Physics of Minerals and Inorganic Materials : An Introduction

The physics of minerals in a broad sense implies the fundamental aspects of understanding mineral matter: the electronic structure of atoms related to their behavior in geochemical processes; the atomic and electronic structures of minerals; the properties of minerals, with their genetic, geophysical, and technical significance, and their pressure and temperature dependence; the mechanisms of phenomena and reactions in mineral formation and transformation processes; the physical me­ thods applied in mineralogical, geochemical and petrological studies, and to a great extent in geological surveys and prospecting. In a narrower sense, it is a branch lying in the border area between mineralogy and solid-state physics, dealing with those aspects of mine­ ralogy which require, for their understanding and investigation, special knowledge in contemporary physics and chemistry of solids. The physics of minerals accounts for the third crucial change within this century in the conceptual foundations of mineralogy: after physi­ cochemical mineralogy, from experimental studies of phase relations to parage netic analyses, and crystal chemistry of minerals, there followed solid-state physics, which has evolved to its present state over the past 25 years. The task of mineralogy has expanded greatly. In addition to the identification and description of minerals, it is becoming necessary to establish the relationships between structure, composition and properties of minerals and their genesis, their distribution within geological regions, magmatic, metamorphic and sedimentary formations and types of ore deposits. The development of new methods of investigation requires an understanding of the physical meaning of the parameters under evaluation.

1 Quantum Theory and the Structure of Atoms.- 1.1 Geochemistry ― History of Self-Consistent Atoms.- 1.2 The Beginnings of Quantum Theory.- 1.2.1 Rutherford-Bohr Model of the Hydrogen Atom and Three Postulates of the “Old Quantum Theory”.- 1.2.2 Calculation of the Radius and Energy of Hydrogen Atom Orbits.- 1.2.3 Atomic Structure and Spectra. The Calculation of Line Spectrum of the Hydrogen Atom.- 1.2.4 Fine Structure of Spectra and Sommerfeld’s Development of the Bohr Theory; Quantum Numbers.- 1.3 The Schrödinger Equation as the Basic Equation of Quantum Mechanics.- 1.3.1 The Physical Bases.- 1.3.2 Derivation of the Schrödinger Equation.- 1.4 Atomic Orbitals (Solutions of the Schrödinger Equation).- 1.4.1 Physical Meaning of the Schrödinger Equation Solutions.- 1.4.2 The Physical Meaning of the Atomic Orbitals.- 1.4.3 The s, p, d, f Systematics of Atomic Orbitals.- 1.5 Orbital Radii (Solutions of the Schrödinger Equation).- 1.5.1 Concerning the Calculations of Electronic Structure of Many-Electron Atoms.- 1.5.2 Orbital Radii and the Wave Functions of Atoms.- 1.6 Electron Spin.- 1.7 Electronic Configurations and the Periodic System of Elements.- 1.8 Term Symbols and Atomic States.- 1.8.1 Description of Atomic States.- 1.8.2 Term Symbols.- 1.8.3 Term Derivation from Electron Configurations.- 1.8.4 Free Atom Energy Levels and Hamiltonian.- 1.8.5 Atomic Spectroscopy and Spectrochemical Analysis of Minerals, Rocks, and Ores; Spectroscopy-Cosmochemistry-Astrophysics.- 2 Crystal Field Theory.- 2.1 The Actions of the Crystal Field upon the Atomic Orbitals and Terms.- 2.1.1 Symmetry of Atomic Orbitals in the Crystal Field; the Concepts of Characters and Irreducible Representations.- 2.1.2 Correlation Tables for the Symmetry Types in Various Point Groups.- 2.1.3 Selection Rules Related to Symmetry Types.- 2.2 Three Types of Ion Behavior in Crystal Fields: Weak, Medium, and Strong Crystalline Fields.- 2.3 Iron Group: Term Splitting by Crystal Field.- 2.3.1 Electron Configurations, Terms, Cubic Field Splitting (Qualitative Schemes).- 2.3.2 Crystal Field Parameters; Tanabe-Sugano Diagrams.- 2.3.3 Splitting by Spin-Orbit Interaction, Jahn-Teller Effect, and Lowering of Symmetry.- 3 Molecular Orbital Theory.- 3.1 Introduction.- 3.2 General Theory of the Chemical Bond; Molecular Orbital Method; Valence Bond Method.- 3.2.1 Description and Systematics of Molecular Orbitals.- 3.2.2 Molecular Orbital Energy and Coefficient Calculations (the H2+ Molecule Ion Example).- 3.2.3 Molecular Orbital Calculation for Octahedral and Tetrahedral Complexes of Transition Metal and Nontransition Element Ions.- 3.2.4 Valence Bond Method; Hybrid Atomic Orbitals.- 3.3 Analysis of the MO Scheme: Information Obtained from MO and Basic Concepts of the Theory of the Chemical Bond.- 3.3.1 Coulomb Integrals HAA in the MO Method-Ionization Potentials-VSIE; Deep Meaning of the Self-Consistency; Electronegativity.- 3.3.2 LCAO Coefficients ci and Electronic Population Analysis; Ionicity ― Covalency of Chemical Bonding and Effective Charge; Valence and Charge.- 3.4 Further Development of Molecular Orbital Methods.- 3.4.1 About the Methods of the MO Calculations for Isolated Clusters.- 3.4.2 Molecular Orbitals for the Larger Clusters.- 3.4.3 Bond Orbital Model.- 4 Energy Band Theory and Reflectance Spectra of Minerals.- 4.1 Basic Principles and Methods of the Energy Band Theory.- 4.1.1 Wave Vector k in the Free-Electron Case.- 4.1.2 Two Approximations of the Energy Band Theory: Nearly Free Electrons and Tight Binding Models.- 4.1.3 Concept of k-Space and Brillouin Zones.- 4.1.4 Classification of Orbitals in Crystals with Respect to Symmetry Types.- 4.1.5 Energy Band Structure Schemes.- 4.1.6 Band Occupation; Densities of States; Fermi Surface.- 4.1.7 The Methods of Band Structure Calculation.- 4.2 Analysis of the Band Schemes and Reflectance Spectra of Minerals.- 4.2.1 Intrinsic Absorption and Reflectance Spectra. Measured and Calculated Parameters.- 4.2.2 Structure Type of NaCl-MgO-PbS.- 4.2.3 Structure Type of Sphalerite (Cubic ZnS).- 4.2.4 Structure Type ofWurtzite (ZnS Hexagonal).- 4.2.5 Data for Other Minerals.- 5 Spectroscopy and the Chemical Bond.- 5.1 General Outline and Parameters of Solid State Spectroscopy.- 5.2 Principal Concepts and Parameters of the Chemical Bond from the Standpoint of Spectroscopy.- 6 Optical Absorption Spectra and Nature of Colors of Minerals.- 6.1 Parameters of Optical Absorption Spectra.- 6.1.1 Units of Measurement of Optical Transition Energies.- 6.1.2 Intensity of Absorption.- 6.1.3 Diffuse Reflectance Spectra.- 6.2 Types of Optical Absorption Spectra and Selection Rules.- 6.3 Analysis and Experimental Survey of Transition Metal Ions Spectra.- 6.4 The Nature of Colors of Minerals.- 6.4.1 Types of Colors of Minerals.- 7 Structure and the Chemical Bond.- 7.1 Contemporary Methods of Description and Calculations of the Chemical Bond in Solids.- 7.1.1 Extension of the Bond Orbital Methods for Cristobalite and Quartz Structures.- 7.2 Lattice Energy of Ionic Crystals.- 7.3 Lattice Sums, Crystal Field Parameters, Spectroscopical Parameters, and Intracrystalline Distribution.- 7.4 Atomic and Ionic, Orbital, and Mean Radii.- 7.4.1 Ionic Radii and Molecular Orbitals.- 7.4.2 Systems of Additive Ionic and Atomic Radii.- 7.4.3 Appraisal of the Systems of Additive Radii.- 7.4.4 Orbital Radii.- 7.4.5 Experimental X-Ray and Electron Diffraction Determinations of Atomic Sizes.- 8 Chemical Bond in Some Classes and Groups of Minerals.- 8.1 Diversity of the Aspects of a Complex Phenomenon of Chemical Bond in Solids.- 8.2 The Chemical Bond in Silicates.- 8.2.1 Description of the Chemical Bond in SiO4?4 in Terms of the Calculated Molecular Orbital Diagram.- 8.2.2 Molecular Orbital Diagram for the SiO4?4 According to X-Ray and ESCA Spectra.- 8.2.3 Effective Charges of Si and Al in the Silicates and Alumino-silicates.- 8.2.4 Silica Polymorphs: Energy Band Schemes; Bond Orbital Model and Calculations of the Electronic Structure and Properties.- 8.2.5 Cation Polyhedra in Crystal Structures of Silicates.- 8.2.6 Degree of Ionicity-Covalency in Cation Polyhedra According to Superfine Structure of Electron Paramagnetic Resonance (EPR) Spectra.- 8.2.7 Energies of the Structural Sites, Energies of Stabilization, and Intracrystalline Fields in Silicates.- 8.2.8 Mössbauer Characteristics of the Bonding of Iron and of the Site Population in Silicate Minerals.- 8.2.9 Crystal-Chemical Meaning of the Nuclear Magnetic Resonance (NMR) Parameters in Silicates.- 8.2.10 Bond Length and Angle Variations; Bridging and Non-bridging Oxygens.- 8.2.11 Interlayer Bonding and Surface Energy Calculations in Sheet Silicates.- 8.2.12 Mantle Properties, High Pressure Spectroscopy, and Electronic Structure of Silicates.- 8.3 The Chemical Bond in Sulfides and Related Compounds.- 8.3.1 Diversity of the Aspects of the Chemical Bond in Sulfide and Related Compounds and the Theoretical Schemes.- 8.3.2 Energy Gaps in Sulfides, Types of Crystal and Types of Optical Transition; Ionicity and Band Scheme.- 8.3.3 Interactions M-M and M-S-M in Transition Metal Sulfides and Their Relation to Properties and Structures.- 8.3.4 States of Iron in Sulfides According to Mössbauer Spectra Parameters.- 8.3.5 Polarity and Donor-Acceptor Bonds in Sulfides and Sulfosalts of As, Sb, Bi According to NQR Data.- 8.3.6 Structural Features of Sulfides and Related Compounds from the Standpoint of the Electronic Structure.- 8.3.7 Survey of Data on the Chemical Bond in Sulfides.- 8.4 Features of Chemical Bonding in Other Classes of Mineral.- References.