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Results for “phase diagram or equation of state”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Characterization of the high-pressure and high-temperature phase diagram and equation of state of chromium

The high-pressure and high-temperature phase diagram of chromium has been investigated both experimentally (in situ), using a laser-heated diamond-anvil cell technique coupled with synchrotron powder X-ray diffraction, and theoretically, using ab initio density-functional theory simulations. In the pressure–temperature range covered experimentally (up to 90 GPa and 4500 K, respectively) only the solid body-centred-cubic and liquid phases of chromium have been observed. Experiments and computer calculations give melting curves in agreement with each other that can both be described by the Simon–Glatzel equation $T_{m}(P) = 2136K (1 + P/25.9)^{0.41}$ In addition, a quasi-hydrostatic equation of state at ambient temperature has been experimentally characterized up to 131 GPa and compared with the present simulations. Both methods give very similar third-order Birch–Murnaghan equations of state with bulk moduli of 182–185 GPa and respective pressure derivatives of 4.74–5.15. According to the present calculations, the obtained melting curve and equation of state are valid up to at least 815 GPa, at which pressure the melting temperature is 9310 K. Finally, from the obtained results, it was possible to determine a thermal equation of state of chromium valid up to 65 GPa and 2100 K.

36 MATERIALS SCIENCE↗
DOE OSTI2022

QCD Equation of State and Phase Diagram from Holographic Black Holes

By using the AdS/CFT correspondence, we construct an Einstein-Maxwell-Dilaton model to map the thermodynamics of strongly interacting matter. The holographic model, constrained to reproduce the lattice QCD equation of state at zero baryon chemical potential, predicts a critical end point and a first order phase transition line. We also obtain the equation of state of the model for a large region of the phase diagram. We characterize the crossover transition region by two lines, one associated to the inflection of the second order baryon susceptibility, and another one associated to the minimum of the square of the speed of sound along trajectories of constant entropy per baryon number. We observe that both lines merge at the critical point.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

The phase diagram of Ti-6Al-4V at high-pressures and high-temperatures

We report results from a series of diamond-anvil-cell synchrotron x-ray diffraction and large-volume-press experiments, and calculations, to investigate the phase diagram of commercial polycrystalline high-strength Ti-6Al-4V alloy in pressure–temperature space. Up to ~30 GPa and 886 K, Ti-6Al-4V is found to be stable in the hexagonal-close-packed, or α phase. The effect of temperature on the volume expansion and compressibility of α–Ti-6Al-4V is modest. The martensitic α → ω (hexagonal) transition occurs at ~30 GPa, with both phases coexisting until at ~38–40 GPa the transition to the ω phase is completed. Between 300 K and 844 K the α → ω transition appears to be independent of temperature. ω–Ti-6Al-4V is stable to ~91 GPa and 844 K, the highest combined pressure and temperature reached in these experiments. Pressure–volume–temperature equations-of-state for the α and ω phases of Ti-6Al-4V are generated and found to be similar to pure Ti. A pronounced hysteresis is observed in the ω–Ti-6Al-4V on decompression, with the hexagonal structure reverting back to the α phase at pressures below ~9 GPa at room temperature, and at a higher pressure at elevated temperatures. Based on our data, we estimate the Ti-6Al-4V α–β–ω triple point to occur at ~900 K and 30 GPa, in good agreement with our calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Femtosecond diffraction studies of the sodium chloride phase diagram under laser shock compression

The phase diagram of sodium chloride (NaCl) under laser shock compression has been studied at Linac Coherent Light Source (LCLS) at the x-ray free-electron laser facility. Both solid–solid (B1 → B2) and solid–liquid (B2 → liquid) transitions have been observed along the Hugoniot over nanosecond time scales. By combining structural measurements through in situ x-ray diffraction, pressure determination through velocimetry, and a thermal equation-of-state, the shock-compressed data are used to constrain the phase diagram of NaCl. Transformation into the B2 phase is found to occur at 28(2) GPa, and B2–liquid coexistence is observed between 54(4) and 66(6) GPa, with near full melt at 66(6) GPa. Late-time pressure release from an initial shocked B2-state results in a B2 → B1 back transformation. Our results show agreement with previous static compression data, suggesting that the time scale for melting is very rapid and that equilibrium states in NaCl are being accessed over nanosecond time scales. Finally, a multiphase equation-of-state description of NaCl incorporated into a one-dimensional hydrocode is used to interpret pressure and temperature evolution over these rapid time scales.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Machine learning the metastable phase diagram of covalently bonded carbon

Abstract Conventional phase diagram generation involves experimentation to provide an initial estimate of the set of thermodynamically accessible phases and their boundaries, followed by use of phenomenological models to interpolate between the available experimental data points and extrapolate to experimentally inaccessible regions. Such an approach, combined with high throughput first-principles calculations and data-mining techniques, has led to exhaustive thermodynamic databases (e.g. compatible with the CALPHAD method), albeit focused on the reduced set of phases observed at distinct thermodynamic equilibria. In contrast, materials during their synthesis, operation, or processing, may not reach their thermodynamic equilibrium state but, instead, remain trapped in a local (metastable) free energy minimum, which may exhibit desirable properties. Here, we introduce an automated workflow that integrates first-principles physics and atomistic simulations with machine learning (ML), and high-performance computing to allow rapid exploration of the metastable phases to construct “metastable” phase diagrams for materials far-from-equilibrium. Using carbon as a prototypical system, we demonstrate automated metastable phase diagram construction to map hundreds of metastable states ranging from near equilibrium to far-from-equilibrium (400 meV/atom). We incorporate the free energy calculations into a neural-network-based learning of the equations of state that allows for efficient construction of metastable phase diagrams. We use the metastable phase diagram and identify domains of relative stability and synthesizability of metastable materials. High temperature high pressure experiments using a diamond anvil cell on graphite sample coupled with high-resolution transmission electron microscopy (HRTEM) confirm our metastable phase predictions. In particular, we identify the previously ambiguous structure of n -diamond as a cubic-analog of diaphite-like lonsdaelite phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Phase diagram to demarcate supercritical, transcritical, and continuous phase regimes for binary fluid equilibrium mixing relevant to combustion applications

Here, a robust methodology to develop phase diagrams of binary fluid mixtures at fixed thermo dynamic conditions (pressure, temperature, and mole fraction) as well as of two initially separated fluids undergoing mixing near critical conditions are presented for fluids and con ditions relevant to rockets, gas turbines, and diesel engine applications. Phase equilibria of mixtures is first examined to provide insight into the continuous-phase mixing behavior (including but not limited to supercritical behavior), and to develop a broadly applicable phase-diagram for binary fluid mixtures at fixed conditions. Next, adiabatic mixing theory and reduced Helmholtz equations of state are used to predict the thermodynamic conditions required to attain continuous-phase binary fluid mixing near critical conditions. Then, a 3D surface diagram (P,T fuel ,T amb ) separating single and two-phase regions is constructed by varying the ambient pressure and the initial temperatures of the two fluids. Polynomial fits of the 3D surfaces for 10 different binary mixtures are tabulated for nitrogen-alkane and methane-oxygen blends relevant to air-breathing and propellant based engines, respectively.

42 ENGINEERING↗
DOE OSTI2022

Ab Initio Phase Diagram of Chromium to 2.5 TPa

Chromium possesses remarkable physical properties such as hardness and corrosion resistance. Chromium is also a very important geophysical material as it is assumed that lighter Cr isotopes were dissolved in the Earth’s molten core during the planet’s formation, which makes Cr one of the main constituents of the Earth’s core. Unfortunately, Cr has remained one of the least studied 3d transition metals. In a very recent combined experimental and theoretical study (Anzellini et al., Scientific Reports, 2022), the equation of state and melting curve of chromium were studied to 150 GPa, and it was determined that the ambient body-centered cubic (bcc) phase of crystalline Cr remains stable in the whole pressure range considered. However, the importance of the knowledge of the physical properties of Cr, specifically its phase diagram, necessitates further study of Cr to higher pressure. In this work, using a suite of ab initio quantum molecular dynamics (QMD) simulations based on the Z methodology which combines both direct Z method for the simulation of melting curves and inverse Z method for the calculation of solid–solid phase transition boundaries, we obtain the theoretical phase diagram of Cr to 2.5 TPa. We calculate the melting curves of the two solid phases that are present on its phase diagram, namely, the lower-pressure bcc and the higher-pressure hexagonal close-packed (hcp) ones, and obtain the equation for the bcc-hcp solid–solid phase transition boundary. We also obtain the thermal equations of state of both bcc-Cr and hcp-Cr, which are in excellent agreement with both experimental data and QMD simulations. We argue that 2180 K as the value of the ambient melting point of Cr which is offered by several public web resources (“Wikipedia,” “WebElements,” “It’s Elemental,” etc.) is most likely incorrect and should be replaced with 2135 K, found in most experimental studies as well as in the present theoretical work.

equation of state↗
DOE OSTI2022

First-principles analysis of the Al-rich corner of Al-Li-Cu phase diagram

The phase diagram of Al-Li-Cu system in the Al-rich region was determined by means of first-principles calculations and statistical mechanics. The mixing enthalpies of many configurations for different lattices in the whole Al-Li-Cu system were determined by density functional theory simulations to find the stable phases in the convex hull. They were fitted with a cluster expansion to calculate the free energy of the configurations with different compositions as a function of temperature in the Al-rich region (Al content > 40 at.%) by means of Monte Carlo simulations. It was found that the ground state phases in the Al-rich part of the Al-Li-Cu phase diagram were α-Al, θ' (Al 2 Cu), $δ$' (Al 3 Li), $δ$ (AlLi) and T 1 (Al 6 Cu 4 Li 3 ), while θ'' (Al 3 Cu), T 1' (Al 2 CuLi) and Al 3 Cu 2 Li were found on the lowest mixing enthalpy surfaces of their lattices and were metastable. α-Al, $δ$ and T 1 are stable phases in the whole temperature range while $δ$' becomes metastable at very low temperature and θ (Al 2 Cu) replaces θ' as the stable phase at approximately 550 K due to the vibrational entropic contribution. In addition, the phase diagram in the Al-rich region was built and it was shown in isothermal sections from 100 to 900 K. They were in good agreement with the limited experimental data in the literature and provided new information regarding the stability, solubility and stoichiometry of the different phases. This information is important to understand the precipitation mechanisms during high temperature aging.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Melting phase diagram of bubble phases in high Landau levels

A low-disorder, two-dimensional electron system (2DES) subjected to a large perpendicular magnetic field and cooled to very low temperatures provides a rich platform for studies of many-body quantum phases. The magnetic field quenches the electrons' kinetic energy and quantizes the energy into a set of Landau levels, allowing the Coulomb interaction to dominate. In excited Landau levels, the fine interplay between short- and long-range interactions stabilizes bubble phases, Wigner crystals with more than one electron per unit cell. In this work, we present the screening properties of bubble phases, probed via a simple capacitance technique where the 2DES is placed between a top and a bottom gate and the electric field penetrating through the 2DES is measured. The bubbles formed at very low temperatures screen the electric field poorly as they are pinned by the residual disorder potential, allowing a large electric field to reach the top gate. As the temperature is increased, the penetrating electric field decreases and, surprisingly, exhibits a pronounced minimum at a temperature that appears to coincide with the melting temperature of the bubble phase. We deduce a quantitative phase diagram, as a function of Landau level filling factor (ν) and temperature, for the transition from the bubble to liquid phases for 4 ≤ ν ≤ 5.

2-dimensional systems↗
DOE OSTI2023

Hot QCD phase diagram from holographic Einstein–Maxwell–Dilaton models

In this review, we provide an up-to-date account of quantitative holographic descriptions of the strongly coupled quark-gluon plasma (QGP) produced in heavy-ion collisions, based on the class of gauge-gravity Einstein-Maxwell-Dilaton (EMD) models. Holography is employed to tentatively map the QCD phase diagram at finite temperature onto a dual theory of charged, asymptotically AdS black holes in 5D. With a quantitative focus on the hot QCD phase diagram, the EMD models reviewed are adjusted to describe lattice results for the finite-temperature QCD equation of state, with 2+1 flavors and physical quark masses, at zero chemical potential and vanishing electromagnetic fields. The predictive power of EMD models is tested by quantitatively comparing their predictions for the hot QCD equation of state at nonzero baryon density and the corresponding state-of-the-art lattice QCD results. The shear and bulk viscosities predicted by these EMD models are also compared to the corresponding profiles favored by the latest phenomenological multistage models describing different heavy-ion data. We report preliminary results from a Bayesian analysis which provide systematic evidence that lattice results at finite temperature and zero baryon density strongly constrains the free parameters of EMD models. Remarkably, the set of parameters constrained by lattice results at zero chemical potential produces EMD models in quantitative agreement with lattice QCD results also at finite baryon density. We also review results for equilibrium and transport properties from magnetic EMD models, describing the QGP at finite temperatures and magnetic fields. Lastly, we provide a critical assessment of the main limitations and drawbacks of the holographic models reviewed in the present work, and point out some perspectives we believe are of fundamental importance for future developments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Ternary Phase Diagram of Water/Bio-Oil/Organic Solvent for Bio-Oil Fractionation

Separating bio-oil by fractionation with different chemical composition is a critical step to refine these oils and obtain high value products. Cold-water precipitation of pyrolytic lignin from bio-oil is the most common approach used. However, the obtained aqueous phase from this method still contain phenols, is diluted and difficult to use. In this study, the use of liquid-liquid extraction with different solvents (1-butanol, ethyl acetate, 1-octanol, dichloromethane, toluene, and hexane) for the separation of targeted molecules (lignin oligomers, sugars, acetic acid) is explored. Ternary phase diagrams for the organic solvent/water/bio-oil are reported. The partition coefficient of compounds of interest (both light and heavy fraction) is reported for the liquid-liquid equilibrium zone. When using butanol as solvent, the highest separation factor of total phenols over total sugars was observed. Furthermore, our results provide information to design L-L separation units with the capacity to selectively recover targeted molecules from pyrolysis oils.

09 BIOMASS FUELS↗
DOE OSTI2025

Magnetic Phase Diagram of 2D Magnet Fe 5– x GeTe 2 Revealed by Cryogenic Lorentz 4D-STEM

A two-dimensional van der Waals ferromagnet Fe 5–x GeTe 2 (F5GT) exhibits room-temperature magnetic transition and magnetic anisotropy. Studies have identified diverse magnetic states, including stripe domains, skyrmionic type-I and topologically trivial type-II bubbles, depending on the magnetic and thermal history. Yet, the underlying micromagnetic energetics driving these states remains unclear. Here, we establish the magnetic phase diagram of bulk F5GT using cryogenic Lorentz four-dimensional scanning transmission electron microscopy. We reveal that stripe domains spontaneously form upon zero-field cooling, while metastable magnetic bubbles are stabilized by external fields. Transitions from type-I to type-II bubbles are driven by an oblique external field. Micromagnetic simulations confirm that these transitions arise from the interplay of uniaxial anisotropy, dipolar interactions, and external fields, without requiring significant Dzyaloshinskii–Moriya Interaction (DMI). In conclusion, these findings clarify the micromagnetic origin of spin textures of F5GT and establish it as a tunable platform for nanoscale topological magnetism.

2D Magnets↗
DOE OSTI2020

Resistivity phase diagram of cuprates revisited

The phase diagram of the cuprate superconductors has posed a formidable scientific challenge for more than three decades. This challenge is perhaps best exemplified by the need to understand the normal-state charge transport as the system evolves from Mott insulator to Fermi- liquid metal with doping. Here in this paper, we report a detailed analysis of the temperature (T) and doping (p) dependence of the planar resistivity of simple-tetragonal HgBa 2 CuO 4+δ (Hg1201), the single- CuO 2 -layer cuprate with the highest optimal superconducting transition temperature, T c . The data allow us to test a recently proposed phenomenological model for the cuprate phase diagram that combines a universal transport scattering rate with spatially inhomogeneous (de)localization of the Mott-localized hole. We find that the model provides a good description of the data. We then extend this analysis to prior transport results for several other cuprates, including the Hall number in the overdoped part of the phase diagram, and find little compound-to-compound variation in (de)localization gap scale. The results point to a robust, universal structural origin of the inherent gap inhomogeneity that is unrelated to doping-related disorder. They are inconsistent with the notion that much of the phase diagram is controlled by a quantum critical point, and instead indicate that the unusual electronic properties exhibited by the cuprates are fundamentally related to strong nonlinearities associated with subtle nanoscale inhomogeneity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Hall effect in LaCrGe 3 at pressures up to 24 kbar and a 𝐻−𝑇 phase diagram of the pressure-induced magnetic phase

LaCrGe 3 is a metallic, itinerant ferromagnet with 𝑇 𝐶 ≈ 86K and an easy magnetic direction along its hexagonal 𝑐 axis. Here we present studies of the 𝐻 ∥ 𝑐 Hall effect in LaCrGe 3 at ambient pressure and under pressures up to 24 kbar. At ambient pressure the anomalous Hall conductivity in the ferromagnetic state reaches a large value of ∼520 Ω − 1 cm −1 . The overall data are consistent with the behavior expected for a ferromagnet with magnetic field applied along its easy axis. Measurements under pressure yield an 𝐻 = 0, 𝑃−𝑇 phase diagram consistent with earlier publications with 𝑇 𝐶 being suppressed with pressure and nonferromagnetic phases appearing for 𝑃 >15 kbar. The data suggest that the observed 𝑇 𝐶 suppression is due to the pressure-dependent exchange interactions rather than suppression of the size of the magnetic moment. Field-dependent Hall resistivity in the higher-pressure, nonferromagnetic state is consistent with the net moment being zero for 𝐻=0. In a finite field there is a sharp anomaly comparable to the one associated with a spin-flip metamagnetic transition. The 𝐻−𝑇 phase diagrams corresponding to a pressure-induced magnetic phase are constructed for several pressures. In conclusion, the Hall data suggest the possibility of the pressure-induced nonferromagnetic phase being a combination of multiple small regions of antiferromagnetic phases with different wave vectors.

Bud'ko, Sergey L. [Ames Laboratory, and Iowa State↗
DOE OSTI2026

Exploring the QCD Phase Diagram

Exploring the QCD phase diagram through relativistic heavy-ion collisions is a primary goal of modern nuclear physics. This contribution focuses on fluctuations and correlations of conserved charges — specifically net-baryon and net-charge cumulants — as sensitive probes of the phase structure and the QCD critical point. We discuss recent theoretical and experimental advancements, highlighting constraints from lattice QCD and new results from the RHIC Beam Energy Scan program. Key challenges in theory-to-experiment comparisons at high baryon density are discussed, alongside the systematic requirements for meaningful physical interpretation. Finally, we identify open issues and outline the discovery potential of future low-energy experiments, such as CBM, in resolving the high-density regime of the phase diagram.

Koch, V. [Lawrence Berkeley National Laboratory (L↗
DOE OSTI2020

Ab Initio Phase Diagram of Tungsten

The phase diagram of tungsten (W) to a pressure (P) of 2500 GPa is investigated using a comprehensive ab initio approach that includes (i) the calculation of the zero temperature (T) free energies (enthalpies) of different solid structures, (ii) the quantum molecular dynamics simulation of the melting curves of different solid structures, (iii) the derivation of the analytic form for the solid-solid phase transition boundary, and (iv) the simulations of the solidification of liquid W into the final solid states on both sides of the solid-solid phase transition boundary, in order to confirm the corresponding analytic form. There are two solid structures confirmed to be present on the phase diagram of W, the ambient body-centered cubic (bcc) and the high-pressure double hexagonal close-packed (dhcp). At T = 0, the bcc-dhcp transition occurs at 1060 GPa, and the transition boundary has a positive slope dT/dP : the bcc-dhcp-liquid triple point is at (P, T) = (1675 GPa, 23680 K).

36 MATERIALS SCIENCE↗
DOE OSTI2023

Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States

The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo–based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗