Donald J. Weidner

Elasticity of α-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio

Laser Brillouin spectroscopy was used to determine the adiabatic single-crystal elastic stiffness coefficients of silicon dioxide (SiO2) in the α-cristobalite structure. This SiO2 polymorph, unlike other silicas and silicates, exhibits a negative Poissons ratio; α-cristobalite contracts laterally when compressed and expands laterally when stretched. Tensorial analysis of the elastic coefficients shows that Poissons ratio reaches a maximum value of –0.5 in some directions, whereas averaged values for the single-phased aggregate yield a Poissons ratio of –0.16.

The deformation-DIA: A new apparatus for high temperature triaxial deformation to pressures up to 15 GPa

A new deformation apparatus has been developed, based on the widely used cubic-anvil apparatus known as the DIA. Two differential rams, introduced in the upper and lower guide blocks, allow independent control of the differential strain and stress field under high confining pressure. Testing experiments with synchrotron x rays have demonstrated that this deformation DIA (D-DIA) is capable of generating up to 30% axial strain on a 1–2 mm long sample under confining pressures up to 15 GPa at simultaneous high temperatures. Various compressional strain rates from 10−3 to about 5×10−6 s−1 have been achieved. Extensional experiments have also been carried out successfully. Strains are measured by x-ray imaging of the sample which has a length measurement precision of ∼0.1 μm; pressures are monitored using standard materials with well established equations of state. X-ray transparent anvils made of sintered polycrystalline cubic boron nitride have been successfully tested, with a two-dimensional x-ray charge co...

P-V-T equation of state of (Mg,Fe)SiO3 perovskite: constraints on composition of the lower mantle

Abstract Unit-cell volumes (V) of Mg 1− x Fe x SiO 3 perovskite ( x = 0.0 and 0.1) have been measured along several isobaric paths up to P = 11 GPa and T = 1300 K using a DIA-type, cubic anvil high-pressure apparatus (SAM-85). With a combination of X-ray diffraction during heating cycles and Raman spectroscopy on recovered samples, pressure and temperature conditions were determined under which the P - V - T behavior of the perovskite remains reversible. At 1 bar, perovskites of both compositions begin to transform to amorphous phases at T ≈ 400 K, accompanied by an irreversible cell volume contraction. Electron microprobe and analytical electron microscopy studies revealed that the iron-rich perovskite decomposed into at least two phases, which were Fe and Si enriched, respectively. At pressures above 4 GPa, the P - V - T behavior of MgSiO 3 perovskite remained reversible up to about 1200 K, whereas the Mg 0.9 Fe 0.1 SiO 3 exhibited an irreversible behavior on heating. Such irreversible behavior makes equation-of-state data on Fe-rich samples dubious. Thermal expansivities ( α V ) of MgSiO 3 perovskite were measured directly as a function of pressure. Overall, our results indicate a weak pressure dependence in α V for MgSiO 3 . Analyses on the P - V - T data using various thermal equations of state yielded consistent results on thermoelastic properties. The temperature derivative of the bulk modulus, ( ∂K T ∂T ) P , is −0.023(±0.011) GPa K −1 for MgSiO 3 perovskite. Using these new results, we examine the constraints imposed by α V and ( ∂K ∂T ) P on the Fe (Mg + Fe) and (Mg + Fe) Si ratios for the lower mantle. For a temperature of 1800 K at the foot of an adiabat (zero depth), these results indicate an overall iron content of Fe (Mg + Fe) = 0.12(1) for a lower mantle composed of perovskite and magnesiowustite. Although the (Mg + Fe) Si ratio is very sensitive to the thermoelastic parameters of the perovskite and it is tentatively constrained between 1.4 and 2.0, these results indicate that it is unlikely for the lower mantle to have a perovskite stoichiometry.

Elastic properties of hydrous ringwoodite (γ-phase) in Mg2SiO4

Abstract Single-crystal elastic properties of hydrous ringwoodite are reported for samples that were synthesized at 19 GPa and 1300°C. The Mg/Si ratio is determined to be ∼1.95 by EPMA, which is slightly lower than that of ideal anhydrous ringwoodite. The H 2 O content determined by SIMS is ∼2.2 wt%, resulting in the stoichiometry Mg 1.89 Si 0.97 O 4 H 0.33 . The lattice parameter ( a =8.0786±4 A) and elastic constants were determined from a single crystal with X-ray diffractometry and Brillouin scattering spectroscopy. The crystal structure is cubic Fd3m, with a unit cell volume which is 0.51% larger than that of the anhydrous ringwoodite. The adiabatic single-crystal elastic moduli of hydrous ringwoodite, in GPa, are: C 11 =281±6, C 44 =117±4, C 12 =92±5. The isotropic properties of hydrous ringwoodite are K VRH =155±4 and G VRH =107±3 which are about 16 and 10% smaller than those of anhydrous ringwoodite. Thus hydrous ringwoodite, if present, drastically reduces the seismic velocity in the mantle transition zone relative to anhydrous ringwoodite. In addition, our results show that the anisotropy is enhanced relative to anhydrous ringwoodite. Using the present results, we discuss the 520 km seismic discontinuity in a wet mantle transition zone.

Single-Crystal Elastic Properties of the Modified Spinel (Beta) Phase of Magnesium Orthosilicate

The single-crystal elastic moduli of the modified spinel structure (beta phase) of magnesium orthosilicate (Mg2SiO4) have been measured by Brillouin spectroscopy under ambient conditions. Single crystals with dimensions up to 500 micrometers were grown at 22 gigapascals and 2000�C over a period of 1 hour. Growth of crystals larger than 100 micrometers was achieved only when the pressure was within 5 percent of the pressure of the phase boundary separating the beta- and gamma-phase stability fields. A comparison of the elastic properties of the modified spinel phase with those of the olivine phase suggests that the 400-kilometer seismic discontinuity in the earths mantle can be described by a mantle with 40 percent olivine. These results confirm that the 400-kilometer discontinuity can be due to the transition from olivine to modified spinel. The amount of olivine that must be present is less than that in a pyrolite model, although the results do not exclude pyrolite as a possible mantle model.

Thermal equation of state of CaSiO3 perovskite

A comprehensive pressure-volume-temperature data set has been obtained for CaSiO3 perovskite up to 13 GPa and 1600 K, using synchrotron X ray diffraction with a cubic-anvil, DIA-6 type apparatus (SAM-85). For each volume measurement, nonhydrostatic stress is determined from the relative shift in the diffraction lines of NaCl, within which the sample was embedded. Heating to above 973 K greatly reduced the strength of NaCl (to below 0.05 GPa), making the measurements hydrostatic. At room temperature the cubic perovskite structure remains metastable at pressures as low as 1 GPa, below which the sample transforms into an amorphous phase as indicated by a large background, a marked decrease in diffraction signals, and an anomalous volume decrease of the remaining crystalline phase. Because our experimental uncertainties are significantly smaller than those in previous measurements, the new data provide a tighter constraint on the zero pressure bulk modulus for CaSiO3 perovskite. A new set of room temperature equation of state parameters are identified so that both our data and the diamond cell data of Mao et al. [1989] are compatible [KT0 = 232(8) GPa, K′T0 = 4.8(3), and V0 = 45.58(4) A3]. Volume measurements along several isotherms under both stable and metastable pressure conditions allow isochoric and isobaric interpolations within the range of experimental pressure and temperature conditions. Analyses using various approaches yielded consistent results for (∂KT/∂T)P of −0.033(8) GPa K−1, and (∂α/∂P)T of −6.3 × 10−7 GPa−1 K−1, with a zero-pressure thermal expansion α0 of 3.0 × 10−5 K−1. The thermal pressure is found to be virtually independent of volume, and thus the Anderson-Gruneisen parameter δT = K′T0 = 4.8. These results are used to predict the bulk modulus and density of CaSiO3 perovskite under lower mantle conditions. Along an adiabat with the foot temperature of 2000 K, the density of the perovskite agrees with that of the preliminary reference Earth model (PREM) within 1% throughout the lower mantle. The bulk modulus shows a smaller pressure dependence along the adiabat; it matches that of PREM at the top of the lower mantle but is about 10% too low near the core-mantle boundary.

Elasticity of diopside

The thirteen single-crystal elastic moduli for diopside as determined by the acoustic technique based on Brillouin scattering are: c11=2.23, c22=1.71, c33=2.35, c44=0.74, c55=0.67, c66=0.66, c12=0.77, c13=0.81, c15=0.17, c23=0.57, c25=0.07, c35=0.43, c46=0.073. The Reuss bound of the adiabatic bulk and shear moduli calculated from these data are Ks=1.08 Mbar and G=0.651 Mbar. The room-pressure isothermal bulk modulus, KT, and the pressure derivative of the bulk modulus, K′T have also been determined on a four-circle diffractometer, from a single crystal mounted in a gasketed opposed-anvil diamond cell, giving values of KT=1.13 Mbar and K′T=4.8. The principal axes of the strain ellipsoid, calculated from the elastic moduli and observed in the static compression data, are identical, and the linear compressibilities are in reasonable agreement. The single-crystal elastic moduli can be correlated with the structural features of diopside.

Elasticity of orthoenstatite

Abstract Elastic constants of orthoenstatite have been determined from Brillouin-scattering measurements. They are c 11 = 2.247, c 22 = 1.779, c 33 = 2.136, c 44 = 0.776, c 55 = 0.759, c 66 = 0.816, c 23 = 0.527, c 31 = 0.541 and c 12 = 0.724 Mbar. Each elastic constant is uniquely defined by the data. Acoustic velocities measured for two directions ultrasonically on the same samples are within 1% of those determined from Brillouin-scattering spectra.

Yield strength at high pressure and temperature

Yield strength is measured at high pressure and temperature using a large volume, high pressure apparatus (SAM85) with synchrotron radiation. A macroscopic deviatoric stress is manifest as a uniform deviatoric strain that is oriented by the geometry of the pressurizing medium. Microscopic deviatoric stress is identified as the elastic broadening of diffraction lines. The deviatoric stress reaches the yield point as evidenced by the uniformity, the saturation, and the temperature dependence of the deviatoric stress. Yield strengths, which correspond to the stress saturation level at a few per cent strain, are determined for NaCl and MgO up to 8 GPa and 1200°C. The results are consistent at room temperature with previous diamond anvil studies and demonstrate the effect of pressure on yield strength. These data demonstrate the feasibility of determining high pressure, high temperature yield strengths for mantle phases.

Elastic properties from acoustic and volume compression experiments

Abstract Hydrostatic compression data for a number of high-pressure phases of oxides and silicates, which have been studied independently by acoustic techniques, have been analyzed by least-squares fitting of the Birch-Murnaghan equation of state to determine the zero-pressure bulk modulus K0 and its pressure derivative K′0 for each material. The standard deviations of K0 and K′0 so determined are generally underestimated unless the experimental errors in the measurements of volume and pressure are explicitly included. When the values of K0 determined from the acoustic and compression techniques are consistent, test results for quartz and rutile demonstrate that constraining K0 to be equal to the acoustic value significantly improves both the accuracy and the precision of K′0 obtained from the compression data. Similar analyses for high-pressure phases (e.g., pyrope garnet and silicate spinels) indicate that by combining the acoustic and P-V data, the standard deviation of K′0 is typically reduced by a factor of three. Thus, we conclude that this approach does allow precise determinations of K′0 even when neither technique alone is able to resolve this parameter. For some materials, however, the P-V and acoustic experiments do not define mutually consistent values of K0, invalidating any combination of these data. The compression data for stishovite clearly exhibit run to run effects, and we infer that systematic errors are present in some of the P-V data which are responsible for many of the interlaboratory inconsistencies. Such systematic biases in the P-V data can at least be partially compensated for by performing several duplicate experimental runs.