Robert C. Liebermann

In situ X-ray observations of the coesite-stishovite transition: reversed phase boundary and kinetics

Using a DIA-type, cubic-anvil, high-pressure apparatus (SAM-85) in conjunction with in situ X-ray diffraction, we have investigated phase relations between coesite and stishovite up to 12 GPa and 1530 °C using synthetic powders of the two phases as the starting materials. The phase transition between coesite and stishovite was identified by observing the first appearance of a phase that did not already exist or by a change in the relative intensity of the two patterns. In most experiments, the diffraction patterns on samples were collected within 10 minutes after reaching a pressure and temperature condition. On this time scale, two phase boundaries associated with the coesite-stishovite transition have been determined: (1) for the stishovite-to-coesite transition, observations were made in the temperature range of 950–1530 °C, and (2) for the coesite-to-stishovite transition from 500 to 1300 °C. These observations reveal that there exists a critical temperature of about 1000 °C to constrain the coesite-stishovite equilibrium phase boundary. Above this temperature, both boundaries are linear, have positive dP/dT slopes, and lie within a pressure interval of 0.4 GPa. Below this temperature, the dP/dT slope for the stishovite-to-coesite phase boundary becomes significantly larger and that for the coesite-tostishovite phase boundary changes from positive to negative. As a result, an equilibrium phase boundary can only be determined from the results above 1000 °C and is described by a linear equation P (GPa)=6.1 (4)+ 0.0026 (2) T (°C). This dP/dT slope is in good agreement with that of Zhang et al. (1993) but more than twice that of Yagi and Akimoto (1976). For the kinetics of the phase transition, preliminary rate data were obtained for the stishovite-to-coesite transition at 1160 and 1430 °C and are in agreement with the simple geometric transformation model of Avrami and Cahn.

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.

Phase equilibria and elastic properties of a pyrolite model for the oceanic upper mantle

The upper-mantle source regions of basaltic magmas in oceanic regions contain both H2O and CO2. If the water content of the upper-mantle peridotite is ( orthopyroxene > garnet > clinopyroxene mineralogy. Temperatures at the top of the LVZ are in the range 1000–1150°C. The lithosphere thickens with age and distance from the mid-oceanic ridges, reaching a stable configuration at a thickness of 85–95 km for t > 80 m.y. With increasing age of the oceanic crust, the velocities in the lithosphere increase, the LVZ becomes thinner, and the velocity contrast between the lithosphere and the LVZ decreases. The pyrolite petrological model and its velocity profile satisfactorily account for most of the geophysical data for various age provinces in oceanic regions.

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.

Elasticity of pyroxene-garnet and pyroxene-ilmenite phase transformations in germanates

Abstract Ultrasonic data for the velocities of the low- and high-pressure polymorphs of germanate compounds undergoing the pyroxene-garnet (CaGeO 3 , CdGeO 3 ) and pyroxene-ilmenite (MgGeO 3 , MnGeO 3 ) phase transformations have been determined as a function of pressure to 7.5 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 60 kbar. These transitions are characterized by the following velocity (υ)-density (ρ) relationships: (1) the velocity jumps are comparable in percentage magnitude to the density jumps, with the exception of shear velocity for the pyroxene-ilmenite transition; (2) the ratio (υ p /υ s ) of the compressional to shear velocity is constant or increases slightly across the transitions; and (3) low slopes (linear or logarithmic) on υ-ρ diagrams. The observed relationships (1) and (2) are similar to those for the coesite-stishovite transition, but are in marked contrast with those from the olivine-spinel and olivine-beta phase transformations. Coordination changes are thus important factors to be considered in establishing velocity-density systematics governing polymorphic transitions. The υ-ρ changes across the pyroxene-garnet and pyroxene-ilmenite transitions are also distinctly smaller than those produced by compression or thermal expansion of a homogeneous material or by varying composition at constant mean atomic weight. Systematic trends in the elastic properties for isostructural sequences support the concept of germanates as models for the elasticity of their silicate analogues; this scheme is applied to estimate the bulk moduli of the garnet (1.80 Mbar) and ilmenite (2.11 Mbar) polymorphs of MgSiO 3 .

Elasticity of single crystal pyrope and implications for garnet solid solution series

Abstract The elastic moduli of a synthetic single crystal of pyrope (Mg 3 Al 2 Si 3 O 12 ) have been determined using a technique based on Brillouin scattering. These results are used in an evaluation of the effect of composition on the elastic properties of silicate garnet solid solution series (Mg, Fe, Mn, Ca) 3 (Al, Fe, Cr) 2 Si 3 O 12 . In the pyralspites (Mg FeMn aluminum garnets), for which a large amount of data is available, this analysis indicates that the bulk modulus K is independent of the Fe 2+ /Mg 2+ ratio, which is similar to the behavior observed in olivines and pyroxenes. However, the shear modulus μ of the garnets increases by 10% from the Mg to the Fe end member, in contrast to the decrease of μ with Fe content which is observed in olivines and pyroxenes. This contrasting behavior is most probably related to the oxygen coordination of the cation site occupied by Mg 2+ and Fe 2+ in these different minerals.

In situ high P‐T X ray diffraction studies on three polymorphs (α, β, γ) of Mg2SiO4

Unit cell volumes of the beta (β) and spinel (γ) phases (Mg2SiO4) have been measured under simultaneous high pressure and high temperature using synchrotron X ray radiation, in a cubic anvil apparatus. With volume-temperature data at constant pressure, we determine the average volume thermal expansion coefficients of the β phase from 724 to 872 K at 7.6 GPa to be 2.28(±0.45)×10−5/K and of the γ phase from 759 to 962 K at 9.8 GPa to be 1.71(±0.14)×10−5/K. Thermodynamic relations are used to constrain the temperature derivative of the isothermal bulk modulus (KT) from the high-pressure thermal expansion data: (∂KT/∂T)P is found to be −2.7(±0.5)×10−2 GPa/K for the β phase and −2.8(±0.3)×10−2 GPs/K for the γ phase. Unit cell volumes of the olivine (α) phase, back-transformed from the β and γ phases at high temperatures, have been measured under pressure at temperatures above the Debye temperature; using thermal pressure equations, we find (∂KT/∂T)P for the α phase to be −2.1(±0.2)×10−2 GPa/K. These new data on the temperature derivatives of the bulk modulus for the three phases are consistent with an upper mantle containing 60 to 65% olivine and the absence of a velocity signature for the β to γ phase transition near 520 km depth.

The elastic properties of (Mg x Fe1?x )O solid solutions

The velocities of compressional (Vp) and shear (Vs) waves in five well-characterized polycrystalline aggregates of (MgxFe1−x)O (0.85≧x>0.23) have been measured as functions of hydrostatic pressure (to 6 kbar) using the techniques of ultrasonic pulse transmission and super-position. Both velocities decrease systematically with increasing iron content. The elastic properties of stoichiometric FeO are inferred by inverting the solid solution data using a model in which the single crystal compliances (sij) vary linearly with the volume fraction of either end member. This model, along with identification of the aggregate moduli with the arithmetic average of the Hashin-Shtrikman bounds, may be used to describe the variation of both bulk (Ks) and shear modulus (μs) with composition for polycrystalline aggregates of phases of arbitrary symmetry. For the case of bulk modulus of an isotropic aggregate of crystals of cubic symmetry, the present model yields the formula first proposed by Liu (1968). The isotropic elastic moduli of FeO thus obtained (Ks=1.82±0.05 Mbar, μs=0.59±0.02 Mbar) are consistent with the wüstite data of Mizutani et al. (1972) but inconsistent with bulk moduli derived from static compression data by Mao et al. (1969) and Rosenhauer et al. (1976). An alternative description of the variation of μ with x based on consideration of the solid solutions as two-phase aggregates is also presented. The observed differences in elastic moduli between MgO (Ks=1.63 Mbar, μs=1.31 Mbar) and FeO (Ks=1.82 Mbar, μs=0.59 Mbar) are consistent with the effects of Mg/Fe substitution in other oxide and silicate crystal structures.

Elasticity of aluminate, titanate, stannate and germanate compounds with the perovskite structure

Abstract Ultrasonic data for the velocities of a large number of perovskite-structure compounds have been determined as a a function of pressure to 6 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 100 kbar in solid-media devices: ScAlO3, GdAlO3, SmAlO3, EuAlO3, YAlO3, CdTiO3, CdSnO3, CaSnO3 and CaGeO3. The elasticity data for these orthorhombic and cubic perovskites define systematic patterns on bulk modulus (KS)-volume (VO) and bulk sound velocity (υφ—mean atomic weight (M) diagrams which are insensitiv to the details of cation chemistry and crystallographic structure. These isostructural trends are used to estimate KS = 2.5 ± 0.3 Mbar and υφ = 7.9 ± 0.4 km/s for the perovskite polymorph of MgSiO3. On a Birch diagram of veloc vs. density, the perovskite data define linear trends which lead to erroneous estimates of velocity for MgSiO3 unless specific account is taken of ionic radius effects in isomorphic substitutions.

Sound velocities of olivine and beta polymorphs of Mg2SiO4 at Earth's transition zone pressures

Sound velocities of olivine (α) and beta (β) polymorphs of Mg2SiO4 are measured to P > 12 GPa at room temperature on polycrystalline samples in a multi-anvil apparatus using ultrasonic interferometry. The new velocity data for olivine are lower by 1% for P waves and 2% for S wave at transition zone pressures than extrapolations of low pressure (<1 GPa) data. However, the elastic bulk (KS) and shear (G) moduli for the polycrystalline olivine exhibit good agreement to 10 GPa with recent Brillouin scattering and ultrasonic data for single crystals. The velocity data for the polycrystalline beta phase at 12 GPa agree within 1% with Eulerian finite strain extrapolations of previous data by Gwanmesia et al. (1990b) for similar specimens. The pressure derivatives of the elastic moduli calculated by linear fittings to KS and G vs. pressure yield K0′ = 4.4 and G0′ = 1.3 for the olivine and K0′ = 4.2 and G0′ = 1.5 for the beta phases. The isothermal velocity contrast at room temperature between these two phases, (Vβ-Vαrpar;/Vα decreases systematically with increasing pressure, reaching 8.0% for P wave and 11.3% for S wave at pressures equivalent to 410 km depth.