transition on Microsegregation for High-Sulfur Steel Solidification

A microsegregation model coupled with inclusion precipitation, variable partition coefficient, and diffusion coefficient of the solute was developed to investigate solute microsegregation for high-sulfur steel solidification. The effects of the solidification path and phase transition on solute microsegregation were explored. The results showed that the solute concentration predicted by the variable partition coefficient was quite different from the solute concentration predicted by the constant partition coefficient, and the percentage differences of solutes Si, P, and S were − 35.5, − 25.0, and 43.0 pct, respectively. For high-sulfur steel solidification, the concentrations of solutes Mn and S would be reduced by 88.3 and 74.9 pct, respectively, due to the precipitation of MnS. The solidification path and phase transition has a significant effect on the solute partition coefficient and microsegregation. With the increase in C content, the fraction of δ-phase decreased while the fraction of the γ-phase increased, and the microsegregation ratio of solutes C and Si decreased while the microsegregation ratio of solute P increased. To predict microsegregation more accurately, all influencing factors of the partition coefficient, inclusion precipitation, and phase transition should be comprehensively considered.

36 MATERIALS SCIENCE↗

High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes

This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit–explicit Runge–Kutta (IMEX-RK) discretization of the semi-discrete equations. The generic multiphysics problem is modeled as a system of n systems of partial differential equations where the i th subsystem is coupled to the other subsystems through a coupling term that can depend on the state of all the other subsystems. This coupled system of partial differential equations reduces to a coupled system of ordinary differential equations via the method of lines where an appropriate spatial discretization is applied to each subsystem. The coupled system of ordinary differential equations is taken as a monolithic system and discretized using an IMEX-RK discretization with a specific implicit–explicit decomposition that introduces the concept of a predictor for the coupling term. We propose four coupling predictors that enable the monolithic system to be solved in a partitioned manner, i.e., subsystem-by-subsystem, and preserve the IMEX-RK structure and therefore the design order of accuracy of the monolithic scheme. The four partitioned solvers that result from these predictors are high-order accurate, allow for maximum re-use of existing single-physics software, and two of the four solvers allow the subsystems to be solved in parallel at a given stage and time step. We also analyze the stability of a coupled, linear model problem with a specific coupling structure and show that one of the partitioned solvers achieves unconditional linear stability for this problem, while the others are unconditionally stable only for certain values of the coupling strength. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems including a simple linear system of ODEs, advection–diffusion–reaction systems, fluid–structure interaction problems, and particle-laden flows, where we verify the design order of the IMEX schemes and study various stability properties.

97 MATHEMATICS AND COMPUTING↗

Quantum chemical calculations to determine partitioning coefficients for HgCl 2 on iron-oxide aerosols

Gas-to-particle phase partitioning controls the pathways for oxidized mercury deposition from the atmosphere to the Earth's surface. The propensity of oxidized mercury species to transition between these two phases is described by the partitioning coefficient (K p ). Experimental measurements of K p values for HgCl 2 in the presence of atmospheric aerosols are difficult and time-consuming. Quantum chemical calculations, therefore, offer a promising opportunity to efficiently estimate partitioning coefficients for HgCl 2 on relevant aerosols. In this study, density functional theory (DFT) calculations are used to predict K p values for HgCl 2 on relevant iron-oxide surfaces. The model is first verified using a NaCl(100) surface, showing good agreement between the calculated (2.8) and experimental (29–43) dimensionless partitioning coefficients at room temperature. Then, the methodology is applied to six atmospherically relevant terminations of α-Fe 2 O 3 (0001): OH-Fe-R, (OH) 3 -Fe-R, (OH) 3 -R, O-Fe-R, Fe-O 3 -R, and O 3 -R (where R denotes bulk ordering). The OH-Fe-R termination is predicted to be the most stable under typical atmospheric conditions, and on this surface termination, a dimensionless HgCl 2 K p value of 5.2 x 10 3 at 295 K indicates a strong preference for the particle phase. Here this work demonstrates DFT as a promising approach to obtain partitioning coefficients, which can lead to improved models for the transport of mercury, as well as for other atmospheric pollutant species, through and between the anthroposphere and troposphere.

54 ENVIRONMENTAL SCIENCES↗

Partitioning of Oxygen Between Ferropericlase and Earth's Liquid Core

Transfer of oxygen between Earth’s core and lowermost mantle is important for determining the chemistry and nature of stratification on both sides of the core-mantle boundary (CMB). Previous studies have found that oxygen enters the metal when Fe-O liquid equilibrates with representative lower mantle materials. However, experiments have not yet been conducted at CMB pressure-temperature conditions. Here we use density functional theory to obtain the first estimates of oxygen partitioning between liquid Fe-O-Si metals and ferropericlase at CMB conditions. Our method successfully reproduces experimentally derived partitioning data at 134 GPa and 3200 K, while our calculations show a strong increase of oxygen partitioning into metal with temperature and a weaker increase with pressure, consistent with previous work. At CMB conditions of 135 GPa and 4000–4700 K oxygen partitioning into metal is higher than previous estimates and increases strongly with metal oxygen concentration. Analysis of the lower mantle chemical boundary layer shows that oxygen transport through the solid is severely limited even with the enhanced partitioning and is unlikely to explain the thickness of a stably stratified layer below the CMB inferred from seismology. However, if the lower mantle was molten in early times, as suggested by core evolution models with high thermal conductivity, then the mass flux and stable layer thickness are significantly increased.

58 GEOSCIENCES↗

Variability of Snow and Rainfall Partitioning Into Evapotranspiration and Summer Runoff Across Nine Mountainous Catchments

Abstract Understanding the partitioning of snow and rain contributing to either catchment streamflow or evapotranspiration (ET) is of critical relevance for water management in response to climate change. To investigate this partitioning, we use endmember splitting and mixing analyses based on stable isotope ( 18 O) data from nine headwater catchments in the East River, Colorado. Our results show that one third of the snow partitions to ET and 13% of the snowmelt sustains summer streamflow. Only 8% of the rainfall contributes to the summer streamflow, because most of the rain (67%) partitions to ET. The spatial variability of precipitation partitioning is mainly driven by aspect and tree cover across the sub‐catchments. Catchments with higher tree cover have a higher share of snow becoming ET, resulting in less snow in summer streamflow. Summer streamflow did not contain more rain with higher rainfall sums, but more rain was taken up in ET.

58 GEOSCIENCES↗

Post-transition state dynamics and product energy partitioning following thermal excitation of the F∙∙∙HCH 2 CN transition state: Disagreement with experiment

Born-Oppenheimer direct dynamics simulations were performed to study atomistic details of the F + CH 3 CN → HF + CH 2 CN H-atom abstraction reaction. The simulation trajectories were calculated with a combined M06-2X/MP2 algorithm utilizing the 6-311++G** basis set. In accord with experiment and assuming the accuracy of transition state theory (TST), the trajectories were initiated at the F-HCH 2 CN abstraction TS with a 300 K Boltzmann distribution of energy and directed towards products. Recrossing of the TS was negligible, confirming the accuracy of TST for the simulation. HF formation was rapid, occurring within 0.014 ps of the trajectory initiation. The intrinsic reaction coordinate (IRC) for reaction involves rotation of HF about CH 2 CN and then trapping in the CH 2 CN-HF post-reaction potential energy well of ~10 kcal/mol with respect to the HF + CH 2 CN products. In contrast to this IRC, five different trajectory types were observed, with the majority involving direct dissociation and only 11% approximately following the IRC. The HF vibrational and rotational quantum numbers, n and J, were calculated when HF was initially formed and they increase as potential energy is released in forming the HF + CH 2 CN products. The population of the HF product vibrational states is only in qualitative agreement with experiment, with the simulations showing depressed and enhanced populations of the n = 1 and 2 states as compared to experiment. From the simulations and with an anharmonic zero-point energy constraint, the percentage partitioning of the product energy to relative translation, HF rotation, HF vibration, CH 2 CN rotation and CH 2 CN vibration is 5, 11, 60, 7, and 16%, respectively. In contrast the experimental energy partitioning percentages to HF rotation and vibration are 6 and 41%. Comparisons are made between the current simulation and those for other F + H-atom abstraction reactions. The simulation product energy partitioning and HF vibrational population for F + CH 3 CN → HF + CH 2 CN are similar to those for these other reactions. Finally, a detailed discussion is given of possible origins of the difference between the simulation and experimental energy partitioning dynamics for the F + CH 3 CN → HF + CH 2 CN reaction. The F + CH 3 CN reaction also forms the CH 3 C(F)N intermediate, in which the F-atom adds to the C≡N bond. However, this intermediate and the F---CH 3 CN and CH 3 CN-F van der Waals complexes are not expected to affect the F + CH 3 CN → HF + CH 2 CN product energy partitioning.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Genetic characterization of a Sorghum bicolor multiparent mapping population emphasizing carbon-partitioning dynamics

Sorghum bicolor, a photosynthetically efficient C4 grass, represents an important source of grain, forage, fermentable sugars, and cellulosic fibers that can be utilized in myriad applications ranging from bioenergy to bioindustrial feedstocks. Sorghum’s efficient fixation of carbon per unit time per unit area per unit input has led to its classification as a preferred biomass crop highlighted by its designation as an advanced biofuel by the U.S. Department of Energy. Due to its extensive genetic diversity and worldwide colonization, sorghum has considerable diversity for a range of phenotypes influencing productivity, composition, and sink/source dynamics. To dissect the genetic basis of these key traits, we present a sorghum carbon-partitioning nested association mapping (NAM) population generated by crossing 11 diverse founder lines with Grassl as the single recurrent female. By exploiting existing variation among cellulosic, forage, sweet, and grain sorghum carbon partitioning regimes, the sorghum carbon-partitioning NAM population will allow the identification of important biomass-associated traits, elucidate the genetic architecture underlying carbon partitioning and improve our understanding of the genetic determinants affecting unique phenotypes within Poaceae. We contrast this NAM population with an existing grain population generated using Tx430 as the recurrent female. Genotypic data are assessed for quality by examining variant density, nucleotide diversity, linkage decay, and are validated using pericarp and testa phenotypes to map known genes affecting these phenotypes. We release the 11-family NAM population along with corresponding genomic data for use in genetic, genomic, and agronomic studies with a focus on carbon-partitioning regimes.

multiparental populations↗

Order conditions for nonlinearly partitioned Runge-Kutta methods

Recently, a new class of nonlinearly partitioned Runge–Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations y' = F(y, y). The target class of problems are those in which different scales, stiffnesses, or physics are coupled in a nonlinear way, wherein the desired partition cannot be written in a classical additive or component-wise fashion. Here we use a rooted-tree analysis to derive full-order conditions for NPRKM methods, where M denotes the number of nonlinear partitions. Due to the nonlinear coupling and thereby the mixed product differentials, it turns out that the standard node-colored rooted tree analysis used in analyzing ODE integrators does not naturally apply. Instead we develop a new edge-colored rooted-tree framework to address the nonlinear coupling. The resulting order conditions are enumerated, are provided directly for up to fourth order with M = 2 and third order with M = 3, and are related to existing order conditions of additive and partitioned RK methods. We conclude with an example that shows how the nonlinear order conditions can be used to obtain an embedded estimate of the state-dependent nonlinear coupling strength in a dynamical system.

97 MATHEMATICS AND COMPUTING↗

Silicon Partitioning Between Iron-Rich Metal and Silicate Melt: New Constraints From Aerodynamic Laser Levitation Furnace Experiments

The partitioning of light elements (e.g., Si, C, H, etc.) between silicate melts and iron metal alloys as a function of pressure and temperature is a critical constraint in defining the compositional evolution of planetary interiors. While there are a significant number of experimental studies in the literature that examine the various influences of oxygen fugacity, temperature, pressure, and composition on the metal-melt partitioning of silicon, it is difficult to disentangle the effects of each variable due to the nominally independent parameters (e.g., pressure, temperature, composition) being collinear. To better test for the independent effects of pressure, temperature, and melt composition on the partitioning of silicon between iron alloy and silicate melt, new high temperature (1800°–2500°C), rapid quench (~700°C/s) aerodynamic levitation laser-heating experiments in the Fe-Si-Mg-O (En65-Fa5-Si3-Fe27) system were conducted. This high temperature, low pressure method is ideal for these experiments because it eliminates the metal container as a sink for elements of interest to partition into, and it has a rapid quench rate that minimizes potential exsolution of silicon from the metal phase during quench cooling. Given the short run times of the levitation experiments (30–60 seconds), a time series at a lower temperature (1700°C) in a vertical gas-mixing muffle tube furnace was also conducted to assess equilibrium times of the bulk composition. All successful runs were imaged using back-scatter electron imaging and analyzed for phase composition using a JEOL 8530F field emission microprobe. These new data were added to a comprehensive and internally consistent data set created from published experiments, and subsequently modeled using parameters designed to minimize collinearity (e.g., optical basicity is used as a proxy for melt composition). High collinearity is found in the data set however between temperature and oxygen fugacity, precluding any model that contains both as nominally independent variables. The resulting model demonstrates a statistically significant effect of pressure, temperature, and melt composition on the partitioning of silicon in Fe-rich metal, which has implications for the formation of planetary cores in rocky planets and provides important constraints on potential bulk core compositions.

Metal↗