The pressure dependence of the R1 ruby fluorescence line has been calibrated at 25 °C against the compression of NaCl. Pressures are determined using the Decker equation of state for NaCl. The dependence is linear to 195 kbar following the equation PNaCl=2.746(Δλ), where P is in kbar and Δλ in A. The uncertainty in the value of the slope, dp/dλ, expressed in terms of a 95% confidence interval is 2.746±0.014 kbar A−1. The coefficient of the quadratic term (Δλ)2 is not significantly different from zero; and the quadratic term makes indeed a negligible contribution to the fit. Taking into account the reported uncertainty associated with the Decker equation of state for NaCl, the value of the slope is 2.740±0.016 kbar A−1 within a 95% confidence interval.

Calibration of the pressure dependence of the R1 ruby fluorescence line to 195 kbar

Preliminaries: Note on conventions Basic homotopy notions Surgery below the middle dimension Appendix: Applications Simple Poincare complexes The main theorem: Statement of results An important special case The even-dimensional case The odd-dimensional case The bounded odd-dimensional case The bounded even-dimensional case Completion of the proof Patterns of application: Manifold structures on Poincare complexes Applications to submanifolds Submanifolds: Other techniques Separating submanifolds Two-sided submanifolds One-sided submanifolds Calculations and applications: Calculations: Surgery obstruction groups Calculations: The surgery obstructions Applications: Free actions on spheres General remarks An extension of the Atiyah-Singer $G$-signature theorem Free actions of $S^1$ Fake projective spaces (real) Fake lens spaces Applications: Free uniform actions on euclidean space Fake tori Polycyclic groups Applications to 4-manifolds Postscript: Further ideas and suggestions: Recent work Function space methods Topological manifolds Poincare embeddings Homotopy and simple homotopy Further calculations Sullivan's results Reformulations of the algebra Rational surgery References Index.

Surgery on compact manifolds

The maturing of the Earth sciences has led to a fragmentation into subdisciplines which speak imperfectly to one another. Some of these subdisciplines are field geology, petrology, mineralogy, geochemistry, geodesy and seismology, and these in turn are split into even finer units. The science has also expanded to include the planets and even the cosmos. The practitioners in each of these fields tend to view the Earth in a completely different way. Discoveries in one field diffuse only slowly into the consciousness of a specialist in another. In spite of the fact that there is only one Earth, there are probably more Theories of the Earth than there are of astronomy, particle physics or cell biology where there are uncountable samples of each object. Even where there is cross-talk among disciplines, it is usually as noisy as static. Too often, one discipline's unproven assumptions or dogmas are treated as firm boundary conditions for a theoretician in a slightly overlapping area. The data of each subdiscipline are usually consistent with a range of hypotheses. The possibilities can be narrowed considerably as more and more diverse data are brought to bear on a particular problem. The questions of origin, composition and evolution of the Earth require input from astronomy, cosmochemistry, meteoritics, planetology, geology, petrology, mineralogy, crystallography, materials science and seismology, at a minimum. To a student of the Earth, these are artificial divisions, however necessary they are to make progress on a given front.

In Theory of the Earth I attempt to assemble the bits and pieces from a variety of disciplines which are relevant to an understanding of the Earth. Rocks and magmas are our most direct source of information about the interior, but they are biased toward the properties of the crust and shallow mantle. Seismology is our best source of information about the deep interior; however, the interpretation of seismic data for purposes other than purely structural requires input from solid-state physics and experimental petrology. Although this is not a book about seismology, it uses seismology in a variety of ways.

The "Theory of the Earth" developed here differs in many respects from conventional views. Petrologists' models for the Earth's interior usually focus on the composition of mantle samples contained in basalts and kimberlites. The simplest hypothesis based on these samples is that the observed basalts and peridotites bear a complementary relation to one another, that peridotites are the source of basalts or the residue after their removal, and that the whole mantle is identical in composition to the inferred chemistry of the upper mantle and the basalt source region. The mantle is therefore homogeneous in composition, and thus all parts of the mantle eventually rise to the surface to provide basalts. Subducted slabs experience no barrier in falling through the mantle to the core-mantle boundary.

Theory of the Earth

The origin of the moon and the single-impact hypothesis III.

Magnetism and thermal evolution of the terrestrial planets

Limits on the Bulk Composition of the Moon

Earth and Venus: A comparative study

Shock-wave data are now available for a variety of rocks, minerals, and oxides of geophysical interest in the pressure range appropriate for the lower mantle. These data are analyzed to obtain equation-of-state parameters with emphasis on the shock-induced high-pressure phases. Of twenty-four materials for which Hugoniot data are analyzed, all but MgO, Al_2O_3, and MnO_2 undergo at least one shock-induced phase change below 800 kb. Birch-Murnaghan parameters for the raw Hugoniots, metastable Hugoniots, adiabats, and 25°C isotherms are obtained for the high-pressure phases. On correcting the raw Hugoniot data for MgO and Al_2O_3 for strength effects, we find that the calculated adiabatic equations of state are in good agreement with recent ultrasonic data. The zero-pressure densities of high-pressure phases are obtained by constraining the adiabats calculated from the Hugoniot data such that the zero-pressure densities and the zero-pressure slopes of the adiabats satisfy Anderson's seismic equation of state.
Probable crystallographic structures of the high-pressure phases are inferred from the classical laws of crystal chemistry and, in some cases, from static high-pressure recovery experiments on analog compounds. Shock data for SiO_2 (stishovite) indicate that transformation to the fluorite-type structure (observed in TiO_2) does not take place under shock, at least to ∼2000 kb. Fe_2O_3 probably transforms to either the perovskite or B rare earth structure with a zero-pressure density of 5.96 g/cm^³. MgAl_2O_4 (spinel) may transform to the CaFe_2O_4 structure with a zero-pressure density of 4.19 g/cm_³. Feldspars transform to the hollandite structure (density, of ∼3.85 g/cm^³). Olivine-rich rocks containing greater than 10% FeO either disproportionate to the ilmenite and rock salt structure or transform to a new post-spinel polymorph having the Sr_2PbO_4 structure. Pyroxenes containing greater than 10% FeO probably transform to the ilmenite structure. High-pressure forms of sillimanite and andalusite have calculated densities of 4.00 and 3.95 g/cm^³, respectively. This probably represents disproportionation reaction products, Al_2O_3 + SiO_2 (stishovite), which would give a density of 4.09 g/cm^³. The Birch-Murnaghan second-order parameter ξ is nearly zero for MgO and Al_2O_3. 0.73 for stishovite, and ∼1 for the high-pressure phases of the olivines and pyroxenes. The values of K′ = dK/dP are calculated along the Hugoniots and adiabats and are found to decrease at a rate of −0.5 to −1.6 cm³/g when the density is increased either by compression or by iron substitution.

/pdf/equations-of-state-and-crystal-structures-of-high-pressure-2q4iyi1mpm.pdf

Equations of State and Crystal Structures of High-Pressure Phases of Shocked Silicates and Oxides

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Limits on the Bulk Composition of the Moon

Earth and Venus: A comparative study

Equations of State and Crystal Structures of High-Pressure Phases of Shocked Silicates and Oxides