Sergio Speziale

Quasi-hydrostatic compression of magnesium oxide to 52 GPa: Implications for the pressure-volume-temperature equation of state

Room temperature static compression of MgO (periclase) was performed under nearly hydrostatic conditions using energy dispersive synchrotron X-ray diffraction in a diamond anvil cell with methanol-ethanol (to 10 GPa) or helium (to 52 GPa) as a pressure-transmitting medium. Highly precise cell parameters were determined with an average relative standard deviation 〈Δa/a〉 = 0.0003 over all the experimental pressure range. Fixing the bulk modulus K0T = 160.2 GPa, a fit of the data to the third-order Birch-Murnaghan equation of state yields: V0 = 74.71±0.01 A3, (∂K0T/∂P)T = 3.99±0.01. A fit of different P-V-T datasets, ranging to 53 GPa and 2500 K, to a Birch-Murnaghan-Debye thermal equation of state constrained the Gruneisen parameter γ0 = 1.49±0.03, but not its volume dependence q, which was constrained to 1.65±0.4 by thermodynamic theory. A model based on a constant value of q cannot explain the ultrahigh pressure (P = 174–203 GPa) shock compression data. We developed a model in which q decreases with compression from 1.65 at 0.1 MPa to 0.01 at 200 GPa. This model, within the framework of the Mie-Gruneisen-Debye assumptions, satisfactorily describes the low-pressure static data (〈ΔV/V〉 = 0.4% to 53 GPa) and the high-pressure Hugoniot data (〈ΔV/V〉 <1% to 203 GPa). Average values of the thermal expansion coefficient α range between 14.1±2.8 and 16.3 ± 2.7 × 10−6 K−1 at P = 174–203 GPa. The pressure dependence of the melting temperature yields an initial pressure derivative ∂Tm/∂P = 98 K/GPa. Our analysis shows that it is possible to develop a simple model of the volume dependence of the Gruneisen parameter that can successfully describe the P-V-T equation of state of MgO from ambient conditions to 203 GPa and 3663 K.

Deformation of (Mg,Fe)SiO3 Post-Perovskite and D'' Anisotropy

Polycrystalline (Mg0.9,Fe0.1)SiO3 post-perovskite was plastically deformed in the diamond anvil cell between 145 and 157 gigapascals. The lattice-preferred orientations obtained in the sample suggest that slip on planes near (100) and (110) dominate plastic deformation under these conditions. Assuming similar behavior at lower mantle conditions, we simulated plastic strains and the contribution of post-perovskite to anisotropy in the D″ region at the Earth core-mantle boundary using numerical convection and viscoplastic polycrystal plasticity models. We find a significant depth dependence of the anisotropy that only develops near and beyond the turning point of a downwelling slab. Our calculated anisotropies are strongly dependent on the choice of elastic moduli and remain hard to reconcile with seismic observations.

Elastic Shear Anisotropy of Ferropericlase in Earth's Lower Mantle

Seismic shear anisotropy in the lowermost mantle most likely results from elastic shear anisotropy and lattice preferred orientation of its constituent minerals, including perovskite, post-perovskite, and ferropericlase. Measurements of the elastic shear anisotropy of single-crystal (Mg0.9Fe0.1)O up to 69 gigapascals (GPa) show that it increased considerably across the pressure-induced spin transition of iron between 40 and 60 GPa. Increasing iron content further enhances the anisotropy. This leads to at least 50% stronger elastic shear anisotropy of (Mg,Fe)O in the lowermost mantle compared to MgO, which is typically used in geodynamic modeling. Our results imply that ferropericlase is the dominant cause of seismic shear anisotropy in the lower mantle.

Sound Velocity and Elasticity of Tetragonal Lysozyme Crystals by Brillouin Spectroscopy

Quasilongitudinal sound velocities and the second-order elastic moduli of tetragonal hen egg-white lysozyme crystals were determined as a function of relative humidity (RH) by Brillouin scattering. In hydrated crystals the measured sound velocities in the [110] plane vary between 2.12 +/- 0.03 km/s along the [001] direction and 2.31 +/- 0.08 km/s along the [110] direction. Dehydration from 98% to 67% RH increases the sound velocities and decreases the velocity anisotropy in (110) from 8.2% to 2.0%. A discontinuity in velocity and an inversion of the anisotropy is observed with increasing dehydration providing support for the existence of a structural transition below 88% RH. Brillouin linewidths can be described by a mechanical model in which the phonon is coupled to a relaxation mode of hydration water with a single relaxation time of 55 +/- 5 ps. At equilibrium hydration (98% RH) the longitudinal moduli C(11) + C(12) + 2C(66) = 12.81 +/- 0.08 GPa, C(11) = 5.49 +/- 0.03 GPa, and C(33) = 5.48 +/- 0.05 GPa were directly determined. Inversion of the measured sound velocities in the [110] plane constrains the combination C(44) + (1/2)C(13) to 2.99 +/- 0.05 GPa. Further constraints on the elastic tensor are obtained by combining the Brillouin quasilongitudinal results with axial compressibilities determined from high-pressure x-ray diffraction. We constrain the adiabatic bulk modulus to the range 2.7-5.3 GPa.

Single-crystal elasticity of brucite, Mg(OH)2, to 15 GPa by Brillouin scattering

Abstract The second-order elastic constants of brucite were determined by Brillouin scattering to 15 GPa in a diamond anvil cell. The experiments were carried out using a 4:1 methanol-ethanol mixture as pressure medium, and ruby as a pressure standard. Two planes, one perpendicular to the c axis (basal plane) and the other containing the c axis (meridian plane), were measured at room pressure and 10 elevated pressures. Individual elastic stiffnesses, aggregate moduli, and their pressure derivatives were obtained by fitting the data to Eulerian finite strain equations. The inversion yields individual elastic constants of C11 = 154.0(14) GPa, C33 = 49.7(7) GPa, C12 = 42.1(17) GPa, C13 = 7.8(25) GPa, C14 = 1.3(10) GPa, C44 = 21.3(4) GPa, and their pressure derivatives of (∂C11/∂P)0 = 9.0(2), (∂C33/∂P)0 = 14.0(5), (∂C12/∂P)0 = 3.2(2), (∂C13/∂P)0 = 5.0(1), (∂C14/∂P)0 = 0.9(1), (∂C44/∂P)0 = 3.9(1). Aggregate moduli and their pressure derivatives are KS0 = 36.4(9) GPa, G0 = 31.3(2) GPa, (∂KS/∂P)T0 = 8.9(4), (∂G/∂P)0 = 4.3(1) for the Reuss bound, and KS0 = 43.8(8) GPa, G0 = 35.2(3) GPa, (∂KS/∂P)T0 = 6.8(2), (∂G/P)0 = 3.4(1) for the Voigt-Reuss-Hill average. The ratio of the linear compressibility along the c and a axes decreased from 4.7 to 1.3 over the examined pressure range. The shear anisotropy (C66/C44) decreased from 2.6(1) at ambient condition to 1.3(1) with increase of pressure to 12 GPa. Axial compressibilities and a compression curve constructed from our Brillouin data are in good agreement with previous X-ray diffraction data. The increased interlayer interactions and hydrogen repulsion that occurs as brucite is compressed produce a continuous variation of elastic properties rather than any abrupt discontinuities.

Elasticity measurements on minerals: a review

The elasticity of minerals is central to our understanding of the structure and properties of the Earth, and other planets. In the last half-century, and in particular within the last 15 years, there have been many new developments in the experimental methods used to determine the elastic properties of minerals. Not only have new techniques become available, but the pressure and temperature ranges over which they can be applied have been greatly extended and the precision and accuracy of the results have been significantly improved. Given these rapid advances in measurement techniques we provide a brief guide to the theory of the elasticity of minerals, and we review and compare the physical principles and the capabilities of the experimental techniques now available.

High-pressure behavior of gypsum: A single-crystal X-ray study

Abstract High-pressure X-ray diffraction was carried out on a single crystal of gypsum compressed in a diamond anvil cell. The sample maintained its crystal structure up to 4.0 ± 0.1 GPa. The fit of pressure dependence of the unit-cell volume to the third-order Birch-Murnaghan equation yielded KT0 = 44(3) GPa and (∂KT/∂P)0 = 3.3(3), where KT0 and (∂KT/∂P)0 are the isothermal bulk modulus and its pressure derivative in ambient conditions. The axial compressibility values, fitting data collected up to 3.94 GPa, were β0aEoS = 6.1(1) and β0cEoS = 5.6(1) 10-3 GPa-1. The value of β0bEoS was 6.2(8) 10-3 GPa-1 fitting the data collected up to 2 GPa, due to non-linearity above this pressure; axial compressibility of gypsum is almost isotropic (β0a:β0b:β0c = 1:1:0.9). This behavior is partly unexpected for a layered mineral based on alternate layers of Ca- and S-polyhedral chains separated by interlayers occupied by water molecules. Above 4.0 GPa the compression curve of gypsum shows a discontinuity with a 2.5% contraction in volume. Structural refinements indicate that SO4 volume and average S-O bond distances remain almost unchanged from room pressure to 3.9 GPa [range 1.637(4)-1.66(9) Å3; 1.4733-1.48 Å]. The SO4 tetrahedron undergoes distortion: the smaller distance decreases from 1.4731(9) to 1.45(2) Å and the larger increases from 1.4735(9) to 1.51(2) Å. In contrast, the calcium polyhedra show expected high-pressure behavior, becoming more regular and decreasing in volume from 25.84(8) Å3 at ambient P to 24.7(1) Å3 at 3.9 GPa. The largest variations were observed in the interlayer region where the water molecules are located. Along the b axis, the two structural layers have very different compressibilities: the polyhedral layer is almost incompressible in the pressure range studied, whereas water layer compressibility is 9.7(3) 10-3 GPa-1, about twice that of the other two lattice parameters. At ambient conditions, water molecules form weak hydrogen bonds with the O atoms of Ca and S polyhedra. With increasing pressure, the weakest hydrogen bond becomes the strongest one: from 0.001 to 4 GPa, the distance changes from 2.806(1) to 2.73(2) Å for OW-H1···O2, and from 2.883(2) to 2.69(3) Å for OW-H2···O2. Structure refinements show that water remains in the structure when P increases. The observed distortion of sulfate tetrahedra explains the splitting of the ν1 sulfate stretching mode, and the various measured compressibilities of the two hydrogen bonds and the coalescence of the Raman stretching mode observed at pressures over 5 GPa.

Single-crystal elasticity of andradite garnet to 11 GPa

The high-pressure elastic properties of single-crystal andradite garnet Ca3Fe 3+ Si3O12 were determined by Brillouin scattering to 11 GPa. The pressure dependence of the elastic stiffness constants and aggregate bulk and shear moduli were obtained by inversion of the data to finite Eulerian strain equations. The inversion yieldsC11 = 286.7 ±0. 6G Pa,C12 = 88.6 ±0. 6G Pa, C44 = 83.8 ± 0. 3G Pa,K0S = 154.5 ± 0. 6G Pa,G0S = 89.7 ± 0. 4G Pa, (∂K0T /∂P)T = 4.71 ± 0.1, and (∂G0/∂P)T = 1.25 ± 0.05. Both individual and aggregate elastic moduli define nearly linear modulus–pressure trends. The elastic anisotropy of andradite garnet si ncr eases weakly in magnitude with compression. Previous studies of the high-pressure elasticity of andradite garnet are highly discrepant, with reported pressure derivatives of the bulk modulus varying by 46% and pressure derivatives of the shear modulus varying by 253%. We are able to provide plausible explanations for these discrepancies. In particular, differences between previous x-ray diffraction data and a static compression curve constructed from our Brillouin data can be attributed to the effects of non-hydrostatic stresses on the x-ray data.

The 3.65 Å phase, MgSi(OH)6: Structural insights from DFT-calculations and T-dependent IR spectroscopy

Abstract First-principles calculations based on density-functional theory (DFT) and low-T IR spectroscopy were performed to gain more insight into the structure of the so-called 3.65 Å phase, a high-pressure phase of the composition MgSi(OH)6. DFT-calculations predict a monoclinic symmetry with ordered sixfold-coordinated Mg and Si and six unique hydrogen sites as the most stable structure. Adapting the structural parameters of the DFT-determined lowest-energy configuration and assuming (MgSi)- ordering, a new Rietveld refinement of the powder XRD pattern of the 3.65 Å phase was performed, which resulted in excellent refinement statistics and successful assignment of X-ray reflections that were unassigned in former structural models with orthorhombic symmetry. A configuration with ordered Mg and Si at the octahedral positions causes a small monoclinic distortion of the network of strongly tilted octahedra and thus leads to space group P21. The structural refinement yields the following unit-cell parameters: a = 5.1131(3), b = 5.1898(3), c = 7.3303(4) Å, β = 90.03(1)°, V = 194.52(2) Å3, space group: P21, Z = 2, ρ = 2.637 g/cm3. The structure of the 3.65 Å phase can be considered as a modified A-site defective perovskite with a unique network of corner-sharing alternating Mg(OH)6 and Si(OH)6 octahedra and is probably related to the structure of stottite group minerals. Low-T IR spectroscopy confirms the presence of 6 different H-positions in the proposed structure. Measured IR-spectra and computed spectra compare favorably, which further supports the computed structure as the correct model for the 3.65 Å phase.

The elasticity of MgAl2O4-MnAl2O4 spinels by Brillouin scattering and an empirical approach for bulk modulus prediction

Abstract The elastic constants Cij of a set of synthetic single crystals belonging to the join MgAl2O4-MnAl2O4 (spinel sensu stricto-galaxite) were determined by Brillouin spectroscopy at ambient conditions. The C11 component tends to remain constant for Mg-rich compositions (XMn < 0.5) and decreases in Mn-rich compositions, whereas C12 increases and C44 decreases almost linearly from MgAl2O4 to MnAl2O4. The bulk modulus KS is weakly dependent upon Mg-Mn substitution within experimental uncertainties, whereas the shear modulus G decreases with increasing Mn2+ content. For MnAl2O4, C11 = 271.3(1.3) GPa, C12 = 164.8(1.3) GPa, C44 = 124.9(5) GPa, KS = 200(1) GPa, and G = 88.7(5) GPa. Based on the “polyhedral approach,” we developed a model that describes the crystal bulk moduli of the MgAl2O4-MnAl2O4 spinels in terms of their cation distribution and the polyhedral bulk moduli of the different cations. We refined a set of values for the effective polyhedral bulk modulus of Mg, Mn2+, and Al in tetrahedral (T) and octahedral (M) sites, which span from 153 to 270 GPa ranking as follows: KMMn < KMMg < KTMg ≈ KTMn < KMAl << KTAl. Crystal bulk modulus was perfectly reproduced within 0.1% for all Mn2+-bearing samples. We also found a high linear correlation between the effective polyhedral bulk modulus and the ionic potential, IP, of the coordinating cations: Kji (GPa) = 20(2) IP + 108(10) (where i indicates the cation and j the polyhedral site). We tested this simple correlation by calculating the specific effective polyhedral bulk modulus of several cations in T and M coordination and then predicting the crystal bulk modulus for several spinel compositions. The success of our simple correlation in modeling the bulk modulus of spinels outside the MgAl2O4-MnAl2O4 system is encouraging, and suggests that the relationships between chemical composition, cation distribution and elastic properties in spinel-structured minerals and materials can indeed be expressed by relatively simple models.