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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

High‐Pressure and High‐Temperature Single‐Crystal Elasticity of Cr‐Pyrope: Implications for the Density and Seismic Velocity of Subcontinental Lithospheric Mantle

Abstract Single‐crystal X‐ray diffraction and Brillouin spectroscopy experiments were performed on a natural Cr‐pyrope (Prp 71.0 Alm 12.6 Sps 0.7 Grs 3.5 Uvr 12.2 ) at high pressure and high temperature up to 11.0 GPa and 800 K. Fitting the collected data to the third‐order finite strain equation yields bulk modulus ( K S 0 ), shear modulus ( G 0 ), their pressure ((∂ K S /∂ P ) T and (∂ G /∂ P ) T ) and temperature (( ∂K S /∂T ) P and ( ∂G/∂T ) P ) derivatives, K S 0 = 167.7(8) GPa, G 0 = 91.5(5) GPa, (∂ K S /∂ P ) T = 4.3(1), (∂ G /∂ P ) T = 1.4(1), ( ∂K S /∂T ) P = − 0.0175(1) GPa/K and ( ∂G/∂T ) P = − 0.0073(1) GPa/K. Using the obtained results, we examined whether the elastic properties of the Cr‐pyrope can be accurately calculated from those of endmembers including pyrope, almandine, grossular, and uvarovite assuming a linear relationship between elastic properties and composition (end‐member model). The results indicate that the end‐member model provides a sufficient approximation for the elastic properties of Cr‐pyrope in calculating the density and velocity of the subcontinental lithospheric mantle (SCLM). We modeled the densities and velocities of three typical types of SCLM (Archon, Proton, and Tecton) in order to investigate how the variation of chemical composition influences the SCLM. We obtained that the compositional change from the Archon to the Tecton increases the density of the SCLM significantly, which can be an important prerequisite for SCLM delamination. However, the compositional variation only slightly changes the velocity of the SCLM and the change is within the uncertainty of the calculation. Moreover, in comparison to the velocity, ρ / V P and ρ / V S are much more sensitive to the compositional change of the SCLM.

Xu, Jingui↗
NASA NTRS2001

Single-Crystal Elastic Constants of Yttria (Y2O3) Measured to High Temperatures

Yttria, or yttrium sesquioxide (Y2O3), has been considered for use in nuclear applications and has gained interest relatively recently for use in infrared optics. Single crystals of yttria have been grown successfully at the NASA Glenn Research Center using a laser-heated float zone technique in a fiber and rod. Such samples allow measurement of the single-crystal elastic properties, and these measurements provide useful property data for the design of components using single crystals. They also yield information as to what degree the elastic properties of yttria ceramics are a result of the intrinsic properties of the yttria crystal in comparison to characteristics that may depend on processing, such as microstructure and intergranular phases, which are common in sintered yttria. The single-crystal elastic moduli are valuable for designing such optical components. In particular, the temperature derivatives of elastic moduli allow the dimensional changes due to heating under physical constraints, as well as acoustic excitation, to be determined. The single-crystal elastic moduli of yttria were measured by Brillouin spectroscopy up to 1200 C. The room-temperature values obtained were C(sub 11) = 223.6 + 0.6 GPa, C(sub 44) = 74.6 + 0.5 GPa, and C(sub 12) = 112.4 + 1.0 GPa. The resulting bulk and (Voigt-Reuss-Hill) shear moduli were K = 149.5 + 1.0 GPa and G(sub VRH) = 66.3 + 0.8 GPa, respectively. Linear least-squares regressions to the variation of bulk and shear moduli with temperature resulted in derivatives of dK/dT = -17 + 2 MPa/C and dG(sub VRH)/dT = -8 + 2 MPa/ C. Elastic anisotropy was found to remain essentially constant over the temperature range studied.

Sayir, Ali↗
NASA NTRS2000

The Single-Crystal Elasticity of Yttria (Y2O3) to High Temperature

The single-crystal elastic moduli of yttria have been measured by Brillouin spectroscopy up to 1200 C. The room temperature values obtained are C11 = 223.6 +/- 0.6 GPa, C44 = 74.6 +/- 0.5 GPa, and C12 = 112.4 +/- 1.0 GPa. The resulting bulk and (Voigt-Reuss-Hill) shear moduli are K = 149.5 +/- 1.0 GPa and G(sub VRH) = 66.3 +/- 0.8 GPa, respectively. These agree much more closely with experimental values reported for polycrystalline samples than do previous single-crystal measurements. Linear least squares regressions to the variation of bulk and shear moduli with temperature result in derivatives of dK/dT = -17 +/- 2 MPa/degC and dG(sub VRH)/dT = -8 +/- 2 MPa/degC. Elastic anisotropy was found to remain essentially constant over the temperature range studied.

Kriven, Waltraud M.↗
DOE OSTI2023

Single-crystal elasticity of (Al,Fe)-bearing bridgmanite up to 82 GPa

Abstract Thermoelastic properties of mantle candidate minerals are essential to our understanding of geophysical phenomena, geochemistry, and geodynamic evolutions of the silicate Earth. However, the lower-mantle mineralogy remains much debated due to the lack of single-crystal elastic moduli (Cij) and aggregate sound velocities of (Al,Fe)-bearing bridgmanite, the most abundant mineral of the planet, at the lower mantle pressure-temperature (P-T) conditions. Here we report single-crystal Cij of (Al,Fe)-bearing bridgmanite, Mg0.88Fe0.1Al0.14Si0.90O3 (Fe10-Al14-Bgm) with Fe3+/ΣFe = ~0.65, up to ~82 GPa using X-ray diffraction (XRD), Brillouin light scattering (BLS), and impulsive stimulated light scattering (ISLS) measurements in diamond-anvil cells (DACs). Two crystal platelets with orientations of (–0.50, 0.05, –0.86) and (0.65, –0.59, 0.48), that are sensitive to deriving all nine Cij, are used for compressional and shear wave velocity (νP and νS) measurements as a function of azimuthal angles over 200° at each experimental pressure. Our results show that all Cij of singe-crystal Fe10-Al14-Bgm increase monotonically with pressure with small uncertainties of 1–2% (±1σ), except C55 and C23, which have uncertainties of 3–4%. Using the third-order Eulerian finite-strain equations to model the elasticity data yields the aggregate adiabatic bulk and shear moduli and respective pressure derivatives at the reference pressure of 25 GPa: KS = 326 ± 4 GPa, µ = 211 ± 2 GPa, KS′ = 3.32 ± 0.04, and µ′ = 1.66 ± 0.02 GPa. The high-pressure aggregate νS and νP of Fe10-Al14-Bgm are 2.6–3.5% and 3.1–4.7% lower than those of MgSiO3 bridgmanite end-member, respectively. These data are used with literature reports on bridgmanite with different Fe and Al contents to quantitatively evaluate pressure and compositional effects on their elastic properties. Comparing with one-dimensional seismic profiles, our modeled velocity profiles of major lower-mantle mineral assemblages at relevant P-T suggest that the lower mantle could likely consist of about 89 vol% (Al,Fe)-bearing bridgmanite. After considering uncertainties, our best-fit model is still indistinguishable from pyrolitic or chondritic models.

Geochemistry & Geophysics↗
NASA NTRS1988

The single crystal elastic constants of hexagonal SiC to 1000 C

The relationships between the sound velocities in the cubic and hexagonal crystal structures and the tensor transformations for the two structures are applied to determine the elastic stiffnesses for the hexagonal structures of SiC to 1000 C. These results are then applied to calculate the polycrystalline elastic moduli, E and G, and their temperature variations. The calculated values for E and G at 20 C are 420 and 180 GPa; for (dE/dT) and (dG/dT), the values are -0.020 and -0.007 GPa/C, respectively.These agree well with published experimental values for E and G of dense polycrystalline alpha silicon carbides.

Li, Z.↗
DOE OSTI2022

Determination of single-crystal elastic moduli of Li RE F 4 ( RE =Y, Gd, and Tb) by resonant ultrasound spectroscopy

The tetragonal fluoro-scheelite Li RE F 4 compounds (RE = rare earth) have been shown to exhibit a variety of useful optical and magnetic properties. While LiYF 4 has been widely studied, many of the fundamental thermodynamic properties of other members of this family remain unknown. Here, we report the complete elastic tensors (C ij ) of single-crystalline LiYF 4 , LiTbF 4 , and LiGdF 4 using resonant ultrasound spectroscopy and density functional theory (DFT). Here we compare the results for LiYF 4 with prior experimental results using time-of-flight ultrasound methods. This is the first report, however, of the experimental elastic tensors of LiTbF 4 and LiGdF 4 . The present results point to a softening of the elastic moduli of the Li RE F 4 system when Y is replaced by the larger ionic radius of Tb or Gd. Furthermore, we find that just 0.3% doping with Nd on the Y site also leads to a slight softening of the moduli. The variation of the elastic moduli as a function of temperature up to 216°C was also measured. A nearly linear softening of all seven independent elastic moduli was observed with increasing temperature. Phonon dispersions and phonon density of states obtained by DFT support the experimental finding of a significantly higher sound velocity due to lighter Y atoms in LiYF 4 , as compared to heavier LiTbF 4 and LiGdF 4 .

36 MATERIALS SCIENCE↗
NASA NTRS1973

Elasticity of some mantle crystal structures. II.

The single-crystal elastic constants are determined as a function of pressure and temperature for rutile structure germanium dioxide (GeO2). The data are qualitatively similar to those of rutile TiO2 measured by Manghnani (1969). The compressibility in the c direction is less than one-half that in the a direction, the pressure derivative of the shear constant is negative, and the pressure derivative of the bulk modulus has a relatively high value of about 6.2. According to an elastic strain energy theory, the negative shear modulus derivative implies that the kinetic barrier to diffusion decreases with increasing pressure.

Wang, H.↗
NASA NTRS1994

Thermal expansion and elastic anisotropy in single crystal Al2O3 and SiC reinforcements

In single crystal form, SiC and Al2O3 are attractive reinforcing components for high temperature composites. In this study, the axial coefficients of thermal expansion and single crystal elastic constants of SiC and Al2O3 were used to determine their coefficients of thermal expansion and Young's moduli as a function of crystallographic orientation and temperature. SiC and Al2O3 exhibit a strong variation of Young's modulus with orientation; however, their moduli and anisotropies are weak functions of temperature below 1000 C. The coefficients of thermal expansion exhibit significant temperature dependence, and that of the non-cubic Al2O3 is also a function of crystallographic orientation.

Salem, Jonathan A.↗
DOE OSTI2022

Development and application of a uranium mononitride (UN) potential: Thermomechanical properties and Xe diffusion

We report that atomic-scale modeling of thermophysical and defect properties of uranium mononitride (UN) plays an important role in establishing a better understanding and improved models of UN fuel performance. Having an accurate interatomic potential is crucial for generating reliable data at finite temperatures using molecular dynamic simulations. We report a new interatomic potential for UN, based on a combination of many-body and pairwise interactions, a simple form that we later show could be easily adapted to include Xe-U and Xe-N interactions, i.e., generating a U-N-Xe interatomic potential. The potential was fitted to experimental thermal expansion and single crystal elastic constants, as well as Frenkel, Schottky, anti-Schottky, and antisite pair reaction energies from density functional theory (DFT) calculations. Using the potential, we successfully reproduced experimental lattice parameters, thermal expansion, single crystal elastic constants, and temperature dependent heat capacity. The potential also performs reasonably well in reproducing the energy of the aforementioned stoichiometric defect reactions and defect migration barriers calculated using DFT. However, the potential underestimates the energy difference between the tetrahedral and dumbbell uranium interstitials, and a more complex potential form might be needed to overcome this issue. The potential was also used to predict UN single crystal elastic constants and elastic properties at different temperatures, showing that UN becomes softer and more compressible with increasing temperature. We also compare our potential against literature data from previous empirical potentials, demonstrating similar or better behavior depending on the property of interest. To enable the simulation of Xe in UN a Buckingham potential has been fitted to DFT-derived Xe incorporation energies. The potential was then used to determine the activation energy for Xe diffusion due to various Xe-containing defects, with {XeU : VU} exhibiting the lowest activation energy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Tensile Deformation of DED Graded IN718-René41 Superalloy at 650°C by in-situ Neutron Diffraction and Digital Image Correlation

A compositionally graded material comprised IN718 (718, γ'/γ" strengthened superalloy) and René41 (R41, a medium γ' strengthened superalloy) was fabricated using laser blown-powder directed energy deposition (DED/LB-M). Hot gas path components that require high and low temperature capabilities at different locations may benefit from such graded superalloy, potentially eliminating the use of welded or mechanically joined components and reducing cost. In the present work, microstructure and 650°C tensile behavior of 718-R41 graded superalloy in as-built and heat-treated states are investigated by Digital Image Correlation (DIC), in-situ neutron diffraction, coupled with conventional characterization techniques. The applied heat treatment generates static recrystallization and equiaxed grains in 718 rich compositions, while R41 rich compositions remain partially or un-recrystallized. Yield strengths of 718 and R41 sections in heat-treated state are comparable to wrought forms but the graded compositions show weakness. From neutron experiment, diffraction elastic constants and single crystal elastic constants are calculated, which show small difference between the as-built and heat-treated states and between the γ and γ' phases. Grain-level load transfer from the (220) grains to (200) grains is found to be composition dependent, and qualitatively agrees with DIC measured macroscopic yield strength. Within the (200) grains, the γ/γ' phases deform elastically until the γ phase yields and afterwards the γ' phase takes load from γ phase.

digital image correlation↗
DOE OSTI2025

Phase-field modeling of orientation-dependent crack growth in ductile single crystals with anisotropic elasticity

Crack growth in ductile single crystals (DuSCs) is orientation dependent due to the anisotropies of crystal plasticity and elastic tensor. This study develops a phase-field model incorporating both crystal plasticity and crack growth and proposes a general method to decompose the elastic energy into compressive and tensile parts to prevent crack growth under compression in the phase-field description. The phase-field model, in combination with three Euler angles, is employed to simulate orientation-dependent crack growth in DuSCs. The contributions from crystal plasticity and anisotropic elasticity are compared, and the former is found to dominate in the anisotropy of crack growth in copper single crystals. Furthermore, the simulation results demonstrate that crystal orientation strongly affects the heterogeneous distribution of plastic strain and the interaction between plastic strain and crack growth. High-throughput phase-field simulations are performed with exhaustive crystal orientations, and the results are explained based on the anisotropy of the Taylor factor.

Computational Solid Mechanics↗
NASA NTRS1971

On the anisotropic elastic properties of hydroxyapatite.

Experimental measurements of the isotropic elastic moduli on polycrystalline specimens of hydroxyapatite and fluorapatite are compared with elastic constants measured directly from single crystals of fluorapatite in order to derive a set of pseudo single crystal elastic constants for hydroxyapatite. The stiffness coefficients thus derived are given. The anisotropic and isotropic elastic properties are then computed and compared with similar properties derived from experimental observations of the anisotropic behavior of bone.

Katz, J. L.↗