Understanding Solids

Preface xix Part I States of Aggregation 1 1 Atoms and Bonding 3 1.1 The Electron Structure of Atoms 3 1.1.1 Hydrogen 3 1.1.2 Many Electron Atoms 4 1.1.3 Orbital Shapes 6 1.1.4 Electron Spin and Electron Configuration 8 1.1.5 Atomic Energy Levels 9 1.2 Ionic Bonding 12 1.2.1 Ionic Size and Bonding 12 1.2.2 Lattice Energies 13 1.2.3 Atomistic Simulation 14 1.3 Covalent Bonding 15 1.3.1 Bond Geometry 15 1.3.2 Bond Energies 18 1.4 Metallic Bonding 21 1.4.1 Molecular Orbitals and Energy Bands 21 1.4.2 The Free Electron Gas 22 1.4.3 Energy Bands 24 1.4.4 Bands in Ionic and Covalent Solids 27 1.5 Weak Chemical Bonds 28 1.6 Computation of Material Properties 31 Further Reading 31 The Following References Expand the Material in this Chapter 31 A Dictionary of Quantum Mechanical Language and Expressions is 32 Ionic Radii are Discussed and Tabulated by 32 The Computation of Properties is Described in 32 Problems and Exercises 32 Calculations and Questions 34 2 Microstructures and Phase Relationships 37 2.1 Macrostructure, Microstructure, and Nanostructure 37 2.1.1 Crystalline Solids 37 2.1.2 Non-crystalline Solids 37 2.1.3 Partly Crystalline Solids 40 2.1.4 Nanoparticles and Nanostructures 40 2.2 The Development of Microstructures 43 2.2.1 Solidification 43 2.2.2 Processing 44 2.3 Phase Diagrams 45 2.3.1 One-Component (Unary) Systems 45 2.3.2 Two-Component (Binary) Systems 48 2.3.2.1 Simple Binary Diagrams: Nickel-Copper as an Example 48 2.3.2.2 Binary Systems Containing a Eutectic Point: Tin-Lead as an Example 49 2.3.2.3 Intermediate Phases 52 2.3.2.4 The Iron-Carbon System Close to Iron 52 2.4 Ternary Systems 54 References 57 Further Reading 58 Problems and Exercises 58 Calculations and Questions 60 3 Crystal Structures and Defects 65 3.1 Crystal Geometry 65 3.1.1 Crystal Systems 65 3.1.2 Crystal Lattices 66 3.1.3 Symmetry and Crystal Classes 68 3.2 Crystal Structures 69 3.2.1 Unit Cells and Atomic Coordinates 69 3.2.2 Crystal Structures 70 3.2.2.1 The Face-Centred Cubic (fcc, A1) Structure 70 3.2.2.2 The Body-Centred Cubic (bcc, A2) Structure 70 3.2.2.3 The Hexagonal Close-Packed (hcp, A3) Structure 70 3.2.2.4 The Diamond Structure 71 3.2.2.5 The Graphite Structure 71 3.2.2.6 The Halite (Rock Salt, Sodium Chloride) Structure 71 3.2.2.7 The Perovskite Structure 72 3.2.2.8 The Spinel Structure 72 3.2.2.9 Lattice Parameters and Vegard's Law 74 3.3 Crystal Planes and Directions 74 3.3.1 Miller Indices 74 3.3.2 Hexagonal Crystals and Miller-Bravais Indices 76 3.3.3 Directions 78 3.3.4 Interplanar Spacings 79 3.4 Crystal Density 80 3.4.1 Density Estimation 80 3.4.2 The Density of NaCl 81 3.4.3 The Density of Crystals with a Variable Composition 81 3.5 Structural Relationships 82 3.5.1 Sphere Packing 82 3.5.2 Ionic Structures in Terms of Anion Packing 84 3.5.3 Polyhedral Representations 86 3.6 Point Defects 87 3.6.1 Point Defects in Crystals of the Elements 88 3.6.2 Solid Solutions 89 3.6.3 The Schottky and Frenkel Defects 90 3.6.4 Non-stoichiometric Compounds 91 3.6.5 Point Defect Notation 93 3.7 Linear, Planar, and Volume defects 95 3.7.1 Dislocations 95 3.7.2 Planar Defects 96 3.7.3 Volume Defects: Precipitates 99 Reference 99 Further Reading 100 Crystal Structures 100 Defects 100 Problems and Exercises 100 Calculations and Questions 102 4 Solids: Overview 109 4.1 Metals 109 4.1.1 Structures 109 4.1.2 Metallic Radii 110 4.1.3 Alloy Solid Solutions 112 4.1.4 Metallic Glasses and Quasicrystals 115 4.1.5 The Principal Properties of Metals 116 4.2 Crystalline Silicates and Inorganic Ceramic Materials 118 4.2.1 Silicate Structures 119 4.2.2 Some Non-silicate Ceramics 122 4.2.3 The Preparation and Processing of Ceramics 125 4.2.4 The Principal Properties of Ceramics 126 4.3 Silicate Glasses 126 4.3.1 Bonding and Structure of Silicate Glasses 127 4.3.2 Glass Deformation 129 4.3.3 Strengthened Glass 131 4.3.4 Glass-Ceramics 132 4.4 Polymers and Organic Materials 133 4.4.1 Polymers 133 4.4.2 Polymer Formation 134 4.4.3 Microstructures of Polymers 138 4.4.4 Elastomers 143 4.4.5 Production of Polymers 145 4.4.6 Organic Framework Structures: MOFs and COFs 148 4.4.7 The Principal Properties of Polymers 151 4.5 Composite Materials 152 4.5.1 Fibre-Reinforced Materials 152 4.5.2 Cement and Concrete 154 Reference 157 Further Reading 157 Metals 157 Bulk Metallic Glasses 157 Ceramics and Glass 157 Zeolites 157 Polymers 157 Metal-organic Frameworks 158 Covalent Organic Frameworks 158 Composites 158 Problems and Exercises 158 Calculations and Questions 160 Part II Reactions and Transformations 165 5 Diffusion and Ionic Conductivity 167 5.1 Self-Diffusion and Tracer Diffusion 167 5.2 Non-steady-state and Steady-State Diffusion 169 5.3 Temperature Variation of Diffusion Coefficient 171 5.4 The Effect of Impurities 171 5.5 RandomWalk Diffusion 171 5.6 Diffusion in Solids 175 5.7 Self-Diffusion in One Dimension 176 5.8 Self-Diffusion in Crystals 178 5.9 The Arrhenius Equation and Point Defects 178 5.10 Correlation Factors for Self-Diffusion 180 5.11 Ionic Conductivity 181 5.12 The Relationship Between Ionic Conductivity and Diffusion Coefficient 183 5.13 Superionic Conductors 184 5.13.1 Disordered Cation Compounds 184 5.13.2 ß-Alumina Oxides 185 5.13.3 Stabilised Zirconia Oxides 188 5.13.4 NASICON-Related Crystals 188 References 189 Further Reading 189 Superionic Conductors: See Also References Therein 190 Problems and Exercises 190 Calculations and Questions 191 6 Phase Transformations and Reactions 195 6.1 Sintering 195 6.1.1 Sintering and Reaction 195 6.1.2 The Driving Force for Sintering 197 6.1.3 The Kinetics of Neck Growth and Grain Growth 198 6.1.4 Rapid Sintering 198 6.2 Phase Transitions 199 6.2.1 First-Order Phase Transitions 200 6.2.2 Second-Order Transitions 201 6.3 Displacive and Reconstructive Transitions 201 6.3.1 Displacive Transitions 201 6.3.2 Reconstructive Transitions 203 6.4 Order-Disorder Transitions 204 6.4.1 Positional Ordering 205 6.4.2 Orientational Ordering 205 6.5 Martensitic Transformations 206 6.5.1 The Austenite-Martensite Transition 207 6.5.2 Martensitic Transformations in Zirconia 210 6.5.3 Martensitic Transitions in Ni-Ti Alloys 211 6.5.4 Shape-Memory Alloys 212 6.6 Phase Diagrams and Microstructures 214 6.6.1 Equilibrium Solidification of Simple Binary Alloys 214 6.6.2 Non-equilibrium Solidification and Coring 214 6.6.3 Solidification in Systems Containing a Eutectic Point 216 6.6.4 Equilibrium Heat Treatment of Steel in the Fe-C Phase Diagram 218 6.7 High Temperature Oxidation of Metals 220 6.7.1 Direct Corrosion 220 6.7.2 The Rate of Oxidation 222 6.7.3 Oxide Film Microstructure 222 6.7.4 Film Growth via Diffusion 223 6.7.5 Alloys 225 6.8 Solid-State Reactions 225 6.8.1 Spinel Formation 225 6.8.2 Photoresists 227 6.8.3 Mechanochemistry 229 Further Reading 230 Sintering and 3D Printing 230 High Temperature Oxidation and Solid-State Reactions 230 For Mechanochemistry See 231 Problems and Exercises 231 Calculations and Questions 233 7 Oxidation and Reduction 239 7.1 Galvanic Cells 239 7.1.1 Cell Basics 239 7.1.2 Standard Electrode Potentials 241 7.1.3 Cell Potential, Gibbs Energy, and Concentration Dependence 243 7.2 Chemical Analysis Using Galvanic Cells 243 7.2.1 pH Meters 243 7.2.2 Ion Selective Electrodes 245 7.2.3 Oxygen Sensors 246 7.3 Batteries 247 7.3.1 Primary Batteries 248 7.3.1.1 'Dry' and Alkaline Primary Batteries 248 7.3.1.2 Lithium-Ion Primary Batteries 249 7.3.1.3 Lithium-Air Batteries 249 7.3.2 Fuel Cells 250 7.3.3 Secondary Batteries 252 7.3.3.1 The Lead-Acid Battery 252 7.3.3.2 Lithium-Ion Batteries 253 7.3.3.3 Dual-Ion Batteries 254 7.4 Corrosion 255 7.4.1 The Reaction of Metals withWater and Aqueous Acids 256 7.4.2 Dissimilar Metal Corrosion 257 7.4.3 Single Metal Electrochemical Corrosion 259 7.5 Electrolysis 260 7.5.1 Electrolytic Cells 260 7.5.2 Electroplating 261 7.5.3 The Amount of Product Produced During Electrolysis 262 7.5.4 The Electrolytic Preparation of Titanium by the FFC Cambridge Process 263 7.6 Pourbaix Diagrams 264 7.6.1 Passivation, Corrosion, and Leaching 264 7.6.2 The Stability Field ofWater 265 7.6.3 Pourbaix Diagrams for a Metal Showing Two Valence States 265 7.6.4 Pourbaix Diagram Displaying Tendency for Corrosion 268 Reference 268 Further Reading 269 For a General Introduction to Electrochemistry See 269 Structure-property Relations and Defects in Electrode and Electrolyte Solids is Described in 269 Batteries 269 Solid Oxide Fuel Cells 269 Corrosion 270 Electroplating 270 Problems and Exercises 270 Calculations and Questions 271 Part III Physical Properties 275 8 Mechanical Properties of Solids 277 8.1 Strength and Hardness 277 8.1.1 Strength 277 8.1.2 Stress and Strain 278 8.1.3 Toughness and Stiffness 280 8.1.4 Superelasticity 282 8.1.5 Hardness 283 8.2 Elastic Moduli 285 8.2.1 Young's Modulus (The Modulus of Elasticity) (E or Y) 286 8.2.2 Poisson's Ratio (nu) 288 8.2.3 The Longitudinal or Axial Modulus (L or M) 289 8.2.4 The Shear Modulus (G or mu), Bulk Modulus (K or B), and Lamé Modulus (lambda) 289 8.2.5 Relationships Between the Elastic Moduli 290 8.2.6 UltrasonicWaves in Elastic Solids 290 8.3 Deformation and Fracture 291 8.3.1 Brittle Fracture 291 8.3.2 Plastic Deformation of Metals 294 8.3.3 Brittle and Ductile Materials 297 8.3.4 Plastic Deformation of Polymers 299 8.3.5 Fracture Following Plastic Deformation 299 8.3.6 Strengthening 301 8.3.7 Computation of Deformation and Fracture 303 8.4 Time-Dependent Properties 304 8.4.1 Fatigue 304 8.4.2 Creep 305 8.5 Nanoscale Properties 309 8.5.1 Solid Lubricants 309 8.5.2 Auxetic Materials 310 8.5.3 Thin Films and Nanowires 312 8.6 Composite Materials 315 8.6.1 Elastic Modulus of Fibre Reinforced Composites 315 8.6.2 Elastic Modulus of a Two-Phase System 316 Further Reading 318 Ductility and Fracture 318 Mechanical Properties of Biological Materials 318 Hall-Petch Effect 318 Computation of Properties 318 Finite Element Methods 319 Nanoscale Methods 319 Composites 319 Problems and Exercises 319 Calculations and Questions 321 9 Insulating Solids 327 9.1 Dielectrics 327 9.1.1 Relative Permittivity and Polarisation 327 9.1.2 Polarisability 330 9.1.3 The Relative Permittivity of Crystals 332 9.2 Piezoelectrics, Pyroelectrics, and Ferroelectrics 334 9.2.1 The Piezoelectric and Pyroelectric Effects 334 9.2.2 Crystal Symmetry and the Piezoelectric and Pyroelectric Effects 335 9.2.3 Piezoelectric Mechanisms 337 9.2.4 Quartz Oscillators 338 9.2.5 Piezoelectric Polymers and Biomolecular Materials 339 9.3 Ferroelectrics 342 9.3.1 Ferroelectric and Antiferroelectric Crystals 343 9.3.2 Hysteresis and Domain Growth in Ferroelectric Crystals 345 9.3.3 The Temperature Dependence of Ferroelectricity and Antiferroelectricity 347 9.3.4 Ferroelectricity Due to Hydrogen Bonds 347 9.3.5 Ferroelectricity Due to Polar Groups 349 9.3.6 Ferroelectricity Due to Medium-Sized Transition-Metal Cations 350 9.3.7 Modification of Properties 352 9.3.8 Relaxor Ferroelectrics 354 9.3.9 Ferroelectric Nanoparticles, Thin Films, and Superlattices 354 9.3.10 Flexoelectricity in Ferroelectrics 356 Reference 358 Flexoelectric Effect 358 Further Reading 358 General 358 Introductory Crystallography with Respect to the Dielectric Properties 358 The Dielectric, Piezoelectric and Ferroelectric Properties of Perovskite Structures are Detailed in 358 Biomolecular Materials are Described in 358 Nanoparticle, Thin Films and Superlattices 358 Problems and Exercises 359 Calculations and Questions 360 10 Magnetic Solids 365 10.1 Magnetic Materials 365 10.1.1 Characterisation of Magnetic Materials 365 10.1.2 Magnetic Dipoles and Magnetic Flux 366 10.1.3 Atomic Magnetism 368 10.1.4 Overview of Magnetic Materials 369 10.2 Paramagnetic Materials 372 10.2.1 The Magnetic Moment of Paramagnetic Atoms and Ions 372 10.2.2 High and Low Spin: Crystal Field Effects 373 10.2.3 Temperature Dependence of Paramagnetic Susceptibility 376 10.2.4 Pauli Paramagnetism 378 10.3 Ferromagnetic Materials 379 10.3.1 Ferromagnetism 379 10.3.2 Exchange Energy 380 10.3.3 Domains 382 10.3.4 Hysteresis 384 10.3.5 Hard and Soft Magnetic Materials 385 10.4 Antiferromagnetic Materials and Superexchange 386 10.5 Ferrimagnetic Materials 387 10.5.1 Cubic Spinel Ferrites 387 10.5.2 Garnet Structure Ferrites 388 10.5.3 Hexagonal Ferrites 389 10.5.4 Double Exchange 390 10.6 Nanostructures 391 10.6.1 Small Particles and Data Recording 391 10.6.2 Superparamagnetism and Thin Films 391 10.6.3 Perovskite Superlattices 392 10.6.4 Photoinduced Magnetism 393 10.7 Magnetic Defects 395 10.7.1 Magnetic Defects in Semiconductors 395 10.7.2 Charge and Spin States in Cobaltites and Manganites 396 Further Reading 399 General 399 Magnetic States 399 A Starting Point for the Detection of Magnetic Fields by Animals 400 Density Functional Theory Calculations of Magnetic Properties is Outlined by 400 Magnetic Superlattices 400 A Starting Point for Studies on Photomagnetism 400 Problems and Exercises 400 Calculations and Questions 402 11 Electronic Conductivity in Solids 405 11.1 Metals 405 11.1.1 Metals, Semiconductors, and Insulators 405 11.1.2 Electronic Conductivity 407 11.1.3 Resistivity 410 11.2 Semiconductors 411 11.2.1 Intrinsic Semiconductors 411 11.2.2 Band Gap Measurement 412 11.2.3 Extrinsic Semiconductors 413 11.2.4 Carrier Concentrations in Extrinsic Semiconductors 415 11.2.5 Characterisation 416 11.2.6 The p-n Junction Diode 419 11.3 Metal-Insulator Transitions 422 11.3.1 Metals and Insulators 422 11.3.2 Electron-Electron Repulsion 423 11.3.3 Modification of Insulators 425 11.3.4 Transparent Conducting Oxides 426 11.4 Conducting Polymers 427 11.5 Superconductivity 431 11.5.1 Superconductors 431 11.5.2 The Effect of Magnetic Fields and Current 432 11.5.3 The BCS Theory of Superconductivity 434 11.5.4 Josephson Junctions 435 11.5.5 Cuprate High Temperature Superconductors 437 11.5.5.1 Lanthanum Cuprate, La2CuO4 437 11.5.5.2 Neodymium Cuprate, Nd2CuO4 438 11.5.5.3 Yttrium Barium Copper Oxide, YBa2Cu3O7 439 11.5.5.4 Perovskite-Related Structures and Series 440 11.5.6 Bi-layer Graphene 444 11.6 Nanostructures and Quantum Confinement of Electrons 445 Further Reading 447 The Band Theory Definition of a Semiconductor is Due to A.H. Wilson 447 Conductivity of (Mainly) Inorganic Solids Due to Defects is Covered In 447 The Metal-Insulator Transition in VO2 447 Polymers 447 Superconductivity 447 The Following Articles in Scientific American Give a Good Overview of the Early Years of High Temperature Superconductivity 448 Graphene Bilayers 448 Quantum Hall Effect 448 Problems and Exercises 448 Calculations and Questions 450 12 Optical Aspects of Solids 455 12.1 Light 455 12.1.1 LightWaves 455 12.1.2 Photons 457 12.1.3 Colour and Appearance 459 12.2 Sources of Light 460 12.2.1 Incandescence 460 12.2.2 Luminescence 461 12.2.3 Fluorescent Lamps 463 12.2.4 Light Emitting Diodes (LEDs) 464 12.2.5 Organic Light Emitting Devices/Diodes (OLEDs) 467 12.2.6 Solid-State Lasers 469 12.2.6.1 The Ruby Laser: Three-Level Lasers 471 12.2.6.2 The Neodymium (Nd3+) Solid State Laser: Four-Level Lasers 473 12.2.6.3 Semiconductor Lasers 474 12.3 Refraction 474 12.3.1 The Refractive Index 474 12.3.2 Refractive Index and Structure 477 12.4 Reflection 477 12.4.1 Reflection from a Surface 477 12.4.2 Reflection from a Transparent Thin Film 478 12.4.3 Low-Reflectivity (Antireflection) and High-Reflectivity Coatings 482 12.4.4 Multiple Thin Films and Dielectric Mirrors 483 12.5 Scattering and Attenuation 483 12.5.1 Scattering 483 12.5.2 Attenuation 485 12.6 Diffraction 486 12.6.1 Diffraction by an Aperture 486 12.6.2 Diffraction Gratings 487 12.6.3 Diffraction from Crystal-like Structures 488 12.6.4 Holograms 490 12.6.4.1 Hologram Formation 490 12.6.4.2 Hologram Recording Media 492 12.7 Fibre Optics 493 12.7.1 Attenuation in Glass Fibres 493 12.7.2 Dispersion and Optical Fibre Design 494 12.7.3 Optical Amplification 496 12.8 Energy Conversion 496 12.8.1 Photoconductivity and Photovoltaic Solar Cells 496 12.8.2 Dye-Sensitised Solar Cells 497 12.8.3 Perovskite Solar Cells 499 12.9 Nanostructures 501 12.9.1 The Optical Properties of QuantumWells 502 12.9.2 The Optical Properties of Nanoparticles 502 12.9.3 Nanoparticle Arrays 504 Further Reading 506 General 506 Much of the Material in this Chapter is Covered in Greater Detail in 506 The Properties of Light with Respect to Colour are Found in 506 The Engineering Aspects of Optical Fibres are Described by 506 Perovskite Solar Cells are Described in 506 For Nanostructures and Surfaces See the Following Review Articles and References Therein 506 Problems and Exercises 507 Calculations and Questions 509 13 Thermal Properties of Solids 515 13.1 Heat Capacity 515 13.1.1 The Heat Capacity of a Solid 515 13.1.2 Theories of Heat Capacity 515 13.1.3 Heat Capacity at Phase Transitions 517 13.2 Thermal Conductivity 518 13.2.1 Heat Transfer 518 13.2.2 Thermal Conductivity and Microstructure 520 13.3 Expansion and Contraction 522 13.3.1 Thermal Expansion 522 13.3.2 Thermal Expansion and Interatomic Potentials 523 13.3.3 Thermal Contraction 524 13.3.4 Zero Thermal Contraction Materials 526 13.4 Thermoelectric Effects 527 13.4.1 Thermoelectric Coefficients 527 13.4.2 Thermoelectric Effects and Charge Carriers 529 13.4.3 The Seebeck Coefficient of Solids Containing Point Defect Populations 530 13.4.4 Thermocouples, Power Generation, and Refrigeration 531 13.5 The Magnetocaloric Effect 533 13.5.1 The Magnetocaloric Effect and Adiabatic Cooling 533 13.5.2 The Giant Magnetocaloric Effect 534 13.6 Thermochromic Effects 535 13.6.1 Liquid Crystal Display Thermometers 535 13.6.2 Vanadium Dioxide 537 References 537 Further Reading 538 General 538 An Interactive Demonstration of the Debye Formula for the Heat Capacity of Solids Is 538 Thermal Conductivity 538 Negative and Zero Thermal Expansion 538 The Magnetocaloric Effect in Alloys 538 Thermoelectric Materials 538 Problems and Exercises 539 Calculations and Questions 540 Part IV Nuclear Properties of Solids 543 14 Radioactivity and Nuclear Reactions 545 14.1 Radioactivity 545 14.1.1 Naturally Occurring Radioactive Elements 545 14.1.2 Isotopes and Nuclides 546 14.1.3 Nuclear Equations 546 14.1.4 Radioactive Series 547 14.1.4.1 The Uranium Series 547 14.1.4.2 The Thorium Series 548 14.1.4.3 The Actinium Series 548 14.1.4.4 The Neptunium/Plutonium Series 550 14.1.5 Nuclear Stability 550 14.2 Artificial Radioactive Atoms 551 14.2.1 Heavy Elements 551 14.2.2 Artificial Radioactivity in Light Elements 553 14.3 Nuclear Decay 554 14.3.1 The Rate of Nuclear Decay 554 14.3.2 Radioactive Dating 555 14.4 Nuclear Energy 557 14.4.1 The Binding Energy of Nuclides 557 14.4.2 Nuclear Fission 558 14.4.3 Thermal Reactors for Power Generation 560 14.4.4 Fuel for Space Exploration 561 14.4.5 Fast Breeder Reactors 561 14.4.6 Fusion and Solar Cycles 562 14.5 NuclearWaste 563 14.5.1 Nuclear Accidents 563 14.5.2 The Storage of NuclearWaste 564 Further Reading 565 The Search for New Heavy Elements 565 Radioactive Dating 565 Nuclear Reactors 566 NuclearWaste 566 Problems and Exercises 566 Calculations and Questions 568 Appendix A 571 Appendix B Energy Levels and Terms of Many-Electron Atoms 573 B.1 Derivation of Atomic Terms 573 B.2 The Ground State Term of an Atom 574 B.3 Energy Levels of Many Electron Atoms 575 Index 577