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Bulk and shear moduli of polycrystalline samples of perovskites with different compositions across the CaTi[O.sub.3]-SrTi[O.sub.3] solid solution have been measured at ambient conditions and in-situ at high pressures by pulse-echo ultrasonic methods. The samples were prepared as dense pellets by hot pressing synthetic powders at ~7.5 GPa and -1000 [degrees]C. Any variations of bulk modulus due to phase transitions are small, but significant anomalies have been observed in the shear modulus at ambient conditions. These are associated with a sequence of symmetry changes Pm[??]m [right arrow] I4/mcm [right arrow] Pbcm [right arrow] Pnma with increasing CaTi[O.sub.3] content. Comparison with variations in elastic properties predicted using Landau theory suggests that a substantial part of the elastic softening observed in tetragonal samples could be due to anelastic contributions from transformation twin walls. This additional softening does not occur in orthorhombic samples, and the transition from tetragonal to orthorhombic symmetry results in a stiffening of the shear modulus. No overt evidence was found for a phase transition I4/mcm [left and right arrow] Pnma at high pressures in [Ca.sub.0.35][Sr.sub.0.65]Ti[O.sub.3] but small changes in the trends of both bulk and shear moduli in the range 2.5-3 GPa could be due either to a different transition or a change in compression mechanism. A Pm[??]m [left and right arrow] I4/mcm transition at ~2 GPa in [Ca.sub.0.05][Sr.sub.0.95]Ti[O.sub.3] shows the same form of softening as observed for the transition as a function of composition. A simple model of twin wall contributions to the compliance of tetragonal samples failed to match the observed variations that, alternatively, seem to follow [DELTA]G [varies] [q.sub.4] where [DELTA]G is the change in shear modulus and [q.sub.4] the driving order parameter for the Pm[??]m [left and right arrow] I4/mcm transition. Analogous elastic behavior is expected to occur in (Mg,Fe)Si[O.sub.3] and CaSi[O.sub.3] perovskites at high pressures and temperatures. Keywords: Elastic constants, phase transitions, CaTi[O.sub.3]-SrTi[O.sub.3] solid solution, anelasticity

We measured the sound velocity of wadsleyite (beta)-Mg(sub 0.88)Fe(sub 0.12)(sub 2)SiO(sub 4) GPa at room temperature using ultrasonic techniques in a uniaxial split-cylinder apparatus using a polycrystalline specimen hot-pressed at 14 GPa and 1200 degrees C. Bench-top velocity measurements yielded V(sub p) = 9.33(3) km/s and V(sub s) = 5.43(2) km/s; the calculated bulk modulus (K) and shear modulus (G) are 172(2) GPa and 106(1) GPa, respectively. These K and G values are indistinguishable from those for single crystal and polycrystalline specimens of Mg(sub 2)SiO(sub 4)-wadsleyite. Pressure derivatives of the bulk and shear moduli have been obtained by fitting the current experimental data to 9.6 GPa using third-order, finite strains equations, yielding K'(sub S0) = 4.6(1) and G'(sub 0) = 1.5(1). From comparison with previous data for similar specimens and techniques, we observe no effect of iron content on the pressure derivatives of either the bulk or shear moduli, within the limited compositional range investigated.

There has been a lack of data available for Si-rich garnets along the Py-Mj join until recently. A project undertook to synthesize a range of samples across the Py-Mj join using recently developed techniques, characterizing elastic behaviour. New sound velocity data for the pyrope end-member of garnet is reported and compared with previous studies.

A polycrystalline sample of MgSi[O.sub.3]-orthopyroxene was hot pressed at a pressure of 4 GPa and temperature of 975 [degrees] C in a multi-anvil apparatus. The recovered specimen has a bulk density within 1% of the X-ray density and compressional and shear wave velocities within 1% of the Hashin-Shtrikman averages of the isotropic velocities calculated from the single-crystal elastic moduli. Compressional and shear wave travel times were measured at pressures up to 10 GPa at room temperature using the phase comparison method of ultrasonic interferometry in a 1000 ton uniaxial split-cylinder apparatus (USCA-1000). The velocities and elastic moduli monotonically increase with pressure; discontinuous behavior is not observed. Both the compressional velocity and bulk modulus, however, exhibit pronounced non-linear dependence on pressure. Fitting a fourth-order Eulerian finite-strain equation of state yield values of the bulk modulus and its first and second pressure derivatives, [K.sub.0], = 104(2) GPa, [K[prime].sub.0] = 10.9(5), and [K[double prime].sub.0] = -1.6(2) [GPa.sup.-1]. In contrast, the shear velocity and modulus are linear with pressure, yielding values of [G.sub.0] = 74.9(1.5) GPa and [G[prime].sub.0] = 1.6(1), when fit to a third-order finite-strain equation of state. A P-V trajectory calculated from these continuous measurements of K vs. P to 8 GPa is in agreement with extant static compression data for this material, without requiring a discontinuous change in K at 4 GPa. The velocities of MgSi[O.sub.3]-orthopyroxene increase more rapidly with pressure than those for [Mg.sub.2]Si[O.sub.4]-olivine (especially for P-waves), such that these two mineral phases are virtually indistinguishable in their velocities at 200 km depth, unless the velocity-temperature dependence of the two phases is dramatically different.

We performed in-situ Raman spectroscopy and X-ray diffraction experiments at high temperature and ambient pressure to investigate the intrinsic anharmonic properties of [Beta]-[Mg.sub.2]Si[O.sub.4] and the mechanism and kinetics of its back-transformation to forsterite. High-temperature Raman spectra of [Beta]-[Mg.sub.2]Si[O.sub.4] and its back-transformed products were recorded up to 1200 K. [Beta]-[Mg.sub.2]Si[O.sub.4] persists metastably up to 800-900 K, and the Raman frequency shifts with temperature were determined. Between 800 and 1000 K, new peaks are observed at about 670 and 1020 [cm.sup.-1]. Above 1000 K, a direct transformation to forsterite occurs. The peaks that appear between 800 and 1000 K are attributed to a defective spinelloid that forms as an intermediate phase during the back-transformation of [Beta]-[Mg.sub.2]Si[O.sub.4] to forsterite. Similar features are observed in the Raman spectrum of partially transformed [Gamma]-[Ni.sub.2]Si[O.sub.4] heated at 1073 K and ambient pressure for 10 min. These results indicate that a two-step mechanism, possibly martensitic, is operative in the back-transformation of the [Beta]- and [Gamma]-phases to olivine at low to moderate temperatures and for a large overstepping of the equilibrium conditions. The kinetics of the [Beta]- to [Alpha]-[Mg.sub.2]Si[O.sub.4] back-transformation were monitored between 1023 and 1120 K at ambient pressure using X-ray powder diffraction. For the kinetic data obtained in air, two regimes are evident from an Avrami analysis. The first regime is characterized by an exponent n [approximately equal to! 2 for a low transformed fraction (X < 0.5); the second has n [approximately equal to] 1 for higher transformed fractions. For this second regime, an activation energy of 432 [+ or -] 64 kJ/mol is derived for the growth process from the kinetic data. A smaller data set collected in vacuum indicates much slower transformation rates and suggests a significant effect of the [O.sub.2] or [H.sub.2]O partial pressures on the kinetics. Intrinsic mode anharmonic parameters can be calculated from the Raman frequency shifts with temperature and used to correct vibrational heat capacity models for intrinsic anharmonic effects. These corrections are slightly higher for the [Beta]-phase than for forsterite but the difference is within the experimental error. This indicates that, within the resolution of our experiments, no significant effect of intrinsic anharmonicity on the location and slope of the [Alpha]-[Beta] phase transition can be predicted.

A modulated microstructure with mutually intersecting linear contrasts parallel to tetragonal planes, having a characteristic modulation wavelength between 150 and 300 Armstrong, is evident from a transmission electron microscopic analysis of Mg end-member majorite crystal prepared at 22 GPa and above 2350 degrees Celsius. A phase conversion in majorite from cubic to tetragonal, near 2350 degrees Celsius and possibly through the alignment of Mg and Si atoms, is responsible for the structural modulation.

The pressure dependence of the elastic wave velocities for hot-pressed, elastically isotropic polycrystals of the Β (modified spinel) phase of magnesium orthosilicate ([Mg.sub.2][SiO.sub.4]) has been determined at room temperature to [...]