Basic Solid State Chemistry

ANTHONY R. WEST,

Department of Chemistry University of Aberdeen

JOHN WILEY & SONS Chichester • New York • Brisbane • Toronto • Singapore

Contents

Chapter 1 Crystal Structures 1 Definitions 1

Unit cells and crystal Systems 1 Symmetry 4 Symmetry and choice of unit cell 6 Lattice, Bravais lattice 8 Lattice planes and Miller indices 9 Indices of directions 12 d-spacing formulae 12 Unit cell contents and crystal densities 13

Description of crystal structures 14 Close packed structures—cubic and hexagonal close packing . . 14 Materials that can be described as close packed 19

Metals 19 Alloys 19 Ionic structures 19 Covalent network structures 22 Molecular structures 23

Structures built of space-filling polyhedra 24 Some important structure types 27

Rock salt, zinc blende or sphalerite, fluorite and antifluorite . . 27 Diamond 37 Wurtzite and nickel arsenide 37 Caesium chloride 44 Other AX structures 45 Rutile, cadmium iodide, cadmium chloride and caesium oxide. . 46 Perovskite 53 Rhenium trioxide and tungsten bronzes 56 Spinel 57 Silicate structures—some tips to understanding them 59

Chapter 2 Bonding in Solids 63 Ionic bonding 64

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Ions and ionic radii 64 Ionic structures—general principles 68 The radius ratio rule 71 Borderline radius ratios and distorted structures 74 Lattice energy of ionic crystals 75 Kapustinskii's equation ' 80 The Born-Haber cycle and thermochemical calculations. . . . 80 Stabilities of real and hypothetical ionic Compounds 83

Inert gas Compounds 83 Lower and higher valence Compounds 84

Partial covalent bonding 85 Coordinated polymeric structures—Sanderson's model . . . . 86 Effective nuclear Charge 87 Atomic radii 87 Electronegativity and partially charged atoms 89 Mooser-Pearson plots and ionicities 92

Bond valence and bond length 94 Non-bonding electron effects 97

d-electron effects 97 Crystal field Splitting of energy levels 97 Jahn-Teller distortions 101 Square planar coordination 103 Tetrahedral coordination 103 Tetrahedral versus octahedral coordination 104

Inert pair effect 106 Metallic bonding and band theory 107

Band structure of metals 112 Band structure of insulators 113 Band structure of semiconductors: Silicon 113 Band structure of inorganic solids 115 Bands or bonds: a final comment 118

Chapter 3 Crystallography and Diffraction Techniques 120 General comments 120

X-ray Diffraction 121 Generation of X-rays 121 An optical grating and diffraction of light 124 Crystals and diffraction of X-rays 126

The Laue equations 126 Bragg's law . 127

The X-ray diffraction experiment 128 The powder method—principles and uses 129 Powder diffractometers and the focusing of X-rays 132 Focusing (Guinier) cameras and crystal monochromators . . . 134 A powder pattern is a crystal's 'fingerprint' 135

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Intensities 137 Scattering of X-rays by an atom 137 Scattering of X-rays by a crystal—systematic absences . . . 139 Intensities—general formulae and a model calculation for CaF2 142

R-factors and structure determination 148 Electron density maps 148 X-ray crystallography and structure determination—what's

involved? 150 The Patterson method 152 Fourier methods 153 Direct methods 153

Electron diffraction 154 Neutron diffraction 155

Crystal structure determination 156 Magnetic structure analysis 156 Inelastic scattering, soft modes and phase transitions 157

Chapter 4 Other Techniques: Microscopy, Spectroscopy, Thermal Analysis . 158

Microscopic techniques 158 Optical microscopy 159

Polarizing microscope 159 Reflected light microscope 160 Applications 160

Crystal morphology and symmetry 160 Phase identification, purity and homogeneity 162 Crystal defects—grain boundaries and dislocations . . . . 163

Electron microscopy 163 Applications . 167

Particle size and shape, texture, surface detail. . . . . . 167 Crystal defects 167 Precipitation and phase transitions 167 Chemical analysis 167 Structure determination 167

Spectroscopic techniques 168 Vibrational spectroscopy: IR and Raman 171 Visible and ultraviolet spectroscopy 173

Structural studies on glass . 1 7 5 Study of laser materials 176

Nuclear magnetic resonance (NMR) spectroscopy 176 Electron spin resonance (ESR) spectroscopy - 1 7 9 X-ray spectroscopies: XRF, AEFS, EXAFS 182

Emission techniques 182 Absorption techniques 185

AEFS 186

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EXAFS 186 Electron spectroscopies: ESCA, XPS, UPS, AES, EELS . . . . 188

Applications 190 Chemical shifts and local structure 190 Bonding and band structure 192 Surface studies 193

Electron energy loss spectroscopy 193 Mössbauer spectroscopy . 1 9 3

Thermal analysis 196 Thermogravimetry (TG) 197 Differential thermal analysis (DTA) and differential scanning

calorimetry (DSC) 198 Applications 200

Chapter 5 Crystal Defects, Non-Stoichiometry and Solid Solutions . . 206 Crystal defects and non-stoichiometry 206

Perfect and imperfect crystals 206 Types of defect 208

Schottky defect 208 Frenkel defect 209

Thermodynamics of Schottky and Frenkel defect formation . . 210 Schottky defects 211 Frenkel defects 212

Colour centres 214 Vacancies and interstitials in non-stoichiometric crystals. . . . 2 1 6 Defect Clusters or aggregates 216 Interchanged atoms 221 Extended defects—crystallographic shear structures 222 Stacking faults 225 Subgrain boundaries and antiphase domains (boundaries) . . . 225

Dislocations and mechanical properties of solids 227 Edge dislocations 227 Screw dislocations 229 Dislocation loops 230 Observation of dislocations 233 Dislocations and crystal structure 234 Mechanical properties of metals 235 Dislocations, vacancies and stacking faults 238 Dislocations and grain boundaries 241

Solid Solutions 242 Substitutional solid Solutions 243 Interstitial solid Solutions 246 More complex solid Solution mechanisms 247

1. Creating cation vacancies 247 2. Creating interstitial anions 248 3. Creating anion vacancies 249

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4. Creating interstitial cations 249 Double Substitution 250 Further comments on the requirements for solid Solution formation 250 Experimental methods for studying solid Solutions 251

X-ray powder diffraction 251 Density measurements 253 Changes in other properties—thermal activity and DTA. . . 255

Chapter 6 Interpretation of Phase Diagrams 256 The phase rule, phases, components and degrees of freedom . . . 256 One-component Systems 260

The system H20. 261 The system Si02 262 Condensed one-component Systems 263

Two-component Condensed Systems 263 A simple eutectic system 263 Binary Systems with Compounds 267 The CaO-Si02 diagram 270 Binary Systems with solid Solutions 271 Binary Systems with solid-solid phase transitions 276 Iron and steel making 279

Chapter 7 Electrical Properties 281 Survey of electrical properties and materials 281 Metallic conductivity: organic metals 283

Conjugated Systems 283 Doped polyacetylene 283 Polyparaphenylene and polypyrrole 286

Organic Charge transfer complexes 286 Superconductivity 287

Ceramic superconductors 287 Structure of YBa2Cu307 290 Applications 292

Semiconductivity 294 Doped Silicon 295 Other semiconductors. 297 Applications 299

Ionic conductivity 300 Alkali halides: vacancy conduction 301 Silver chloride: interstitial conduction 308 Alkaline earth fluorides 311 Solid electrolytes (or fast ion conductors, superionic conductors). 311

ß-alumina 313 AgI and Ag+ ion solid electrolytes 319 Anion conductors 322 Requirements for high ionic conductivity: other ionic conductors 323

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Applications 325 Intercalation electrodes 330

Dielectric materials 330 Ferroelectricity 331 Pyroelectricity 338 Piezoelectricity 339

Applications of ferro-, pyro- and piezoelectrics 340

Chapter8 Magnetic and Optica! Properties 342 Magnetic properties 342

Behaviour of substances in a magnetic field 342 Effects of temperature: Curie and Curie-Weiss laws 344 Calculation of magnetic moments 346 Mechanisms of ferro- and antiferromagnetic ordering:

superexchange 348 Some more definitions 349

Selected examples of magnetic materials, their structures and properties 350

Metals and alloys 350 Transition metal oxides 354 Spineis 356 Garnets 359 Ilmenites and perovskites 362 Magnetoplumbites , . . 363 Applications: structure-property relations 363

Transformer cores 363 Information storage 364 Magnetic bubble memory devices 365 Permanent magnets 365

Optical properties: luminescence, lasers 365 Luminescence and phosphors 365 Configurational coordinate model 368 Some phosphor materials 370 Anti-Stokes phosphors 372 Lasers 372

The ruby laser 373 Neodymium lasers 374

Further reading 376 Appendices . 380

1. Interplanar spacings and unit cell volumes 380 2. Model building . 381 3. Geometrical considerations in crystal chemistry . . . . . . 385 4. The elements and some of their properties . . . . . . . . 389

Questions 393 Index 402