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At least 1,531 records · Page 85

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DOE OSTI2020

Probing interfacial momentum closures in two-phase bubbly flow with machine learning-aided methods

Computational fluid dynamics (CFD) approach has already reached a high level of maturity for single-phase flows, however the development of closure models for two-phase flow requires additional attention. Multiphase CFD (M-CFD) methods resolve the conservation equations for mass, momentum and energy while differing in the approaches and strategies adopted in the physical closure models. The most widely adopted framework for M-CFD is the Eulerian-Eulerian two-fluid approach which assumes that all phases are co-existing inside each computational cell. For each fluid, the full set of conservation equations is solved; therefore, each fluid has a different velocity field. For adiabatic two-phase flow, the mechanisms of the interfacial momentum transfer are modeled by the interfacial forces representing different physical mechanisms. One of the crucial issues in the development and application of two-fluid model is the understanding of the interfacial momentum closures which determines the bubble distribution and migration behaviors. Dedicated experiments are performed to support the physical understanding and drive the closures’ development. However, limitations exist due to the uncertainties in the experimental measurement and the simplified analytical assumptions which have difficulties on representing the complex non-linear flow fields. In this paper, a data-driven approach, Feature Similarity Measurement (FSM), is developed and proposed to resolve the challenges of modeling the interfacial forces closures. Case study is performed with two-phase flow scenarios where the high-fidelity experimental data is available. Within the Eulerian-Eulerian two-fluid framework, only momentum equations for gas and liquid phases are solved and reduced-order interfacial momentum closures are aided with FSM. Predictions of void fraction and velocity fields are analyzed and demonstrate the potential of machine learning-driven interfacial forces closures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Evaluation of liquid-phase thermometry in impinging jet sprays using synchrotron x-ray scattering

Liquid thermometry during primary and secondary breakup of liquid sprays is challenging due to the presence of highly dynamic, optically complex flow features. This work evaluates the use of x-ray scattering from a focused, monochromatic beam of the Advanced Photon Source at Argonne National Laboratory for the measurement of liquid temperatures within the mixing zone of an impinging jet spray. The measured scattering profiles are converted to temperature through a previously developed two-component partial least squares (PLS) regression model. Transmitive mixing during jet merging is inferred through spatial mapping of temperatures within the impingement region. In this work, the technique exhibits uncertainties of ±2K in temperature and 2% in capturing the correct scattering profile, showing its potential utility for probing liquid temperature distributions in multiphase flows.

42 ENGINEERING↗

DOE OSTI2015

Inflow/outflow boundary conditions for particle-based blood flow simulations: Application to arterial bifurcations and trees

When blood flows through a bifurcation, red blood cells (RBCs) travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and R- BCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon valida- tion of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the \all-or-nothing" phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Lastly, we demonstrated the new methodology for simulating blood flow in ves- sels with multiple inlets and outlets, constructed using an angiogenesis model.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

Receptor Activation of HIV-1 Env Leads to Asymmetric Exposure of the gp41 Trimer

Structural rearrangements of HIV-1 glycoprotein Env promote viral entry through membrane fusion. Env is a symmetric homotrimer with each protomer composed of surface subunit gp120 and transmembrane subunit gp41. Cellular CD4- and chemokine receptor-binding to gp120 coordinate conformational changes in gp41, first to an extended prehairpin intermediate (PHI) and, ultimately, into a fusogenic trimer-of-hairpins (TOH). HIV-1 fusion inhibitors target gp41 in the PHI and block TOH formation. To characterize structural transformations into and through the PHI, we employed asymmetric Env trimers containing both high and low affinity binding sites for individual fusion inhibitors. Asymmetry was achieved using engineered Env heterotrimers composed of protomers deficient in either CD4- or chemokine receptor-binding. Linking receptor engagement to inhibitor affinity allowed us to assess conformational changes of individual Env protomers in the context of a functioning trimer. We found that the transition into the PHI could occur symmetrically or asymmetrically depending on the stoichiometry of CD4 binding. Sequential engagement of multiple CD4s promoted progressive exposure of individual fusion inhibitor binding sites in a CD4-dependent fashion. By contrast, engagement of only a single CD4 molecule led to a delayed, but symmetric, exposure of the gp41 trimer. This complex coupling between Env-CD4 interaction and gp41 exposure explained the multiphasic fusion-inhibitor titration observed for a mutant Env homotrimer with a naturally asymmetric gp41. Our results suggest that the spatial and temporal exposure of gp41 can proceed in a nonconcerted, asymmetric manner depending on the number of CD4s that engage the Env trimer. The findings have important implications for the mechanism of viral membrane fusion and the development of vaccine candidates designed to elicit neutralizing antibodies targeting gp41 in the PHI.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Challenges in correlating oxygen stable isotope ratios of hydrates on uranium ore concentrates to process waters

Exchange of oxygen stable isotopes (δ 18 O values) between precipitation waters and uranium oxides is governed by thermodynamics or kinetics. It has been assumed that meteoric waters can be related to precipitation waters in uranium ore concentrates and their calcination and reduced uranium oxide products. With this assumption, the δ 18 O values of uranium materials could provide forensic signatures that identify the production history and geolocation of nuclear materials. To further exploit the potential of δ 18 O values in nuclear material analysis, this study examines the oxygen stable isotope exchange in two UOCs, magnesium diuranate (MDU) and sodium diuranate (SDU). MDU and SDU were synthesized from solutions of uranyl nitrate hexahydrate using precipitation waters with unique oxygen isotope compositions. The structures of the MDU and SDU were analyzed using powder X-ray diffraction (p-XRD) and thermal mass loss curves, while the δ 18 O values of waters generated during thermal decomposition were analyzed using a thermogravimetric analyzer coupled to an isotope ratio infrared spectrometer (TGA-IRIS). By p-XRD, the MDU was uniform and amorphous across all syntheses with residual crystalline material incorporated as a minor component. Combined with the TGA results, all of the MDU is likely amorphous MgU 2 O 7 ·3H 2 O with MgO impurities present throughout. In contrast, the SDU synthesis resulted in multiple phases with many samples exhibiting crystalline phases including a combination of Na(UO 2 ) 4 O 2 (OH) 5 ·5H 2 O and Na 2 (UO2) 6 O 4 (OH) 6 ·8H 2 O with a Na 2 U 2 O 7 minor phase. A small fraction of the SDU samples were amorphous with no crystalline XRD peaks observed. Mass loss curves of the SDU samples revealed that the amorphous samples contained inclusions of similar crystalline phases compared to the crystalline materials. The uniformity of the MDU samples enabled highly reproducible measurements of δ 18 O values of the water vapor yielded for two dehydration events at 170 °C and 500 °C. In contrast, the multiphase composition of the SDU samples resulted in poor reproducibility in δ 18 O values. In conclusion, neither system revealed any correlation between the δ 18 O values of precipitation water, and the waters released during dehydration of the UOCs.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2019

Predicting sedimentary bedrock subsurface weathering fronts and weathering rates: Dataset

Although bedrock weathering strongly influences water quality and global carbon and nitrogen budgets, the weathering depths and rates within subsurface are not well understood nor predictable. Determination of both porewater chemistry and subsurface water flow are needed in order to develop more complete understanding and obtain weathering rates. In a long-term field study, we applied a multiphase approach along a mountainous watershed hillslope transect underlain by marine shale. Here we report three findings. First, the deepest extent of the water table determines the weathering front, and the range of annually water table oscillations determines the thickness of the weathering zone. Below the lowest water table, permanently water-saturated bedrock remains reducing, preventing deeper pyrite oxidation. Secondly, carbonate minerals and potentially rock organic matter share the same weathering front depth with pyrite, contrary to models where weathering fronts are stratified. Thirdly, the measurements-based weathering rates from subsurface shale are high, amounting to base cation exports of about 70 kmolc ha−1 y−1, yet consistent with weathering of marine shale. Finally, by integrating geochemical and hydrological data we present a new conceptual model that can be applied in other settings to predict weathering and water quality responses to climate change.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

An overview of interface-dominated deformation mechanisms in metallic nanocomposites elucidated using in situ straining in a TEM

Nanostructured multiphase metallic materials present extraordinary properties, such as high strength, enhanced fatigue and radiation resistance, and thermal stability, compared to conventional bulk metallic materials. Previous research studies have shown that their deformation and fracture behavior are dominated by defect interactions at internal interfaces. In situ straining, including nanoindentation, compression, and tension, in a transmission electron microscope (TEM) has emerged as a powerful tool to investigate the physics of defect–interface interactions at the nano-scale and even atomic scale. Here, the mechanistic insights gained from these experiments coupled with dislocation theory and atomistic modeling has helped develop a fundamental understanding of the mechanical properties. In this article, through some recent investigations on observing dislocation and interface activities, crack propagation, and nanopillar compression, we present current progress in utilizing in situ TEM straining to examine interface-dominated deformation mechanisms.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Microstructural characterization of phase-separated co-deposited Cu–Ta immiscible alloy thin films

Elevated temperature co-sputtering of immiscible elements ends in a variety of self-organized morphologies due to phase separation. Cu–Ta is used as a model system to understand the evolution of phase-separated microstructural morphologies by co-sputtering thin films with nominal 50–50 at.% composition at four temperatures: 25, 400, 600, and 800 °C. Scanning/transmission electron microscopy of the film cross sections showed the microstructure morphology varied from nanocrystalline Cu–Ta at 25 °C to a wavy ribbon-like structure at 400 °C, to Cu-rich agglomerates surrounded by Ta-rich veins at 600 and 800 °C. In the agglomerate-vein morphology, microstructural features were present on two length scales, from a few nanometers to a few tens of nanometers, thus making the structures hierarchical. On the nanoscale, the Cu-rich agglomerates contained Ta precipitates, whereas the Ta-rich veins had embedded Cu nanocrystals. The various microstructures can be attributed to the highly disparate constituent element interdiffusion at the deposition temperatures with the Cu having orders of magnitude higher mobility than Ta at the deposition temperatures. This research of processing–microstructure relationship will be useful in guiding the design of hierarchical multiphase microstructures in binary or multicomponent thin films with tailored mechanical properties.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Quantitative microstructural imaging by scanning Laue x-ray micro- and nanodiffraction

We present that local crystal structure, crystal orientation, and crystal deformation can all be probed by Laue diffraction using a submicron x-ray beam. This technique, employed at a synchrotron facility, is particularly suitable for fast mapping the mechanical and microstructural properties of inhomogeneous multiphase polycrystalline samples, as well as imperfect epitaxial films or crystals. As synchrotron Laue x-ray microdiffraction enters its 20th year of existence and new synchrotron nanoprobe facilities are being built and commissioned around the world, we take the opportunity to overview current capabilities as well as the latest technical developments. Fast data collection provided by state-of-the-art area detectors and fully automated pattern indexing algorithms optimized for speed make it possible to map large portions of a sample with fine step size and obtain quantitative images of its microstructure in near real time. Lastly, we extrapolate how the technique is anticipated to evolve in the near future and its potential emerging applications at a free-electron laser facility.

36 MATERIALS SCIENCE↗

DOE OSTI2018

A Numerical Study of Two-Phase Flow and Interfacial Mass Transfer in a Wetted Wall Column for Counter-Current Gas Absorption

We present a numerical study to investigate the effects of surface waves of falling films on the mass transfer from flowing gas phase into the liquid film. The model employs the volume of fluid method to explicitly track the gas-liquid phase interface and a one-fluid formulation to model the multiphase flow coupled with mass transfer between the two phases. The surface waves are generated by the time-varying injection rate of the falling film. The effects of surface wave frequencies and amplitudes on the overall mass transfer also are investigated for a counter-current gas-liquid flow of oxygen and water. Because of the solubility difference in the two phases, the model can capture the concentration discontinuity across the liquid-gas interface. Good agreement is obtained between the numerical results and experimental data reported in the literature. By systematically varying the frequencies and amplitudes of flow rate for the falling film, the surface waves generated on the film surface enhance mass transfer in general. Here, the model prediction shows a proportional increase in mass transfer for small frequencies of surface waves, but saturation at higher frequencies.

42 ENGINEERING↗

DOE OSTI2022

NUMERICAL INVESTIGATION OF AIR DEHUMIDIFICATION THROUGH WATER DROPLETS DIELECTROPHORESIS

This paper numerically investigated the dehumidification of moist airflow in a converging rectangular duct with electrically enhanced condensation. The aim was to develop a condensation model that predicted water vapor condensation by employing the dielectrophoresis principle. The charged droplets were injected into the computational domain to produce a gradient electric field. The dielectrophoretic interaction between the droplets and vapor molecules of the humid air resulted in local water vapor condensation at the vapor and liquid droplet interface. This phenomenon is described in detail in this paper. A hybrid Eulerian-Lagrangian solver SprayFoam was developed based on OpenFOAM® to simulate condensation in two-phase gas-liquid mixtures. The following developments were made based on the standard compressible multiphase flow solver SprayFoam in OpenFOAM®: (1) Eulerian solver for gas phase (2) multi-component species transport, and (3) Lagrangian solver for gas-droplet two-phase flows and sub-models for liquid droplets. The newly developed numerical model was experimentally validated with data from a series of tests conducted in the authors' laboratory. The results showed that the simulations followed the same trends as the data, and the model predicted the condensation due to the electro-spray injection process in the air stream. The injected water droplets, which are electrically charged to their Rayleigh limits, increased in size while wiping out the humidity from the air. The simulations indicated that the dehumidification was about 1% for 0.5 cubic feet per minute airflow rate. Scaling up to larger flows is a future follow-up work.

Yel Mahi, *Maliha↗

DOE OSTI2019

AMReX: a framework for block-structured adaptive mesh refinement

AMReX is a C++ software framework that supports the development of block-structured adaptive mesh refinement (AMR) algorithms for solving systems of partial differential equations (PDEs) with complex boundary conditions on current and emerging architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving the local descriptions of different physical processes in complex multiphysics algorithms. Current AMReX-based application codes span a number of areas, including atmospheric modeling, astrophysics, combustion, cosmology, fluctuating hydrodynamics, multiphase flows, and particle accelerators. In particular, the AMReX-Astro GitHub repository holds a number of astrophysical modeling tools based on AMReX. The origins of AMReX trace back to the BoxLib software framework. AMReX supports a number of different time-stepping strategies and spatial discretizations. Solution strategies supported by AMReX range from level-by-level approaches (with or without subcycling in time) with multilevel synchronization to full-hierarchy approaches, and any combination thereof. User-defined kernels that operate on patches of data can be written in C++ or Fortran; there is also a Fortran-interface functionality which wraps the core C++ data structures and operations in Fortran wrappers so that an application code based on AMReX can be written entirely in Fortran.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

A Numerical Study of Factors Affecting Fracture-Fluid Cleanup and Produced Gas/Water in Marcellus Shale: Part II

Horizontal wells combined with successful multi-stage hydraulic fracture treatments are currently the most established method for effectively stimulating and enabling economic development of gas bearing organic-rich shale formations. Fracture cleanup in the Stimulated Reservoir Volume (SRV) is critical to stimulation effectiveness and long-term well performance. However, fluid cleanup is often hampered by formation damage, and post-fracture well performance frequently falls below expectations. A systematic study of the factors that hinder fracture fluid cleanup in shale formations can help optimize fracture treatments and better quantify long term volumes of produced water and gas. Fracture fluid cleanup is a complex process influenced by multi-phase flow through porous media (relative permeability hysteresis, capillary pressure etc.), reservoir rock and fluid properties, fracture fluid properties, proppant placement, fracture treatment parameters, and subsequent flowback and field operations. Changing SRV and fracture conductivity as production progresses further adds to the complexity of this problem. Numerical simulation is the best, and most practical approach to investigate such a complicated blend of mechanisms, parameters, their interactions, and subsequent impact on fracture fluid cleanup and well deliverability. In this paper, a 3-dimensional, 2-phase, dual-porosity model was used to investigate the impact of multiphase flow, proppant crushing, proppant diagenesis, shut-in time, reservoir rock compaction, gas slippage, and gas desorption on fracture fluid cleanup, and well performance in Marcellus shale. The research findings have shed light on the factors that substantially constrains efficient fracture fluid cleanup in gas shales, and provided guidelines for improved fracture treatment designs and water management.

58 GEOSCIENCES↗

DOE OSTI2018

Interaction Between Proppant Compaction and Single-/Multiphase Flows in a Hydraulic Fracture

Understanding proppant-transport and -deposition patterns in a hydraulic fracture is vital for effective and economical production of petroleum hydrocarbons. In this research, a numerical-modeling approach, combining the discrete-element method (DEM) with single-/multiphase lattice Boltzmann (LB) simulation, was adopted to advance understanding of the interaction between reservoir depletion, proppant-particle compaction, and single-/multiphase flows in a hydraulic fracture. DEM was used to simulate effective-stress increase and the resultant proppant-particle movement and rearrangement during the process of reservoir depletion caused by hydrocarbon production. Simulated pore structure of the proppant pack was extracted and used as boundary conditions in the LB simulation to calculate the time-dependent permeability of the proppant pack. We first validated the DEM-LB numerical work flow, and the simulated proppant-pack permeabilities as functions of effective stress were in good agreement with laboratory measurements. Furthermore, three proppant packs with the same average particle diameter but different diameter distributions were generated to study the role of proppant-size heterogeneity (variation in particle diameter). Specifically, we used the coefficient of variation (COV) of diameter, defined as the ratio of standard deviation of diameter to mean diameter, to characterize the heterogeneity of particle size. We obtained proppant-pack porosity, permeability, and fracture-width reduction (closure distance) as functions of effective stress. Under the same effective stress, a proppant pack with a higher diameter COV had lower porosity and permeability and larger fracture-width reduction. This was because the high diameter COV gave rise to a wider diameter distribution of proppant particles; smaller particles were compressed into the pore space between larger particles with increasing stress, leading to larger closure distance and lower porosity and permeability. With multiphase LB simulation, relative permeability curves were obtained, which are critical for larger-scale reservoir simulations under various effective stresses. The relative permeability of the oil phase was more sensitive to changes in geometry and stress, compared with the wetting phase. This was because the oil phase occupied larger pores; compaction of the proppant pack affected the structure of the pores, because the pores were farther from the grain contacts and thus more susceptible to collapse. It is also interesting to note that when effective stress increased continuously, oil relative permeability increased first and then decreased. This nonmonotonic behavior was the result of the nonmonotonic development of pore structure and oil connectivity under increasing stress.

Fan, Ming↗

DOE OSTI2014

Pore-Water Extraction from Unsaturated Porous Media: Intermediate-Scale Laboratory

As a remedial approach, vacuum-induced pore-water extraction offers the possibility of contaminant and water removal from the vadose zone, which may be beneficial in reducing the flux of vadose zone contaminants to groundwater. Vadose zone water extraction is being considered at the Hanford Site in Washington State as a means to remove technetium-99 contamination from low permeability sediments with relatively high water contents. A series of intermediate-scale laboratory experiments have been conducted to improve the fundamental understanding and limitations of the technique. Column experiments were designed to investigate the relations between imposed suctions, water saturations, and water production. Flow cell experiments were conducted to investigate the effects of high-permeability layers and near-well compaction on pore-water extraction efficiency. Results show that water extraction from unsaturated systems can be achieved in low permeability sediments, provided that the initial water saturations are relatively high. The presence of a high-permeability layer decreased the yield, and compaction near the well screen had a limited effect on overall performance. In all experiments, large pressure gradients were observed near the extraction screen. Minimum requirements for water extraction include an imposed vacuum-induced suction larger than the initial sediment capillary pressure, in combination with a fully saturated seepage-face boundary. A numerical multiphase simulator with a coupled seepage-face boundary conditions was used to simulate the experiments. Reasonable matches were obtained between measured and simulated results for both water extraction and capillary pressures, suggesting that numerical simulations may be used as a design tool for field-scale applications of pore-water extraction.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2019

Investigation of Gravity-Driven Infiltration Instabilities in Smooth and Rough Fractures Using a Pairwise-Force Smoothed Particle Hydrodynamics Model

In this work, we use a three-dimensional multiphase pairwise-force smoothed particle hydrodynamics (PF-SPH) method to simulate infiltration dynamics in smooth and rough fractures. We investigate the influence of roughness and injection rate on the fluid flow profile and flow velocity. Three types of fractures are considered with different degrees of roughness, including a smooth fracture. Both the rough and smooth fractures exhibit flow instability, fingering, and intermittent flow regimes for low infiltration rates. A stable fluid profile only is achieved for high fluxes when fractures are fully saturated. In all considered fractures, the mean flow velocity exponentially increases with increasing infiltration rate. To characterize the flow instability, we calculate standard deviations of the velocity in different sections of the fracture relative to the mean flow velocity. For the considered infiltration rates, we find that roughness decreases the flow velocity and increases the velocity standard deviations. Hence, we observe that the likelihood of discontinuities in flow regimes increases with the degree of roughness.

58 GEOSCIENCES↗

DOE OSTI2019

Heat‐Generating Nuclear Waste in Salt: Field Testing and Simulation

Core Ideas A field‐scale experiment and numerical simulations confirm salt backfill behavior. Simulations closely match temperature around and under the piled salt backfill. Results indicate limited dissolution–precipitation reactions around the heat source. Alteration of backfill is unlikely if the drift is allowed to dry before emplacement. Investigations relating to in‐drift disposal of heat‐generating nuclear waste in salt have raised questions about heat–brine interactions in the unsaturated run‐of‐mine (RoM) salt pile used as backfill. These interactions have the potential to change the structure of the RoM salt surrounding the canister, possibly altering long‐term containment of the source. An experiment is in progress at the Waste Isolation Pilot Plant (WIPP), New Mexico, in which a heated canister was placed on the floor of an open drift, covered in a pile of RoM salt, and energized with 1000 W. Temperature in the RoM salt pile had stabilized after about 15 d, allowing evaluation of the heat‐up period of the ongoing experiment. Using a multiphase porous flow simulator that has been modified to handle salt‐specific coupled processes, we examined coupled thermal–hydrological–chemical behavior in the RoM salt pile. Our simulations suggest that for the relatively dry cases examined, porosity changes within RoM salt in a generic salt repository are likely to be minor in the period between waste emplacement and plastic closure of the drift. The primary sensitivity for porosity change is to the early moisture content of the RoM salt used to cover the canister. Secondary influences include moisture availability from the disturbed rock zone (DRZ) surrounding the drift and the capillary pressure ratio between the DRZ and the RoM salt. Early changes in porosity and permeability may be affected by moisture content, but this was not observed in the test. Such changes would be most likely to occur when using damp RoM salt or if waste is emplaced in a drift immediately following opening of the drift before evaporative dewatering of the drift walls occurs.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2014

SESAME 96170, a solid-liquid equation of state for CeO2

I describe an equation of state (EOS) for the low-pressure solid phase and liquid phase of cerium (IV) oxide, CeO 2 . The models and parameters used to calculate the EOS are presented in detail, and I compare with data for the full-density crystal. Hugoniot data are available only for high-porosity powders, and I discuss difficulties in comparing with such data. I have constructed SESAME 96170, an EOS for cerium (IV) oxide that includes the ambient solid and liquid phases. The EOS extends over the full standard SESAME range, but should not be used at low temperatures and high densities because of the lack of a high-pressure solid phase. I have described the models used to compute the three terms of the EOS (cold curve, nuclear, and thermal electronic), and I have given the parameters used in the models. They were determined by comparison with experimental data at P = 1 atm, including the constant-pressure specific heat, coefficient of thermal expansion, and melting and boiling points. The EOS compares well with data in its intended range of validity, but the presence of high-frequency optical modes in its phonon spectrum limits the agreement of our models with thermal data. The next step is to construct a multiphase EOS that includes the low- and high-pressure solid phases and the liquid. The DAC data from Duclos will most strongly constrain the parameters of the high-pressure solid. A remaining issue is the comparison of the crystal-density EOS with experimental Hugoniot data, which are taken at much lower initial data because the samples are porous powders. A satisfactory means of modeling porosity, allowing comparison of theory and experiment, has not yet been produced.

36 MATERIALS SCIENCE↗