Elasticity of CaTiO3, SrTiO3 and BaTiO3 perovskites up to 3.0 Gpa: the effect of crystallographic structure

Elasticity of CaTiO₃, SrTiO₃ and BaTiO₃ perovskites has been experimentally investigated as a function of pressure up to 3.0 GPa in a liquid-medium piston cylinder apparatus using a high precision ultrasonic interferometric technique. Specimens used are hot-pressed fine-grained (3–10 μm) polycrystalline aggregates with low porosity (<1.5%). Compressional and shear wave velocities and their pressure derivatives have been measured. The results are compared with previous studies on other perovskites and the role of structural transitions is examined. We find that the role of Ti-O₆ polyhedral tilting (such as observed in CaTiO₃) is small in the sense that a single well-defined general trend exists in perovskites with a wide range of tilting angles, although there is suggestion that cubic perovskites have slightly higher bulk modulus than orthorhombic perovskites. In contrast, cation-anion displacement that changes crystal symmetry from cubic to tetragonal in BaTiO₃ has very large effects on elasticity. This distortion significantly reduces the bulk modulus (but not much the shear modulus) and results in an unusually large pressure derivative of bulk modulus (dK/dP～10). A large change in elasticity in BaTiO₃ associated with the structural transition (without a significant volume change) is a clear example of the breakdown of the Birch's law between densities and elastic wave velocities.     

Grain growth in CaTiO3-perovskite + FeO-wüstite aggregates

Grain growth kinetics in CaTiO₃-perovskite + FeO-wüstite aggregates were studied at the conditions of T = 1223–1623 K, P = 0.1 MPa and P = 200 MPa. Starting samples were fabricated by hot-pressing mechanically mixed powders of CaTiO₃ + FeO with FeO = 0%, 1%, 3%, 6%, 10%, 20% and 100% by weight in a gas-medium apparatus at 1323 K and 300 MPa for 5 h. The increase of grain size (G) of CaTiO₃ with time (t) follows a growth law: G ⁿ −G ⁿ ₀ = κ·t(κ=κ₀exp(−(Q/RT)). Two grain growth regimes are observed at T < 1523 K and T ≥ 1523 K. For T < 1523 K, the best fits of the data to the growth law yield growth exponents of n = 2.2 ± 0.2, 3.0 ± 0.3 and 3.5 ± 0.3 for samples with FeO = 0%, 3% and 10% respectively. Under these conditions the rate constants, κ, obey an Arrhenius relation with Q = 206 ± 35 kJ/mol and 385 ± 65 kJ/mol for samples with FeO = 3% and 10%. Grain growth of CaTiO₃ becomes sluggish when FeO content exceeds 6%. For T ≥ 1523 K, the best fits of the data to the growth law yield n = 2.5 ± 0.2 for both samples with FeO = 3% and 10%. The activation energies (Q ) were determined as 71 ± 30 kJ/mol and 229 ± 45 kJ/mol for samples with FeO = 3% and 10%, respectively. The TEM observations show a remarkable difference in the distribution and geometry of FeO below and above 1523 K: nanometer-sized particles of FeO were observed along CaTiO₃ grain boundaries in samples annealed at T < 1523 K. No FeO particles were detected along CaTiO₃ grain boundaries in samples annealed at T ≥ 1523 K, but large clusters of FeO particles are observed locally indicating a fast separation of FeO from CaTiO₃. Thus we conclude that the slow growth rate of CaTiO₃ at T < 1523 K is due to the pinning by FeO particles at grain boundary, and that the change of grain growth kinetics in CaTiO₃ at T ≥ 1523 K may relate to the separation of FeO from CaTiO₃, which we interpret as due to the phase transformation of CaTiO₃ at around 1523 K. Received: 19 June 1998 / Revised, accepted: 24 March 1999     

Electrical conductivity of talc aggregates at 0.5 GPa: influence of dehydration

Electrical conductivity of talc was measured at 0.5 GPa and ~473 to ~1,300 K by using impedance spectroscopy both before and after dehydration. Before dehydration, the electrical conductivity of talc increased with temperature and is ~10^?4 S/m at 1,078 K. After dehydration, most of the talc changed to a mixture of enstatite and quartz and the total water content is reduced by a factor 6 or more. Despite this large reduction in the total water content, the electrical conductivity increased. The activation enthalpy of electrical conductivity (~125 kJ/mol) is too large for the conduction by free water but is consistent with conduction by small polaron. Our results show that a majority of hydrogen atoms in talc do not enhance electrical conductivity, implying the low mobility of the hydrogen atoms in talc. The observed small increase in conductivity after dehydration may be attributed to the increase in oxygen fugacity that enhances conductivity due to small polaron.     

Grain-growth kinetics in wadsleyite: Effects of chemical environment

Grain-growth kinetics in wadsleyite was investigated using a multianvil high-pressure apparatus. Fine-grained wadsleyite aggregates were synthesized by isostatic hot-pressing and were subsequently annealed under high pressure and temperature in a controlled chemical environment. Wadsleyite samples show normal grain-growth characterized by a log-normal grain-size distribution following the relation, where n is a constant, L the grain-size at time t, L₀ the grain-size at time t = 0 and k is a rate constant that depends on temperature T and chemical environments (fO₂: oxygen fugacity in Pa, C_OH: water content in H/10⁶Si) as:

     

Some Issues on the Strength of the Lithosphere

The strength of the oceanic and continental lithosphere has important controls on some of the major geological processes on earth including the operation of plate tectonics and the long-term stability of the continental roots.However,explaining these major geological features from the experimental and theoretical studies on the strength of rocks is challenging and some of the existing models for the strength of the lithosphere do not explain these main geological observations.A brief review is provided to s...     

The misorientation index: Development of a new method for calculating the strength of lattice-preferred orientation

Using orientation data from experimentally deformed olivine, we explore some practical problems with the J-index, a commonly applied measure of fabric strength. We show that the J-index is highly dependent on several factors, including the number of discrete data in the orientation distribution function (ODF), and arbitrary numerical parameters specified for its calculation. Because of this non-uniqueness, we conclude that the J-index is difficult to interpret and should only be applied with caution. As an alternative to the J-index, we propose a new measure of fabric strength that is based on the distribution of uncorrelated misorientation angles. This “M-index” is shown to be insensitive to the parameters specified for its calculation. For typical deformed olivine samples, we show that 150 discrete data are adequate to quantify fabric strength using the M-index technique. The M-index correlates well with seismic anisotropy, particularly for materials of the same fabric type. Therefore, we conclude that the M-index technique is well-suited for the quantification of fabric strength and the comparison of like materials.     

Core formation and chemical equilibrium in the Earth—I. Physical considerations

Current models of planetary formation suggest a hierarchy in the size of planetesimals from which planets were formed, causing formation of a hot magma ocean through which metal-silicate separation (core formation) may have occurred. We analyze chemical equilibrium during metal-silicate separation and show that the size of iron as well as the thermodynamic conditions of equilibrium plays a key role in determining the chemistry of the mantle (silicates) and core (iron) after core formation. A fluid dynamical analysis shows that the hydrodynamically stable size of iron droplets is less than 10⁻² m for which both chemical and thermal equilibrium should have been established during the separation from the surrounding silicate magma. However, iron may have been separated from silicates as larger bodies when accumulation of iron on rheological boundaries and resultant large scale gravitational instability occurred or when the core of colliding planetesimals directly plunged into the pre-existing core. In these cases, iron to form the core will be chemically in dis-equilibrium with surrounding silicates during separation. The relative role of equilibrium and dis-equilibrium separation has been examined taking into account of the effects of rheological structure of a growing earth that contains a completely molten near surface layer followed by a partially molten deep magma ocean and finally a solid innermost proto-nucleus. We show that the separation of iron through a completely molten magma ocean likely occurred with iron droplets assuming a hydrodynamically stable size ( 10⁻² m) at chemical equilibrium, but the sinking iron droplets are likely to have been accumulated on top of the partially molten layer to form a layer (or a lake) of molten iron which sank to deeper portions as a larger droplet. The degree of chemical equilibrium during this process is determined by the size of droplets which is in turn controlled by the size and frequency of accreting planetesimals and the rheological properties of silicate matrix. For a plausible range of parameters, most of the iron that formed the core is likely to have been separated as large droplets or bodies and chemical equilibrium with silicate occurred only at relatively low temperatures and pressures in a shallow magma ocean or in their parental bodies. However, a small portion of iron that separated as small droplets was in chemical equilibrium with silicate at high temperatures and pressures in a deep magma ocean during the later stage of core formation. Therefore the chemistry of the core is mostly controlled by the chemical equilibrium with silicates at relatively low temperatures and pressures, whereas the chemistry of the mantle controlled by the interaction with iron during core formation is likely to have been determined mostly by the chemical equilibrium with a small amount of iron at high temperatures and pressures.