Thomas J. Shankland

Laboratory‐based electrical conductivity in the Earth's mantle

Recent laboratory measurements of electrical conductivity of mantle minerals are used in forward calculations for mantle conditions of temperature and pressure. The electrical conductivity of the Earths mantle is influenced by many factors, which include temperature, pressure, the coexistence of multiple mineral phases, and oxygen fugacity. In order to treat these factors and to estimate the resulting uncertainties, we have used a variety of spatial averaging schemes for mixtures of the mantle minerals and have incorporated effects of oxygen fugacity. In addition, to better calculate lower mantle conductivities, we report new measurements for electrical conductivity of magnesiowustite (Mg0.89Fe0.11)O. Because the effective medium theory averages lie between the Hashin-Shtrikman bounds for the whole mantle, a laboratory-based conductivity-depth profile was constructed using this averaging scheme. Comparison of apparent resistivities calculated from the laboratory-based conductivity profile with those from field geophysical models shows that the two approaches agree well.

The electrical conductivity of an isotropic olivine mantle

In order to extend the useful temperature range of interpretation of olivine electrical conductivity σ we have used the nonlinear iterative Marquardt technique to fit experimental data over the range 720°–1500°C to the parametric form σ = σ1e−A1/kT + σ2e−A2/kT, where k is Boltzmanns constant and T is absolute temperature. The model describes conduction by migration of two different thermally activated defect populations with activation energies A1 and A2, and preexponential terms σ1 and σ2 that depend on number of charge carriers and their mobility and that may be different for each crystallographic direction. A combined interpretation of recent high (San Carlos olivine) and low (Jackson County dunite) temperature measurements has been made that demonstrates that a single activation energy A1 for all three crystallographic directions adequately fits the data. The parametric fits show that the high-temperature conduction mechanism has far greater anisotropy than the low-temperature mechanism, consistent with previous assignments to ionic and electronic conduction, respectively. The geometric mean of the conductivity in the three directions is approximately –¯=102.402e-1.60eV/kT+109.17e-4.25eV/kT S/m and is presented as a model for isotropic olivine, SO2, appropriate from 720°C to above 1500°C, at oxygen fugacities near the center of the olivine stability field. It is observed that the magnitudes of σ1 for the three crystal directions are similar to the ratios of the inter-ionic distances between the M1 magnesium sites in olivine, to within 5%, consistent with Fe3+ preferring the M1 site below 1200°C.

Pressure effect on electrical conductivity of mantle olivine

Abstract We report new measurements of electrical conductivity of olivine that were made in a multi-anvil press using solid buffers (Mo–MoO2) to stabilize oxygen partial pressure. The temperature range was 1000°C–1400°C and the pressure range was 4–10 GPa. When pressure effects are interpreted as activation volumes in the Arrhenius equation, they yield values of order 0.6±0.6 cm3/mole. Values of the pre-exponential factor σ0 are of the order of hundreds of S/m, and the zero-pressure activation energy is about 1.5 eV, in agreement with laboratory measurements at lower pressure conditions. In addition, we analyzed older literature data, which produced a similar result but with larger variation. The common practice of assuming that the pressure effect on electrical conductivity of olivine in the Earths upper mantle depends weakly on pressure has rested on uncertain grounds. These new observations suggest that for upper mantle conditions (depths of 80–200 km) neglecting pressure effects on olivine conductivity is justified. A weak pressure effect also supports the small polaron (Fe3+) model as the dominant conduction mechanism, although the mainly positive activation volumes argue for a component of lattice deformation. When applied to the depth range 200–400 km in the Earth, the laboratory data yield conductivities of order 10−2 S/m, slightly lower than the range of geophysical conductivity profiles but well within this range after allowing for probable effects of oxygen activity and temperature uncertainty.

Electrical conduction in rocks and minerals: Parameters for interpretation

Abstract Recent studies of electrical properties have clarified the important parameters governing electrical conductivity in minerals — temperature, oxygen fugacity, stoichiometry, iron content — and in porous rocks — shape and interconnections of fluid-filled pore spaces. These parameters are discussed in terms of: (1) how they contribute to bulk conduction mechanisms within minerals; and (2) how they pertain to the conditions of rocks in situ.

Thermoelastic equation of state of jadeite NaAlSi2O6: An energy‐dispersive Reitveld Refinement Study of low symmetry and multiple phases diffraction

We report the first measurement of a complete set of thermoelastic equation of state of a clinopyroxene mineral. We have conducted an in situ synchrotron x-ray diffraction study of jadeite at simultaneous high pressures and high temperatures. A modified Rietveld profile refinement program has been applied to refine the diffraction spectra of low symmetry and multiple phases observed in energy dispersive mode. Unit cell volumes, measured up to 8.2 GPa and 1280 K, are fitted to a modified high-temperature Birch-Murnaghan equation of state. The derived thermoelastic parameters of the jadeite are: bulk modulus K=125 GPa with assumed pressure derivative of bulk modulus K′ = ∂K/∂P = 5.0, temperature derivative of bulk modulus , and volumetric thermal expansivity α = a + bT with values of a=2.56×10−5K−1 and b=0.26x10−8 K−2. We also derived thermal Gruneisen parameter γth=1.06 for ambient conditions; Anderson-Gruneisen parameter δTo=5.02, and pressure derivative of thermal expansion ∂α/∂P = −1.06×10−6 K−1 GPa−1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at five constant pressures of 1.0, 2.5, 4.0, 5.5, and 7.5 GPa are calculated. The derived pressure dependence of thermal expansion is: Δα/ΔP = −0.97×10−6K−1GPa−1, in good agreement with the thermodynamic relations.

Homogeneity and temperatures in the lower mantle

Abstract Using the three global seismic profiles, model 1066B, PEM, and PREM, we have calculated adiabatic temperature profiles, corrections arising from the differences between adiabatic self compression on the seismic and convective time scales, and the superadiabatic profiles from inhomogeneity. The three adiabatic temperature profiles are virtually identical and provide a net change of 600 K across the lower mantle; the net superadiabatic temperature changes from inhomogeneity are also similar and provide a further 200 K. If elastic relaxation corrections of 400–700 K are included in addition to a thermal boundary layer arising from heat transfer from the core to the base of the mantle, then it is possible to construct mantle profiles beginning with 1600°C at 670 km and yielding temperatures at the core-mantle boundary within the range 3300 ± 500°C inferred from shock melting experiments on iron.

Electrical conductivity of orthopyroxene and its high pressure phases

Electrical conductivity of orthopyroxene, clinopyroxene, and ilmenite + garnet with the same starting material San Carlos orthopyroxene (Mg 0.92 Fe 0.08 )SiO 3 containing 2.89 % Al 2 O 3 by weight were measured within their respective stability fields in a multi-anvil press. In the formula for conductivity σ = σ 0 exp(-ΔH/kT), pre-exponential factors σ 0 of orthopyroxene, clinopyroxene, and ilmenite + garnet are 5248, 1778, 2239 S/m, respectively, and the activation enthalpies are 1.80, 1.87 and 1.66 eV, respectively. These results are required for defining a laboratory-based conductivity-depth profile of the upper mantle.

Increase of electrical conductivity with pressure as an indicator of conduction through a solid phase in midcrustal rocks

Rocks freshly cored from depth at the German continental scientific drilling site (KTB) offer an opportunity to study transport properties in relatively unaltered samples resembling material in situ. Electrical conductivity σ was measured to 250 MPa pressure, and room temperature on 1 M NaCl-saturated amphibolites from 4 to 5 km depth. An unexpected feature was an increase of σ with pressure P that appeared (anisotropically) in most samples. To characterize this behavior, we fitted the linear portion of log σ versus P to obtain two parameters: the slope dlogσ/dP (of order 10−3 MPa−1) and the zero-pressure intercept σ0. Samples of positive and negative slopes behave differently. Those having negative slopes show strong correlation of σ0 with a fluid property (permeability). This behavior indicates that fluids exert the dominant control on σ0 at low pressure when σ0 is greatest, which is typical behavior observed in previous studies. In contrast, samples with positive slopes lack a correlation of σ0 with permeability, indicating that fluids are less important to positive pressure behavior. Another result is that samples of negative dlogσ/dP have uncorrelated slopes and initial conductivities. In significant contrast, samples of positive slopes have the greatest P dependence for lowest initial conductivity σ0, that is, the less fluid, the more positive dlogσ/dP. Hence positive dlogσ/dP is consistent with reconnection of solid phases into a conductive texture better resembling that of rock at depth. Detailed examination of one sample by electron probe and scanning electron microscope reveals the presence of carbon on internal cleavage surfaces in amphibole, the most abundant mineral present. Thus carbon probably dominates the reconnection, but total σ still involves fluids as well as Fe-Ti oxides. For the KTB location it is inferred that the reason mid to deep crustal electrical conductivities modeled from geophysical measurements are so much higher than conductivities of silicates is the presence of interconnected good conductors involving films of carbon on surfaces and other solid phases.

General relationships among sound speeds: II. Theory and discussion

Abstract The dependence of bulk sound speed Vφ upon mean atomic weight m and density ρ can be expressed in a single equation: V φ =Bρ λ ( m 0 m [ 1 2 +λ(1−c)] ( km/sec ) Here B is an empirically determined “universal” parameter equal to 1.42, m 0 = 20.2 , a reference mean atomic weight for which well-determined elastic properties exist, and λ = 1.25 is a semi empirical parameter equal to γ − 1 3 where γ is a Gruneisen parameter. The constant c = (∂ ln VM/∂ ln m ) X , where VM is molar volume, is in general different for different crystal structure series and different cation substitutions. However, it is possible to use cFe = 0.14 for Fe2+Mg2+ and GeSi substitutions and cCa ≅ 1.3 for CaMg substitutional series. With these values it is pos to deduce from the above equation Birchs law, its modifications introduced by Simmons to account for Ca-bearing minerals, variations in the seismic equation of state observed by D.L. Anderson, and the apparent proportionality of bulk modulus K to VM−4.

Laboratory study of linear and nonlinear elastic pulse propagation in sandstone

Linear and nonlinear elastic wave pulse propagation experiments were performed in sandstone rods, both at ambient conditions and in vacuum. The purpose of these experiments was to obtain a quantitative measure of the extremely large nonlinear response found in microcracked (i.e., micro‐inhomogeneous) media like rock. Two rods were used, (1) a 2‐m‐long, 5‐cm‐diam rod of Berea sandstone (with embedded detectors) used in previously published experiments and (2) a somewhat smaller 1.8‐m‐long, 3.8‐cm‐diam rod. In the earlier experiments, wave scattering from the embedded detectors was a critical problem. In most of the experiments reported here, this problem was avoided by mounting accelerometers directly to the outside surface of the rod. Linear results show out of vacuum attenuations varied from 1.7 Np/m at 15 kHz (Q=10) for the large rod to 0.4 Np/m at 15 kHz (Q=55) for the small rod; attenuations for the small rod in vacuum were much less, typically about 0.15 Np/m at 15 kHz (Q=150). Wave velocities ranged...