Preface 1. Origin and history of the Solar System 2. Composition of the Earth 3. Radioactivity, isotopes and dating 4. Isotopic clues to the age and origin of the Solar System 5. Evidence of the Earth's evolutionary history 6. Rotation, figure of the Earth and gravity 7. Precession, wobble and rotational irregularities 8. Tides and the evolution of the lunar orbit 9. The satellite geoid, isostasy and post-glacial rebound 10. Elastic and inelastic properties 11. Deformation of the crust: rock mechanics 12. Tectonics 13. Convective and tectonic stresses 14. Kinematics of the earthquake process 15. Earthquake dynamics 16. Seismic wave propagation 17. Seismological determination of Earth structure 18. Finite strain and high pressure equations of state 19. Thermal properties 20. The surface heat flux 21. The global energy budget 22. Thermodynamics of convection 23. Thermal history 24. The geomagnetic field 25. Rock magnetism and paleomagnetism 26. Alternative energy sources and natural climate variations: some geophysical background Appendix A. General reference data Appendix B. Orbital dynamics (Kepler's laws) Appendix C. Spherical harmonic functions Appendix D. Relationships between elastic moduli of an isotropic solid Appendix E. Thermodynamic parameters and derivative properties Appendix F. An Earth model: mechanical properties Appendix G. A thermal model of the Earth Appendix H. Radioactive isotopes Appendix I. A geological time scale 2004 Appendix J. Problems References Index.

Physics of the Earth

Boron carbide is characterized by a unique combination of properties that make it a material of choice for a wide range of engineering applications. Boron carbide is used in refractory applications due to its high melting point and thermal stability; it is used as abrasive powders and coatings due to its extreme abrasion resistance; it excels in ballistic performance due to its high hardness and low density; and it is commonly used in nuclear applications as neutron radiation absorbent. In addition, boron carbide is a high temperature semiconductor that can potentially be used for novel electronic applications. This paper provides a comprehensive review of the recent advances in understanding of structural and chemical variations in boron carbide and their influence on electronic, optical, vibrational, mechanical, and ballistic properties. Structural instability of boron carbide under high stresses associated with external loading and the nature of the resulting disordered phase are also discussed.

Boron Carbide: Structure, Properties, and Stability under Stress

The determination of the elastic properties of composite materials (multiphase aggregates, polycrystals, and porous or cracked solids) from the elastic properties of the components may be approached in several ways. The problem may be treated statistically, via scattering theory, through variational principles, or by the assumption of specific geometries for the material under consideration. Each of these methods is reviewed in turn. The widely used Voigt-Reuss-Hill average can be a poor approximation for both two-phase composites and polycrystals, and its replacement by the two Hashin-Shtrikman bounds is recommended. For pore-containing or crack-containing media, specific geometry models must be considered if useful results are to be obtained. If aggregate theory is used to estimate the moduli of individual components of a composite whose bulk properties are known, the shear moduli of the component phases must be matched (within a factor of 2 or 3) for the method to be useful. Results for nonlinear composites (which allow calculation of the pressure variation of aggregate moduli) have been obtained for only a few special cases.

The Elastic Properties of Composite Materials

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

Chapter vii – the equation of state of solids from shock wave studies

Shock-wave data have been obtained for the following rocks: one albitite, one anorthosite, two bronzitites, two diabases, two dunites, two eclogites, one granite, and one Jadeite. The experimental pressure range is from slightly over 0.1 to about 1.0 Mb. There is evidence that all rocks investigated exhibit a phase change. It is estimated that the transformations occur at about 0.1 Mb for the low-density rocks and between 0.3 and 0.6 Mb for the high-density rocks. A single-shock Hugoniot consistent with the data has been determined for the high-pressure modification of some of these rocks. These equations of state are compared with similar equations of state derived from geophysical data for the earth. This comparison supports the model of a mantle composed of high-pressure modifications of these basic rocks with an iron content lying somewhere between that of Twin Sisters dunite and Hortonolite dunite. Other thermodynamic quantities have been calculated based on estimates of the specific heat and the Gruneisen parameter.

Hugoniot equation of state of twelve rocks

Because of the discovery and subsequent synthesis of stishovite, a high-density polymorph of silica, Wackerle's shock-wave data on quartz have been re-examined to see if the high-pressure phase he reports could indeed be stishovite. Although the temperatures used for synthesis are about 1000°C higher than the temperature calculated by Wackerle for the transformation, the fact that the pressures are nearly the same (about 140 kb) is the prime evidence that the two transformations are the same, since the small change in entropy for a solid-solid phase change and the large observed volume change indicate that the slope of the phase line, dP/dT, should be quite small. The large increase in density shown by the shock-wave data above the transformation is comparable to the increase in density of quartz to stishovite; this gives additional support for identification of the transformations. On the assumptions that Wackerle's high-pressure data, for both crystalline and vitreous quartz, correspond to stishovite, a Hugoniot equation of state has been found for stishovite. This material has a Gruneisen ratioV(∂P/∂E)υ = 0.9, a heat of formation relative to quartz of 1.5×1010 ergs/g, and a bulk sound speed of about 10 km/sec.

On the equation of state of stishovite

Numerical calculations have been made that determine the equation of state of the materials which constitute the mantle and core of the earth. These calculations are based on the observed seismic velocities and the known mass and moment of inertia of the earth. Comparison of these equations of state with those obtained experimentally indicate the type of materials which may exist in the various regions. The general features of these calculations are in close agreement with the conclusions reached by F. Birch and others; namely, the mantle is made up of high-density oxides of silicon, iron, and magnesium, and the core is mostly iron. Density and pressure variations throughout the earth are also obtained.

J. N. Fritz

Papers

Chapter vii – the equation of state of solids from shock wave studies

Hugoniot equation of state of twelve rocks

On the equation of state of stishovite

On the composition of the Earth's interior

Hugoniot equation of state of the lanthanides