Single-crystal Elastic Moduli Research Articles

Single-crystal elastic moduli, anisotropy, and the B1–B2 phase transition of NaCl at high pressures

Pressure dependences of the highest and lowest possible longitudinal sound velocities in single crystals of the B1 and B2 phases of NaCl were extracted from examination of their polycrystalline samples using the technique of time-domain Brillouin scattering. Based on the data collected up to 41 GPa, we largely extended the pressure range where single-crystal elastic moduli, Cij(P), and elastic anisotropy of the two cubic phases are measured, especially the experimental data for the B2 phase formed upon the reconstructive phase transition. The B1 phase of NaCl exhibits strong and growing anisotropy with increasing pressure, while that of the B2 phase is much weaker. Comparing with the previous experimental Cij(P) of other compounds exhibiting or expected to exhibit the B1–B2 phase transition, such as CaO, MgO, and (Mg1−x, Fex)O, we concluded that the transition is initiated by the shear instability due to violation of the Born stability criterion [C44(P)–P] > 0 and predicted the presently-not-verified transition pressures for MgO and (Mg1−x, Fex)O.

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

AbstractThermoelastic 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.

Effect of structural water on the elasticity of orthopyroxene

AbstractAs a major nominally anhydrous mineral (NAM) in the Earth’s upper mantle, orthopyroxene could host up to several hundred parts per million H2O in its crystal structure and transport the H2O to the deep Earth. To study the effect of structural H2O on the elasticity of orthopyroxene, we have measured the single-crystal elasticity of Mg1.991Al0.065Si1.951O6 with 842–900 ppm H2O and 1.64 ± 0.20 wt% Al2O3 at ambient conditions using Brillouin spectroscopy. The best-fit single-crystal elastic moduli (Cijs), bulk (KS0), and shear (G0) modulus of the hydrous Al-bearing orthopyroxene were determined as: C11 = 235(2) GPa, C22 = 173(2) GPa, C33 = 222(2) GPa, C44 = 86(1) GPa, C55 = 82(1) GPa, C66 = 82(1) GPa, C12 = 75(3) GPa, C13 = 67(2) GPa, and C23 = 49(2) GPa, KS0 = 111(2) GPa, and G0 = 78(1) GPa. Systematic analysis based on the results presented in this and previous studies suggests that the incorporation of 842–900 ppm H2O would increase C13 by 12.0(7)% and decrease C23 by 8.6(8)%. The effects on C11, C22, C33, C44, C66, KS0, and VP are subtle if not negligible when considering the uncertainties. The C55, C12, G0, and VS are not affected by the presence of structural H2O. Although laboratory experiments show that Fe,Al-bearing orthopyroxenes can host up to 0.8 wt% H2O in its structure, future high-pressure-temperature elasticity measurements on orthopyroxene with higher H2O content are needed to help better quantify this effect.

The Water-Fe-Pressure dependent single-crystal elastic properties of wadsleyite: Implications for the seismic anisotropy in the upper Mantle Transition Zone

Recent seismic studies suggested an anisotropic Mantle Transition Zone (MTZ) in areas adjacent to subducted slabs. Wadsleyite is the main anisotropy contributor in the upper MTZ, therefore the interpretation of these seismic observations requires the knowledge of single-crystal elastic moduli (Cijs) and the deformation-induced lattice preferred orientation (LPO) of wadsleyite. Wadsleyite can host up to 3 wt% water in its crystal structure as point defects in the form of hydroxyl groups, however, the combined effect of water content, Fe content, and pressure on the Cijs of wadsleyite remains unclear. In this study, we measured the high-pressure single-crystal elasticity of a synthetic hydrous Fe-bearing wadsleyite (0.14 (4) wt% water, Fe#=9.4, Fe3+/ΣFe=0.3) up to 18.2 (2) GPa. In combination with previous experimental data, we separated the effects of pressure, water, and Fe contents on the Cijs and intrinsic elastic anisotropy of wadsleyite. Our results suggest that the intrinsic elastic anisotropy of wadsleyite decreases with pressure, water, and Fe contents. At 15 GPa, increasing the water content by 0.1 wt% or Fe# by 1 decreases the VP and VS anisotropy of wadsleyite by ∼1.1-1.3%, and ∼0.8-1.3% in average, respectively. Combining the LPO determined in previous deformation experiments, we modeled the seismic anisotropy in the upper MTZ generated by a sub-vertical mantle flow near cold subducted slabs and a sub-horizontal mantle flow in the ambient mantle. In both scenarios, the LPO of wadsleyite leads to VSV (vertically polarized shear wave velocity) >VSH (horizontally polarized shear wave velocity). Our results suggest that wadsleyite may account for a weak anisotropic MTZ (<1%) on the global scale. Considering the fact that water decreases the elastic anisotropy but promotes LPO of wadsleyite, seismic anisotropy may not be a good water sensor in the upper MTZ.

The seismically fastest chemical heterogeneity in the Earth's deep upper mantle—implications from the single-crystal thermoelastic properties of jadeite

Jadeite is a major mineral phase (up to 50 vol%) in the subducted sediments/crust with continental origin, which are one of the major heterogeneities and important enriched geochemical reservoirs (such as EM-1 and EM-2) for incompatible elements in the Earth's interior. Identifying and locating the enriched geochemical heterogeneities requires knowledge of the elastic properties of relevant mineral phases at high pressure-temperature conditions. Unfortunately, the single-crystal elastic properties of jadeite have never been measured at high-pressure conditions, partially due to its low crystal symmetry. In this study, we have experimentally determined the single-crystal elastic moduli of jadeite at high pressures for the first time up to 18 GPa at the ambient temperature condition using Brillouin spectroscopy. Fitting the third-order finite strain equation of state to the velocity-pressure data yields KS0′=3.9(1), G0′=1.09(4) with ρ0=3.302(5) g/cm3, KS0=138(3) GPa, and G0=84(2) GPa. In addition, we have also conducted synchrotron single-crystal X-ray diffraction experiments up to 25 GPa and 700 K. The fitting of a Holland-Powell type thermal-pressure Birch-Murnaghan equation of state yields KT0′=3.8(2) and α0=3.4(5) ×10−5 K−1. Based on the obtained thermoelastic parameters of jadeite, the density and seismic velocities of continent-derived sediments/crust are modeled at the depth range from 200 to 500 km. The seismic velocities of the subducted continental sediments/crust become extremely fast at depths greater than ∼300 km, up to 11.8% and 14.7% faster than the Vp and Vs of the ambient mantle, and 5.6% and 7.3% faster than the Vp and Vs of the subducted oceanic crust. The existence of even a small amount of the subducted continental sediments/crust can result in strong seismic anomalies in the Earth's interior.

Single Crystal Elastic Properties of Hemimorphite, a Novel Hydrous Silicate

Hemimorphite, with the chemical formula Zn4Si2O7(OH)2·H2O, contains two different types of structurally bound hydrogen: molecular water and hydroxyl. The elastic properties of single-crystal hemimorphite have been determined by Brillouin spectroscopy at ambient conditions, yielding tight constraints on all nine single-crystal elastic moduli (Cij). The Voigt–Reuss–Hill (VRH) averaged isotropic aggregate elastic moduli are KS (VRH) = 74(3) GPa and μ (VRH) = 27(2) GPa, for the adiabatic bulk modulus and shear modulus, respectively. The average of the Hashin–Shtrickman (HS) bounds are Ks (HS) = 74.2(7) GPa and and μ (HS) = 26.5(6) GPa. Hemimorphite displays a high degree of velocity anisotropy. As a result, differences between upper and lower bounds on aggregate properties are large and the main source of uncertainty in Ks and μ. The HS average P wave velocity is VP = 5.61(4) km/s, and the HS S-wave velocity is VS = 2.77(3) km/s. The high degree of elastic anisotropy among the on-diagonal longitudinal and pure shear moduli of hemimorphite are largely explained by its distinctive crystal structure.

Elasticity of single-crystal Fe-enriched diopside at high-pressure conditions: Implications for the origin of upper mantle low-velocity zones

AbstractDiopside is one of the most important end-members of clinopyroxene, which is an abundant mineral in upper-mantle petrologic models. The amount of clinopyroxene in upper-mantle pyrolite can be ∼15 vol%, while pyroxenite can contain as high as ∼60 vol% clinopyroxene. Knowing the elastic properties of the upper-mantle diopside at high pressure-temperature conditions is essential for constraining the chemical composition and interpreting seismic observations of region. Here we have measured the single-crystal elasticity of Fe-enriched diopside (Di80Hd20, Di-diopside, and Hd-hedenbergite; also called Fe-enriched clinopyroxene) at high-pressure conditions up to 18.5 GPa by using in situ Brillouin light-scattering spectroscopy (BLS) and synchrotron X-ray diffraction in a diamond-anvil cell. Our experimental results were used in evaluating the effects of pressure and Fe substitution on the full single-crystal elastic moduli across the Di-Hd solid-solution series to better understand the seismic velocity profiles of the upper mantle. Using the third- or fourth-order Eulerian finite-strain equations of state to model the elasticity data, the derived aggregate adiabatic bulk and shear moduli (KS0, G0) at ambient conditions were determined to be 117(2) and 70(1) GPa, respectively. The first- and second-pressure derivatives of bulk and shear moduli at 300 K were (∂KS/∂P)T = 5.0(2), (∂2KS/∂P2)T = –0.12(4) GPa−1 and (∂G/∂P)T = 1.72(9), (∂2G/∂P2)T = –0.05(2) GPa−1, respectively. A comparison of our results with previous studies on end-member diopside and hedenbergite in the literatures shows systematic linear correlations between the Fe composition and single-crystal elastic moduli. An addition of 20 mol% Fe in diopside increases KS0 by ∼1.7% (∼2 GPa) and reduces G0 by ∼4.1% (∼3 GPa), but has a negligible effect on the pressure derivatives of the bulk and shear moduli within experimental uncertainties. In addition, our modeling results show that substitution of 20 mol% Fe in diopside can reduce VP and VS by ∼1.8% and ∼3.5%, respectively, along both an expected normal mantle geotherm and a representative cold subducted slab geotherm. Furthermore, the modeling results show that the VP and VS profiles of Fe-enriched pyroxenite along the cold subducted slab geotherm are ∼3.2% and ∼2.5% lower than AK135 model at 400 km depth, respectively. Finally, we propose that the presence of Fe-enriched pyroxenite (including Fe-enriched clinopyroxene, Fe-enriched orthopyroxene, and Fe-enriched olivine), can be an effective mechanism to cause low-velocity anomalies in the upper mantle regions atop the 410 km discontinuity at cold subudcted slab conditions.

Elastic anisotropy and single-crystal moduli of solid argon up to 64 GPa from time-domain Brillouin scattering

Single-crystal elastic moduli ${C}_{ij}$, shear modulus $G$, and Zener anisotropic ratio $A$ of solid argon having the face-centered cubic (fcc) structure were determined at high pressures between 12 and 64 GPa using a combination of experimental and theoretical approaches. The experimental data, namely, the maximal and minimal values of the product of the longitudinal sound velocity and refractive index $n\ifmmode\cdot\else\textperiodcentered\fi{}{V}_{L}$, were obtained from the 3D scanning of elastic inhomogeneities in compressed samples of argon using the technique of time-domain Brillouin scattering. These inhomogeneities, caused by elastic anisotropy of solid argon, were revealed to be about twice as strong as those reported in the earlier experiments using classical Brillouin light scattering (BLS). To derive the ${V}_{L}$ values, we used the refractive index obtained here from ab initio calculations which also permitted us to rule out any contribution to the amplitude of the observed elastic inhomogeneities of the hexagonal close-packed phase of argon, proposed to coexist with the fcc phase at high pressures. From the measured ${C}_{ij}(P)$, we derived pressure dependence of shear modulus of the fcc argon ${G}_{H}(P)$ using the Voigt-Reuss-Hill approximation and found a very good agreement with the earlier $G(P)$ obtained from shear sound velocities in the classical BLS measurements. Our results agree very well with the earlier predictions based on a relatively simple many-body model employing the Buckingham pair potential. Finally, our measurements show a much weaker change of the Cauchy discrepancy $({C}_{12}\ensuremath{-}{C}_{44}\ensuremath{-}2P)$ of the fcc argon with pressure than reported in all earlier experimental and theoretical works.

Structure and Properties of Ice Phase States

The structure, equation of state, mechanical and vibrational properties of single crystals of ices II, VIII, XI and ice in a previously predicted phase bct-4 are studied within the Hartree-Fock method using the density functional theory (B3LYP hybrid functional) with localized Gaussian atomic orbitals as implemented in the “CRYSTAL14” software package. Calculated lattice parameters, elastic moduli of single crystals, and mechanical parameters of polycrystalline samples are shown to meet the criteria of mechanical stability. Parameters of the Vinet equation of state are obtained. Energy band widths and Mulliken atomic charges are determined using obtained energy and spatial distribution of electrons. The frequencies of long-wave vibrations are calculated and vibrational spectra are constructed.

Finite temperature elastic properties of equiatomic CoCrFeNi from first principles

The finite temperature elastic properties of the equiatomic CoCrFeNi medium-entropy alloy has been studied by density functional theory. Besides atomic vibrations and electronic free energy, the predictive model developed here includes contributions from spin fluctuations (SFs) in determining the elastic properties of CoCrFeNi. Including SFs changes the magnitude of the temperature derivatives of the poly-crystal elastic moduli, resulting in a close agreement between simulation and experimentally measured trends. How the single-crystal elastic moduli depend on SFs and how these dependencies influence changes in the poly-crystal elastic moduli are analyzed systematically. Finally, the elemental sources to the simulated trends are identified.

Fe–Mg substitution in aluminate spinels: effects on elastic properties investigated by Brillouin scattering

We investigated by a multi-analytical approach (Brillouin scattering, X-ray diffraction and electron microprobe) the dependence of the elastic properties on the chemical composition of six spinels in the series (Mg1−x,Fex)Al2O4 (0 ≤ x ≤ 0.5). With the exception of C12, all the elastic moduli (C11, C44, KS0 and G) are insensitive to chemical composition for low iron concentration, while they decrease linearly for higher Fe2+ content. Only C12 shows a continuous linear increase with increasing Fe2+ across the whole compositional range under investigation. The high cation disorder showed by the sample with x = 0.202 has little or no influence on the elastic parameters. The range 0.202 < x < 0.388 bounds the percolation threshold (pc) for nearest neighbor interaction of Fe in the cation sublattices of the spinel structure. Below x = 0.202, the iron atoms are diluted in the system and far from each other, and the elastic moduli are nearly constant. Above x = 0.388, Fe atoms form extended interconnected clusters and show a cooperative behavior thus affecting the single-crystal elastic moduli. The elastic anisotropy largely increases with the introduction of Fe2+ in substitution of magnesium in spinel. This behavior is different with respect to other spinels containing transition metals such as Mn2+ and Co2+.

Extrapolation of bulk rock elastic moduli of different rock types to high pressure conditions and comparison with texture-derived elastic moduli

In this study elastic moduli of three different rock types of simple (calcite marble) and more complex (amphibolite, micaschist) mineralogical compositions were determined by modeling of elastic moduli using texture (crystallographic preferred orientation; CPO) data, experimental investigation and extrapolation. 3D models were calculated using single crystal elastic moduli, and CPO measured using time-of-flight neutron diffraction at the SKAT diffractometer in Dubna (Russia) and subsequently analyzed using Rietveld Texture Analysis. To define extrinsic factors influencing elastic behaviour, P-wave and S-wave velocity anisotropies were experimentally determined at 200, 400 and 600 MPa confining pressure. Functions describing variations of the elastic moduli with confining pressure were then used to predict elastic properties at 1000 MPa, revealing anisotropies in a supposedly crack-free medium. In the calcite marble elastic anisotropy is dominated by the CPO. Velocities continuously increase, while anisotropies decrease from measured, over extrapolated to CPO derived data. Differences in velocity patterns with sample orientation suggest that the foliation forms an important mechanical anisotropy. The amphibolite sample shows similar magnitudes of extrapolated and CPO derived velocities, however the pattern of CPO derived velocity is closer to that measured at 200 MPa. Anisotropy decreases from the extrapolated to the CPO derived data. In the micaschist, velocities are higher and anisotropies are lower in the extrapolated data, in comparison to the data from measurements at lower pressures. Generally our results show that predictions for the elastic behavior of rocks at great depths are possible based on experimental data and those computed from CPO. The elastic properties of the lower crust can, thus, be characterized with an improved degree of confidence using extrapolations. Anisotropically distributed spherical micro-pores are likely to be preserved, affecting seismic velocity distributions. Compositional variations in the polyphase rock samples do not significantly change the velocity patterns, allowing the use of RTA-derived volume percentages for the modeling of elastic moduli.

Single-crystal elasticity of MgAl2O4-spinel up to 10.9 GPa and 1000 K: Implication for the velocity structure of the top upper mantle

The combined effect of pressure and temperature on the single-crystal elasticity of MgAl2O4-spinel has been studied using Brillouin scattering and X-ray diffraction up to 10.9 GPa and 1000 K in externally-heated diamond anvil cells. The obtained single-crystal elastic moduli of MgAl2O4-spinel at ambient conditions are consistent with literature values and follow a linear increase with pressure at high temperatures. More importantly, the pressure dependence of the elastic moduli at high temperatures is much smaller than that at 300 K, indicating a stronger temperature effect on the elastic moduli of MgAl2O4-spinel at high pressures. Our new results were applied to model the sound velocity of MgAl2O4-spinel at relevant pressure and temperature conditions of the top upper mantle, showing that MgAl2O4-spinel has the greatest velocity and the VP/VS ratio among major mantle minerals. We further modeled the velocity of spinel-peridotite at the top upper mantle. Varying the composition of spinel-peridotite can lead to up to 2.1% variation in VP and 1.3% in VS. The top upper mantle with greater VP and VS should contain more olivine and spinel but less orthopyroxene. The velocity of the top upper mantle is thus strongly correlated with the composition of the region. Our results are thus important in understanding the composition and velocity of the top upper mantle.

A numerical method for predicting Rayleigh surface wave velocity in anisotropic crystals

A numerical method was developed for calculating the Rayleigh Surface Wave (RSW) velocity in arbitrarily oriented single crystals in 360 degrees of propagation. This method relies on the results from modern analysis of RSW behavior with the Stroh formalism to restrict the domain in which to search for velocities by first calculating the limiting velocity. This extension of existing numerical methods also leads to a natural way of determining both the existence of the RSW as well as the possibility of encountering a pseudo-surface wave. Furthermore, the algorithm is applied to the calculation of elastic properties from measurement of the surface wave velocity in multiple different directions on a single crystal sample. The algorithm was tested with crystal symmetries and single crystal elastic moduli from literature. It was found to be very robust and efficient in calculating RSW velocity curves in all cases.

A monodisperse microspheres/silk fibroin nanofiber composite with controlled release of biomolecules for vascular tissue engineering

In this study elastic moduli of three different rock types of simple (calcite marble) and more complex (amphibolite, micaschist) mineralogical compositions were determined by modeling of elastic moduli using texture (crystallographic preferred orientation; CPO) data, experimental investigation and extrapolation. 3D models were calculated using single crystal elastic moduli, and CPO measured using time-of-flight neutron diffraction at the SKAT diffractometer in Dubna (Russia) and subsequently analyzed using Rietveld Texture Analysis. To define extrinsic factors influencing elastic behaviour, P-wave and S-wave velocity anisotropies were experimentally determined at 200, 400 and 600 MPa confining pressure. Functions describing variations of the elastic moduli with confining pressure were then used to predict elastic properties at 1000 MPa, revealing anisotropies in a supposedly crack-free medium. In the calcite marble elastic anisotropy is dominated by the CPO. Velocities continuously increase, while anisotropies decrease from measured, over extrapolated to CPO derived data. Differences in velocity patterns with sample orientation suggest that the foliation forms an important mechanical anisotropy. The amphibolite sample shows similar magnitudes of extrapolated and CPO derived velocities, however the pattern of CPO derived velocity is closer to that measured at 200 MPa. Anisotropy decreases from the extrapolated to the CPO derived data. In the micaschist, velocities are higher and anisotropies are lower in the extrapolated data, in comparison to the data from measurements at lower pressures. Generally our results show that predictions for the elastic behavior of rocks at great depths are possible based on experimental data and those computed from CPO. The elastic properties of the lower crust can, thus, be characterized with an improved degree of confidence using extrapolations. Anisotropically distributed spherical micro-pores are likely to be preserved, affecting seismic velocity distributions. Compositional variations in the polyphase rock samples do not significantly change the velocity patterns, allowing the use of RTA-derived volume percentages for the modeling of elastic moduli.

Elasticity of calcium and calcium-sodium amphiboles

Measurements of single-crystal elastic moduli under ambient conditions are reported for nine calcium to calcium-sodium amphiboles that lie in the composition range of common crustal constituents. Velocities of body and surface acoustic waves measured by Impulsive Stimulated Light Scattering (ISLS) were inverted to determine the 13 moduli characterizing these monoclinic samples. Moduli show a consistent pattern: C33>C22>C11 and C23>C12>C13 and C44>C55∼C66 and for the uniquely monoclinic moduli, |C35|≫C46∼|C25|>|C15|∼0. Most of the compositionally-induced variance of moduli is associated with aluminum and iron content. Seven moduli (C11C12C13C22C44C55C66) increase with increasing aluminum while all diagonal moduli decrease with increasing iron. Three moduli (C11, C13 and C44) increase with increasing sodium and potassium occupancy in A-sites. The uniquely monoclinic moduli (C15C25 and C35) have no significant compositional dependence. Moduli associated with the a∗ direction (C11C12C13C55 and C66) are substantially smaller than values associated with structurally and chemically related clinopyroxenes. Other moduli are more similar for both inosilicates. The isotropically averaged adiabatic bulk modulus does not vary with iron content but increases with aluminum content from 85GPa for tremolite to 99GPa for pargasite. Increasing iron reduces while increasing aluminum increases the isotropic shear modulus which ranges from 47GPa for ferro-actinolite to 64GPa for pargasite. These results exhibit far greater anisotropy and higher velocities than apparent in earlier work. Quasi-longitudinal velocities are as fast as ∼9km/s and (intermediate between the a∗- and c-axes) are as slow as ∼6km/s. Voigt-Reuss-Hill averaging based on prior single crystal moduli resulted in calculated rock velocities lower than laboratory measurements, leading to adoption of the (higher velocity) Voigt bound. Thus, former uses of the upper Voigt bound can be understood as an ad hoc decision that compensated for inaccurate data. Furthermore, because properties of the end-member amphiboles deviate substantially from prior estimates, all predictions of rock velocities as a function of modal mineralogy and elemental partitioning require reconsideration.

The elastic anisotropy of clay minerals

The layered structure of clay minerals produces large elastic anisotropy due to the presence of strong covalent bonds within layers and weaker electrostatic bonds in between. Technical difficulties associated with small grain size preclude experimental measurement of single-crystal elastic moduli. However, theoretical calculations of the complete elastic tensors of several clay minerals have been reported, using either first-principle calculations based on density functional theory or molecular dynamics. Because of the layered microstructure, the elastic stiffness tensor obtained from such calculations can be approximated to good accuracy as a transversely isotropic (TI) medium. The TI-equivalent elastic moduli of clay minerals indicate that Thomsen’s anisotropy parameters [Formula: see text] and [Formula: see text] are large and positive, whereas [Formula: see text] is small or negative. A least-squares inversion for the elastic properties of a best-fitting equivalent TI medium consisting of two isotropic layers to the elastic properties of clay minerals indicates that the shear modulus of the stiffest layer is considerably larger than the softest layer, consistent with the expected high compliance of the interlayer region in clay minerals. It is anticipated that the elastic anisotropy parameters derived from the best-fitting TI approximation to the elastic stiffness tensor of clay minerals will find applications in rock physics for seismic imaging, amplitude variation with offset analysis, and geomechanics.

Diffraction and single-crystal elastic constants of Inconel 625 at room and elevated temperatures determined by neutron diffraction

In this work, diffraction and single-crystal elastic constants of Inconel 625 have been determined by means of in situ loading at room and elevated temperatures using time-of-flight neutron diffraction. Theoretical models proposed by Voigt, Reuss, and Kroner were used to determine single-crystal elastic constants from measured diffraction elastic constants, with the Kroner model having the best ability to capture experimental data. The magnitude of single-crystal elastic moduli, computed from single-crystal elastic constants, decreases and the single crystal anisotropy increases as temperature increases, indicating the importance of texture in affecting macroscopic stress at elevated temperatures. The experimental data reported here are of great importance in understanding additive manufacturing of metallic components as: diffraction elastic constants are required for computing residual stresses from residual lattice strains measured using neutron diffraction, which can be used to validate thermomechanical models of additive manufacturing, while single-crystal elastic constants can be used in crystal plasticity modeling, for example, to understand mechanical deformation behavior of additively manufactured components.

Large elastoplasticity under static megabar pressures: Formulation and application to compression of samples in diamond anvil cells

In high pressure research, static megabar pressures are typically produced by compression of a thin sample by two diamonds in various types of diamond anvil cells. This process is accompanied by large plastic deformation (sample thickness is reduced by a factor of 30), and finite elastic deformation of a sample and even the diamond. A thermodynamically consistent system of equations for large elastic and plastic deformation of an isotropic material obeying nonlinear elasticity and pressure dependent yield condition is formulated. The Murnaghan elasticity law and pressure-dependent J2 plasticity are utilized. The finite-strain third-order elasticity law for cubic crystals is utilized for diamond. A computational algorithm is presented with emphasis on the stress update procedure and derivation of the consistent tangent moduli. It is implemented as a user material subroutine in the finite element code ABAQUS. Material parameters for a rhenium sample, as an example, and a diamond are calibrated based on the experimental and atomistic simulation results in the literature. The evolution of the stress and strain tensor fields in the sample and diamond is studied up to a pressure of 300 GPa. Good correspondence between numerical and experimental pressure distributions at the diamond-sample contact surface is obtained. Because there is a significant scatter of the magnitude of reported third-order single-crystal elastic moduli for diamond, their effect on strains and stresses is studied in detail. With the smaller third-order elastic moduli, the phenomenon of cupping of the diamond-sample contact surface is reproduced, which plays an important role in increasing maximum pressures for a given anvil geometry. The results provide important insight into the mechanical response in diamond anvil cells, interpretation of materials properties under extreme conditions from heterogeneous fields, and optimum design of cells for reaching the maximum static pressure in a volume sufficient for the desired measurements.

Uncertainty Quantification in Prediction of the In-Plane Young's Modulus of Thin Films With Fiber Texture

Electrodeposited thin films in MEMS devices often show fiber texture resulting in transverse isotropic, effective elastic properties. It is of interest to predict these elastic properties since they play a role in device performance. In addition to predicting effective material properties of the devices, we quantify the uncertainty in our predictions of these material properties for use in downstream simulations aimed at studies of performance, lifetime, or reliability. In this paper, we estimate the numerical value of the effective in-plane Young's modulus of thin nickel polycrystalline films using numerical simulation. We also examine the variability and sensitivity of the in-plane Young's modulus due to uncertainties in microstructure geometry, crystallographic texture, and numerical values of single-crystal elastic constants. The importance of accurate characterization of the texture is shown, as is the sensitivity of the effective in-plane Young's modulus to single-crystal elastic moduli.