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NASA NTRS1992

Cohesive Energy-Lattice Constant and Bulk Modulus-Lattice Constant Relationships: Alkali Halides, Ag Halides, Tl Halides

In this note we present two expressions relating the cohesive energy, E(sub coh), and the zero pressure isothermal bulk modulus, B(sub 0), of the alkali halides. Ag halides and TI halides, with the nearest neighbor distances, d(sub nn). First, we show that the product E(sub coh)d(sub 0) within families of halide crystals with common crystal structure is to a good approximation constant, with maximum rms deviation of plus or minus 2%. Secondly, we demonstrate that within families of halide crystals with a common cation and common crystal structure the product B(sub 0)d(sup 3.5)(sub nn) is a good approximation constant, with maximum rms deviation of plus or minus 1.36%.

Schlosser, Herbert↗

DOE OSTI2023

Electronic Structure and Mechanical Properties of Solvated Montmorillonite Clay Using Large-Scale DFT Method

Montmorillonite clay (MMT) has been widely used in engineering and environmental applications as a landfill barrier and toxic waste repository due to its unique property as an expandable clay mineral that can absorb water easily. This absorption process rendered MMT to be highly exothermic due to electrostatic interactions among molecules and hydrogen bonds between surface atoms. A detailed study of a large supercell model of structural clay enables us to predict long-term nuclear waste storage. Herein, a large solvent MMT model with 4071 atoms is studied using ab initio density functional theory. The DFT calculation and analysis clarify the important issues, such as bond strength, solvation effect, elasticity, and seismic wave velocities. These results are compared to our previous study on crystalline MMT (dry). The solvated MMT has reduced shear modulus (G), bulk modulus (K), and Young’s modulus (E). We observe that the conduction band (CB) in the density of states (DOS) of solvated MMT model has a single, conspicuous peak at –8.5 eV. Moreover, the atom-resolved partial density of states (PDOS) summarizes the roles played by each atom in the DOS. These findings illuminate numerous potential sophisticated applications of MMT clay.

36 MATERIALS SCIENCE↗

NASA NTRS1978

Elastic constants at low temperatures - Recent measurements on technological materials at NBS

Solid-state low-temperature elastic properties have been experimentally studied at the NBS Cryogenic Division for four years. Most studies were between room temperature and liquid-helium temperature; some were only to liquid-nitrogen temperature. Two dynamic (high-frequency) experimental methods were used, pulse-echo and resonance, resulting in adiabatic elastic constants. The present paper reviews these studies for 47 technological materials - metals, alloys, and composites. The elastic constants primarily discussed are Young's modulus, the shear modulus, the bulk modulus (reciprocal compressibility), and Poisson's ratio. A summary table is presented to show which base metals tend to exhibit regular, irregular, or anomalous behavior in their elastic constant/temperature curves.

Ledbetter, H. M.↗

DOE OSTI2022

Thermal equation of state for zoisite: Implications for the transportation of water into the upper mantle and the high-velocity anomaly in the Farallon plate

Seismic tomography studies have revealed a high-velocity anomaly at depths between 100 km and 300 km in the Farallon plate. However, the reasons for the high-velocity anomaly continue to be debated. An analysis of the mineral proportions of eclogites exhumed from the Farallon plate shows that the average amount of zoisite in eclogite is ∼16.0 vol%. Therefore, the presence of zoisite eclogite needs to be considered to explain the high-velocity anomaly of the Farallon plate. However, the thermal equation of state and stability of zoisite have not been fully investigated under high pressure−temperature (P-T) conditions. We investigated the high-pressure and high-temperature behavior of natural zoisite utilizing synchrotron single crystal-X-ray diffraction (XRD). The results indicate that zoisite is metastable up to 24.8 GPa and 700 K. We obtained the ambient unit-cell volume V0 = 901.26(3) Å3 by synchrotron single crystal-XRD measurement. We also fitted the pressure-volume-temperature data to a high-temperature Birch-Murnaghan equation of state and obtained the zero-pressure bulk modulus K0 = 134.7(8) GPa, the temperature derivative of the bulk modulus (∂K/∂T)P = −0.011(4) GPa/K, and the thermal expansion coefficients α0V = 1.9(7) × 10−5 K−1 and α1V = 3(2) × 10−8 K−2 when the pressure derivative of bulk modulus (K′0) is fixed at 4. By incorporating the results from previous studies, we calculated the density and bulk sound velocity profiles of zoisite eclogite along the Farallon plate geotherm. Finally, we infer that zoisite could carry water to depths of ∼300 km within cold subducting slabs and that the bulk sound velocity of typical zoisite eclogite with ∼61.0 vol% omphacite, ∼23.0 vol% garnet, and ∼16.0 vol% zoisite could cause the high-velocity anomalies at depths of 100−300 km in the Farallon plate.

Geology↗

NASA NTRS1985

Elastic constant versus temperature behavior of three hardened maraging steels

Elastic constants of three maraging steels were determined by measuring ultrasonic velocities. Annealed steels show slightly lower bulk moduli and considerably lower shear moduli than hardened steels. All the elastic constants (Young's modulus, shear modulus, bulk modulus and Poisson's ratio) show regular temperature behavior between 76 and 400 K. Young's modulus and the shear modulus increase with increasing yield strength, but the bulk modulus and Poisson's ratio are relatively unchanged. Elastic anisotropy is quite small.

Ledbetter, H. M.↗

DOE OSTI2023

Graph neural networks predict energetic and mechanical properties for models of solid solution metal alloy phases

Here, we developed a PyTorch-based architecture called HydraGNN that implements graph convolutional neural networks (GCNNs) to predict the formation energy and the bulk modulus for models of solid solution alloys for various atomic crystal structures and relaxed volumes. We trained the GCNN surrogate model on a dataset for nickel–niobium (NiNb) generated by the embedded atom model (EAM) empirical interatomic potential for demonstration purposes. The dataset was generated by calculating the formation energy and the bulk modulus as a prototypical elastic property for optimized geometries starting from initial body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal compact packed (HCP) crystal structures, with configurations spanning the possible compositional range for each of the three types of initial crystal structures. Numerical results show that the GCNN model effectively predicts both the formation energy and the bulk modulus as function of the optimized crystal structure, relaxed volume, and configurational entropy of the model structures for solid solution alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Shear strength of a refractory high entropy alloy MoNbTaVW under high pressure

Radial X-ray diffraction (R-XRD) was performed in situ using a Panoramic Diamond Anvil Cell on the refractory high entropy alloy MoNbTaVW. The lattice parameters were determined through a Le Bail fit using a body centered cubic (BCC) lattice of symmetry $Im$$\overline{3}$$m$ (international space group number 229). Upper and lower bounds to the shear strength were determined up to 80 GPa nonhydrostatically using copper as a pressure standard. The equation of state was derived at the magic angle ψ = 54.7° and yielded a bulk modulus of K 0 = 220.8 ± 1.65 GPa. The experimental lattice parameters and bulk modulus match closely with corresponding density functional theory (DFT) calculations. The BCC phase remains stable up to the highest pressure of 80 GPa studied and is shown to be elastically anisotropic. The shear strength was found to saturate around 70 GPa with a value of τ = 1.75 GPa, and the shear moduli are presented in different limits of iso-strain and iso-stress.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Single-crystal X-ray diffraction of fluorapatite to 61 GPa

Apatite is a mineral of widespread importance in Earth and planetary science. Here we examine the behavior of a natural fluorapatite (FAp) crystal from Durango (Mexico) under compression to 61 GPa. Single-crystal X-ray diffraction experiments were carried out in a diamond-anvil cell using a synchrotron source. The apatite structure persists up to 32.4 GPa. Birch-Murnaghan equation of state parameters were fit to the pressure-volume data for fluorapatite for two cases: fixing V 0 at its measured ambient value resulted in a bulk modulus, K 0T , of 97.0(8) GPa and a pressure derivative of the bulk modulus, K' 0T , of 3.3(1), while fixing V 0 and K 0T at its ambient value 90.5 GPa (derived from ultrasonically measured elastic constants) resulted in a K' 0T value of 4.1(1). At 35.6 GPa, fluorapatite transforms to a triclinic phase (P$\bar{1}$, Z = 4), designated here as fluorapatite II (FAp-II). This phase persists up to at least 61 GPa. The major structural differences between FAp and FAp-II involve the buckling of the Ca polyhedra along the c-axis and changes in the number and coordination of the Ca sites. Furthermore, our study extends the pressure range over which fluorapatite has been examined by more than a factor of three, providing new insights into its structural response to high-pressure conditions.

58 GEOSCIENCES↗

NASA NTRS1982

Solid impingement erosion mechanisms and characterization of erosion resistance of ductile metals

Experimental results pertaining to spherical glass bead and angular crushed glass particle impingement are presented. A concept of energy adsorption to explain the failure of material is proposed. The erosion characteristics of several pure metals were correlated with the proposed energy parameters and with other properties. Correlations of erosion and material properties were also carried out with these materials to study the effect of the angle of impingement. Analyses of extensive erosion data indicate that surface energy, strain energy, melting point, bulk modulus, hardness, ultimate resilience, atomic volume and product of linear coefficient of thermal expansion, bulk modulus, and temperature rise required for melting, and ultimate resilience, and hardness exhibit the best correlations. It appears that both energy and thermal properties contribute to the total erosion.

Rao, V. P.↗

NASA NTRS1985

Characterization of solid particle erosion resistance of ductile metals based on their properties

This paper presents experimental results pertaining to spherical glass bead and angular crushed glass particle impingement. A concept of energy absorption to explain the failure of material is proposed and is correlated with the erosion characteristics of several pure metals. Analyses of extensive erosion data indicate that the properties - surface energy, specific melting energy, strain energy, melting point, bulk modulus, hardness, atomic volume - and the product of the parameters - linear coefficient of thermal expansion x bulk modulus x temperature rise required for melting, and ultimate resilience x hardness - exhibit the best correlations. The properties of surface energy and atomic volume are suggested for the first time for correlation purposes and are found to correlate well with erosion rates at different angles of impingement. It further appears that both energy and thermal properties contribute to the total erosion.

Rao, P. V.↗

NASA NTRS1983

Compression, nonstoichiometry and bulk viscosity of wuestite

New and existing data on the elasticity of wuestite which indicate virtually no correlation between the bulk modulus and stoichiometry are summarized. There appears, however, to be a systematic difference between static and dynamic measurements. This behavior suggests the presence of a frequency dependence to the bulk modulus that can be formally ascribed to a finite bulk viscosity of Fe(1-x)O. Such an effect has not previously been described in oxide or silicate minerals, and it presumably is caused by pressure-induced changes in defect ordering and subsequent relaxation within the incommensurate structure of wuestite.

Jeanloz, R.↗

DOE OSTI2022

Synthesis and Ultrahigh Pressure Compression of High-Entropy Boride (Hf0.2Mo0.2Nb0.2Ta0.2Zr0.2)B2 to 220 GPa

The high-entropy boride (Hf0.2Mo0.2Nb0.2Ta0.2Zr0.2)B2 material was synthesized under high-pressures and high-temperatures in a large-volume Paris-Edinburgh (PE) press from a ball-milled powder mix of HfO2, MoO3, Nb2O5, Ta2O5, ZrO2, carbon black, and boron carbide. The transformation process was monitored in situ by energy-dispersive x-ray diffraction with conversion starting at 1100 °C and completed by 2000 °C with the formation of a single hexagonal AlB2-type phase. The synthesized sample was recovered, powdered, and mixed with platinum pressure marker and studied under high pressure by angle-dispersive x-ray diffraction in a diamond anvil cell. The hexagonal AlB2-type phase of (Hf0.2Mo0.2Nb0.2Ta0.2Zr0.2)B2 was found to be stable up to the highest pressure of 220 GPa reached in this study (volume compression V/V0 = 0.70). The third order Birch-Murnaghan equation of state fit to the high-pressure data up to 220 GPa results in an ambient pressure unit cell volume V0=28.16±0.04 Å3, bulk modulusKo = 407 ± 6 GPa, pressure derivative of bulk-modulus K0′ = 2.73 ± 0.045 GPa. Our study indicates that this high-entropy boride (Hf0.2Mo0.2Nb0.2Ta0.2Zr0.2)B2 material is stable to ultrahigh pressures and temperatures and exhibit high bulk modulus similar to other incompressible transition metal borides like ReB2 and Os2B3.

36 MATERIALS SCIENCE↗

NASA NTRS1973

Evaluation of a high response electrohydraulic digital control valve

The application is described of a digital control valve on an electrohydraulic servo actuator. The digital control problem is discussed in general as well as the design and evaluation of a breadboard actuator. The evaluation revealed a number of problems associated with matching the valve to a hydraulic load. The problems were related to lost motion resulting from bulk modulus and leakage. These problems were effectively minimized in the breadboard actuator by maintaining a 1000 psi back pressure on the valve circuit and thereby improving the effective bulk modulus.

Anderson, R. L.↗

DOE OSTI2023

Temperature-dependent elastic constants of thorium dioxide probed using time-domain Brillouin scattering

Herein we report the adiabatic elastic constants of single-crystal thorium dioxide over a temperature range of 77–350 K. Time-domain Brillouin scattering, an all-optical, non-contact picosecond ultrasonic technique, is used to generate and detect coherent acoustic phonons that propagate in the bulk perpendicular to the surface of the crystal. These coherent acoustic lattice vibrations have been monitored in two hydrothermally grown single-crystal thorium dioxide samples along the (100) and (311) crystallographic directions. The three independent elastic constants of the cubic crystal (C 11 , C 12 , and C 44 ) are determined from the measured bulk acoustic velocities. The longitudinal wave along the (100) orientation provided a direct measurement of C 11 . Measurement of C 44 and C 12 was achieved by enhancing the intensity of quasi-shear mode in a (311) oriented crystal by adjusting the polarization angle relative to the crystal axes. We find the magnitude of softening of the three elastic constants to be ~2.5% over the measured temperature range. Good agreement is found between the measured elastic constants with previously reported values at room temperature, and between the measured temperature-dependent bulk modulus with calculated values. We find that semi-empirical models capturing lattice anharmonicity adequately reproduce the observed trend. We also determine the acoustic Grüneisen anharmonicity parameter from the experimentally derived temperature-dependent bulk modulus and previously reported temperature-dependent values of volumetric thermal expansion coefficient and heat capacity. This work presents measurements of the temperature-dependent elasticity in single-crystal thorium dioxide at cryogenic temperature and provides a basis for testing ab initio theoretical models and evaluating the impact of anharmonicity on thermophysical properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1986

Hydrostatic compression of Fe(1-x)O wuestite

Hydrostatic compression measurements on Fe(0.95)O wuestite up to 12 GPa yield a room temperature value for the isothermal bulk modulus of K(ot) = 157 (+ or - 10) GPa at zero pressure. This result is in accord with previous hydrostatic and nonhydrostatic measurements of K(ot) for wuestites of composition: 0.89 = Fe/O 0.95. Dynamic measurements of the bulk modulus by ultrasonic, shock-wave and neutron-scattering experiments tend to yield a larger value: K(ot) approximately 180 GPa. The discrepancy between static and dynamic values cannot be explained by the variation of K(ot) with composition, as has been proposed. This conclusion is based on high-precision compression data and on theoretical models of the effects of defects on elastic constants. Barring serious errors in the published measurements, the available data suggest that wuestite exhibits a volume relaxation under pressure.

Jeanloz, R.↗

NASA NTRS1993

Physical and chemical properties of some new perfluoropolyalkylether lubricants prepared by direct fluorination

A series of perfluoropolyalkylether (PFPAE) fluids was synthesized by direct fluorination. Viscosity-temperature properties, oxidation stabilities, oxidation-corrosion properties, bulk modulus, lubricity, surface tension and density were measured. It was shown that as the carbon to oxygen ratio in the polymer repeating unit decreases, the viscometric properties improve, the fluids may become poorer boundary lubricants, the bulk modulus increases, the surface tension increases and the fluid density increases. The presence of difluoromethylene oxide units in the polymer does not significantly lower the oxidation and oxidation-corrosion stabilities as long as the difluoromethylene oxide units are separated by other units.

Jones, W. R., Jr.↗

DOE OSTI2026

Crystal structure, compressibility, and thermal expansion of uranium mononitride

The behavior of the uranium mononitride (UN) crystal structure at nonambient conditions is disputed, with studies proposing various mutually exclusive distortions and transformations of the conventional face-centered-cubic structure at extreme temperatures and pressures. Here, in this study, we investigated the UN lattice with diamond anvil cell x-ray diffraction experiments at pressures up to 92 GPa and with density functional theory calculations at temperatures up to 1000 K and pressures up to 90 GPa. We determined that while the UN structure is nearly cubic at ambient conditions, its lattice angle (𝛼) varies as a function of pressure and temperature, meaning its structure can be more precisely described as face-centered-rhombohedral with 𝛼 ≈ 90∘. Over the range of conditions we investigated, UN exhibits a single, isostructural phase transition at ≈ 35 GPa, where 𝛼 collapses to ≈ 86°. Measurements and calculations agree that the compressibility of UN increases significantly beyond this transition, with the bulk modulus falling from ≈ 200 GPa in the low-pressure phase to 121 ± 3 GPa (according to calculations) or 58 ± 4 GPa (according to measurements) in the high-pressure phase. Our measurements also allowed us to constrain the bulk modulus of 𝛼−U 2 ⁢N 3 to 240 ± 10 GPa.

36 MATERIALS SCIENCE↗

NASA NTRS1988

The development of new, low-cost perfluoroalkylether fluids with excellent low and high-temperature properties

A series of perfluoroalkylether (PFAE) fluids were synthesized by direct fluorination. Viscosity-temperature properties, oxidation stabilities, oxidation-corrosion properties, and lubricity were determined. The fluids were tested in the presence of common elastomers to check for compatibility. The bulk modulus of each was measured to determine if any could be used as nonflammable aircraft hydraulic fluid. It was determined that as the carbon to oxygen ratio decreases, the viscometric properties improve, the fluids may become poor lubricants, the bulk modulus increases, the surface tension increases, and the fluid density increases. The presence of difluoromethylene oxide units in the polymer does not seriously lower the oxidation and oxidation-corrosion stabilities as long as the difluoromethylene oxide units are separated by other units.

Bierschenk, Thomas R.↗