Understanding Solids

Preface to the Second Edition xvii Preface to the First Edition xix PART 1 STRUCTURES AND MICROSTRUCTURES 1 1 The electron structure of atoms 3 1.1 The hydrogen atom 3 1.1.1 The quantum mechanical description 3 1.1.2 The energy of the electron 4 1.1.3 Electron orbitals 5 1.1.4 Orbital shapes 5 1.2 Many-electron atoms 7 1.2.1 The orbital approximation 7 1.2.2 Electron spin and electron configuration 7 1.2.3 The periodic table 9 1.3 Atomic energy levels 11 1.3.1 Spectra and energy levels 11 1.3.2 Terms and term symbols 11 1.3.3 Levels 13 1.3.4 Electronic energy level calculations 14 Further reading 15 Problems and exercises 16 2 Chemical bonding 19 2.1 Ionic bonding 19 2.1.1 Ions 19 2.1.2 Ionic size and shape 20 2.1.3 Lattice energies 21 2.1.4 Atomistic simulation 23 2.2 Covalent bonding 24 2.2.1 Valence bond theory 24 2.2.2 Molecular orbital theory 30 2.3 Metallic bonding and energy bands 35 2.3.1 Molecular orbitals and energy bands 36 2.3.2 The free electron gas 37 2.3.3 Energy bands 40 2.3.4 Properties of metals 41 2.3.5 Bands in ionic and covalent solids 43 2.3.6 Computation of properties 44 Further reading 45 Problems and exercises 46 3 States of aggregation 49 3.1 Weak chemical bonds 49 3.2 Macrostructures, microstructures and nanostructures 52 3.2.1 Structures and scale 52 3.2.2 Crystalline solids 52 3.2.3 Quasicrystals 53 3.2.4 Non-crystalline solids 54 3.2.5 Partly crystalline solids 55 3.2.6 Nanoparticles and nanostructures 55 3.3 The development of microstructures 57 3.3.1 Solidification 58 3.3.2 Processing 58 3.4 Point defects 60 3.4.1 Point defects in crystals of elements 60 3.4.2 Solid solutions 61 3.4.3 Schottky defects 62 3.4.4 Frenkel defects 63 3.4.5 Non-stoichiometric compounds 64 3.4.6 Point defect notation 66 3.5 Linear, planar and volume defects 68 3.5.1 Edge dislocations 68 3.5.2 Screw dislocations 69 3.5.3 Partial and mixed dislocations 69 3.5.4 Planar defects 69 3.5.5 Volume defects: precipitates 70 Further reading 73 Problems and exercises 73 4 Phase diagrams 77 4.1 Phases and phase diagrams 77 4.1.1 One-component (unary) systems 77 4.1.2 The phase rule for one-component (unary) systems 79 4.2 Binary phase diagrams 80 4.2.1 Two-component (binary) systems 80 4.2.2 The phase rule for two-component (binary) systems 81 4.2.3 Simple binary diagrams: nickel–copper as an example 81 4.2.4 Binary systems containing a eutectic point: tin–lead as an example 83 4.2.5 Intermediate phases and melting 87 4.3 The iron–carbon system near to iron 88 4.3.1 The iron–carbon phase diagram 88 4.3.2 Steels and cast irons 89 4.3.3 Invariant points 89 4.4 Ternary systems 90 4.5 Calculation of phase diagrams: CALPHAD 93 Further reading 94 Problems and exercises 94 5 Crystallography and crystal structures 101 5.1 Crystallography 101 5.1.1 Crystal lattices 101 5.1.2 Crystal systems and crystal structures 102 5.1.3 Symmetry and crystal classes 104 5.1.4 Crystal planes and Miller indices 106 5.1.5 Hexagonal crystals and Miller-Bravais indices 109 5.1.6 Directions 110 5.1.7 Crystal geometry and the reciprocal lattice 112 5.2 The determination of crystal structures 114 5.2.1 Single crystal X-ray diffraction 114 5.2.2 Powder X-ray diffraction and crystal identification 115 5.2.3 Neutron diffraction 118 5.2.4 Electron diffraction 118 5.3 Crystal structures 118 5.3.1 Unit cells, atomic coordinates and nomenclature 118 5.3.2 The density of a crystal 119 5.3.3 The cubic close-packed (A1) structure 121 5.3.4 The body-centred cubic (A2) structure 121 5.3.5 The hexagonal (A3) structure 122 5.3.6 The diamond (A4) structure 122 5.3.7 The graphite (A9) structure 123 5.3.8 The halite (rock salt, sodium chloride, B1) structure 123 5.3.9 The spinel (H11) structure 125 5.4 Structural relationships 126 5.4.1 Sphere packing 126 5.4.2 Ionic structures in terms of anion packing 128 5.4.3 Polyhedral representations 129 Further reading 131 Problems and exercises 131 PART 2 CLASSES OF MATERIALS 137 6 Metals, ceramics, polymers and composites 139 6.1 Metals 139 6.1.1 The crystal structures of pure metals 140 6.1.2 Metallic radii 141 6.1.3 Alloy solid solutions 142 6.1.4 Metallic glasses 145 6.1.5 The principal properties of metals 146 6.2 Ceramics 147 6.2.1 Bonding and structure of silicate ceramics 147 6.2.2 Some non-silicate ceramics 149 6.2.3 The preparation and processing of ceramics 152 6.2.4 The principal properties of ceramics 154 6.3 Silicate glasses 154 6.3.1 Bonding and structure of silicate glasses 155 6.3.2 Glass deformation 157 6.3.3 Strengthened glass 159 6.3.4 Glass-ceramics 160 6.4 Polymers 161 6.4.1 Polymer formation 162 6.4.2 Microstructures of polymers 165 6.4.3 Production of polymers 170 6.4.4 Elastomers 173 6.4.5 The principal properties of polymers 175 6.5 Composite materials 177 6.5.1 Fibre-reinforced plastics 177 6.5.2 Metal-matrix composites 177 6.5.3 Ceramic-matrix composites 178 6.5.4 Cement and concrete 178 Further reading 181 Problems and exercises 182 PART 3 REACTIONS AND TRANSFORMATIONS 189 7 Diffusion and ionic conductivity 191 7.1 Self-diffusion, tracer diffusion and tracer impurity diffusion 191 7.2 Non-steady-state diffusion 194 7.3 Steady-state diffusion 195 7.4 Temperature variation of diffusion coefficient 195 7.5 The effect of impurities 196 7.6 Random walk diffusion 197 7.7 Diffusion in solids 198 7.8 Self-diffusion in one dimension 199 7.9 Self-diffusion in crystals 201 7.10 The Arrhenius equation and point defects 202 7.11 Correlation factors for self-diffusion 204 7.12 Ionic conductivity 205 7.12.1 Ionic conductivity in solids 205 7.12.2 The relationship between ionic conductivity and diffusion coefficient 208 Further reading 209 Problems and exercises 209 8 Phase transformations and reactions 213 8.1 Sintering 213 8.1.1 Sintering and reaction 213 8.1.2 The driving force for sintering 215 8.1.3 The kinetics of neck growth 216 8.2 First-order and second-order phase transitions 216 8.2.1 First-order phase transitions 217 8.2.2 Second-order transitions 217 8.3 Displacive and reconstructive transitions 218 8.3.1 Displacive transitions 218 8.3.2 Reconstructive transitions 219 8.4 Order–disorder transitions 221 8.4.1 Positional ordering 221 8.4.2 Orientational ordering 222 8.5 Martensitic transformations 223 8.5.1 The austenite–martensite transition 223 8.5.2 Martensitic transformations in zirconia 226 8.5.3 Martensitic transitions in Ni–Ti alloys 227 8.5.4 Shape-memory alloys 228 8.6 Phase diagrams and microstructures 230 8.6.1 Equilibrium solidification of simple binary alloys 230 8.6.2 Non-equilibrium solidification and coring 230 8.6.3 Solidification in systems containing a eutectic point 231 8.6.4 Equilibrium heat treatment of steel in the Fe–C phase diagram 233 8.7 High-temperature oxidation of metals 236 8.7.1 Direct corrosion 236 8.7.2 The rate of oxidation 236 8.7.3 Oxide film microstructure 237 8.7.4 Film growth via diffusion 238 8.7.5 Alloys 239 8.8 Solid-state reactions 240 8.8.1 Spinel formation 240 8.8.2 The kinetics of spinel formation 241 Further reading 242 Problems and exercises 242 9 Oxidation and reduction 247 9.1 Galvanic cells 247 9.1.1 Cell basics 247 9.1.2 Standard electrode potentials 249 9.1.3 Cell potential and Gibbs energy 250 9.1.4 Concentration dependence 251 9.2 Chemical analysis using galvanic cells 251 9.2.1 pH meters 251 9.2.2 Ion selective electrodes 253 9.2.3 Oxygen sensors 254 9.3 Batteries 255 9.3.1 ‘Dry’ and alkaline primary batteries 255 9.3.2 Lithium-ion primary batteries 256 9.3.3 The lead–acid secondary battery 257 9.3.4 Lithium-ion secondary batteries 257 9.3.5 Lithium–air batteries 259 9.3.6 Fuel cells 260 9.4 Corrosion 262 9.4.1 The reaction of metals with water and aqueous acids 262 9.4.2 Dissimilar metal corrosion 264 9.4.3 Single metal electrochemical corrosion 265 9.5 Electrolysis 266 9.5.1 Electrolytic cells 267 9.5.2 Electroplating 267 9.5.3 The amount of product produced during electrolysis 268 9.5.4 The electrolytic preparation of titanium by the FFC Cambridge Process 269 9.6 Pourbaix diagrams 270 9.6.1 Passivation, corrosion and leaching 270 9.6.2 The stability field of water 270 9.6.3 Pourbaix diagram for a metal showing two valence states, M2þ and M3þ 271 9.6.4 Pourbaix diagram displaying tendency for corrosion 273 Further reading 274 Problems and exercises 275 PART 4 PHYSICAL PROPERTIES 279 10 Mechanical properties of solids 281 10.1 Strength and hardness 281 10.1.1 Strength 281 10.1.2 Stress and strain 282 10.1.3 Stress–strain curves 283 10.1.4 Toughness and stiffness 286 10.1.5 Superelasticity 286 10.1.6 Hardness 287 10.2 Elastic moduli 289 10.2.1 Young’s modulus (the modulus of elasticity) (E or Y) 289 10.2.2 Poisson’s ratio (n) 291 10.2.3 The longitudinal or axial modulus (L or M) 292 10.2.4 The shear modulus or modulus of rigidity (G or m) 292 10.2.5 The bulk modulus, K or B 293 10.2.6 The Lame modulus (l) 293 10.2.7 Relationships between the elastic moduli 293 10.2.8 Ultrasonic waves in elastic solids 293 10.3 Deformation and fracture 295 10.3.1 Brittle fracture 295 10.3.2 Plastic deformation of metals 298 10.3.3 Dislocation movement and plastic deformation 298 10.3.4 Brittle and ductile materials 301 10.3.5 Plastic deformation of polymers 302 10.3.6 Fracture following plastic deformation 302 10.3.7 Strengthening 304 10.3.8 Computation of deformation and fracture 306 10.4 Time-dependent properties 307 10.4.1 Fatigue 307 10.4.2 Creep 308 10.5 Nanoscale properties 312 10.5.1 Solid lubricants 312 10.5.2 Auxetic materials 313 10.5.3 Thin films and nanowires 315 10.6 Composite materials 317 10.6.1 Young’s modulus of large particle composites 317 10.6.2 Young’s modulus of fibre-reinforced composites 318 10.6.3 Young’s modulus of a two-phase system 319 Further reading 320 Problems and exercises 321 11 Insulating solids 327 11.1 Dielectrics 327 11.1.1 Relative permittivity and polarisation 327 11.1.2 Polarisability 329 11.1.3 Polarisability and relative permittivity 330 11.1.4 The frequency dependence of polarisability and relative permittivity 331 11.1.5 The relative permittivity of crystals 332 11.2 Piezoelectrics, pyroelectrics and ferroelectrics 333 11.2.1 The piezoelectric and pyroelectric effects 333 11.2.2 Crystal symmetry and the piezoelectric and pyroelectric effects 335 11.2.3 Piezoelectric mechanisms 336 11.2.4 Quartz oscillators 337 11.2.5 Piezoelectric polymers 338 11.3 Ferroelectrics 340 11.3.1 Ferroelectric crystals 340 11.3.2 Hysteresis and domain growth in ferroelectric crystals 341 11.3.3 Antiferroelectrics 344 11.3.4 The temperature dependence of ferroelectricity and antiferroelectricity 344 11.3.5 Ferroelectricity due to hydrogen bonds 345 11.3.6 Ferroelectricity due to polar groups 347 11.3.7 Ferroelectricity due to medium-sized transition-metal cations 348 11.3.8 Poling and polycrystalline ferroelectric solids 349 11.3.9 Doping and modification of properties 349 11.3.10 Relaxor ferroelectrics 351 11.3.11 Ferroelectric nanoparticles, thin films and superlattices 352 11.3.12 Flexoelectricity in ferroelectrics 353 Further reading 354 Problems and exercises 355 12 Magnetic solids 361 12.1 Magnetic materials 361 12.1.1 Characterisation of magnetic materials 361 12.1.2 Magnetic dipoles and magnetic flux 362 12.1.3 Atomic magnetism 363 12.1.4 Overview of magnetic materials 365 12.2 Paramagnetic materials 368 12.2.1 The magnetic moment of paramagnetic atoms and ions 368 12.2.2 High and low spin: crystal field effects 369 12.2.3 Temperature dependence of paramagnetic susceptibility 371 12.2.4 Pauli paramagnetism 373 12.3 Ferromagnetic materials 374 12.3.1 Ferromagnetism 374 12.3.2 Exchange energy 376 12.3.3 Domains 378 12.3.4 Hysteresis 380 12.3.5 Hard and soft magnetic materials 380 12.4 Antiferromagnetic materials and superexchange 381 12.5 Ferrimagnetic materials 382 12.5.1 Cubic spinel ferrites 382 12.5.2 Garnet structure ferrites 383 12.5.3 Hexagonal ferrites 383 12.5.4 Double exchange 384 12.6 Nanostructures 385 12.6.1 Small particles and data recording 385 12.6.2 Superparamagnetism and thin films 386 12.6.3 Superlattices 386 12.6.4 Photoinduced magnetism 387 12.7 Magnetic defects 389 12.7.1 Magnetic defects in semiconductors 389 12.7.2 Charge and spin states in cobaltites and manganites 390 Further reading 393 Problems and exercises 393 13 Electronic conductivity in solids 399 13.1 Metals 399 13.1.1 Metals, semiconductors and insulators 399 13.1.2 Electron drift in an electric field 401 13.1.3 Electronic conductivity 402 13.1.4 Resistivity 404 13.2 Semiconductors 405 13.2.1 Intrinsic semiconductors 405 13.2.2 Band gap measurement 407 13.2.3 Extrinsic semiconductors 408 13.2.4 Carrier concentrations in extrinsic semiconductors 409 13.2.5 Characterisation 411 13.2.6 The p-n junction diode 413 13.3 Metal–insulator transitions 416 13.3.1 Metals and insulators 416 13.3.2 Electron–electron repulsion 417 13.3.3 Modification of insulators 418 13.3.4 Transparent conducting oxides 419 13.4 Conducting polymers 420 13.5 Nanostructures and quantum confinement of electrons 423 13.5.1 Quantum wells 424 13.5.2 Quantum wires and quantum dots 425 13.6 Superconductivity 426 13.6.1 Superconductors 426 13.6.2 The effect of magnetic fields 427 13.6.3 The effect of current 428 13.6.4 The nature of superconductivity 428 13.6.5 Josephson junctions 430 13.6.6 Cuprate high-temperature superconductors 430 Further reading 438 Problems and exercises 438 14 Optical aspects of solids 445 14.1 Light 445 14.1.1 Light waves 445 14.1.2 Photons 447 14.2 Sources of light 449 14.2.1 Incandescence 449 14.2.2 Luminescence and phosphors 450 14.2.3 Light-emitting diodes (LEDs) 453 14.2.4 Solid-state lasers 454 14.3 Colour and appearance 460 14.3.1 Luminous solids 460 14.3.2 Non-luminous solids 460 14.3.3 Attenuation 461 14.4 Refraction and dispersion 462 14.4.1 Refraction 462 14.4.2 Refractive index and structure 464 14.4.3 The refractive index of metals and semiconductors 465 14.4.4 Dispersion 465 14.5 Reflection 466 14.5.1 Reflection from a surface 466 14.5.2 Reflection from a single thin film 467 14.5.3 The reflectivity of a single thin film in air 469 14.5.4 The colour of a single thin film in air 469 14.5.5 The colour of a single thin film on a substrate 470 14.5.6 Low-reflectivity (antireflection) and high-reflectivity coatings 471 14.5.7 Multiple thin films and dielectric mirrors 471 14.6 Scattering 472 14.6.1 Rayleigh scattering 472 14.6.2 Mie scattering 475 14.7 Diffraction 475 14.7.1 Diffraction by an aperture 475 14.7.2 Diffraction gratings 476 14.7.3 Diffraction from crystal-like structures 477 14.7.4 Photonic crystals 478 14.8 Fibre optics 479 14.8.1 Optical communications 479 14.8.2 Attenuation in glass fibres 479 14.8.3 Dispersion and optical fibre design 480 14.8.4 Optical amplification 482 14.9 Energy conversion 483 14.9.1 Photoconductivity and photovoltaic solar cells 483 14.9.2 Dye sensitized solar cells 485 14.10 Nanostructures 486 14.10.1 The optical properties of quantum wells 486 14.10.2 The optical properties of nanoparticles 487 Further reading 489 Problems and exercises 489 15 Thermal properties 495 15.1 Heat capacity 495 15.1.1 The heat capacity of a solid 495 15.1.2 Classical theory of heat capacity 496 15.1.3 Quantum theory of heat capacity 496 15.1.4 Heat capacity at phase transitions 497 15.2 Thermal conductivity 498 15.2.1 Heat transfer 498 15.2.2 Thermal conductivity of solids 498 15.2.3 Thermal conductivity and microstructure 500 15.3 Expansion and contraction 501 15.3.1 Thermal expansion 501 15.3.2 Thermal expansion and interatomic potentials 502 15.3.3 Thermal contraction 503 15.3.4 Zero thermal contraction materials 505 15.4 Thermoelectric effects 506 15.4.1 Thermoelectric coefficients 506 15.4.2 Thermoelectric effects and charge carriers 508 15.4.3 The Seebeck coefficient of solids containing point defect populations 509 15.4.4 Thermocouples, power generation and refrigeration 509 15.5 The magnetocaloric effect 512 15.5.1 The magnetocaloric effect and adiabatic cooling 512 15.5.2 The giant magnetocaloric effect 513 Further reading 514 Problems and exercises 514 PART 5 NUCLEAR PROPERTIES OF SOLIDS 517 16 Radioactivity and nuclear reactions 519 16.1 Radioactivity 519 16.1.1 Naturally occurring radioactive elements 519 16.1.2 Isotopes and nuclides 520 16.1.3 Nuclear equations 520 16.1.4 Radioactive series 521 16.1.5 Nuclear stability 523 16.2 Artificial radioactive atoms 524 16.2.1 Transuranic elements 524 16.2.2 Artificial radioactivity in light elements 527 16.3 Nuclear decay 527 16.3.1 The rate of nuclear decay 527 16.3.2 Radioactive dating 529 16.4 Nuclear energy 531 16.4.1 The binding energy of nuclides 531 16.4.2 Nuclear fission 532 16.4.3 Thermal reactors for power generation 533 16.4.4 Fuel for space exploration 535 16.4.5 Fast breeder reactors 535 16.4.6 Fusion 535 16.4.7 Solar cycles 536 16.5 Nuclear waste 536 16.5.1 Nuclear accidents 537 16.5.2 The storage of nuclear waste 537 Further reading 538 Problems and exercises 539 Subject Index 543