Structure of materials: an introduction to crystallographyPDF电子书下载

1 Materials and material properties 1

1.1 Materials and structure 1

1.2 Organization of the book 2

1.3 About length scales 3

1.4 Wave-particle duality and the de Broglie relationship 7

1.5 What is a material property？ 9

1.5.1 Definition of a material property 9

1.5.2 Directional dependence of properties 10

1.5.3 A first encounter with symmetry 12

1.5.4 A first encounter with magnetic symmetry 15

1.6 So，what is this book all about？ 17

1.7 Chapter summary 19

1.8 Historical notes 20

1.9 Selected problems 21

2 The periodic table of the elements and interatomic bonds 23

2.1 About atoms 23

2.1.1 The electronic structure of the atom 23

2.1.2 The hydrogenic model 24

2.2 The periodic table 26

2.2.1 Layout of the periodic table 28

2.2.2 Trends across the table 31

2.3 Interatomic bonds 34

2.3.1 Quantum chemistry 34

2.3.2 Interactions between atoms 34

2.3.3 The ionic bond 36

2.3.4 The covalent bond 38

2.3.5 The metallic bond 39

2.3.6 The van der Waals bond 40

2.3.7 Mixed bonding 41

2.3.8 Electronic states and symmetry 41

2.3.9 Overview of bond types and material properties 42

2.4 Chapter summary 43

2.5 Historical notes 43

2.6 Selected problems 47

3 What is a crystal structure？ 49

3.1 Periodic arrangements of atoms 49

3.2 The space lattice 51

3.2.1 Basis vectors and translation vectors 51

3.2.2 Some remarks about notation 52

3.2.3 More about lattices 54

3.3 The four 2-D crystal systems 56

3.4 The seven 3-D crystal systems 57

3.5 The five 2-D Bravais nets and fourteen 3-D Bravais lattices 60

3.6 Other ways to define a unit cell 64

3.7 2-D and 3-D magnetic Bravais lattices 66

3.8 Chapter summary 71

3.9 Historical notes 72

3.10 Selected problems 73

4 Crystallographic computations 75

4.1 Directions in the crystal lattice 75

4.2 Distances and angles in a 3-D lattice 76

4.2.1 Distance between two points 76

4.2.2 The metric tensor 78

4.2.3 The dot product in a crystallographic reference frame 80

4.3 Worked examples 82

4.3.1 Computation of the length of a vector 82

4.3.2 Computation of the distance between two atoms 83

4.3.3 Computation of the angle between atomic bonds 84

4.3.4 Computation of the angle between lattice directions 84

4.3.5 An alternative method for the computation of angles 85

4.3.6 Further comments 85

4.4 Chapter summary 86

4.5 Historical notes 87

4.6 Selected problems 89

5 Lattice planes 90

5.1 Miller indices 90

5.2 Families of planes and directions 93

5.3 Special case：the hexagonal system 94

5.4 Crystal forms 96

5.5 Chapter summary 101

5.6 Historical notes 101

5.7 Selected problems 102

6 Reciprocal space 104

6.1 The reciprocal basis vectors 104

6.2 Reciprocal space and lattice planes 108

6.3 The reciprocal metric tensor 110

6.3.1 Computation of the angle between planes 112

6.3.2 Computation of the length of the reciprocal lattice vector 112

6.4 Worked examples 114

6.5 Chapter summary 119

6.6 Historical notes 119

6.7 Selected problems 120

7 Additional crystallographic computations 122

7.1 The stereographic projection 122

7.2 About zones and zone axes 125

7.2.1 The vector cross product 126

7.2.2 About zones and the zone equation 130

7.2.3 The reciprocal lattice and zone equation in the hexagonal system 131

7.3 Relations between direct space and reciprocal space 133

7.4 Coordinate transformations 135

7.4.1 Transformation rules 135

7.4.2 Example of a coordinate transformation 138

7.4.3 Converting vector components into Cartesian coordinates 140

7.5 Examples of stereographic projections 143

7.5.1 Stereographic projection of a cubic crystal 143

7.5.2 Stereographic projection of a monoclinic crystal 146

7.6 Chapter summary 149

7.7 Historical notes 150

7.8 Selected problems 151

8 Symmetry in crystallography 152

8.1 Symmetry of an arbitrary object 152

8.2 Symmetry operations 158

8.2.1 Basic isometric transformations 159

8.2.2 Compatibility of rotational symmetries with crystalline translational periodicity 160

8.2.3 Operations of the first kind：pure rotations 162

8.2.4 Operations of the first kind：pure translations 164

8.2.5 Operations of the second kind：pure reflections 166

8.2.6 Operations of the second kind：inversions 167

8.2.7 Symmetry operations that do not pass through the origin 168

8.3 Magnetic symmetry operations 169

8.3.1 Time-reversal symmetry and axial vectors 169

8.3.2 Time-reversing symmetry operations 173

8.4 Combinations of symmetry operations 175

8.4.1 Combination of rotations with the inversion center 175

8.4.2 Combination of rotations and mirrors 177

8.4.3 Combination of rotations and translations 178

8.4.4 Combination of mirrors and translations 181

8.4.5 Relationships and differences between operations of the first and second kind 183

8.4.6 Combinations of magnetic and regular symmetry operators 184

8.5 Point symmetry 186

8.6 Chapter summary 188

8.7 Historical notes 190

8.8 Selected problems 191

9 Point groups 193

9.1 What is a group？ 193

9.1.1 A simple example 193

9.1.2 Group axioms 194

9.1.3 Principal properties of groups 196

9.2 3-D crystallographic point symmetries 197

9.2.1 Step Ⅰ：the proper rotations 198

9.2.2 Step Ⅱ：combining proper rotations with two-fold rotations 199

9.2.3 Step Ⅲa：combining proper rotations with inversion symmetry 201

9.2.4 Step Ⅲb：combining proper rotations with perpendicular reflection elements 203

9.2.5 Step Ⅳ：combining proper rotations with coinciding reflection elements 204

9.2.6 Step Ⅴa：combining inversion rotations with coinciding reflection elements 204

9.2.7 Step Ⅴb：combining proper rotations with coinciding and perpendicular reflection elements 205

9.2.8 Step Ⅵ：combining proper rotations 206

9.2.9 Step Ⅶ：adding reflection elements to Step Ⅵ 207

9.2.10 General remarks 208

9.3 2-D crystallographic point symmetries 220

9.4 Magnetic point groups 221

9.4.1 Derivation 221

9.4.2 Visualization of the magnetic point groups 223

9.4.3 Color，charge，and time reversal 225

9.5 Chapter summary 227

9.6 Historical notes 228

9.7 Selected problems 228

10 Plane groups and space groups 230

10.1 Combining translations with point group symmetry 230

10.2 Plane groups 231

10.2.1 A simple example 231

10.2.2 A more complex example 233

10.2.3 The 17 plane groups 235

10.3 Space groups 236

10.3.1 A simple example 236

10.3.2 A second simple example 238

10.3.3 A more complex example 239

10.3.4 The symmorphic space groups 240

10.3.5 The non-symmorphic space groups 242

10.3.6 Space group generators 243

10.3.7 General remarks 247

10.4 The International Tables for Crystallography 248

10.5 Magnetic space groups 253

10.6 Chapter summary 255

10.7 Historical notes 256

10.8 Selected problems 257

11 X-ray diffraction：geometry 259

11.1 Properties and generation of X-rays 259

11.1.1 How do we generate X-rays？ 261

11.1.2 Wavelength selection 265

11.2 X-rays and crystal lattices 268

11.2.1 Scattering of X-rays by lattice planes 272

11.2.2 Bragg’s law in reciprocal space 276

11.3 Basic experimental X-ray diffraction techniques 280

11.3.1 The X-ray powder diffractometer 281

11.4 Chapter summary 289

11.5 Historical notes 289

11.6 Selected problems 290

12 X-ray diffraction：intensities 291

12.1 Scattering by electrons，atoms，and unit cells 291

12.1.1 Scattering by a single electron 291

12.1.2 Scattering by a single atom 293

12.1.3 Scattering by a single unit cell 298

12.2 The structure factor 300

12.2.1 Lattice centering and the structure factor 300

12.2.2 Symmetry and the structure factor 304

12.2.3 Systematic absences and the International Tables for Crystallography 307

12.2.4 Examples of structure factor calculations 307

12.3 Intensity calculations for diffracted and measured intensities 309

12.3.1 Description of the correction factors 310

12.3.2 Expressions for the total measured intensity 315

12.4 Chapter summary 317

12.5 Historical notes 317

12.6 Selected problems 318

13 Other diffraction techniques 320

13.1 Introductory remarks 320

13.2 Neutron diffraction 321

13.2.1 Neutrons：generation and properties 323

13.2.2 Neutrons：wavelength selection 325

13.2.3 Neutrons：atomic scattering factors 326

13.2.4 Neutrons：scattering geometry and diffracted intensities 330

13.2.5 Neutrons：example powder pattern 334

13.3 Electron diffraction 335

13.3.1 The electron as a particle and a wave 335

13.3.2 The geometry of electron diffraction 337

13.3.3 The transmission electron microscope 338

13.3.4 Basic observation modes in the TEM 340

13.3.5 Convergent beam electron diffraction 343

13.4 Synchrotron X-ray sources for scattering experiments 347

13.4.1 Synchrotron accelerators 348

13.4.2 Synchrotron radiation：experimental examples 350

13.5 Chapter summary 352

13.6 Historical notes 352

13.7 Selected problems 354

14 About crystal structures and diffraction patterns 356

14.1 Crystal structure descriptions 356

14.1.1 Space group description 356

14.1.2 Graphical representation methods 357

14.2 Crystal structures?powder diffraction patterns 360

14.2.1 The Ni powder pattern，starting from the known structure 361

14.2.2 The NaCl powder pattern，starting from the known structure 365

14.2.3 The Ni structure，starting from the experimental powder diffraction pattern 369

14.2.4 The NaCl structure，starting from the experimental powder diffraction pattern 372

14.2.5 General comments about crystal structure determination 375

14.3 Chapter summary 380

14.4 Historical notes 380

14.5 Selected problems 382

15 Non-crystallographic point groups 383

15.1 Example of a non-crystallographic point group symmetry 383

15.2 Icosahedral and related five-fold symmetry groups 384

15.2.1 The icosahedral point groups 384

15.2.2 Fullerene molecular structures 385

15.2.3 Icosahedral group representations 387

15.2.4 Other non-crystallographic point groups with five-fold symmetries 390

15.2.5 Descents in symmetry：decagonal and pentagonal groups 393

15.3 Non-crystallographic point groups with octagonal symmetry 395

15.4 Chapter summary 400

15.5 Historical notes 400

15.6 Selected problems 402

16 Periodic and aperiodic tilings 403

16.1 2-D plane tilings 403

16.1.1 2-D regular tilings 404

16.1.2 2-D Archimedean tilings 405

16.1.3 k-uniform regular tilings 406

16.1.4 Dual tilings - the Laves tilings 407

16.1.5 Tilings without regular vertices 408

16.2 Color tilings 408

16.3 Quasiperiodic tilings 410

16.4 Regular polyhedra and n-D regular polytopes 411

16.5 Crystals with stacking of 36 tilings 415

16.5.1 Simple close-packed structures：ABC stacking 415

16.5.2 Interstitial sites in close-packed structures 416

16.5.3 Representation of close-packed structures 417

16.5.4 Polytypism and properties of SiC semiconductors 419

16.5.5 36 close-packed tilings of polyhedral faces 420

16.6 Chapter summary 421

16.7 Historical notes 422

16.8 Selected problems 424

17 Metallic structures Ⅰ：simple，derivative，and superlattice structures 425

17.1 Introductory comments 425

17.2 Classification of structures 426

17.2.1 Strukturbericht symbols 426

17.2.2 Pearson symbols 427

17.2.3 Structure descriptions in this book 427

17.3 Parent structures 428

17.3.1 Geometrical calculations for cubic structures 430

17.4 Atomic sizes，bonding，and alloy structure 431

17.4.1 Hume-Rothery rules 432

17.4.2 Bonding in close-packed rare gas and metallic structures 433

17.4.3 Phase diagrams 437

17.5 Superlattices and sublattices：mathematical definition 438

17.6 Derivative structures and superlattice examples 439

17.6.1 fcc-derived structures and superlattices 439

17.6.2 bcc-derived superlattices 444

17.6.3 Diamond cubic derived superlattices 446

17.6.4 Hexagonal close-packed derived superlattices 448

17.7 Elements with alternative stacking sequences or lower symmetry 450

17.7.1 Elements with alternative stacking sequences 450

17.7.2 Elements with lower-symmetry structures 451

17.8 Natural and artificial superlattices 455

17.8.1 Superlattice structures based on the L12 cell 455

17.8.2 Artificial superlattices 457

17.8.3 X-ray scattering from long-period multi-layered systems 459

17.8.4 Incommensurate superlattices 459

17.9 Interstitial alloys 461

17.10 Chapter summary 462

17.11 Historical notes 463

17.12 Selected problems 464

18 Metallic structures Ⅱ：complex geometrically determined structures 466

18.1 Electronic states in metals 466

18.2 Topological close packing 468

18.2.1 The Kasper polyhedra 469

18.2.2 Connectivity of Kasper polyhedra 471

18.2.3 Metallic radii 471

18.3 Frank-Kasper alloy phases 472

18.3.1 A1 5 phases and related structures 472

18.3.2 The Laves phases and related structures 479

18.3.3 The sigma phase 486

18.3.4 The μ-phase and the M-，P-，and R-phases 488

18.4 Quasicrystal approximants 490

18.4.1 Mg32（Al，Zn）49 and α-Al-Mn-Si crystal structures 490

18.4.2 Mg32（Al，Zn）49 and α-Al-Mn-Si shell models 491

18.5 Chapter summary 494

18.6 Historical notes 495

18.7 Selected problems 496

19 Metallic structures Ⅲ：quasicrystals 497

19.1 Introductory remarks 497

19.2 The golden mean and pentagonal symmetry 498

19.3 1-D quasicrystals 501

19.3.1 The Fibonacci sequence and lattice derived by recursion 501

19.3.2 Lattice positions in the Fibonacci lattice 503

19.3.3 Construction of the Fibonacci lattice by the projection method 504

19.3.4 The Fourier transform of the Fibonacci lattice 505

19.4 2-D quasicrystals 507

19.4.1 2-D quasicrystals：Penrose tilings 507

19.4.2 The Penrose tiling derived by projection 512

19.4.3 2-D quasicrystals：other polygonal quasicrystals 514

19.5 3-D quasicrystals 516

19.5.1 3-D Penrose tilings 517

19.5.2 Indexing icosahedral quasicrystal diffraction patterns 519

19.5.3 Icosahedral quasicrystal diffraction patterns and quasilattice constants 521

19.5.4 3-D Penrose tiles：stacking，decoration，and quasilattice constants 522

19.5.5 3-D Penrose tiles：projection method 524

19.6 Multiple twinning and icosahedral glass models 525

19.7 Microscopic observations of quasicrystal morphologies 526

19.8 Chapter summary 528

19.9 Historical notes 528

19.10 Selected problems 530

20 Metallic structures Ⅳ：amorphous metals 531

20.1 Introductory comments 531

20.2 Order in amorphous and nanocrystalline alloys 532

20.3 Atomic positions in amorphous alloys 535

20.4 Atomic volume，packing，and bonding in amorphous solids 536

20.4.1 DRPHS model 537

20.4.2 Binding in clusters：crystalline and icosahedral short-range order 539

20.4.3 Icosahedral short-range order models 539

20.5 Amorphous metal synthesis 540

20.6 Thermodynamic and kinetic criteria for glass formation 542

20.7 Examples of amorphous metal alloy systems 543

20.7.1 Metal-metalloid systems 544

20.7.2 Rare earth-transition metal systems 545

20.7.3 Early transition metal-late transition metal systems 546

20.7.4 Multi-component nanocomposite systems 546

20.7.5 Multi-component bulk amorphous systems 548

20.8 X-ray scattering in amorphous materials 550

20.9 Extended X-ray absorption fine structure （EXAFS） 554

20.10 Mossbauer spectroscopy 557

20.11 Chapter summary 558

20.12 Historical notes 558

20.13 Selected problems 560

21 Ceramic structures Ⅰ：basic structure prototypes 561

21.1 Introductory remarks 561

21.2 Ionic radii 562

21.3 Bonding energetics in ionic structures 565

21.4 Rules for packing and connectivity in ionic crystals 566

21.4.1 Pauling’s rules for ionic structures 566

21.4.2 Radius ratio rules for ionic compounds 567

21.5 Oxides of iron 570

21.6 Halide salt structures：CsCl，NaCl，and CaF2 571

21.7 Close-packed sulfide and oxide structures：ZnS and Al2O3 574

21.8 Perovskite and spinel structures 577

21.8.1 Perovskites：ABO3 577

21.8.2 Spinels：AB2O4 580

21.9 Non-cubic close-packed structures：NiAs，CdI2，and TiO2 584

21.10 Layered structures 585

21.10.1 Magnetoplumbite phases 586

21.10.2 Aurivillius phases 586

21.10.3 Ruddlesden-Popper phases 588

21.10.4 Tungsten bronzes 589

21.10.5 Titanium carbosulfide 591

21.11 Additional remarks 591

21.12 Point defects in ceramics 592

21.13 Chapter summary 594

21.14 Historical notes 594

21.15 Selected problems 596

22 Ceramic structures Ⅱ：high-temperature superconductors 597

22.1 Introductory remarks about superconductivity 597

22.2 High-temperature superconductors：nomenclature 598

22.3 Perovskite-based high-temperature superconductors 599

22.3.1 Single-layer perovskite high-temperature superconductors 599

22.3.2 Triple-layer perovskite-based high-temperature superconductors 601

22.4 BSCCO，TBCCO，HBCCO，and ACBCCO HTSC layered structures 606

22.4.1 The BSCCO double-layer high-temperature superconductors 606

22.4.2 The TBCCO double-layer high-temperature superconductors 608

22.4.3 The TBCCO single-layer high-temperature superconductors 611

22.4.4 The HBCCO high-temperature superconductors 613

22.4.5 The ACBCCO high-temperature superconductors 615

22.4.6 Rutheno-cuprate high-temperature superconductors 615

22.4.7 Infinite-layer high-temperature superconductors 616

22.5 Chapter summary 616

22.6 Historical notes 617

22.7 Selected problems 619

23 Ceramic structures Ⅲ：terrestrial and extraterrestrial minerals 620

23.1 Classification of minerals 620

23.2 Silicates overview 622

23.2.1 Orthosilicates （nesosilicates） 624

23.2.2 Pyrosilicates （sorosilicates） 629

23.2.3 Chains of tetrahedra，metasilicates （inosilicates） 630

23.2.4 Double chains of tetrahedra 633

23.2.5 Sheets of tetrahedra，phyllosilicates 634

23.2.6 Networks of tetrahedra，tectosilicates 635

23.2.7 Random networks of tetrahedra：silicate glasses 639

23.2.8 Mesoporous silicates 641

23.2.9 Sol-gel synthesis of silicate nanostructures 642

23.3 Magnetic minerals on Mars and their biogenic origins 643

23.3.1 Hydroxides 646

23.3.2 Sulfates 649

23.4 Chapter summary 650

23.5 Historical notes 651

23.6 Selected problems 652

24 Molecular solids and biological materials 653

24.1 Introductory remarks 653

24.2 Simple molecular crystals：ice，dry ice，benzene，the clathrates，and self-assembled structures 654

24.2.1 Solid H2O：ice 654

24.2.2 Solid CO2：dry ice 656

24.2.3 Hydrocarbon crystals 657

24.2.4 Clathrates 658

24.2.5 Amphiphiles and micelles 659

24.3 Polymers 660

24.3.1 Polymer classification 661

24.3.2 Polymerization reactions and products 662

24.3.3 Polymer chains：spatial configurations 664

24.3.4 Copolymers and self-assembly 666

24.3.5 Conducting and superconducting polymers 668

24.3.6 Polymeric derivatives of fullerenes 670

24.4 Biological macromolecules 671

24.4.1 DNA and RNA 671

24.4.2 Virus structures 674

24.5 Fullerene-based molecular solids 677

24.5.1 Fullerites 679

24.5.2 Fullerides 681

24.5.3 Carbon nanotubes 681

24.6 Chapter summary 685

24.7 Historical notes 685

24.8 Selected problems 687

References 688

Index 716