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.
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Shear properties of MgO inferred using neural networks
Abstract. Shear properties of mantle minerals are vital for interpreting seismic shear wave speeds and therefore inferring the composition and dynamics of a planetary interior. Shear wave speed and elastic tensor components, from which the shear modulus can be computed, are usually measured in the laboratory mimicking the Earth's (or a planet's) internal pressure and temperature conditions. A functional form that relates the shear modulus to pressure (and temperature) is fitted to the measurements and used to interpolate within and extrapolate beyond the range covered by the data. Assuming a functional form provides prior information, and the constraints on the predicted shear modulus and its uncertainties might depend largely on the assumed prior rather than the data. In the present study, we propose a data-driven approach in which we train a neural network to learn the relationship between the pressure, temperature and shear modulus from the experimental data without prescribing a functional form a priori. We present an application to MgO, but the same approach works for any other mineral if there are sufficient data to train a neural network. At low pressures, the shear modulus of MgO is well-constrained by the data. However, our results show that different experimental results are inconsistent even at room temperature, seen as multiple peaks and diverging trends in probability density functions predicted by the network. Furthermore, although an explicit finite-strain equation mostly agrees with the likelihood predicted by the neural network, there are regions where it diverges from the range given by the networks. In those regions, it is the prior assumption of the form of the equation that provides constraints on the shear modulus regardless of how the Earth behaves (or data behave). In situations where realistic uncertainties are not reported, one can become overconfident when interpreting seismic models based on those defined equations of state. In contrast, the trained neural network provides a reasonable approximation to experimental data and quantifies the uncertainty from experimental errors, interpolation uncertainty, data sparsity and inconsistencies from different experiments.
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- Award ID(s):
- 2009935
- NSF-PAR ID:
- 10438238
- Date Published:
- Journal Name:
- European Journal of Mineralogy
- Volume:
- 35
- Issue:
- 1
- ISSN:
- 1617-4011
- Page Range / eLocation ID:
- 45 to 58
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Single‐crystal X‐ray diffraction and Brillouin spectroscopy experiments were performed on a natural Cr‐pyrope (Prp71.0Alm12.6Sps0.7Grs3.5Uvr12.2) 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 )Pand (∂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 andρ /V S are much more sensitive to the compositional change of the SCLM. -
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Abstract It is well known that elasticity is a key physical property in the determination of the structure and composition of the Earth and provides critical information for the interpretation of seismic data. This study investigates the stress‐induced variation in elastic wave velocities, known as the acoustoelastic effect, in San Carlos olivine. A recently developed experimental ultrasonic acoustic system, the Directly Integrated Acoustic System Combined with Pressure Experiments (DIASCoPE), was used with the D‐DIA multi‐anvil apparatus to transmit ultrasonic sound waves and collect the reflections. We use the DIASCoPE to obtain longitudinal (
P ) and shear (S ) elastic wave velocities from San Carlos olivine at pressures ranging from 3.2–10.5 GPa and temperatures from 450–950°C which we compare to the stress state in the D‐DIA derived from synchrotron X‐ray diffraction. We use elastic‐plastic self‐consistent (EPSC) numerical modeling to forward model X‐ray diffraction data collected in D‐DIA experiments to obtain the macroscopic stress on our sample. We can observe the relationship between the relative elastic wave velocity change (ΔV /V ) and macroscopic stress to determine the acoustoelastic constants, and interpret our observations using the linearized first‐order equation based on the model proposed by Hughes and Kelly (1953),https://doi.org/10.1103/physrev.92.1145 . This work supports the presence of the acoustoelastic effect in San Carlos olivine, which can be measured as a function of pressure and temperature. This study will aid in our understanding of the acoustoelastic effect and provide a new experimental technique to measure the stress state in elastically deformed geologic materials at high pressure conditions. -
null (Ed.)Abstract Calcium carbonate (CaCO3) is one of the most abundant carbonates on Earth's surface and transports carbon to Earth's interior via subduction. Although some petrological observations support the preservation of CaCO3 in cold slabs to lower mantle depths, the geophysical properties and stability of CaCO3 at these depths are not known, due in part to complicated polymorphic phase transitions and lack of constraints on thermodynamic properties. Here we measured thermal equation of state of CaCO3-Pmmn, the stable polymorph of CaCO3 through much of the lower mantle, using synchrotron X-ray diffraction in a laser-heated diamond-anvil cell up to 75 GPa and 2200 K. The room-temperature compression data for CaCO3-Pmmn are fit with third-order Birch-Murnaghan equation of state, yielding KT0 = 146.7 (±1.9) GPa and K′0 = 3.4(±0.1) with V0 fixed to the value determined by ab initio calculation, 97.76 Å3. High-temperature compression data are consistent with zero-pressure thermal expansion αT = a0 + a1T with a0 = 4.3(±0.3)×10-5 K-1, a1 = 0.8(±0.2)×10-8 K-2, temperature derivative of the bulk modulus (∂KT/∂T)P = –0.021(±0.001) GPa/K; the Grüneisen parameter γ0 = 1.94(±0.02), and the volume independent constant q = 1.9(±0.3) at a fixed Debye temperature θ0 = 631 K predicted via ab initio calculation. Using these newly determined thermodynamic parameters, the density and bulk sound velocity of CaCO3-Pmmn and (Ca,Mg)-carbonate-bearing eclogite are quantitatively modeled from 30 to 80 GPa along a cold slab geotherm. With the assumption that carbonates are homogeneously mixed into the slab, the results indicate the presence of carbonates in the subducted slab is unlikely to be detected by seismic observations, and the buoyancy provided by carbonates has a negligible effect on slab dynamics.more » « less
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Abstract In this study, we have investigated the crystal structure and equation of state of tetragonal CaSiO3-perovskite up to 200 GPa using synchrotron X-ray diffraction in laser-heated diamond-anvil cells. X-ray diffraction patterns of the quenched CaSiO3-perovskite above 148 GPa clearly show that 200, 211, and 220 peaks of the cubic phase split into 004+220, 204+312, and 224+400 peak pairs, respectively, in the tetragonal structure, and their calculated full-width at half maximum (FWHM) exhibits a substantial increase with pressure. The distribution of diffraction peaks suggests that the tetragonal CaSiO3-perovskite most likely has an I4/mcm space group at 300 K between 148 and 199 GPa, although other possibilities might still exist. Using the Birch-Murnaghan equations, we have determined the equation of state of tetragonal CaSiO3-perovskite, yielding the bulk modulus K0T = 227(21) GPa with the pressure derivative of the bulk modulus, K0T′ = 4.0(3). Modeled sound velocities at 580 K and around 50 GPa using our results and literature values show the difference in the compressional (VP) and shear-wave velocity (VS) between the tetragonal and cubic phases to be 5.3 and 6.7%, respectively. At ~110 GPa and 1000 K, this phase transition leads to a 4.3 and 9.1% jump in VP and VS, respectively. Since the addition of Ti can elevate the transition temperature, the transition from the tetragonal to cubic phase may have a seismic signature compatible with the observed mid-lower mantle discontinuity around the cold subduction slabs, which needs to be explored in future studies.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.5194/ejm-35-45-2023
