Lithium transition metal phosphates have become of great interest as storage cathodes for rechargeable lithium batteries because of their high energy density, low raw materials cost, environmental friendliness and safety. Their key limitation has been extremely low electronic conductivity, until now believed to be intrinsic to this family of compounds. Here we show that controlled cation non-stoichiometry combined with solid-solution doping by metals supervalent to Li+ increases the electronic conductivity of LiFePO4 by a factor of approximately 10(8). The resulting materials show near-theoretical energy density at low charge/discharge rates, and retain significant capacity with little polarization at rates as high as 6,000 mA x g(-1). In a conventional cell design, they may allow development of lithium batteries with the highest power density yet.

Electronically conductive phospho-olivines as lithium storage electrodes

Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Theory of Reflectance and Emittance Spectroscopy

The thermodynamic properties of 254 end-members, including 210 mineral end-members, 18 silicate liquid end-members and 26 aqueous fluid species are presented in a revised and updated internally consistent thermodynamic data set. The PVT properties of the data set phases are now based on a modified Tait equation of state (EOS) for the solids and the Pitzer & Sterner (1995) equation for gaseous components. Thermal expansion and compressibility are linked within the modified Tait EOS (TEOS) by a thermal pressure formulation using an Einstein temperature to model the temperature dependence of both the thermal expansion and bulk modulus in a consistent way. The new EOS has led to improved fitting of the phase equilibrium experiments. Many new end-members have been added, including several deep mantle phases and, for the first time, sulphur-bearing minerals. Silicate liquid end-members are in good agreement with both phase equilibrium experiments and measured heat of melting. The new dataset considerably enhances the capabilities for thermodynamic calculation on rocks, melts and aqueous fluids under crustal to deep mantle conditions. Implementations are already available in thermocalc to take advantage of the new data set and its methodologies, as illustrated by example calculations on sapphirine-bearing equilibria, sulphur-bearing equilibria and calculations to 300 kbar and 2000 °C to extend to lower mantle conditions.

An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids

The elastic moduli of a solid permeated with an isotropic distribution of flat cracks have been calculated from the energy of a single crack by use of a self-consistent approximation. The results are applicable for a dense network of cracks and give physically reasonable results up to the point that the shear modulus vanishes. Results for both circular and elliptical cracks are essentially the same if the crack density is characterized by 2N〈A2/P〉/π, where N is the number of cracks per unit volume, A is the area of crack, and P is the perimeter of cracks; for circular cracks of radius a this becomes N〈a3〉. This crack density parameter can be related quantitatively to crack traces observed in thin section. Results for completely dry or saturated cracks, for mixtures of dry and saturated cracks, and for cracks saturated with a compressible fluid are presented. For all cases, both seismic wave velocities decrease with increasing crack density. The velocity ratio VP/VS decreases for dry cracks and increases for saturated cracks. For the analysis of data a plot of VP/VS versus VS uniquely specifies the crack density. Comparison of the theory with wave velocities measured in laboratory rock samples demonstrates its validity for large crack densities. Interpretation of velocity changes before the San Fernando earthquake indicates that the region contained a substantial density of cracks at all times, that the anomalous decrease in VP/VS was due to the vaporization of pore fluid in nearly all of the previously saturated cracks without the introduction of new dry cracks, and that during the period of the recovery of the velocities to previous values the number of cracks in the region away from the epicentral zone decreased as they were resaturated, whereas the crack density increased following resaturation in the epicentral zone. Such use of the theoretical results may be useful in further investigations of preseismic phenomena.

Seismic velocities in dry and saturated cracked solids

In this paper, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically homogeneous and heterogeneous rocks are considered. The latter are characterized by large-scale spatial variations and correlations in their effective properties and include rocks that may be characterized by several distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity---those of the pores and of the fractures. First, the diagenetic processes that give rise to the present reservoir rocks are discussed and a few geometrical models of such processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topology, and pore surface roughness, and morphological properties of fracture networks are discussed. It is shown that fractal and percolation concepts play important roles in the characterization of rocks, from the smallest length scale at the pore level to the largest length scales at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to these phenomena are compared. The first approach is based on the classical equations of transport supplemented with constitutive equations describing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the phenomena at the smallest scale, a pore or fracture, and then employs large-scale simulation and modern concepts of the statistical physics of disordered systems, such as scaling and universality, to obtain the macroscopic properties of the system. The fundamental roles of the interconnectivity of the rock and its wetting properties in dispersion and two-phase flows, and those of microscopic and macroscopic heterogeneities in miscible displacements are emphasized. Two important conceptual advances for modeling fractured rocks and studying flow phenomena in porous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its structure. The second, simulated annealing, borrowed from optimization processes and the statistical mechanics of spin glasses, is used for finding the optimum structure of a fractured reservoir that honors a limited amount of experimental data.

Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing

Summary. A Debye model using two cut-off frequencies corresponding to compressional and shear velocities is used to calculate mineral entropies. This model permits entropy and heat capacity in the Earth to be calculated from seismic profiles, and iteration yields temperature profiles along an isentrope. With an adiabatic temperature profile it is possible to obtain Griineisen’s parameter and thermal expansion as a function of depth. Only in the lower mantle is the calculated Griineisen’s parameter along an isentrope approximately proportional to volume.

/pdf/thermodynamic-parameters-in-the-earth-as-determined-from-1wah9p6vzb.pdf

Thermodynamic parameters in the Earth as determined from seismic profiles

For mantle regions of anomalously high electrical conductivity (greater than 0.1 S/m) the bulk conductivity is modeled by effective medium theory as a basalt melt fraction within a mainly olivine matrix. In order for the highly conducting melt to affect the bulk conductivity it must form interconnections, so that the very existence of mantle conductivity anomalies constitutes evidence for such interconnections. The inclusion of petrological data on the partial melting of peridotite strongly constrains the range of temperatures and melt fractions that can be used to yield an observed electrical conductivity. Thus from anomalous conductivities which are observed under rift zones, volcanic belts, geothermal areas, and beneath the oceans, it is possible to estimate both the temperature and the degree of partial melting. While other mechanisms for mantle conductivity enhancement may exist, e.g., contributions from contaminated grain boundaries or high volatile contents, these explanations associate a chemical differentiation in the mantle with thermal manifestations and in most cases create conditions that favor melting.

Partial melting and electrical conductivity anomalies in the upper mantle

We have compiled both laboratory and worldwide field data on electrical conductivity to help understand the physical implications of deep crustal electrical profiles. Regional heat flow was used to assign temperatures to each layer in regional electrical conductivity models: we avoided those data where purely conductive heat flow suggested temperatures more than about 1000/sup 0/C, substantially higher than solidus temperatures and outside the range of validity of heat flow models. The resulting plots of log conductivity sigma versus 1/T demonstrate that even low-conductivity layers (LCL) have conductivities several orders of magnitude higher than dry laboratory samples and that the data can be represented by straight line fits. In addition, tectonically active regions show systematically higher conductivities than do shield areas. Because volatiles are usually lost in laboratory measurements and their absence is a principal difference between laboratory and field conditions, these materials probably account for the relatively higher conductivities of rocks in situ in the crust; free water in amounts of 0.01--0.1% in fracture porosity could explain crustal conductivities. Other possibilities are graphite, hydrated minerals in rare instances, and sulfur in combination with other volatiles. As most of the temperatures are less than 700/sup 0/C, partial melting seems likely onlymore » in regions of highest heat flow where the conductive temperature profiles are inappropriate. Another result is that at a given temperature, crustal high-conductivity layes (HCL) are more conductive by another order of magnitude and show more scatter than do LCL's.« less

Electrical conductivity, temperatures, and fluids in the lower crust

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 Earth's 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.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB900299

Laboratory-based electrical conductivity in the Earth's mantle

Geophysical models show that electrical conductivity in Earth9s mantle rises about two orders of magnitude through the transition zone in the depth range 410 to 660 kilometers. Impedance measurements obtained on Mg1.8Fe0.2SiO4 olivine, wadsleyite, and ringwoodite at up to 20 gigapascals and 1400°C show that the electrical conductivities of wadsleyite and ringwoodite are similar and are almost two orders of magnitude higher than that of olivine. A conductivity-depth profile to 660 kilometers, based on these laboratory data, shows a conductivity increase of almost two orders of magnitude across the 410-kilometer discontinuity; such a profile favors a two-layer model for the upper mantle. Activation enthalpies of 1.2 to 1.7 electron volts permit appreciable lateral variations of conductivity with lateral temperature variations.

https://science.sciencemag.org/content/sci/280/5368/1415.full.pdf

Thomas J. Shankland

Papers

Thermodynamic parameters in the Earth as determined from seismic profiles

Partial melting and electrical conductivity anomalies in the upper mantle

Electrical conductivity, temperatures, and fluids in the lower crust

Laboratory-based electrical conductivity in the Earth's mantle

Electrical Conductivity of Olivine, Wadsleyite, and Ringwoodite Under Upper-Mantle Conditions