Single-crystal Elasticity Research Articles

A Library of Elastic Tensors for Lowermost Mantle Seismic Anisotropy Studies and Comparison With Seismic Observations

AbstractThe exact mechanism for lowermost mantle seismic anisotropy remains unknown; however, work on the elasticity and deformation of lower mantle materials has constrained a few possible options. The most probable minerals producing anisotropy are bridgmanite, postperovskite, and ferropericlase. While there is an extensive literature on the elasticity and deformation of lower mantle minerals, we create a comprehensive uniform database of D″ anisotropy scenarios. In order to characterize a range of the possible fabrics for D″ anisotropy, we carry out VPSC (visco‐plastic self‐consistent modeling) to predict textures for each proposed mineral and dominant slip system. We numerically deform each mineral under different geometrical scenarios: simple shear, pure shear, and extension. By using published single crystal elasticity values, we produce a library of 336 candidate elastic tensors. We used the elastic tensor library to revisit previously published D″‐associated seismic anisotropy studies for crossing raypaths (Siberia, North America, the Afar region of Africa, and Australia). While we cannot identify a single, unique mechanism that explains all of these data sets, we find that postperovskite (dominant slip on [100](010) or [100](001)) and periclase (dominant slip on {100}<011>) provide the best fit to the observations and suggest reasonable shear directions for each region of interest. Bridgmanite generally provides a poor fit to the observations; however, we cannot completely rule out any particular model. As the number of anisotropy observations for D″ increases, this elastic tensor library will be helpful for observational seismologists in identifying possible mechanisms of anisotropy and shear directions at in the lowermost mantle.

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.

Single-crystal elasticity of iron-bearing phase E and seismic detection of water in Earth's upper mantle

AbstractThe elastic properties of Mg2.12(2)Fe0.21(2)Ni0.01Si1.15(1)O6H2.67(8) phase E single crystals with Fe3+/ΣFe = 0.25(3) have been determined by Brillouin spectroscopy at ambient conditions. We find that that the elasticity of iron-bearing phase E is described by the six independent stiffness tensor components (all in units of GPa): C11 = 192.2(6), C12 = 56.4(8), C13 = 43.5(8), C14 = –4.3(3), C33 = 192.1(7), C44 = 46.4(3). The Voigt-Reuss-Hill averages of bulk and shear moduli are 95.9(4) and 59.6(2) GPa, respectively. The aggregate velocities of iron-bearing phase E are νP = 7.60(2) and νS = 4.43(1) km/s, markedly lower than those of major mantle minerals at ambient conditions. Modeling based on our results suggests that the presence of iron-bearing phase E may reduce the sound wave velocities in upper mantle and transition zone rocks, making it a possible target for future seismological investigations aiming to map hydration in subducting slabs.

High-pressure phase stability and elasticity of ammonia hydrate

Abstract Phase stability and elasticity of ammonia hydrate have been studied using Raman spectroscopy and Brillion scattering in diamond-anvil cells up to 53 GPa at 300 K. Here we have established the high-pressure phase diagram of ammonia hydrate in three different compositions, including ammonia monohydrate (AMH, NH3·H2O), dihydrate (ADH, NH3·2H2O), and trihydrate (ATH, NH3·3H2O). In contrast to previous experimental results, our Raman and Brillouin measurements at 300 K have shown that all three ammonia hydrates start to dehydrate at 2.1–2.2 GPa. Dehydration of the ammonia hydrate leads to the formation of single-crystal ice-VII and an increase in the concentration of NH3 in the residual liquid. The residual liquid finally turns into solid ammonia hemihydrate phase II (AHH-II) at 4–4.6 GPa, leading to a 28% jump in the compressional-wave velocity (VP). Considering a 10–15 vol% NH3 in the mantle of ice giants, AHH should thus be the dominant form of NH3 coexisting with H2O-ice in the ice giants. Further Brillouin measurements provide crucial constraints on the VP of AHH and the single-crystal elasticity of ice-VII at high pressures and 300 K. VP of AHH increases smoothly with pressure. No anomalous change in VP of AHH was identified up to 39 GPa, although a solid to solid phase transition was noted to occur at ~18 GPa by Raman measurements. In addition, the elasticity of single-crystal ice-VII, which was the dehydration product of ammonia hydrate, has been determined up to 53 GPa at 300 K. The deviation of C12 from C44 observed at 11.4 and 14.6 GPa could be caused by the hydrogen bond symmetrizations or the ordering of dipole of single-crystal ice-VII. An abnormal softening in the elastic moduli C11, C12, and the adiabatic moduli KS together with stiffening in C44 was observed between 42 and 53 GPa, which should be caused by the transition from ice-VII to its pre-transitional state. Of particular interest is the dramatic increase in the anisotropy of ice-VII with increasing pressure. Combining the sound velocity of AHH and ice-VII, we have modeled the VP of ice giants with a volume ratio of 20% AHH and 80% ice-VII in the mantle. The obtained high-pressure phase diagram and elastic properties of ammonia hydrate could contribute to understanding the structure of the mantle in the ice giants and satellites.

The single-crystal elastic properties of the jadeite-diopside solid solution and their implications for the composition-dependent seismic properties of eclogite

Abstract The 13 single-crystal adiabatic elastic moduli (Cij) of a C2/c jadeite sample close to the ideal composition (NaAlSi2O6) and a natural P2/n diopside-rich omphacite sample have been measured at ambient condition by Brillouin spectroscopy. The obtained Cij values for the jadeite sample are: C11 = 265.4(9) GPa, C22 = 247(1) GPa, C33 = 274(1) GPa, C44 = 85.8(7) GPa, C55 = 69.3(5) GPa, C66 = 93.0(7) GPa, C12 = 84(1) GPa, C13 = 66(1) GPa, C23 = 87(2) GPa, C15 = 5.4(7) GPa, C25 = 17(1) GPa, C35 = 28.7(6) GPa, C46 = 14.6(6) GPa. Voigt-Reuss-Hill averaging of the Cij values yields aggregate bulk modulus KS = 138(3) GPa and shear modulus G = 84(2) GPa for jadeite. Systematic analysis combing previous single-crystal elasticity measurements within the diopside-jadeite solid solution indicates that the linear trends are valid for most Cij values. The νp and νs of omphacite decrease with diopside content, though the velocity changes are small as diopside component exceeds 70%. We also found that both the isotropic νp and νs, as well as the seismic anisotropy of eclogite, changed strongly with the bulk-chemical composition. The relationship between the anisotropic velocities of eclogite and the chemical composition can be a useful tool to trace the origin of the eclogitic materials in the Earth's mantle.

Elasticity of single-crystal low water content hydrous pyrope at high-pressure and high-temperature conditions

AbstractThe elasticity of single-crystal hydrous pyrope with ~900 ppmw H2O has been derived from sound velocity and density measurements using in situ Brillouin light spectroscopy (BLS) and synchrotron X-ray diffraction (XRD) in the diamond-anvil cell (DAC) up to 18.6 GPa at room temperature and up to 700 K at ambient pressure. These experimental results are used to evaluate the effect of hydration on the single-crystal elasticity of pyrope at high pressure and high temperature (P-T) conditions to better understand its velocity profiles and anisotropies in the upper mantle. Analysis of the results shows that all of the elastic moduli increase almost linearly with increasing pressure at room temperature, and decrease linearly with increasing temperature at ambient pressure. At ambient conditions, the aggregate adiabatic bulk and shear moduli (KS0, G0) are 168.6(4) and 92.0(3) GPa, respectively. Compared to anhydrous pyrope, the presence of ~900 ppmw H2O in pyrope does not significantly affect its KS0 and G0 within their uncertainties. Using the third-order Eulerian finite-strain equation to model the elasticity data, the pressure derivatives of the bulk [(∂KS/∂P)T] and shear moduli [(∂G/∂P)T] at 300 K are derived as 4.6(1) and 1.3(1), respectively. Compared to previous BLS results of anhydrous pyrope, an addition of ~900 ppmw H2O in pyrope slightly increases the (∂KS/∂P)T, but has a negligible effect on the (∂G/∂P)T within their uncertainties. The temperature derivatives of the bulk and shear moduli at ambient pressure are (∂KS/∂T)P = –0.015(1) GPa/K and (∂G/∂T)P = –0.008(1) GPa/K, which are similar to those of anhydrous pyrope in previous BLS studies within their uncertainties. Meanwhile, our results also indicate that hydrous pyrope remains almost elastically isotropic at relevant high P-T conditions, and may have no significant contribution to seismic anisotropy in the upper mantle. In addition, we evaluated the seismic velocities (νP and νS) and the νP/νS ratio of hydrous pyrope along the upper mantle geotherm and a cold subducted slabs geotherm. It displays that hydrogen also has no significant effect on the seismic velocities and the νP/νS ratio of pyrope at the upper mantle conditions.

Determination of single-crystal elasticity constants of the beta phase in a multiphase tungsten thin film using impulse excitation technique, X-ray diffraction and micro-mechanical modeling

The scope of this work is to propose a methodology allowing the determination of the single-crystal elasticity constants of a phase included in a multiphase thin film taking into account its microstructure (crystallographic and morphological texture, porosity and multiphase aspect). The methodology is based on the use of a macro-mechanical test, the impulse excitation technique, a micro-mechanical test, X-ray diffraction and the Kröner-Eshelby scale transition model. As a supporting example, it was applied to determine the single-crystal elasticity constants of the Wβ tungsten metastable phase embedded in a two phases (α+β) tungsten thin film deposited on a steel substrate by DC magnetron sputtering. The effects of the grain-shape, the crystallographic texture, the porosity and the Wβ volume fraction on the macroscopic elasticity constants were studied. Among all these effects, it was found that the effect of the Wβ volume fraction was the most pronounced. The effects of the crystallographic and morphological texture on the microscopic elastic behavior of the film were evaluated. No dominance of the crystallographic or morphological texture effect was observed and their contributions depend on the crystallographic plane and the measurement direction.

Effect of calcium on the elasticity of majoritic garnets and the seismic gradients in the mantle transition zone

Brillouin scattering spectroscopy was applied to investigate the effect of calcium on the single-crystal elasticity of majorite garnet, Mj42Py50.5Gr7.5, up to 25 GPa, spanning the conditions of the mantle transition zone. The adiabatic bulk and shear moduli, and their pressure derivatives are Ks = 159(2) GPa, μ = 87(1) GPa, KS′ = 4.3(2) and μ′ = 1.2(1). Calcium substitution has a small but resolvable effect on the elasticity of the majorite-pyrope join and lowers both Ks and μ by 6 and 3% respectively compared to the calcium-free counterparts. The elasticity results, along with literature data, were employed to compute shear seismic gradients associated to the exsolution of CaSiO3 perovskite (CaPv) in pyrolite and MORB below 520 km depth. The results show that the exsolution of 18 vol% of CaPv is required to produce gradients comparable to PREM at the bottom of the transition zone, although these amounts are compatible with calcium contents in MORB but too high for pyrolite mineralogy. We conclude that the steep shear seismic gradients in the transition zone are compatible with progressive calcium enrichment likely supplied by subducted oceanic crust accumulated at the bottom of the transition zone by stagnating slabs.

Single-crystal elasticity of (Al,Fe)-bearing bridgmanite and seismic shear wave radial anisotropy at the topmost lower mantle

In this study, we investigated the single-crystal elasticity of (Al,Fe)-bearing bridgmanite (Bgm) with chemical compositions of Mg0.95Fe0.0332+Fe0.0273+Al0.04Si0.96O3 (Fe6-Al4-Bgm) and Mg0.89Fe0.0242+Fe0.0963+Al0.11Si0.89O3 (Fe12-Al11-Bgm) using combined experimental results from Brillouin light scattering (BLS), impulsive stimulated light scattering (ISLS), and X-ray diffraction (XRD) measurements in diamond anvil cells at 25 and 35 GPa. Based on experimentally measured compressional and shear wave velocities (VP, VS) as a function of azimuthal angles within selected crystal platelets that are sensitive to derivation of nine elastic constants for each composition, we reliably derived the full elastic constants of Fe6-Al4-Bgm and Fe12-Al11-Bgm at the two experimental pressures. Our results show that the combined Fe and Al substitution results in a reduction of both VS and VP in Fe12-Al11-Bgm up to 2.6(±0.5)% and 1.5(±0.3)%, respectively, compared with those in Fe6-Al4-Bgm at the experimental pressures. In particular, we observed strong combined Fe and Al effects on VS splitting anisotropy of (Al,Fe)-bearing Bgm at the two experimental pressures: Fe6-Al4-Bgm exhibits the highest VS splitting anisotropy of ∼8.23-9.0% along the [001] direction, while the direction shifts to the midway between [100] and [001] directions for Fe12-Al11-Bgm with VS splitting anisotropy of ∼7.68-11.06%. Combining the single-crystal elasticity data of Fe6-Al4-Bgm and Fe12-Al11-Bgm with the crystallographic preferred orientation (CPO) results of deformed Bgm at relevant lower-mantle pressure-temperature (P-T) conditions from literature, we modeled the seismic VS radial anisotropy of deformed (Al,Fe)-bearing Bgm near a subducting slab at conditions relevant to the topmost lower mantle. Taking into account the Fe and Al contents in (Al,Fe)-bearing Bgm with depth in the Earth's topmost lower mantle, the results of our model show that the deformation of Fe6-Al4-Bgm and Fe12-Al11-Bgm crystals would produce ∼0.9% and ∼0.8% VS radial anisotropy at depths of ∼670 and ∼920 km, respectively. These findings provide mineral physics explanations to the distinct seismically-detected VS radial anisotropies at the topmost lower mantle near subducted slabs, especially in the Tonga-Kermadec subduction region.

The extreme acoustic anisotropy and fast sound velocities of cubic high-pressure ice polymorphs at Mbar pressure

We presented the experimentally determined single-crystal elasticity model of ice up to 103(3) GPa, based on the sound velocity measurements of high-P ice polymorphs within multiple diamond anvil cells using Brillouin spectroscopy. We have not observed any discontinuities of the P-wave (Vp) or S-wave (Vs) velocities over the entire P range. The elastic moduli of high-P ice show a close to linear P dependence. In comparison with the high-P silicate minerals in terrestrial planetary bodies, the Vp and Vs values of ice exceed those of both bridgmanite and ferropericlase at P > 80–90 GPa, counter-intuitively indicating that the high-P ice, if existing in the deep terrestrial planets' interior, is not a slow phase. Instead, the high-P ice shows extremely strong elastic anisotropy, reaching 27% and 74% at 100 GPa for Vp and Vs, respectively. The presence of high-P ice in terrestrial planets' interior, even on a small scale may lead to the observable anisotropic signatures, such as the 25% Vs anisotropy in the deep earthquake-generating zone in subducting slabs. We anticipate our measurements to serve as an important base for explaining and modeling the geophysical observations for various types of planetary bodies.

Brillouin Light Scattering: Development of a Near Century-Old Technique for Characterizing the Mechanical Properties of Materials.

Brillouin light scattering (BLS), a technique theoretically described nearly a century back by the French physicist Léon Brillouin in 1922, is a light-scattering method for determining the mechanical properties of materials. This inelastic scattering method is described by the Bragg diffraction of light from a propagating fluctuation in the local dielectric. These fluctuations arise spontaneously from thermally populated sound waves intrinsic to all materials, and thus BLS may be broadly applied to transparent samples of any phase. This review begins with a brief historical overview of the development of BLS, from its theoretical prediction to the current state of the art, and notes specific technological advancements that enabled the development of BLS. Despite the broad utility of BLS, no commercial spectrometer is currently available for purchase, but rather individual components are assembled to suit a specific application. Central to any BLS spectrometer is the interferometer, and its performance characteristics-scanning or non-scanning, multi-passing, and stabilization-are critical considerations for spectrometer design. Consistent with any light-scattering method, the frequency shift is a key observable in BLS, and we summarize the connection of this measurement to evaluate the mechanical properties of materials. With emphasis toward pharmaceutical materials analysis, we introduce the traditional BLS approach for single-crystal elasticity, and this is followed by a discussion of more recent developments in powder BLS. We conclude our review with a perspective on future developments in BLS that may enable BLS as a novel addition to the current catalog of process analytical technologies.

Effect of H on elastic properties of Mg<sub>2</sub>Si by the first principles calculation

The mechanical properties of Al-Mg-Si-type aluminum alloys may degenerate due to the hydrogen damage during servicing in hydrogen environment. The Mg<sub>2</sub>Si is the main strengthening phases in Al-Mg-Si-type aluminum alloys. Therefore, the mechanical properties of Mg<sub>2</sub>Si directly determine the strengths of Al-Mg-Si-type aluminum alloys. In this work, the effects of hydrogen atoms on the mechanical properties of Mg<sub>2</sub>Si are investigated by first principle calculation, which is based on the density function theory. First of all, we calculate the single crystal elasticity constants of <i>C</i><sub>11</sub>, <i>C</i><sub>12</sub> and <i>C</i><sub>44</sub>. Then the elasticity modulus, Poisson’s ratio and hardness of polycrystalline are calculated by using the crystal elasticity constants. Furthermore, we also calculate the tensile properties of Mg<sub>2</sub>Si with and without H atoms. The difference between the densities of states with and without H atoms is used to investigate the change of Mg<sub>2</sub>Si induced by H atoms. The results show that hydrogen atoms significantly reduce the shear modulus and elastic modulus of Mg<sub>2</sub>Si, resulting in the strength and hardness decreasing, but the toughness increasing. The calculations of tensile properties indicate that H atoms reduce the fracture strength but enhance the fracture elongation of Mg<sub>2</sub>Si. The analysis of density of states indicates that hydrogen atoms will induce the properties of Mg<sub>2</sub>Si to transform from semiconductor to metal properties. The calculated results in this paper can provide a reference basis for revealing the mechanism of strength reduction of Mg<sub>2</sub>Si materials in a hydrogen environment.

Single-crystal elasticity of the rhodochrosite at high pressure by Brillouin scattering spectroscopy

ABSTRACTThe sound velocity properties of single-crystal rhodochrosite (MnCO3) were determined up to 9.7 GPa at ambient temperature by Brillouin scattering spectroscopy. Six elastic constants were calculated by a genetic algorithm method using the Christoffel's equations at each pressure. The elastic constants increased linearly as a function of pressure and its pressure derivatives ∂Cij/∂P for C11, C33, C44, C12, C13, C14 were 5.86 (±0.36), 3.82 (±0.44), 2.06 (±0.39), 5.07 (±0.27), 5.34 (±0.44), 1.52 (±0.24), respectively. Based on the derived elastic constants of rhodochrosite, the aggregate adiabatic bulk and shear moduli (Ks and G) were calculated using the Voigt-Reuss-Hill averages and the linear fitting coefficients (∂Ks/∂P)T and (∂G/∂P)T were 5.05(±0.26) and 0.73(±0.05), respectively. The aggregate Vp of rhodochrosite increased clearly as a function of pressure and its pressure derivative ∂Vp/∂P was 7.99(±0.53) × 10−2 km/(s GPa), while the aggregate Vs increased slowly and ∂Vs/∂P was only 1.19(±0.12) × 10−2 km/(s GPa). The anisotropy factor for As of rhodochrosite increased from ∼40% at 0.8 GPa to ∼48% at 9.7 GPa, while Ap decreased from ∼19% to ∼16% at the corresponding pressure.

High-pressure single-crystal elasticity of wadsleyite and the seismic signature of water in the shallow transition zone

Earth's transition zone at depths between 410 km and 660 km plays a key role in Earth's deep water cycle since large amounts of hydrogen can be stored in the nominally anhydrous minerals wadsleyite and ringwoodite, (Mg,Fe)2SiO4. Previous mineral physics experiments on iron-free wadsleyite proposed low seismic velocities as an indicative feature for hydration in the transition zone. Here we report simultaneous sound wave velocity and density measurements on iron-bearing wadsleyite single crystals with 0.24 wt-% H2O. By comparison with earlier studies, we show that pressure suppresses the velocity reduction caused by higher degrees of hydration in iron-bearing wadsleyite, ultimately leading to a velocity cross-over for both P-waves and S-waves. Modeling based on our experimental results shows that wave speed variations within the transition zone as well as velocity jumps at the 410-km seismic discontinuity, both of which have been used in previous work to detect mantle hydration, are poor water sensors. Instead, the impedance contrast across the 410-km seismic discontinuity that is reduced in the presence of water can serve as a more robust indicator for hydrated parts of the transition zone.

Seismically invisible water in Earth's transition zone?

Ringwoodite, the dominant mineral at depths between 520 km and 660 km, can store up to 2–3 wt.% of water in its crystal structure, making the Earth's transition zone a plausible water reservoir that plays a central role in Earth's deep water cycle. Experiments show that hydration of ringwoodite significantly reduces elastic wave velocities at room pressure, but the effect of pressure remains poorly constrained. Here, a novel experimental setup enables a direct quantification of the effect of hydration on ringwoodite single-crystal elasticity and density at pressures of the Earth's transition zone and high temperatures. Our data show that the hydration-induced reduction of seismic velocities almost vanishes at conditions of the transition zone. Seismic data thus agree with a wide range of water contents in the transition zone.

Single crystal elasticity of natural topaz at high-temperatures

Topaz is an aluminosilicate mineral phase stable in the hydrothermally altered pegmatitic rocks and also in subducted sedimentary lithologies. In nature, topaz often exhibits solid solution between fluorine and hydrous end members. We investigated elasticity of naturally occurring single crystal topaz (Al2SiO4F1.42(OH)0.58) using Resonant Ultrasound Spectroscopy. We also explored the temperature dependence of the full elastic constant tensor. We find that among the various minerals stable in the Al2O3-SiO2-H2O ternary system, topaz exhibits moderate elastic anisotropy. As a function of temperature, the sound velocity of topaz decreases with frac{{boldsymbol{d}}{{boldsymbol{V}}}_{{boldsymbol{P}}}}{{boldsymbol{d}}{boldsymbol{T}}} and frac{{boldsymbol{d}}{{boldsymbol{V}}}_{{boldsymbol{S}}}}{{boldsymbol{d}}{boldsymbol{T}}} being −3.10 and −2.30 × 10−4 km/s/K. The elasticity and sound velocity of topaz also vary as a function of OH and F content. The effect of composition ({{boldsymbol{x}}}_{{boldsymbol{O}}{boldsymbol{H}}}) on the velocity is equally important as that of the effect of temperature. We also note that the Debye temperature ({{boldsymbol{Theta }}}_{{boldsymbol{D}}}) of topaz at room temperature condition is 910 K and decreases at higher temperature. The Debye temperature shows positive correlation with density of the mineral phases in the Al2O3-SiO2-H2O ternary system.

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.

Single crystal elasticity of gold up to ∼20 GPa: Bulk modulus anomaly and implication for a primary pressure scale

We measured the elasticity of single crystal gold (Au) and its lattice parameters under high pressure using inelastic X-ray scattering (IXS). The elastic moduli were obtained at five pressure points between 0 and 20 GPa. The pressure variation of the bulk modulus displays anomalous behavior, being nearly constant up to ∼5 GPa, and then steeply increasing at higher pressure. A similar anomaly is observed in first-principles calculations. An absolute pressure scale was derived by direct numerical integration of the bulk modulus over volume change. This yields a scale that gives slightly lower pressure values than those of previous work, about 5–10% lower at ∼20 GPa.

40 years of mineral elasticity: a critical review and a new parameterisation of equations of state for mantle olivines and diamond inclusions

Elasticity is a key property of materials, not only for predicting volumes and densities of minerals at the pressures and temperatures in the interior of the Earth, but also because it is a major factor in the energetics of structural phase transitions, surface energies, and defects within minerals. Over the 40 years of publication of Physics and Chemistry of Minerals, great progress has been made in the accuracy and precision of the measurements of both volumes and elastic tensors of minerals and in the pressures and temperatures at which the measurements are made. As an illustration of the state of the art, all available single-crystal data that constrain the elastic properties and pressure–volume–temperature equation of state (EoS) of mantle-composition olivine are reviewed. Single-crystal elasticity measurements clearly distinguish the Reuss and Voigt bulk moduli of olivine at all conditions. The consistency of volume and bulk modulus data is tested by fitting them simultaneously. Data collected at ambient pressure and data collected at ambient temperature up to 15 GPa are consistent with a Mie–Grunesien–Debye thermal-pressure EoS in combination with a third-order Birch–Murnaghan (BM) compressional EoS, the parameter V 0 = 43.89 cm3 mol−1, isothermal Reuss bulk modulus $$K_{\text{TR,0}} = 126.3(2){\text{ GPa}}$$ , $$K^{\prime}_{\text{TR,0}} = 4.54(6)$$ , a Debye temperature $$\theta_{\text{D}} = 644(9)\;{\text{K}}$$ , and a Gruneisen parameter γ 0 = 1.044(4), whose volume dependence is described by q = 1.9(2). High-pressure softening of the bulk modulus at room temperature, relative to this EoS, can be fit with a fourth-order BM EoS. However, recent high-P, T Brillouin measurements are incompatible with these EoS and the intrinsic physics implied by it, especially that $$\left( {\frac{{\partial K^{\prime}_{\text{TR}} }}{\partial T}} \right)_{P} > 0$$ . We introduce a new parameterisation for isothermal-type EoS that scales both the Reuss isothermal bulk modulus and its pressure derivative at temperature by the volume, $$K_{\text{TR}} (T,P = 0) = K_{\text{TR,0}} \left[ {\frac{{V_{0} }}{V(T)}} \right]^{{\delta_{\text{T}} }}$$ and $$K^{\prime}_{\text{TR}} (T,P = 0) = K^{\prime}_{\text{TR,0}} \left[ {\frac{V(T)}{{V_{0} }}} \right]^{{\delta^{\prime}}}$$ , to ensure thermodynamic correctness at low temperatures. This allows the elastic softening implied by the high-P, T Brillouin data for mantle olivine to be fit simultaneously and consistently with the same bulk moduli and pressure derivatives (at room temperature) as the MGD EoS, and with the additional parameters of α V0 = 2.666(9) × 10−5 K−1, $$\theta_{\text{E}} = 484(6)$$ , $$\delta_{\text{T}}$$ = 5.77(8), and $$\delta^{\prime}$$ = −3.5(1.1). The effects of the differences between the two EoS on the calculated density, volume, and elastic properties of olivine at mantle conditions and on the calculation of entrapment conditions of olivine inclusions in diamonds are discussed, and approaches to resolve the current uncertainties are proposed.

Evidence for a Fe3+-rich pyrolitic lower mantle from (Al,Fe)-bearing bridgmanite elasticity data.

The chemical composition of Earth's lower mantle can be constrained by combining seismological observations with mineral physics elasticity measurements. However, the lack of laboratory data for Earth's most abundant mineral, (Mg,Fe,Al)(Al,Fe,Si)O3 bridgmanite (also known as silicate perovskite), has hampered any conclusive result. Here we report single-crystal elasticity data on (Al,Fe)-bearing bridgmanite (Mg0.9Fe0.1Si0.9Al0.1)O3 measured using high-pressure Brillouin spectroscopy and X-ray diffraction. Our measurements show that the elastic behaviour of (Al,Fe)-bearing bridgmanite is markedly different from the behaviour of the MgSiO3 endmember. We use our data to model seismic wave velocities in the top portion of the lower mantle, assuming a pyrolitic mantle composition and accounting for depth-dependent changes in iron partitioning between bridgmanite and ferropericlase. We find excellent agreement between our mineral physics predictions and the seismic Preliminary Reference Earth Model down to at least 1,200 kilometres depth, indicating chemical homogeneity of the upper and shallow lower mantle. A high Fe3+/Fe2+ ratio of about two in shallow-lower-mantle bridgmanite is required to match seismic data, implying the presence of metallic iron in an isochemical mantle. Our calculated velocities are in increasingly poor agreement with those of the lower mantle at depths greater than 1,200 kilometres, indicating either a change in bridgmanite cation ordering or a decrease in the ferric iron content of the lower mantle.