Understanding Solids

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 Second Edition xvii Preface to the First Edition xixPART 1 STRUCTURES AND MICROSTRUCTURES 11 The electron structure of atoms 31.1 The hydrogen atom 31.1.1 The quantum mechanical description 31.1.2 The energy of the electron 41.1.3 Electron orbitals 51.1.4 Orbital shapes 51.2 Many-electron atoms 71.2.1 The orbital approximation 71.2.2 Electron spin and electron configuration 71.2.3 The periodic table 91.3 Atomic energy levels 111.3.1 Spectra and energy levels 111.3.2 Terms and term symbols 111.3.3 Levels 131.3.4 Electronic energy level calculations 14Further reading 15Problems and exercises 162 Chemical bonding 192.1 Ionic bonding 192.1.1 Ions 192.1.2 Ionic size and shape 202.1.3 Lattice energies 212.1.4 Atomistic simulation 232.2 Covalent bonding 242.2.1 Valence bond theory 242.2.2 Molecular orbital theory 302.3 Metallic bonding and energy bands 352.3.1 Molecular orbitals and energy bands 362.3.2 The free electron gas 372.3.3 Energy bands 402.3.4 Properties of metals 412.3.5 Bands in ionic and covalent solids 432.3.6 Computation of properties 44Further reading 45Problems and exercises 463 States of aggregation 493.1 Weak chemical bonds 493.2 Macrostructures, microstructures and nanostructures 523.2.1 Structures and scale 523.2.2 Crystalline solids 523.2.3 Quasicrystals 533.2.4 Non-crystalline solids 543.2.5 Partly crystalline solids 553.2.6 Nanoparticles and nanostructures 553.3 The development of microstructures 573.3.1 Solidification 583.3.2 Processing 583.4 Point defects 603.4.1 Point defects in crystals of elements 603.4.2 Solid solutions 613.4.3 Schottky defects 623.4.4 Frenkel defects 633.4.5 Non-stoichiometric compounds 643.4.6 Point defect notation 663.5 Linear, planar and volume defects 683.5.1 Edge dislocations 683.5.2 Screw dislocations 693.5.3 Partial and mixed dislocations 693.5.4 Planar defects 693.5.5 Volume defects: precipitates 70Further reading 73Problems and exercises 734 Phase diagrams 774.1 Phases and phase diagrams 774.1.1 One-component (unary) systems 774.1.2 The phase rule for one-component (unary) systems 794.2 Binary phase diagrams 804.2.1 Two-component (binary) systems 804.2.2 The phase rule for two-component (binary) systems 814.2.3 Simple binary diagrams: nickel–copper as an example 814.2.4 Binary systems containing a eutectic point: tin–lead as an example 834.2.5 Intermediate phases and melting 874.3 The iron–carbon system near to iron 884.3.1 The iron–carbon phase diagram 884.3.2 Steels and cast irons 894.3.3 Invariant points 894.4 Ternary systems 904.5 Calculation of phase diagrams: CALPHAD 93Further reading 94Problems and exercises 945 Crystallography and crystal structures 1015.1 Crystallography 1015.1.1 Crystal lattices 1015.1.2 Crystal systems and crystal structures 1025.1.3 Symmetry and crystal classes 1045.1.4 Crystal planes and Miller indices 1065.1.5 Hexagonal crystals and Miller-Bravais indices 1095.1.6 Directions 1105.1.7 Crystal geometry and the reciprocal lattice 1125.2 The determination of crystal structures 1145.2.1 Single crystal X-ray diffraction 1145.2.2 Powder X-ray diffraction and crystal identification 1155.2.3 Neutron diffraction 1185.2.4 Electron diffraction 1185.3 Crystal structures 1185.3.1 Unit cells, atomic coordinates and nomenclature 1185.3.2 The density of a crystal 1195.3.3 The cubic close-packed (A1) structure 1215.3.4 The body-centred cubic (A2) structure 1215.3.5 The hexagonal (A3) structure 1225.3.6 The diamond (A4) structure 1225.3.7 The graphite (A9) structure 1235.3.8 The halite (rock salt, sodium chloride, B1) structure 1235.3.9 The spinel (H11) structure 1255.4 Structural relationships 1265.4.1 Sphere packing 1265.4.2 Ionic structures in terms of anion packing 1285.4.3 Polyhedral representations 129Further reading 131Problems and exercises 131PART 2 CLASSES OF MATERIALS 1376 Metals, ceramics, polymers and composites 1396.1 Metals 1396.1.1 The crystal structures of pure metals 1406.1.2 Metallic radii 1416.1.3 Alloy solid solutions 1426.1.4 Metallic glasses 1456.1.5 The principal properties of metals 1466.2 Ceramics 1476.2.1 Bonding and structure of silicate ceramics 1476.2.2 Some non-silicate ceramics 1496.2.3 The preparation and processing of ceramics 1526.2.4 The principal properties of ceramics 1546.3 Silicate glasses 1546.3.1 Bonding and structure of silicate glasses 1556.3.2 Glass deformation 1576.3.3 Strengthened glass 1596.3.4 Glass-ceramics 1606.4 Polymers 1616.4.1 Polymer formation 1626.4.2 Microstructures of polymers 1656.4.3 Production of polymers 1706.4.4 Elastomers 1736.4.5 The principal properties of polymers 1756.5 Composite materials 1776.5.1 Fibre-reinforced plastics 1776.5.2 Metal-matrix composites 1776.5.3 Ceramic-matrix composites 1786.5.4 Cement and concrete 178Further reading 181Problems and exercises 182PART 3 REACTIONS AND TRANSFORMATIONS 1897 Diffusion and ionic conductivity 1917.1 Self-diffusion, tracer diffusion and tracer impurity diffusion 1917.2 Non-steady-state diffusion 1947.3 Steady-state diffusion 1957.4 Temperature variation of diffusion coefficient 1957.5 The effect of impurities 1967.6 Random walk diffusion 1977.7 Diffusion in solids 1987.8 Self-diffusion in one dimension 1997.9 Self-diffusion in crystals 2017.10 The Arrhenius equation and point defects 2027.11 Correlation factors for self-diffusion 2047.12 Ionic conductivity 2057.12.1 Ionic conductivity in solids 2057.12.2 The relationship between ionic conductivity and diffusion coefficient 208Further reading 209Problems and exercises 2098 Phase transformations and reactions 2138.1 Sintering 2138.1.1 Sintering and reaction 2138.1.2 The driving force for sintering 2158.1.3 The kinetics of neck growth 2168.2 First-order and second-order phase transitions 2168.2.1 First-order phase transitions 2178.2.2 Second-order transitions 2178.3 Displacive and reconstructive transitions 2188.3.1 Displacive transitions 2188.3.2 Reconstructive transitions 2198.4 Order–disorder transitions 2218.4.1 Positional ordering 2218.4.2 Orientational ordering 2228.5 Martensitic transformations 2238.5.1 The austenite–martensite transition 2238.5.2 Martensitic transformations in zirconia 2268.5.3 Martensitic transitions in Ni–Ti alloys 2278.5.4 Shape-memory alloys 2288.6 Phase diagrams and microstructures 2308.6.1 Equilibrium solidification of simple binary alloys 2308.6.2 Non-equilibrium solidification and coring 2308.6.3 Solidification in systems containing a eutectic point 2318.6.4 Equilibrium heat treatment of steel in the Fe–C phase diagram 2338.7 High-temperature oxidation of metals 2368.7.1 Direct corrosion 2368.7.2 The rate of oxidation 2368.7.3 Oxide film microstructure 2378.7.4 Film growth via diffusion 2388.7.5 Alloys 2398.8 Solid-state reactions 2408.8.1 Spinel formation 2408.8.2 The kinetics of spinel formation 241Further reading 242Problems and exercises 2429 Oxidation and reduction 2479.1 Galvanic cells 2479.1.1 Cell basics 2479.1.2 Standard electrode potentials 2499.1.3 Cell potential and Gibbs energy 2509.1.4 Concentration dependence 2519.2 Chemical analysis using galvanic cells 2519.2.1 pH meters 2519.2.2 Ion selective electrodes 2539.2.3 Oxygen sensors 2549.3 Batteries 2559.3.1 ‘Dry’ and alkaline primary batteries 2559.3.2 Lithium-ion primary batteries 2569.3.3 The lead–acid secondary battery 2579.3.4 Lithium-ion secondary batteries 2579.3.5 Lithium–air batteries 2599.3.6 Fuel cells 2609.4 Corrosion 2629.4.1 The reaction of metals with water and aqueous acids 2629.4.2 Dissimilar metal corrosion 2649.4.3 Single metal electrochemical corrosion 2659.5 Electrolysis 2669.5.1 Electrolytic cells 2679.5.2 Electroplating 2679.5.3 The amount of product produced during electrolysis 2689.5.4 The electrolytic preparation of titanium by the FFC Cambridge Process 2699.6 Pourbaix diagrams 2709.6.1 Passivation, corrosion and leaching 2709.6.2 The stability field of water 2709.6.3 Pourbaix diagram for a metal showing two valence states, M2þ and M3þ 2719.6.4 Pourbaix diagram displaying tendency for corrosion 273Further reading 274Problems and exercises 275PART 4 PHYSICAL PROPERTIES 27910 Mechanical properties of solids 28110.1 Strength and hardness 28110.1.1 Strength 28110.1.2 Stress and strain 28210.1.3 Stress–strain curves 28310.1.4 Toughness and stiffness 28610.1.5 Superelasticity 28610.1.6 Hardness 28710.2 Elastic moduli 28910.2.1 Young’s modulus (the modulus of elasticity) (E or Y) 28910.2.2 Poisson’s ratio (n) 29110.2.3 The longitudinal or axial modulus (L or M) 29210.2.4 The shear modulus or modulus of rigidity (G or m) 29210.2.5 The bulk modulus, K or B 29310.2.6 The Lame modulus (l) 29310.2.7 Relationships between the elastic moduli 29310.2.8 Ultrasonic waves in elastic solids 29310.3 Deformation and fracture 29510.3.1 Brittle fracture 29510.3.2 Plastic deformation of metals 29810.3.3 Dislocation movement and plastic deformation 29810.3.4 Brittle and ductile materials 30110.3.5 Plastic deformation of polymers 30210.3.6 Fracture following plastic deformation 30210.3.7 Strengthening 30410.3.8 Computation of deformation and fracture 30610.4 Time-dependent properties 30710.4.1 Fatigue 30710.4.2 Creep 30810.5 Nanoscale properties 31210.5.1 Solid lubricants 31210.5.2 Auxetic materials 31310.5.3 Thin films and nanowires 31510.6 Composite materials 31710.6.1 Young’s modulus of large particle composites 31710.6.2 Young’s modulus of fibre-reinforced composites 31810.6.3 Young’s modulus of a two-phase system 319Further reading 320Problems and exercises 32111 Insulating solids 32711.1 Dielectrics 32711.1.1 Relative permittivity and polarisation 32711.1.2 Polarisability 32911.1.3 Polarisability and relative permittivity 33011.1.4 The frequency dependence of polarisability and relative permittivity 33111.1.5 The relative permittivity of crystals 33211.2 Piezoelectrics, pyroelectrics and ferroelectrics 33311.2.1 The piezoelectric and pyroelectric effects 33311.2.2 Crystal symmetry and the piezoelectric and pyroelectric effects 33511.2.3 Piezoelectric mechanisms 33611.2.4 Quartz oscillators 33711.2.5 Piezoelectric polymers 33811.3 Ferroelectrics 34011.3.1 Ferroelectric crystals 34011.3.2 Hysteresis and domain growth in ferroelectric crystals 34111.3.3 Antiferroelectrics 34411.3.4 The temperature dependence of ferroelectricity and antiferroelectricity 34411.3.5 Ferroelectricity due to hydrogen bonds 34511.3.6 Ferroelectricity due to polar groups 34711.3.7 Ferroelectricity due to medium-sized transition-metal cations 34811.3.8 Poling and polycrystalline ferroelectric solids 34911.3.9 Doping and modification of properties 34911.3.10 Relaxor ferroelectrics 35111.3.11 Ferroelectric nanoparticles, thin films and superlattices 35211.3.12 Flexoelectricity in ferroelectrics 353Further reading 354Problems and exercises 35512 Magnetic solids 36112.1 Magnetic materials 36112.1.1 Characterisation of magnetic materials 36112.1.2 Magnetic dipoles and magnetic flux 36212.1.3 Atomic magnetism 36312.1.4 Overview of magnetic materials 36512.2 Paramagnetic materials 36812.2.1 The magnetic moment of paramagnetic atoms and ions 36812.2.2 High and low spin: crystal field effects 36912.2.3 Temperature dependence of paramagnetic susceptibility 37112.2.4 Pauli paramagnetism 37312.3 Ferromagnetic materials 37412.3.1 Ferromagnetism 37412.3.2 Exchange energy 37612.3.3 Domains 37812.3.4 Hysteresis 38012.3.5 Hard and soft magnetic materials 38012.4 Antiferromagnetic materials and superexchange 38112.5 Ferrimagnetic materials 38212.5.1 Cubic spinel ferrites 38212.5.2 Garnet structure ferrites 38312.5.3 Hexagonal ferrites 38312.5.4 Double exchange 38412.6 Nanostructures 38512.6.1 Small particles and data recording 38512.6.2 Superparamagnetism and thin films 38612.6.3 Superlattices 38612.6.4 Photoinduced magnetism 38712.7 Magnetic defects 38912.7.1 Magnetic defects in semiconductors 38912.7.2 Charge and spin states in cobaltites and manganites 390Further reading 393Problems and exercises 39313 Electronic conductivity in solids 39913.1 Metals 39913.1.1 Metals, semiconductors and insulators 39913.1.2 Electron drift in an electric field 40113.1.3 Electronic conductivity 40213.1.4 Resistivity 40413.2 Semiconductors 40513.2.1 Intrinsic semiconductors 40513.2.2 Band gap measurement 40713.2.3 Extrinsic semiconductors 40813.2.4 Carrier concentrations in extrinsic semiconductors 40913.2.5 Characterisation 41113.2.6 The p-n junction diode 41313.3 Metal–insulator transitions 41613.3.1 Metals and insulators 41613.3.2 Electron–electron repulsion 41713.3.3 Modification of insulators 41813.3.4 Transparent conducting oxides 41913.4 Conducting polymers 42013.5 Nanostructures and quantum confinement of electrons 42313.5.1 Quantum wells 42413.5.2 Quantum wires and quantum dots 42513.6 Superconductivity 42613.6.1 Superconductors 42613.6.2 The effect of magnetic fields 42713.6.3 The effect of current 42813.6.4 The nature of superconductivity 42813.6.5 Josephson junctions 43013.6.6 Cuprate high-temperature superconductors 430Further reading 438Problems and exercises 43814 Optical aspects of solids 44514.1 Light 44514.1.1 Light waves 44514.1.2 Photons 44714.2 Sources of light 44914.2.1 Incandescence 44914.2.2 Luminescence and phosphors 45014.2.3 Light-emitting diodes (LEDs) 45314.2.4 Solid-state lasers 45414.3 Colour and appearance 46014.3.1 Luminous solids 46014.3.2 Non-luminous solids 46014.3.3 Attenuation 46114.4 Refraction and dispersion 46214.4.1 Refraction 46214.4.2 Refractive index and structure 46414.4.3 The refractive index of metals and semiconductors 46514.4.4 Dispersion 46514.5 Reflection 46614.5.1 Reflection from a surface 46614.5.2 Reflection from a single thin film 46714.5.3 The reflectivity of a single thin film in air 46914.5.4 The colour of a single thin film in air 46914.5.5 The colour of a single thin film on a substrate 47014.5.6 Low-reflectivity (antireflection) and high-reflectivity coatings 47114.5.7 Multiple thin films and dielectric mirrors 47114.6 Scattering 47214.6.1 Rayleigh scattering 47214.6.2 Mie scattering 47514.7 Diffraction 47514.7.1 Diffraction by an aperture 47514.7.2 Diffraction gratings 47614.7.3 Diffraction from crystal-like structures 47714.7.4 Photonic crystals 47814.8 Fibre optics 47914.8.1 Optical communications 47914.8.2 Attenuation in glass fibres 47914.8.3 Dispersion and optical fibre design 48014.8.4 Optical amplification 48214.9 Energy conversion 48314.9.1 Photoconductivity and photovoltaic solar cells 48314.9.2 Dye sensitized solar cells 48514.10 Nanostructures 48614.10.1 The optical properties of quantum wells 48614.10.2 The optical properties of nanoparticles 487Further reading 489Problems and exercises 48915 Thermal properties 49515.1 Heat capacity 49515.1.1 The heat capacity of a solid 49515.1.2 Classical theory of heat capacity 49615.1.3 Quantum theory of heat capacity 49615.1.4 Heat capacity at phase transitions 49715.2 Thermal conductivity 49815.2.1 Heat transfer 49815.2.2 Thermal conductivity of solids 49815.2.3 Thermal conductivity and microstructure 50015.3 Expansion and contraction 50115.3.1 Thermal expansion 50115.3.2 Thermal expansion and interatomic potentials 50215.3.3 Thermal contraction 50315.3.4 Zero thermal contraction materials 50515.4 Thermoelectric effects 50615.4.1 Thermoelectric coefficients 50615.4.2 Thermoelectric effects and charge carriers 50815.4.3 The Seebeck coefficient of solids containing point defect populations 50915.4.4 Thermocouples, power generation and refrigeration 50915.5 The magnetocaloric effect 51215.5.1 The magnetocaloric effect and adiabatic cooling 51215.5.2 The giant magnetocaloric effect 513Further reading 514Problems and exercises 514PART 5 NUCLEAR PROPERTIES OF SOLIDS 51716 Radioactivity and nuclear reactions 51916.1 Radioactivity 51916.1.1 Naturally occurring radioactive elements 51916.1.2 Isotopes and nuclides 52016.1.3 Nuclear equations 52016.1.4 Radioactive series 52116.1.5 Nuclear stability 52316.2 Artificial radioactive atoms 52416.2.1 Transuranic elements 52416.2.2 Artificial radioactivity in light elements 52716.3 Nuclear decay 52716.3.1 The rate of nuclear decay 52716.3.2 Radioactive dating 52916.4 Nuclear energy 53116.4.1 The binding energy of nuclides 53116.4.2 Nuclear fission 53216.4.3 Thermal reactors for power generation 53316.4.4 Fuel for space exploration 53516.4.5 Fast breeder reactors 53516.4.6 Fusion 53516.4.7 Solar cycles 53616.5 Nuclear waste 53616.5.1 Nuclear accidents 53716.5.2 The storage of nuclear waste 537Further reading 538Problems and exercises 539Subject Index 543

“Summing Up: Recommended.  Lower-division undergraduates and two-year technical program students.”  (Choice, 1 February 2014)