The Chemical Structure of Solids

The last quarter-century has been marked by the extremely rapid growth of the solid-state sciences. They include what is now the largest subfield of physics, and the materials engineering sciences have likewise flourished. And, playing an active role throughout this vast area of science and engineer­ ing have been very large numbers of chemists. Yet, even though the role of chemistry in the solid-state sciences has been a vital one and the solid-state sciences have, in turn, made enormous contributions to chemical thought, solid-state chemistry has not been recognized by the general body of chemists as a major subfield of chemistry. Solid-state chemistry is not even well defined as to content. Some, for example, would have it include only the quantum chemistry of solids and would reject thermodynamics and phase equilibria; this is nonsense. Solid-state chemistry has many facets, and one of the purposes of this Treatise is to help define the field. Perhaps the most general characteristic of solid-state chemistry, and one which helps differentiate it from solid-state physics, is its focus on the chemical composition and atomic configuration of real solids and on the relationship of composition and structure to the chemical and physical properties of the solid. Real solids are usually extremely complex and exhibit almost infinite variety in their compositional and structural features.

of Volume 1.- 1 Chemical Bonds in Solids.- 1. Why Solids Are Different from Molecules.- 1.1. Quantum Theory of Chemical Bonds.- 1.2. The Five Solid Types.- 1.3. Bonds and/or Bands?.- 2. Crystal Structures and Cohesive Energies of the Elements.- 2.1. Valence Groupings.- 2.2. Shell Effects.- 2.3. Transition Series.- 3. Binary Compounds and Alloys.- 3.1. Minerals.- 3.2. Semiconductors.- 3.3. Intermetallic Solutions.- 4. Chemical Bonding and Physical Properties.- 4.1. Classical Polarizabilities.- 4.2. Dispersion.- 4.3. Covalent and Ionic Energies.- 4.4. Chemical Trends in Physical Properties.- 5. Summary.- References.- 2 Energy Bands.- 1. Introduction.- 1.1. Historical Remarks.- 1.2. The Independent-Electron Approximation.- 2. Energy Bands in General.- 3. The Classical Descriptions of Energy Bands in Periodic Systems.- 3.1. Introduction.- 3.2. Two Classical Limits—Tight Binding and Nearly Free Electron.- 3.3. Tight Binding Theory.- 3.4. Wannier Functions.- 3.5. Nearly-Free-Electron Theory.- 3.6. Pseudopotentials.- 3.7. The Cellular Method.- 3.8. Orthogonalized Plane Wave, Augmented Plane Wave, and Related Methods.- 4. Approximations, Interpolations, Perturbations.- 4.1. Introduction.- 4.2. Moment Methods.- 4.3. Nearly-Free-Electron Perturbation Theory.- 4.4. The k · p Method.- 4.5. Small-k Expansions for KKR Theory.- 5. Some Relevant Experiments.- 5.1. Introduction.- 5.2. Soft X-Ray Emission and Absorption.- 5.3. Optical Spectroscopy.- 5.4. Fermi Surface Analysis.- 6. Typical Band Structures.- 6.1. Introduction.- 6.2. Simple Metals.- 6.3. Alkali Halides.- 6.4. Group IV Semiconductors.- 6.5. The III–V and II–VI Semiconductors.- 6.6. Silicon Dioxide.- 6.7. Transition Metals.- 6.8. Transition Metal Compounds.- 7. Disordered Solids.- 7.1. Introduction.- 7.2. Definition of Problems.- 7.3. The Density of States in an Alloy.- 7.4. The Anderson Problem.- 7.5. Topological Disorder.- 7.6. Applications.- 8. Conclusion.- Acknowledgments.- References.- 3 Factors Controlling the Formation and Structure of Phases.- 1. Introduction.- 2. Practical Prediction of Phase Stability.- 2.1. Metals: Use of Thermodynamic Data.- 2.2. Valence Compounds: Use of Crystal Chemical Knowledge.- 3. General Structural Consequences of Bonding Types.- 3.1. Ionic Crystals.- 3.2. Compounds with Saturated Covalent Bonds.- 3.3. Metallic Phases.- 3.4. A Priori Separation of Structure Types.- 4. Atomic Size and Structural Constraint.- 5. Factors Influencing the Stability of Crystal Structures.- 5.1. Electrochemical Factor.- 5.2. Geometric Effects.- 5.3. Energy Band Effects.- 5.4. Environmental Factors.- 6. Distortions of Crystal Structures.- 6.1. Distortions Arising from Cation-Cation Bonds.- 6.2. Jahn-Teller Distortions.- 6.3. Spin-Orbit Coupling Distortions.- 6.4. Magnetic Exchange Energies.- 6.5. Mechanical Instability.- 7. Epilogue.- Appendix—Structure Diagrams.- Acknowledgments.- References.- 4 Structure and Composition in Relation to Properties.- 1. Magnetic Behavior.- 1.1. Introduction.- 1.2. The 3d Transition Elements.- 1.3. Rare Earth Metals.- 1.4. Role of Local Atomic Environment Regarding Development of Atomic Moments and Long-Range Order.- 1.5. Directional Ordering and Magnetic Anisotropy.- 1.6. Magnetic Oxides.- 1.7. Magnetic Semiconductors.- 1.8. Linear and Two-Dimensional Magnetic Behavior.- 1.9. Amorphous Magnetic Materials.- 1.10. Summary.- 2. Superconducting Behavior.- 2.1. Introduction.- 2.2. The Cr3Si (?-W) and Transition Metal Nitride and Carbide Phases. Electron Concentration and Lattice Instability.- 2.3. Role of Stoichiometry and Atomic Order.- 2.4. Metastable Superconducting Phases.- 2.5. Paramagnetic Impurities in Superconductors.- 2.6. Ternary Superconducting Chalcogenides.- 2.7. Superconductivity of Degenerate Semiconductors.- 2.8. Summary.- 3. Dielectric Materials.- 3.1. Ferroelectrics.- 3.2. Piezoelectrics.- 3.3. Nonlinear Optical Materials.- 3.4. Electrooptic and Pyroelectric Materials.- 3.5. Summary.- 4. Mechanical Behavior.- 4.1. Introduction.- 4.2. Elastic Behavior.- 4.3. Plastic Behavior.- 4.4. Summary.- Acknowledgments.- References.- 5 Introduction to Chemical and Structural Defects in Crystalline Solids.- 1. Introduction.- 2. Point Defects.- 3. Dislocations.- 4. Planar Defects.- 5. Volumetric Defects.- Acknowledgments.- References.- 6 Defect Equilibria in Solids.- 1. Introduction.- 1.1. Native Defects.- 1.2. Law of Mass Action and Point Defects.- 1.3. Electronic Defects.- 1.4. Energetics of Defect Formation.- 2. Native Defects.- 2.1. Defect Equilibria in Elemental Crystals.- 2.2. Defect Equilibria in Binary Compounds.- 2.3. Nonstoichiometry—Equilibria with External Phases.- 2.4. Ionization of Defects.- 2.5. Relationship between Mass Action Law and Statistical Thermodynamics.- 2.6. Defect Interactions.- 3. Multicomponent Systems.- 3.1. Equilibria Involving Foreign Atoms.- 3.2. Multicomponent Compounds.- 4. Extended Defects.- Acknowledgment.- References.- 7 Characterization of Solids—Chemical Composition.- 1. Introduction.- 2. Current Capability for Determination of Chemical Composition.- 2.1. Introduction.- 2.2. General Over iew.- 2.3. Analytical Techniques: Present Status.- 2.4. Precision and Sensitivity of Analytical Techniques.- 3. Application of Current Techniques to Characterization of Materials.- 3.1. Characterization of Major Phase.- 3.2. Characterization of Minor Phases and Impurities.- 3.3. Characterization of Surfaces.- 4. Utilization of Existing Techniques.- 4.1. Literature Examples.- 4.2. Factors Determining Use.- Acknowledgments.- References.- 8 Structural Characterization of Solids.- 1. Introduction.- 2. Structural Characterization by Optical Techniques.- 2.1. Morphology.- 2.2. Bulk Optical Properties.- 2.3. Scattering Studies.- 2.4. Surface Characterization.- 2.5. Particle Size and Shape.- 3. Structural Characterization by X-Ray Diffraction.- 3.1. X-Ray Powder Methods.- 3.2. Single-Crystal X-Ray Methods.- 3.3. Temperature and Pressure Experiments.- 3.4. X-Ray Topography and Interferometry.- 4. Electron Methods for Materials Characterization.- 4.1. Electron Microscopy.- 4.2. Electron Diffraction.- 4.3. Scanning Electron Microscopy.- 5. Neutron Scattering from Solids.- 5.1. Neutron Sources.- 5.2. Interactions with Matter.- 5.3. Structure Analysis with Neutrons.- 5.4. Magnetic Structure Analysis.- 5.5. Lattice and Spin Dynamics.- 6. Spectroscopy and Local Symmetry.- 6.1. Absorption Spectra in the Visible Range.- 6.2. Infrared Absorption Spectroscopy.- 6.3. Raman Spectra.- 6.4. Soft X-Ray Spectra.- 6.5. Electron Spin Resonance.- 6.6. Nuclear Magnetic Resonance.- 6.7. Mössbauer Effect.- 6.8. Electron Spectroscopy.- 6.9. Acoustic Spectroscopy.- 7. Physical Properties as Characterization Tools.- 7.1. Introduction.- 7.2. Some Crystal Physical Generalizations.- 7.3. Dielectric Measurements.- 7.4. Electrical Characterization of Solids.- 7.5. Magnetic Measurements.- 7.6. Calorimetric Measurements.- Acknowledgment.- References.