Search NASA⌕ Search

SEARCH · Search NASA

Results for “TWO-PHASE SYSTEM”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Implementation of a Drift Flux Model into SAM with Development of a Verification and Validation Test Suite for Modeling of Noncondensable Gas Mixtures

The advanced thermal-hydraulic system code, System Analysis Module (SAM), was originally developed for the modeling of single-phase flow in advanced reactors. It has since been expanded to include a four-equation drift flux model for the modeling of two-phase flows containing a noncondensable gas. The model was expanded to support the modeling of molten salt reactor (MSR) designs in which the fuel is directly dissolved in the circulating coolant. These designs have shown that circulating gas bubbles can play an important role in the management of fission products and the operational behavior of the reactor. A drift flux model was implemented to more accurately capture the localized behavior of the void in the core and its impact on the mass transfer of fission products. A thorough assessment of the new model was performed by developing a verification and validation test suite. Verification problems were designed to test all major terms in the new governing equations. The new model converged to the correct solution at the expected order of accuracy for all verification cases. The validation cases included a wide range of flow and void conditions in different pipe geometries. Although higher void experiments show a slight underprediction of void by the drift flux model, experiments that aim to reproduce Molten Salt Reactor Experiment (MSRE) experimental conditions show good agreement with the model. The gas transport model was activated for a SAM model of the MSRE to demonstrate that it can be used in a more complex model. Finally, this gas transport model will be used along with an interfacial area transport equation being implemented in SAM for the prediction of mass transport behavior in MSR conditions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Pore-scale simulation of drying in porous media using a hybrid lattice Boltzmann: pore network model

In this work, a hybrid method coupling a pseudo-potential lattice Boltzmann model (LBM) and a pore network model (PNM) to simulate drying in porous media is proposed. Based on the watershed method, the porous medium is firstly decomposed into pore regions. According to the liquid–vapor phase distribution at a given time, the pore regions are further divided into four pore types, namely two-phase pores where a liquid–vapor interface exists, buffer pores next to the two-phase pores, single-liquid and single-vapor phase pores. The pseudo-potential LBM is used in the two-phase and buffer pores to simulate liquid drying and track the movement of the interfaces, while the single-phase PNM simulations are conducted in the buffer and single-phase pores to simulate vapor or liquid flow. LBM and PNM are coupled in the buffer pores through exchange of boundary information. The hybrid method is applied to simulate liquid drying in a porous medium. The whole-domain LBM simulation is considered as the reference solution to validate the hybrid method. Liquid saturation variation during the drying process and detailed phase and pressure distributions obtained by the two methods match quite well, demonstrating the accuracy of the hybrid method. For the specific case studied, the hybrid method saves more than 60% computational time compared to the whole-domain LBM simulation. In addition, the speedup of the hybrid method becomes more significant for a larger computational domain. In summary, the hybrid method developed in this work combines the accuracy of LBM and the efficiency of PNM to simulate drying in porous media at pore scale and can lead to significant reduction of computation time, thus allowing the pore-scale consideration of drying in larger porous systems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A high-dimensional neural network potential for molecular dynamics simulations of condensed phase nickel and phase transitions

A high-dimensional neural network interatomic potential was developed and used in molecular dynamics simulations of condensed phase Ni and Ni systems with liquid–solid phase coexistence. The reference data set was generated by sampling the potential energy surface over a broad temperature-pressure domain using ab initio MD simulations to train a unified potential. Excellent agreement was achieved between bulk face-centered cubic nickel thermal expansion simulations and relevant experimental data. The same potential also yields accurate structures and diffusivities in the liquid state. The phase transition between liquid and solid phases was simulated using the two-phase interface method. The predicted melting point temperature is within a few kelvins of the literature value. Here, the general methodology could be applied to describe crystals with much more complex phase behaviors.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Enhancing superconductivity of Y 5 Rh 6 Sn 18 by atomic disorder

Here, we investigate the effect of enhancement of superconducting transition temperature $T_c$ by nonmagnetic atom disorder in the filled skutterudite-related tetragonal Y 5 Rh 6 Sn 18 compound doped with Ca. We documented experimentally that Y 5 Rh 6 Sn 18 and its Ca-doped alloys are electronically inhomogeneous at the nanoscale, when Ca content is smaller than ~1.5 in the Y 5– x Ca x Rh 6 Sn 18 system, while for $\textit{x}$ ≥ 1.5 much stronger chemical phase inhomogeneity is observed with an about 20% volume fraction of the second 3:4:13 cubic phase, which we interpret as a fluctuation of stoichiometry within the bulk sample. Then the enhancement of $T_c$ vs $\textit{x}$ could be modeled by a mechanism proposed in recent theoretical reports for increasing the mean-field transition temperature $T_c$ in the presence of nonmagnetic disorder. The increase in disorder with doping increases the sample inhomogeneity and causes a systematic increase in $T_c$, while for two-phase $\textit{x}$ ≥ 1.5 samples the critical temperature $T^{\star}_c ≈ 2 × T_c$ rapidly increases. Based on band structure calculations performed under pressure, we demonstrate how the change in density of states would affect $T_c$ of Y 5 Rh 6 Sn 18 . We obtained the Grüneisen parameter $γ_G$ larger for the inhomogeneous phase with respect to $γ_G$ of the bulk $T_c$ phase and attribute the enhancement of $T_c$ to larger stiffening of the high-temperature $T^{\star}_c$ phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Spinodal electronic phase separation during insulator-metal transitions

Electronic phase transitions such as insulator-metal transitions are common in strongly correlated systems. Here, using a combination of thermodynamic linear-stability analysis and phase-field simulations and employing VO 2 as a prototypical example, we predict that an insulator-metal transition driven by photoexcitation may involve an intermediate, modulated charge density state with a temperature-dependent characteristic wavelength. It is shown that such an intermediate two-phase electronic state is formed through a spinodal mechanism and that its formation can be generic for insulator-metal transitions driven by fast stimuli. This transient electronic phase separation is expected to stimulate future experimental and computational efforts.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Extended families of critical and stationary droplets for nonequilibrium phase transitions in spatially discrete bistable systems

Bistable nonequilibrium systems are realized in catalytic reaction-diffusion processes, biological transport and regulation, spatial epidemics, etc. Behavior in spatially continuous formulations, described at the mean-field level by reaction-diffusion type equations (RDEs), often mimics that of classic equilibrium van der Waals type systems. When accounting for noise, similarities include a discontinuous phase transition at some value, p eq , of a control parameter, p , with metastability and hysteresis around p eq . For each p , there is a unique critical droplet of the more stable phase embedded in the less stable or metastable phase which is stationary (neither shrinking nor growing), and with size diverging as p → p eq . Spatially discrete analogs of these mean-field formulations, described by lattice differential equations (LDEs), are more appropriate for some applications, but have received less attention. It is recognized that LDEs can exhibit richer behavior than RDEs, specifically propagation failure for planar interphases separating distinct phases. Herein, we show that this feature, together with an orientation dependence of planar interface propagation also deriving from spatial discreteness, results in the occurrence of entire families of stationary droplets. The extent of these families increases approaching the transition and can be infinite if propagation failure is realized. In addition, there can exist a regime of generic two-phase coexistence where arbitrarily large droplets of either phase always shrink. Such rich behavior is qualitatively distinct from that for classic nucleation in equilibrium and spatially continuous nonequilibrium systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Effect of transport mechanism on the coarsening of bicontinuous structures: A comparison between bulk and surface diffusion

Here, coarsening of bicontinuous microstructures is observed in a variety of systems, such as nanoporous metals and mixtures that have undergone spinodal decomposition. To better understand the morphological evolution of these structures during coarsening, we compare the morphologies resulting from two different coarsening mechanisms, surface and bulk diffusion. We perform phase-field simulations of coarsening via each mechanism in a two-phase mixture at nominal volume fractions of 50%-50% and 36%-64%, and the simulated structures are characterized in terms of topology (genus density), the interfacial shape distribution, structure factor, and autocorrelations of phase and mean curvature. We observe self-similar evolution of morphology and topology and agreement with the expected power laws for dynamic scaling, in which the characteristic length scale increases over time proportionally to t 1/4 for surface diffusion and t 1/3 for bulk diffusion. While we observe the expected difference in the coarsening kinetics, we find that differences in self-similar morphology due to coarsening mechanism are relatively small, although typically they are larger at 36% volume fraction than at 50% volume fraction. In particular, we find that bicontinuous structures coarsened via surface diffusion have lower scaled genus densities than structures coarsened via bulk diffusion. We also compare the self-similar morphologies to those in literature and to two model bicontinuous structures, namely, constant-mean-curvature surfaces based on the Schoen G minimal surface and random leveled-wave structures. The average scaled mean curvatures of these model structures agree reasonably with those of the coarsened structures at both 36% and 50%, but we find substantial disagreements in the scaled genus densities and the standard deviations of mean curvature.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Interface pinning causes the hysteresis of the hydride transformation in binary metal hydrides

Hydriding and dehydriding transitions in bulk and nanocrystalline binary metal hydrides were studied using the Pd-H model system by measuring pressure-composition isotherms with in situ x-ray diffractometry. Nanocrystalline Pd showed a smaller pressure hysteresis, solvus hysteresis, and hysteresis in lattice parameter, compared to bulk Pd. The time-dependence of pressure equilibration was measured after dosing with aliquots of hydrogen, giving equilibration times that were much faster in the single-phase regions than in the two-phase plateaus. In the broad two-phase plateaus, the pressure relaxations were exponential functions of time. An explanation of hysteresis is developed that is based on a dissipative potential barrier that impedes the motion of the interface due to interactions between lattice defects and the two-phase interface. The exponential pressure relaxations and hysteresis are consistent for this mechanism. For a simple model of the pinning potential, the potential barrier maximum is an order of magnitude less than typical grain boundary energies. These pinning effects are substantially different in the nanocrystalline Pd, suggesting differences in the hydriding mechanism.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Three and Two Phase Rotating Field Inductive Couplers for Wireless Power Transfer with One Phase per Layer Windings

Multiphase inductive wireless charging coils have been proposed recently to improve coupler surface power density, reduce component stress and size, and provide near-constant power delivery to charge mobile electric systems. Several aspects for the fundamental characterization of multiphase coils are explored up to six phases including approximate mutual inductance with size and turn variation, induced voltage, and output power estimation. The relative component stress and size of passive components for resonant operation are compared between the multiphase variants. A combination of an experimentally validated 3D electromagnetic finite element analysis (FEA) and power electronic co-simulations are used to validate the estimated quantities approximated with a mixture of analytical equations and an artificial neural network model for mutual inductance. A novel three-phase transmitter, two-phase receiver coil pair is also proposed for electric vehicle charging to reduce the number of connections and compensation complexity on the vehicle-side with improved power output compared to a two-phase configuration.

Lewis, Donovin D. [University of Kentucky]↗
DOE OSTI2023

Understanding the Effect of Electrochemical Properties and Microstructure on the Microgalvanic Corrosion of Mg Alloys via Phase-Field Simulations

In this work, we apply a phase-field model to gain insights into the corrosion behavior of Mg alloys. Specifically, we study the effect of electrochemical properties of the materials and their environment and the spatial distribution of second phases in a magnesium alloy. To this end, we perform sensitivity analyses in which we separately vary the exchange current density and corrosion potential of the second phase, as well as the electrolyte conductivity. We describe the effects of these parameters on the corrosion current and the resulting corrosion-front morphology. We also confirm that the ratio between the Wagner length, calculated for the anodic phase, and the initial width of the anodic domain is a good predictor of the morphological characteristic of the corroding surface. In addition, we examine the effect of the microstructure on the corrosion behavior in both 2D and 3D systems by varying the shape, size, and distribution of the second-phase regions. Our findings provide insights into the influence of the two-phase microstructure on the corrosion behavior in a magnesium alloy.

Electrochemistry↗
DOE OSTI2019

A two-phase substrate model for enzymatic hydrolysis of lignocellulose: application to batch and continuous reactors

Abstract Background Enzymatic hydrolysis continues to have a significant projected production cost for the biological conversion of biomass to fuels and chemicals, motivating research into improved enzyme and reactor technologies in order to reduce enzyme usage and equipment costs. However, technology development is stymied by a lack of accurate and computationally accessible enzymatic-hydrolysis reaction models. Enzymatic deconstruction of cellulosic materials is an exceedingly complex physico-chemical process. Models which elucidate specific mechanisms of deconstruction are often too computationally intensive to be accessible in process or multi-physics simulations, and empirical models are often too inflexible to be effectively applied outside of their batch contexts. In this paper, we employ a phenomenological modeling approach to represent rate slowdown due to substrate structure (implemented as two substrate phases) and feedback inhibition, and apply the model to a continuous reactor system. Results A phenomenological model was developed in order to predict glucose and solids concentrations in batch and continuous enzymatic-hydrolysis reactors from which liquor is continuously removed by ultrafiltration. A series of batch experiments were performed, varying initial conditions (solids, enzyme, and sugar concentrations), and best-fit model parameters were determined using constrained nonlinear least-squares methods. The model achieved a good fit for overall sugar yield and insoluble solids concentration, as well as for the reduced rate of sugar production over time. Additionally, without refitting model coefficients, good quantitative agreement was observed between results from continuous enzymatic-hydrolysis experiments and model predictions. Finally, the sensitivity of the model to its parameters is explored and discussed. Conclusions Although the phenomena represented by the model correspond to behaviors that emerge from clusters of mechanisms, and hence a set of model coefficients are unique to the substrate and the enzyme system, the model is efficient to solve and may be applied to novel reactor schema and implemented in computational fluid dynamics (CFD) simulations. Hence, this modeling approach finds the right balance between model complexity and computational efficiency. These capabilities have broad application to reactor design, scale-up, and process optimization.

09 BIOMASS FUELS↗
DOE OSTI2025

Data for "Anti-Pdc1p Nanobody as a Genetically Encoded Inhibitor of Ethanol Production Enables Dual Transcriptional and Post-translational Controls of Yeast Fermentations"

Microbial fermentation provides a sustainable method of producing valuable chemicals. Adding dynamic control to fermentations can significantly improve titers, but most systems rely on transcriptional controls of metabolic enzymes, leaving existing intracellular enzymes unregulated. This limits the ability of transcriptional controls to switch off metabolic pathways, especially when metabolic enzymes have long half-lives. We developed a two-layer transcriptional/post-translational control system for yeast fermentations. Specifically, the system uses blue light to transcriptionally activate the major pyruvate decarboxylase PDC1 , required for cell growth and concomitant ethanol production. Switching to darkness transcriptionally inactivates PDC1 and instead activates the anti-Pdc1p nanobody, NbJRI, to act as a genetically encoded inhibitor of Pdc1p accumulated during the growth phase. This dual transcriptional/post-translational control improves the production of 2,3-BDO and citramalate by up to 100 and 92% compared to using transcriptional controls alone in dynamic two-phase fermentations. This study establishes the NbJRI nanobody as an effective genetically encoded inhibitor of Pdc1p that can enhance the production of pyruvate-derived chemicals.

metabolic engineering↗
DOE OSTI2023

Parametric and Sensitivity Analysis of a Steam Generator Model Using Python and Machine-Learning Tools

For this study, we used Python and machine-learning tools to perform a comprehensive parametric and sensitivity analysis on a steam generator (SG) model. (The Python model was based on a previously completed MATLAB framework for the Holtec SMR-160 SG.) We investigated the influence of various input parameters (e.g., heat transfer coefficient [HTC], Nusselt number, and heat exchanger effectiveness) on the system’s output. With machine-learning tools such as the Risk Analysis Virtual Environment (RAVEN), which was developed at Idaho National Laboratory, we were then able to perform an automated analysis of the SG inputs’ effect on the HTC. The analysis results give valuable insights into the performance and optimization of SG systems. We found the inlet mass flow rate (MFR) to have the greatest impact on the HTC, followed closely by the inlet temperature, and then pressure. Shifting of the input parameters causes the location of the maximum HTC along the SG length to change incrementally. The cold leg (CL) MFR was also found to impact the HTC magnitude as well as the location of the maximum HTC. At between 0.4–0.9 of the total SG length, the input parameters experience maximum impact on the HTC, leading us to suggest that sensors be efficiently placed on the SG so as to closely and effectively monitor thermal-hydraulic properties during reactor operation. We also found that the sensitivity data calculated manually agrees with the RAVEN – based data, confirming the same range of maximum sensitivity. However, the RAVEN-based analysis showed that cold leg pressure and hot leg temperature have a greater impact on the heat transfer coefficient than the mass flow rate, implying that a manual sensitivity study taking only two samples is not accurate.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

FY-25 Progress on Computational Modeling of the Water Based NSTF

This report summarizes the system level modeling using RELAP5-3D of the Natural Convection Shutdown Heat Removal Test Facility (NSTF) completed in FY25. This year’s work focuses on a new tank configuration where the inlet of the tank was lowered in elevation by 45”. The stability boundaries of the NSTF are thoroughly studied and stability maps are constructed based on the stability and the oscillation patterns of the system. Five distinct operational modes are identified, namely single-phase liquid, uniform double peak oscillations, uniform sinusoidal oscillations, stable two-phase flow, and non-uniform oscillations. Next, the riser inlet throttling case of experimental test Run-104 is simulated with the RELAP5 model where good agreement is obtained between the model and the experimental data. The simulation also highlights the effects of backflow of water from the tank to the upper region of the chimney. Additionally, the decay heat removal test of Run-99 is simulated with the RELAP5 model. Comparison is carried out between this run and a similar run with the mid-tank inlet of Run-74 performed in FY22. With the lower tank inlet, the RELAP5 model is able to predict the experimental data more accurately than the previous mid tank inlet configuration. The discrepancy in model prediction accuracy highlights the non-symmetrical spatial effects in the tank that would otherwise be more easily captured with higher fidelity models. Lastly, two exploratory studies are conducted to investigate the behaviors of the NSTF when 1) heating is provided to the downcomer and 2) a bypass channel is added between the horizontal chimney section to the downcomer.

42 ENGINEERING↗
DOE OSTI2026

SULI Report - Development of a Molten Salt Circulation Loop for in-situ Spectroscopy

This project supports the development of real time optical monitoring capabilities for molten salt reactor (MSR) environments by designing, testing, and refining a molten salt circulation loop suitable for combined laser induced breakdown spectroscopy (LIBS) and ultraviolet visible (UV Vis) absorption measurements. Online spectroscopic monitoring is increasingly important for nuclear safeguards, corrosion tracking, and material accountancy, yet MSR process fluids present substantial challenges due to their chemical complexity and hazards such as high temperatures and radiation. To address these needs, this work focuses on Phase I, the development of a room temperature aqueous circulation loop that serves as a surrogate platform for evaluating flow behavior, optical access, and component performance prior to high temperature salt operation. Initial testing identified several practical issues—including leaks, obstructions, and two-phase flow through the absorption cell—that were systematically resolved through hardware replacement, flow path redesign, and venturi pressure optimization. Relocating the flow cell upstream of the primary venturi enabled periods of stable single-phase flow, demonstrating the feasibility of integrating optical diagnostics into a circulation system. The results of Phase I provide essential design insight for Phase II, which will incorporate furnace compatible materials and LiCl KCl eutectic salt. Completion of the molten salt system will deliver a reusable testbed for evaluating multimodal spectroscopic techniques, advancing nondestructive, real time monitoring tools for future MSR and nuclear fuel cycle applications.

98 - NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL↗
DOE OSTI2025

Derivation of A Representative Elementary Volume (REV) for Upscaled Two-Phase Flow in Porous Media

Relative permeability plays an important role in the upscaling of multiphase flow in porous media from the pore scale to the Darcy scale. The entire concept of relative permeability is contingent on the existence of a representative elementary volume (REV). As we move to smaller samples to measure relative permeability, such as with digital core analysis, the concept of a classical REV has become increasingly unlikely when using the conventional approach to defining a representative volume. The “‘conventional”’ understanding of an REV is that a large enough volume must be considered such that spatial variability averages out. In digital rock methods, such as pore-scale simulations based on micro-computed tomography (CT) images, the domain size is typically 2 to 4 mm. This is approximately the length scale of a single-phase flow REV using the classic REV approach. However, the single-phase perspective does not consider the complex dynamics and fluctuations often observed in multiphase flow systems, even at centimeter-scale experiments and/or simulations. A fundamental question is, therefore, whether the domain size commonly used in digital rock simulations can provide a consistent energy budget such that the concept of relative permeability exists. Based on first principles, relative permeability accounts for the rate of energy dissipated in a stationary process. If the dynamics are fluctuating, the energy dissipated can vary but will average out over a long enough timescale. The key to determining the validity of the relative permeability is the timescale of the measurement, not the spatial scale. The conventional REV theory assumes that spatial, temporal, and ensemble averages are equivalent in an ergodic system, but it does not provide a way to test this assumption. We provide a formal way to identify the timescale where the relative permeability accurately captures energy dissipation as a way to validate relative permeability measurements and quantitatively assess their accuracy. This result will be tested for a practical SCAL test, determining how long a flow experiment needs to be run to accurately characterize the rate of energy dissipation by the flow. The outcome will be a best practice guide for the determination of relative permeability from core-scale experiments and/or digital core simulations that ensure the energy budget is fully accounted for in the relative permeability coefficient.

Mcclure, James [Virginia Tech, Blacksburg]↗
DOE OSTI2020

Time-Domain Nuclear Magnetic Resonance Determination of Wettability Alteration: Analysis for Low-Salinity Water

Wettability has been shown to influence oil recovery. This property has become central to low-salinity (LSW) and smart (SWF) water flooding recovery mechanisms research. The challenge lies in the fact that oil recovery results from the combined effects of solid-liquid and liquid-liquid interactions. This demands methods that allow an independent interpretation of wettability alteration contributions. The primary objective of this work is to assess changes in wettability through the application of Time-Domain Nuclear Magnetic Resonance (TD-NMR) T 2 distribution and diffusion coefficient, starting with a well-controlled porous system, that is, glass beads, and then a model rock (Berea), in the presence of one phase, either oil or brine exclusively. Subsequently, two-phase fluid saturation was tested. For the glass beads, dimethyldichlorosilane was used to induce a hydrophobic response, as confirmed by contact angle experiments on slides of the same material. Sodium sulfate was used for its known positive influence on oil recovery during LSW and SWF. In cases where alteration of surface properties was expected, a leftward shift of the average T 2 distribution curve modes, accompanied by a reduction on the diffusion coefficient during the aging process was observed. The results of this work confirm that fluid-solid interactions during LSW and SWF, namely a shift in wettability, take place after the injection of low-salinity water.

42 ENGINEERING↗
DOE OSTI2022

A Modeling and Neutron Diffraction Study of the High Temperature Properties of Sub-Stoichiometric Yttrium Hydride for Novel Moderator Applications

Low-enriched-uranium (LEU) reactor systems utilize moderators to improve neutron economy. Solid yttrium hydride is one of the primary moderator candidates for high-temperature (>700 °C) nuclear reactor applications. This is due to its ability to retain hydrogen at elevated temperatures compared to other metal hydrides. For reactor modeling purposes, both neutronic and thermos-mechanical modeling, several high-temperature properties for sub-stoichiometric yttrium hydride (YH2−x) are needed. In this paper, we present an atomistics and a neutron diffraction study of the high-temperature properties of Y and YH2−x. Specifically, we focus on the thermal lattice expansion effects in yttrium metal and yttrium hydride, which also govern bulk thermal expansion. Previously reported physical and mechanical properties for sub-stoichiometric yttrium hydride at ambient conditions are expanded using lattice dynamics to take into account high-temperature effects. Accordingly, an array of newly generated properties is presented that enables high-fidelity neutronics, and thermomechanical modeling. These properties include various elastic moduli, thermal expansion parameters for yttrium and yttrium hydride, and single-phase (YH2−x) and two-phase (Y + YH2−x) density as a function of stoichiometry and density.

36 MATERIALS SCIENCE↗