Understanding Solids: The Science of Materials

Understanding Solids......Page 4
Contents......Page 10
Preface......Page 24
PART 1 STRUCTURES AND MICROSTRUCTURES......Page 26
1.1 Atoms......Page 28
1.2.1 The quantum mechanical description of a hydrogen atom......Page 30
1.2.2 The energy of the electron......Page 31
1.2.3 The location of the electron......Page 32
1.2.4 Orbital shapes......Page 33
1.3.1 The orbital approximation......Page 35
1.3.2 Electron spin and electron configuration......Page 36
1.3.3 The periodic table......Page 38
1.4.2 The vector model......Page 40
1.4.3 Terms and term schemes......Page 41
Why does the periodic table summarise both the chemical and the physical properties of the elements?......Page 42
Problems and exercises......Page 43
2.1.1 Ions......Page 48
2.1.3 Madelung energy......Page 49
2.1.5 Lattice energy......Page 51
2.1.6 The formulae and structures of ionic compounds......Page 52
2.1.7 Ionic size and shape......Page 53
2.1.8 Ionic structures......Page 54
2.2.1 Molecular orbitals......Page 55
2.2.2 The energies of molecular orbitals in diatomic molecules......Page 56
2.2.3 Bonding between unlike atoms......Page 59
2.2.4 Electronegativity......Page 60
2.2.5 Bond strength and direction......Page 61
2.2.6 Orbital hybridisation......Page 62
2.2.7 Multiple bonds......Page 65
2.2.8 Resonance......Page 68
2.3.2 Chemical bonding......Page 69
2.3.4 Divalent and other metals......Page 71
2.3.5 The classical free-electron gas......Page 72
2.3.6 The quantum free-electron gas......Page 73
2.3.7 The Fermi energy and Fermi surface......Page 74
2.3.8 Energy bands......Page 76
2.3.10 Alloys and noncrystalline metals......Page 78
2.3.11 Bands in ionic and covalent solids......Page 79
Further reading......Page 81
Problems and exercises......Page 82
3.1.1 Weak chemical bonds......Page 86
3.1.2 Chemical names and formulae......Page 89
3.1.3 Polymorphism and other transformations......Page 90
3.2.1 Structures and microstructures......Page 91
3.2.3 Noncrystalline solids......Page 92
3.2.4 Partly crystalline solids......Page 94
3.2.5 Nanostructures......Page 95
3.3.1 Solidification......Page 96
3.4.1 Point defects in crystals of elements......Page 98
3.4.3 Schottky defects......Page 100
3.4.4 Frenkel defects......Page 102
3.4.5 Nonstoichiometric compounds......Page 103
3.4.6 Edge dislocations......Page 104
3.4.7 Screw dislocations......Page 105
3.4.8 Partial and mixed dislocations......Page 106
3.4.9 Multiplication of dislocations......Page 107
3.4.10 Planar defects......Page 108
3.4.11 Volume defects: precipitates......Page 109
Further reading......Page 110
Problems and exercises......Page 111
4.1.1 One-component (unary) systems......Page 116
4.2.2 Simple binary phase diagrams: nickel–copper......Page 119
4.2.3 Binary systems containing a eutectic point: lead–tin......Page 121
4.2.4 Solid solution formation......Page 124
4.2.5 Binary systems containing intermediate compounds......Page 125
4.2.6 The iron–carbon phase diagram......Page 126
4.2.7 Steels and cast irons......Page 128
4.3.1 Ternary phase diagrams......Page 129
Further reading......Page 132
Problems and exercises......Page 133
5.1.1 Crystal lattices......Page 140
5.1.2 Crystal structures and crystal systems......Page 142
5.1.3 Symmetry and crystal classes......Page 143
5.1.4 Crystal planes and Miller indices......Page 144
5.1.5 Hexagonal crystals and Miller-Bravais indices......Page 145
5.1.6 Directions......Page 146
5.1.7 The reciprocal lattice......Page 147
5.2 The determination of crystal structures......Page 148
5.2.2 Powder X-ray diffraction and crystal identification......Page 149
5.2.4 Electron diffraction......Page 151
5.3.1 Unit cells, atomic coordinates and nomenclature......Page 152
5.3.2 The density of a crystal......Page 153
5.3.3 The cubic close-packed (A1) structure......Page 154
5.3.5 The hexagonal (A3) structure......Page 155
5.3.7 The hexagonal (graphite), A9 structure......Page 156
5.3.9 The halite (rock salt, sodium chloride, B1) structure......Page 157
5.3.10 The spinel (H1(1)) structure......Page 158
5.4.1 Sphere packing......Page 159
5.4.2 Ionic structures in terms of anion packing......Page 161
5.4.3 Polyhedral representations......Page 163
What is meant by a (100) plane?......Page 165
Problems and exercises......Page 166
PART 2 CLASSES OF MATERIALS......Page 174
6.1 Metals......Page 176
6.1.1 The crystal structures of pure metals......Page 177
6.1.2 Metallic radii......Page 178
6.1.3 Alloy solid solutions......Page 179
6.1.4 Metallic glasses......Page 182
6.1.5 The principal properties of metals......Page 183
6.2.1 Bonding and structure of silicate ceramics......Page 184
6.2.2 Bonding and structure of nonsilicate ceramics......Page 188
6.2.4 The principal properties of ceramics......Page 190
6.3.1 Bonding and structure of silicate glasses......Page 191
6.3.2 Glass deformation......Page 193
6.3.4 Glass ceramics......Page 195
6.4.1 The chemical structure of some polymers......Page 197
6.4.2 Microstructures of polymers......Page 201
6.4.3 Production of polymers......Page 205
6.4.4 Elastomers......Page 208
6.4.5 The principal properties of polymers......Page 210
6.5.1 Fibre-reinforced plastics......Page 212
6.5.4 Cement and concrete......Page 213
Are polymers glasses?......Page 216
Problems and exercises......Page 217
PART 3 REACTIONS AND TRANSFORMATIONS......Page 226
7.1 Self-diffusion, tracer diffusion and tracer impurity diffusion......Page 228
7.2 Nonsteady-state diffusion......Page 231
7.4 Temperature variation of the diffusion coefficient......Page 233
7.5 The effect of impurities......Page 234
7.7 Self-diffusion mechanisms......Page 235
7.8 Atomic movement during diffusion......Page 236
7.10 Self-diffusion in crystals......Page 237
7.11 The Arrhenius equation and the effect of temperature......Page 238
7.12 Correlation factors for self-diffusion......Page 239
7.13 Ionic conductivity......Page 240
7.14 The relationship between ionic conductivity and the diffusion coefficient......Page 242
Problems and exercises......Page 243
8.1.1 Reversible reactions and equilibrium......Page 250
8.1.2 Equilibrium constants......Page 251
8.1.4 Equilibrium conditions......Page 252
8.1.5 Pseudochemical equilibrium......Page 253
8.2.1 Equilibrium solidification of simple binary alloys......Page 254
8.2.2 Nonequilibrium solidification and coring......Page 255
8.2.3 Solidification in systems containing a eutectic point......Page 256
8.2.4 Equilibrium heat treatment of steels......Page 258
8.2.5 Rapid cooling of steels......Page 261
8.3.1 Displacive transitions......Page 262
8.3.2 Martensitic transitions in alloys......Page 263
8.3.3 Shape-memory alloys......Page 264
8.4.1 Sintering and reaction......Page 266
8.4.2 The driving force for sintering......Page 267
8.4.3 The kinetics of neck growth......Page 268
8.5.2 The rate of oxidation......Page 269
8.5.3 Mechanisms of oxidation......Page 270
8.6.1 Spinel formation......Page 272
What is dynamic equilibrium?......Page 274
Further reading......Page 275
Problems and exercises......Page 276
9.1.1 Oxidation and reduction......Page 282
9.2.1 The Daniel cell......Page 283
9.2.2 Standard electrode potentials......Page 284
9.2.3 Cell potential and free energy......Page 286
9.2.4 Concentration dependence......Page 287
9.2.5 Chemical analysis using galvanic cells......Page 288
9.3.1 ‘Dry’ and alkaline primary batteries......Page 290
9.3.2 Lithium-ion primary batteries......Page 291
9.3.4 Nickel–cadmium (Ni–Cd, nicad) rechargable batteries......Page 292
9.3.5 Nickel-metal-hydride rechargeable batteries......Page 293
9.3.6 Lithium-ion rechargeable batteries......Page 294
9.3.7 Fuel cells......Page 295
9.4.1 The reaction of metals with water and aqueous acids......Page 297
9.4.2 Dissimilar-metal corrosion......Page 299
9.4.3 Single-metal electrochemical corrosion......Page 300
9.5.2 Electrolysis of fused salts......Page 302
9.5.3 The electrolytic preparation of titanium by the Fray-Farthing-Chen Cambridge process......Page 303
9.5.4 Electrolysis of aqueous solutions......Page 305
9.5.5 The amount of product produced during electrolysis......Page 306
9.5.6 Electroplating......Page 307
9.6.2 Variable valence states......Page 308
9.6.3 Pourbaix diagram for a metal showing two valence states, M(2+) and M(3+)......Page 309
9.6.5 Limitations of Pourbaix diagrams......Page 310
What information is contained in a Pourbaix diagram?......Page 311
Problems and exercises......Page 312
PART 4 PHYSICAL PROPERTIES......Page 318
10 Mechanical properties of solids......Page 320
10.1.2 Stress and strain......Page 321
10.1.3 Stress-strain curves......Page 322
10.1.4 Elastic deformation: the elastic (Young’s) modulus......Page 325
10.1.5 Poisson’s ratio......Page 326
10.1.7 Brittle fracture......Page 327
10.1.8 Plastic deformation of metals and ceramics......Page 330
10.1.9 Dislocation movement and plastic deformation......Page 331
10.1.10 Brittle and ductile materials......Page 332
10.1.11 Plastic deformation of polymers......Page 335
10.1.12 Fracture following plastic deformation......Page 336
10.1.13 Strengthening......Page 338
10.1.14 Hardness......Page 339
10.2.1 Fatigue......Page 341
10.2.2 Creep......Page 342
10.3.1 Solid lubricants......Page 345
10.3.2 Auxetic materials......Page 347
10.3.3 Thin films......Page 348
10.4.2 Elastic modulus of fibre-reinforced composites......Page 351
How are stress and strain defined?......Page 353
What are solid lubricants?......Page 354
Problems and exercises......Page 355
11.1.1 Relative permittivity and polarisation......Page 362
11.1.2 Polarisability......Page 364
11.1.3 Polarisability and relative permittivity......Page 365
11.1.4 The frequency dependence of polarizability and relative permittivity......Page 366
11.2.1 The piezoelectric and pyroelectric effects......Page 368
11.2.2 Piezoelectric mechanisms......Page 370
11.2.3 Piezoelectric polymers......Page 372
11.2.4 The pyroelectric effect......Page 374
11.3.1 Ferroelectric crystals......Page 375
11.3.3 Antiferroelectrics......Page 376
11.3.5 Ferroelectricity due to hydrogen bonds......Page 377
11.3.7 Ferroelectricity due to medium-sized transition-metal cations......Page 379
11.3.8 Poling and polycrystalline ferroelectric solids......Page 380
How are the relative permittivity and refractive index of a transparent solid related?......Page 381
Further reading......Page 382
Problems and exercises......Page 383
12.1.1 Characterisation of magnetic materials......Page 388
12.1.2 Types of magnetic material......Page 389
12.1.3 Atomic magnetism......Page 392
12.2.2 Paramagnetic materials......Page 393
12.2.3 The temperature dependence of paramagnetic susceptibility......Page 396
12.3.1 Ferromagnetism......Page 397
12.3.2 Exchange energy......Page 398
12.3.3 Antiferromagnetism and superexchange......Page 399
12.3.4 Ferrimagnetism and double exchange......Page 400
12.3.5 Cubic spinel ferrites......Page 401
12.3.6 Hexagonal ferrites......Page 402
12.4.1 Domains......Page 403
12.4.2 Hysteresis......Page 404
12.4.3 Hysteresis loops: hard and soft magnetic materials......Page 405
12.5.1 Pauli paramagnetism......Page 406
12.5.2 Transition metals......Page 407
12.6.2 Superparamagnetism and thin films......Page 408
12.6.3 Molecular magnetism......Page 409
What is a ferrimagnetic material?......Page 410
Problems and exercises......Page 411
13.1.1 Metals, semiconductors and insulators......Page 416
13.1.2 Conductivity of metals and alloys......Page 418
13.2.1 Intrinsic semiconductors......Page 421
13.2.2 Carrier concentrations in intrinsic semiconductors......Page 423
13.2.3 Extrinsic semiconductors......Page 424
13.2.4 Carrier concentrations in extrinsic semiconductors......Page 425
13.2.5 Characterisation......Page 426
13.2.6 The p-n junction diode......Page 430
13.2.8 Conducting polymers......Page 433
13.3.1 Quantum wells......Page 437
13.3.2 Quantum wires and quantum dots......Page 439
13.4.2 The effect of magnetic fields......Page 440
13.4.4 The nature of superconductivity......Page 442
13.4.5 Ceramic ‘high-temperature’ superconductors......Page 443
13.4.6 Josephson junctions......Page 446
Further reading......Page 447
Problems and exercises......Page 448
14.1.1 Light waves......Page 456
14.1.3 The interaction of light with matter......Page 458
14.2.1 Luminescence......Page 459
14.2.2 Incandescence......Page 460
14.2.3 Fluorescence and solid-state lasers......Page 461
14.2.4 The ruby laser: three-level lasers......Page 462
14.2.5 The neodymium (Nd(3+)) solid-state laser: four-level lasers......Page 463
14.2.6 Light-emitting diodes......Page 464
14.3.2 Nonluminous solids......Page 466
14.4.1 Refraction......Page 468
14.4.2 Refractive index and structure......Page 470
14.4.4 Dispersion......Page 471
14.5.1 Reflection from a surface......Page 472
14.5.2 Reflection from a single thin film......Page 473
14.5.4 The colour of a single thin film in air......Page 474
14.5.6 Low-reflectivity (antireflection) and high-reflectivity coatings......Page 475
14.5.7 Multiple thin films and dielectric mirrors......Page 476
14.6.1 Rayleigh scattering......Page 477
14.6.2 Mie scattering......Page 478
14.7.1 Diffraction by an aperture......Page 479
14.7.2 Diffraction gratings......Page 480
14.7.4 Photonic crystals......Page 481
14.8.1 Optical communications......Page 482
14.8.2 Attenuation in glass fibres......Page 483
14.8.3 Dispersion and optical fibre design......Page 484
14.8.4 Optical amplification......Page 485
14.9.1 Nonlinear optics......Page 486
14.10.1 Photoconductivity and photovoltaic solar cells......Page 487
14.10.2 Photoelectrochemical cells......Page 488
14.11 Nanostructures......Page 489
14.11.2 Quantum wires and quantum dots......Page 490
Further reading......Page 491
Problems and exercises......Page 492
15.1.1 Heat capacity......Page 498
15.1.2 Theory of heat capacity......Page 499
15.1.4 Thermal conductivity......Page 500
15.1.6 Thermal expansion......Page 503
15.1.7 Thermal expansion and interatomic potentials......Page 505
15.1.8 Thermal contraction......Page 506
15.2.1 Thermoelectric coefficients......Page 508
15.2.2 Thermoelectric effects and charge carriers......Page 509
15.2.3 Thermocouples, power generation and refrigeration......Page 510
Problems and exercises......Page 512
PART 5 NUCLEAR PROPERTIES OF SOLIDS......Page 516
16.1.1 Radioactive elements......Page 518
16.1.3 Nuclear equations......Page 519
16.1.4 Radioactive series......Page 520
16.1.6 Artificial radioactivity......Page 522
16.2.2 The rate of nuclear decay......Page 524
16.2.3 Radioactive dating......Page 526
16.3.1 The binding energy of nuclides......Page 527
16.3.2 Nuclear fission......Page 528
16.3.3 Thermal reactors for power generation......Page 529
16.3.6 Fusion......Page 530
16.4 Nuclear waste......Page 531
16.4.2 The storage of nuclear waste......Page 532
What is the difference between an isotope and a nuclide?......Page 533
Problems and exercises......Page 534
SUPPLEMENTARY MATERIAL......Page 538
S1.1 Chemical equations and units......Page 540
S1.2.2 The electron configurations of the 3d transition metals......Page 541
S1.3.1 Energy levels and terms schemes of many-electron atoms......Page 542
S1.4 Madelung constants......Page 544
S1.5.1 The phase rule for one-component (unary) sytems......Page 545
S1.5.2 The phase rule for two-component (binary) systems......Page 546
S1.8 Construction of a reciprocal lattice......Page 547
S2.1.1 Hydrocarbons......Page 550
S2.1.2 Functional groups......Page 554
S3.1.1 The relationship between D and diffusion distance......Page 556
S3.1.2 Atomic migration and the diffusion coefficient......Page 557
S3.1.3 Ionic conductivity......Page 558
S3.2.2 Reactions......Page 559
S3.2.3 Oxidation......Page 560
S3.2.5 Activity......Page 561
S3.4 Cell notation......Page 562
S3.5 The stability field of water......Page 563
S3.6.1 Corrosion of iron......Page 564
S3.6.2 The simplified Pourbaix diagram for iron in water and air......Page 565
S4.1.2 The shear modulus or modulus of rigidity, G......Page 568
S4.1.3 The bulk modulus, K or B......Page 569
S4.1.7 The calculation of elastic and bulk moduli......Page 570
S4.2.1 Estimation of the fracture strength of a brittle solid......Page 572
S4.2.2 Estimation of the fracture strength of a brittle solid containing a crack......Page 573
S4.3 Formulae and units used to describe the electrical properties of insulators......Page 574
S4.4 Formulae and units used to describe the magnetic properties of materials......Page 575
S4.4.1 Conversion factors for superconductivity......Page 576
S4.5 Crystal field theory and ligand field theory......Page 577
S4.6 Electrical resistance and conductivity......Page 578
S4.7 Current flow......Page 579
S4.8 The electron and hole concentrations in intrinsic semiconductors......Page 580
S4.10 Rates of absorption and emission of energy......Page 582
S4.11 The colour of a thin film in white light......Page 584
S4.12 Classical and quantum statistics......Page 585
S4.13 Physical properties and vectors......Page 586
Answers to problems and exercises......Page 588
Chemical Index......Page 600
Subject Index......Page 610