Richard J. D. Tilley D. Sc, Ph. D, is Emeritus Professor in the School of Engineering at the University of Cardiff, Wales, U.K. He has published extensively in the area of solid-state materials science, including four books for Wiley, 180 papers, and 15 fifteen book chapters.

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

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