The composition of the Earth

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

The study of preferred orientation of minerals in rocks dates back to Omalius d’Halloy (1833) who attributes a special significance to the alignment of crystals as an indicator of the formation process. Much later the influence of crystal alignment on physical properties was quantified (e.g., Weissenberg 1922, Voigt 1928, Reuss 1929). Only recently has this field emerged as a coherent part of earth science research linking such branches as mineralogy, petrology, structural geology, geodynamics and seismology. The reason for this was the emergence of quantitative methods to analyze preferred orientation, or “texture” as it was first called by Naumann (1850). These methods were largely developed in collaboration with materials science and mechanics. Quantitative measurements, detailed field studies, rigorous data analysis, theories to predict textures, and improvements in characterizing seismic anisotropy in the Earth are leading to a coherent picture that is now being refined.

Though seismologists have long accepted that there is a causal relationship between anisotropic propagation of seismic waves, the deformation field and crystal orientation, the prevailing view is still largely the mythological concept that seismic fast directions align with the flow direction. While this may be approximately the case for olivine deformed under certain conditions, it is certainly no universal law, as we will try to illustrate in this review. The “fast” direction of a crystal depends on the mineral species and its crystal structure. The alignment of crystals depends on microscopic, intra-crystalline deformation systems and the deformation history. Both relationships are complex and not intuitive, but there are well-established theories to compute single crystal physical properties as well as orientation patterns. Simulations can be compared with experimental data and then applied with some caution to the macroscopic Earth.

This review is intended to provide a brief introduction, highlighting some of the issues with …

Texture and Anisotropy

Mobile colloids—suspended particles in the submicrometre size range—are known to occur naturally in ground water1, 2 and have the potential to enhance transport of non-soluble contaminants through sorption3. The possible implications of this transport mechanism are of particular concern in the context of radionuclide transport. Significant quantities of the element plutonium have been introduced into the environment as a result of nuclear weapons testing and production, and nuclear power-plant accidents. Moreover, many countries anticipate storing nuclear waste underground. It has been argued that plutonium introduced into the subsurface environment is relatively immobile owing to its low solubility in ground water4 and strong sorption onto rocks5. Nonetheless, colloid-facilitated transport of radionuclides has been implicated in field observations6, 7, but unequivocal evidence of subsurface transport is lacking3, 8, 9. Moreover, colloid filtration models predict transport over a limited distance resulting in a discrepancy between observed and modelled behaviour3. Here we report that the radionuclides observed in groundwater samples from aquifers at the Nevada Test Site, where hundreds of underground nuclear tests were conducted, are associated with the colloidal fraction of the ground water. The 240 Pu/239 Pu isotope ratio of the samples establishes that an underground nuclear test 1.3 km north of the sample site is the origin of the plutonium. We argue that colloidal groundwater migration must have played an important role in transporting the plutonium. Models that either predict limited transport or do not allow for colloid-facilitated transport may thus significantly underestimate the extent of radionuclide migration.

Migration of plutonium in ground water at the Nevada Test Site

Light elements in the Earth's outer core: A critical review

Results are reported on a room temperature static compression study of iron and the Fe(0.8)Ni(0.2) alloy to above 260 GPa, which provide direct pressure-volume measurements on geophysically important materials at the conditions close to those at the inner core boundary. The diffraction patterns obtained by XRD indicate that pure iron remains in the hcp structure to 304 GPa and that Fe(0.8)Ni(0.2) is stable to at least 255 GPa. The results of this study, in conjunction with work at higher temperatures, will make it possible to address directly the question of the composition of the inner core with a level of certainty that were previously applicable only to the mantle.

Static compression of iron to 300 GPa and Fe0.8Ni0.2 alloy to 260 GPa: Implications for composition of the core

High-pressure, high-temperature properties of MgSiO3, (Fe01Mg09)SiO3, and (Fe02Mg08)SiO3 perovskites have been investigated using a newly developed X ray diffraction technique involving monochromatic synchrotron radiation The first direct measurements of unit cell distortions and equation-of-state parameters of the orthorhombic perovskite as functions of composition and simultaneous high pressure and high temperature were obtained The experiments were conducted under hydrostatic pressure up to 30 GPa, into the stability field of the perovskite The results demonstrate that the perovskite is elastically anisotropic, with the lattice parameter b being 25% less compressible than a and c Under increasing pressures the orthorhombic perovskite is distorted further away from the ideal cubic structure in agreement with theoretical predictions The 298-K isothermal equations of state of the three perovskites are indistinguishable within the uncertainty limits of the experiment The zero-pressure bulk modulus KT0 = 261 (±4) GPa with its pressure derivative KT0′ = 4 is close to that determined in previous static high pressure measurements The thermal expansion obtained from the high P - T experiments are consistent with previous measurements carried out at zero pressure but shows a strong volume dependence The temperature derivative of the isothermal bulk modulus at constant pressure (∂KT/∂T)p is −63(±05)×10−2 GPa/K Analyses of the high-temperature data give a value for the Anderson-Gruneisen parameter δT of 65–75, which is significantly higher than that used in recent lower mantle models

Effect of pressure, temperature, and composition on lattice parameters and density of (Fe,Mg)SiO3-perovskites to 30 GPa

The stability and P-V equation of state of CaSiO3 have been investigated using in situ diamond-anvil X ray diffraction techniques to 134 GPa, a pressure equivalent to that at the core-mantle boundary. Samples were heated by YAG laser at each pressure increment at high pressures to accelerate phase transitions. X ray diffraction measurements were carried out at 300 K using both energy-dispersive synchrotron and sealed-tube film techniques. Quenched CaSiO3-perovskite was observed to remain metastable close to 0.1 MPa, and to convert rapidly to an amorphous phase on pressure release. The simple cubic perovskite phase of CaSiO3 was found to be the stable phase for all lower mantle pressure conditions. All 47 P-V data points were used to obtain a third-order Birch-Murnaghan equation of state with zero-pressure parameters: unit cell volume V0 = 45.37±(0.08) A3, density ρ0 = 4.252(±0.008) Mg/m3, and bulk modulus K0 = 281(±4) GPa, with an assumed bulk modulus pressure K0′ = 4. These parameters are close to those of (Mg0.88Fe0.12)SiO3-perovskite and to those inferred by the Preliminary Reference Earth Model for the lower mantle. Hence, CaSiO3 must be considered an invisible component, in terms of density and bulk modulus constraints, in the lower mantle. Mantle composition models with both high and low calcium content can satisfy existing seismological constraints for the lower mantle.

Y. Wu

Papers

Static compression of iron to 300 GPa and Fe0.8Ni0.2 alloy to 260 GPa: Implications for composition of the core

Effect of pressure, temperature, and composition on lattice parameters and density of (Fe,Mg)SiO3-perovskites to 30 GPa

Stability and equation of state of CaSiO3-perovskite to 134 GPa