Structure of materials: an introduction to crystallographyPDF|Epub|txt|kindle电子书版本网盘下载

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1 Materials and material properties1

1.1 Materials and structure1

1.2 Organization of the book2

1.3 About length scales3

1.4 Wave-particle duality and the de Broglie relationship7

1.5 What is a material property？9

1.5.1 Definition of a material property9

1.5.2 Directional dependence of properties10

1.5.3 A first encounter with symmetry12

1.5.4 A first encounter with magnetic symmetry15

1.6 So，what is this book all about？17

1.7 Chapter summary19

1.8 Historical notes20

1.9 Selected problems21

2 The periodic table of the elements and interatomic bonds23

2.1 About atoms23

2.1.1 The electronic structure of the atom23

2.1.2 The hydrogenic model24

2.2 The periodic table26

2.2.1 Layout of the periodic table28

2.2.2 Trends across the table31

2.3 Interatomic bonds34

2.3.1 Quantum chemistry34

2.3.2 Interactions between atoms34

2.3.3 The ionic bond36

2.3.4 The covalent bond38

2.3.5 The metallic bond39

2.3.6 The van der Waals bond40

2.3.7 Mixed bonding41

2.3.8 Electronic states and symmetry41

2.3.9 Overview of bond types and material properties42

2.4 Chapter summary43

2.5 Historical notes43

2.6 Selected problems47

3 What is a crystal structure？49

3.1 Periodic arrangements of atoms49

3.2 The space lattice51

3.2.1 Basis vectors and translation vectors51

3.2.2 Some remarks about notation52

3.2.3 More about lattices54

3.3 The four 2-D crystal systems56

3.4 The seven 3-D crystal systems57

3.5 The five 2-D Bravais nets and fourteen 3-D Bravais lattices60

3.6 Other ways to define a unit cell64

3.7 2-D and 3-D magnetic Bravais lattices66

3.8 Chapter summary71

3.9 Historical notes72

3.10 Selected problems73

4 Crystallographic computations75

4.1 Directions in the crystal lattice75

4.2 Distances and angles in a 3-D lattice76

4.2.1 Distance between two points76

4.2.2 The metric tensor78

4.2.3 The dot product in a crystallographic reference frame80

4.3 Worked examples82

4.3.1 Computation of the length of a vector82

4.3.2 Computation of the distance between two atoms83

4.3.3 Computation of the angle between atomic bonds84

4.3.4 Computation of the angle between lattice directions84

4.3.5 An alternative method for the computation of angles85

4.3.6 Further comments85

4.4 Chapter summary86

4.5 Historical notes87

4.6 Selected problems89

5 Lattice planes90

5.1 Miller indices90

5.2 Families of planes and directions93

5.3 Special case：the hexagonal system94

5.4 Crystal forms96

5.5 Chapter summary101

5.6 Historical notes101

5.7 Selected problems102

6 Reciprocal space104

6.1 The reciprocal basis vectors104

6.2 Reciprocal space and lattice planes108

6.3 The reciprocal metric tensor110

6.3.1 Computation of the angle between planes112

6.3.2 Computation of the length of the reciprocal lattice vector112

6.4 Worked examples114

6.5 Chapter summary119

6.6 Historical notes119

6.7 Selected problems120

7 Additional crystallographic computations122

7.1 The stereographic projection122

7.2 About zones and zone axes125

7.2.1 The vector cross product126

7.2.2 About zones and the zone equation130

7.2.3 The reciprocal lattice and zone equation in the hexagonal system131

7.3 Relations between direct space and reciprocal space133

7.4 Coordinate transformations135

7.4.1 Transformation rules135

7.4.2 Example of a coordinate transformation138

7.4.3 Converting vector components into Cartesian coordinates140

7.5 Examples of stereographic projections143

7.5.1 Stereographic projection of a cubic crystal143

7.5.2 Stereographic projection of a monoclinic crystal146

7.6 Chapter summary149

7.7 Historical notes150

7.8 Selected problems151

8 Symmetry in crystallography152

8.1 Symmetry of an arbitrary object152

8.2 Symmetry operations158

8.2.1 Basic isometric transformations159

8.2.2 Compatibility of rotational symmetries with crystalline translational periodicity160

8.2.3 Operations of the first kind：pure rotations162

8.2.4 Operations of the first kind：pure translations164

8.2.5 Operations of the second kind：pure reflections166

8.2.6 Operations of the second kind：inversions167

8.2.7 Symmetry operations that do not pass through the origin168

8.3 Magnetic symmetry operations169

8.3.1 Time-reversal symmetry and axial vectors169

8.3.2 Time-reversing symmetry operations173

8.4 Combinations of symmetry operations175

8.4.1 Combination of rotations with the inversion center175

8.4.2 Combination of rotations and mirrors177

8.4.3 Combination of rotations and translations178

8.4.4 Combination of mirrors and translations181

8.4.5 Relationships and differences between operations of the first and second kind183

8.4.6 Combinations of magnetic and regular symmetry operators184

8.5 Point symmetry186

8.6 Chapter summary188

8.7 Historical notes190

8.8 Selected problems191

9 Point groups193

9.1 What is a group？193

9.1.1 A simple example193

9.1.2 Group axioms194

9.1.3 Principal properties of groups196

9.2 3-D crystallographic point symmetries197

9.2.1 Step Ⅰ：the proper rotations198

9.2.2 Step Ⅱ：combining proper rotations with two-fold rotations199

9.2.3 Step Ⅲa：combining proper rotations with inversion symmetry201

9.2.4 Step Ⅲb：combining proper rotations with perpendicular reflection elements203

9.2.5 Step Ⅳ：combining proper rotations with coinciding reflection elements204

9.2.6 Step Ⅴa：combining inversion rotations with coinciding reflection elements204

9.2.7 Step Ⅴb：combining proper rotations with coinciding and perpendicular reflection elements205

9.2.8 Step Ⅵ：combining proper rotations206

9.2.9 Step Ⅶ：adding reflection elements to Step Ⅵ207

9.2.10 General remarks208

9.3 2-D crystallographic point symmetries220

9.4 Magnetic point groups221

9.4.1 Derivation221

9.4.2 Visualization of the magnetic point groups223

9.4.3 Color，charge，and time reversal225

9.5 Chapter summary227

9.6 Historical notes228

9.7 Selected problems228

10 Plane groups and space groups230

10.1 Combining translations with point group symmetry230

10.2 Plane groups231

10.2.1 A simple example231

10.2.2 A more complex example233

10.2.3 The 17 plane groups235

10.3 Space groups236

10.3.1 A simple example236

10.3.2 A second simple example238

10.3.3 A more complex example239

10.3.4 The symmorphic space groups240

10.3.5 The non-symmorphic space groups242

10.3.6 Space group generators243

10.3.7 General remarks247

10.4 The International Tables for Crystallography248

10.5 Magnetic space groups253

10.6 Chapter summary255

10.7 Historical notes256

10.8 Selected problems257

11 X-ray diffraction：geometry259

11.1 Properties and generation of X-rays259

11.1.1 How do we generate X-rays？261

11.1.2 Wavelength selection265

11.2 X-rays and crystal lattices268

11.2.1 Scattering of X-rays by lattice planes272

11.2.2 Bragg’s law in reciprocal space276

11.3 Basic experimental X-ray diffraction techniques280

11.3.1 The X-ray powder diffractometer281

11.4 Chapter summary289

11.5 Historical notes289

11.6 Selected problems290

12 X-ray diffraction：intensities291

12.1 Scattering by electrons，atoms，and unit cells291

12.1.1 Scattering by a single electron291

12.1.2 Scattering by a single atom293

12.1.3 Scattering by a single unit cell298

12.2 The structure factor300

12.2.1 Lattice centering and the structure factor300

12.2.2 Symmetry and the structure factor304

12.2.3 Systematic absences and the International Tables for Crystallography307

12.2.4 Examples of structure factor calculations307

12.3 Intensity calculations for diffracted and measured intensities309

12.3.1 Description of the correction factors310

12.3.2 Expressions for the total measured intensity315

12.4 Chapter summary317

12.5 Historical notes317

12.6 Selected problems318

13 Other diffraction techniques320

13.1 Introductory remarks320

13.2 Neutron diffraction321

13.2.1 Neutrons：generation and properties323

13.2.2 Neutrons：wavelength selection325

13.2.3 Neutrons：atomic scattering factors326

13.2.4 Neutrons：scattering geometry and diffracted intensities330

13.2.5 Neutrons：example powder pattern334

13.3 Electron diffraction335

13.3.1 The electron as a particle and a wave335

13.3.2 The geometry of electron diffraction337

13.3.3 The transmission electron microscope338

13.3.4 Basic observation modes in the TEM340

13.3.5 Convergent beam electron diffraction343

13.4 Synchrotron X-ray sources for scattering experiments347

13.4.1 Synchrotron accelerators348

13.4.2 Synchrotron radiation：experimental examples350

13.5 Chapter summary352

13.6 Historical notes352

13.7 Selected problems354

14 About crystal structures and diffraction patterns356

14.1 Crystal structure descriptions356

14.1.1 Space group description356

14.1.2 Graphical representation methods357

14.2 Crystal structures?powder diffraction patterns360

14.2.1 The Ni powder pattern，starting from the known structure361

14.2.2 The NaCl powder pattern，starting from the known structure365

14.2.3 The Ni structure，starting from the experimental powder diffraction pattern369

14.2.4 The NaCl structure，starting from the experimental powder diffraction pattern372

14.2.5 General comments about crystal structure determination375

14.3 Chapter summary380

14.4 Historical notes380

14.5 Selected problems382

15 Non-crystallographic point groups383

15.1 Example of a non-crystallographic point group symmetry383

15.2 Icosahedral and related five-fold symmetry groups384

15.2.1 The icosahedral point groups384

15.2.2 Fullerene molecular structures385

15.2.3 Icosahedral group representations387

15.2.4 Other non-crystallographic point groups with five-fold symmetries390

15.2.5 Descents in symmetry：decagonal and pentagonal groups393

15.3 Non-crystallographic point groups with octagonal symmetry395

15.4 Chapter summary400

15.5 Historical notes400

15.6 Selected problems402

16 Periodic and aperiodic tilings403

16.1 2-D plane tilings403

16.1.1 2-D regular tilings404

16.1.2 2-D Archimedean tilings405

16.1.3 k-uniform regular tilings406

16.1.4 Dual tilings - the Laves tilings407

16.1.5 Tilings without regular vertices408

16.2 Color tilings408

16.3 Quasiperiodic tilings410

16.4 Regular polyhedra and n-D regular polytopes411

16.5 Crystals with stacking of 36 tilings415

16.5.1 Simple close-packed structures：ABC stacking415

16.5.2 Interstitial sites in close-packed structures416

16.5.3 Representation of close-packed structures417

16.5.4 Polytypism and properties of SiC semiconductors419

16.5.5 36 close-packed tilings of polyhedral faces420

16.6 Chapter summary421

16.7 Historical notes422

16.8 Selected problems424

17 Metallic structures Ⅰ：simple，derivative，and superlattice structures425

17.1 Introductory comments425

17.2 Classification of structures426

17.2.1 Strukturbericht symbols426

17.2.2 Pearson symbols427

17.2.3 Structure descriptions in this book427

17.3 Parent structures428

17.3.1 Geometrical calculations for cubic structures430

17.4 Atomic sizes，bonding，and alloy structure431

17.4.1 Hume-Rothery rules432

17.4.2 Bonding in close-packed rare gas and metallic structures433

17.4.3 Phase diagrams437

17.5 Superlattices and sublattices：mathematical definition438

17.6 Derivative structures and superlattice examples439

17.6.1 fcc-derived structures and superlattices439

17.6.2 bcc-derived superlattices444

17.6.3 Diamond cubic derived superlattices446

17.6.4 Hexagonal close-packed derived superlattices448

17.7 Elements with alternative stacking sequences or lower symmetry450

17.7.1 Elements with alternative stacking sequences450

17.7.2 Elements with lower-symmetry structures451

17.8 Natural and artificial superlattices455

17.8.1 Superlattice structures based on the L12 cell455

17.8.2 Artificial superlattices457

17.8.3 X-ray scattering from long-period multi-layered systems459

17.8.4 Incommensurate superlattices459

17.9 Interstitial alloys461

17.10 Chapter summary462

17.11 Historical notes463

17.12 Selected problems464

18 Metallic structures Ⅱ：complex geometrically determined structures466

18.1 Electronic states in metals466

18.2 Topological close packing468

18.2.1 The Kasper polyhedra469

18.2.2 Connectivity of Kasper polyhedra471

18.2.3 Metallic radii471

18.3 Frank-Kasper alloy phases472

18.3.1 A1 5 phases and related structures472

18.3.2 The Laves phases and related structures479

18.3.3 The sigma phase486

18.3.4 The μ-phase and the M-，P-，and R-phases488

18.4 Quasicrystal approximants490

18.4.1 Mg32（Al，Zn）49 and α-Al-Mn-Si crystal structures490

18.4.2 Mg32（Al，Zn）49 and α-Al-Mn-Si shell models491

18.5 Chapter summary494

18.6 Historical notes495

18.7 Selected problems496

19 Metallic structures Ⅲ：quasicrystals497

19.1 Introductory remarks497

19.2 The golden mean and pentagonal symmetry498

19.3 1-D quasicrystals501

19.3.1 The Fibonacci sequence and lattice derived by recursion501

19.3.2 Lattice positions in the Fibonacci lattice503

19.3.3 Construction of the Fibonacci lattice by the projection method504

19.3.4 The Fourier transform of the Fibonacci lattice505

19.4 2-D quasicrystals507

19.4.1 2-D quasicrystals：Penrose tilings507

19.4.2 The Penrose tiling derived by projection512

19.4.3 2-D quasicrystals：other polygonal quasicrystals514

19.5 3-D quasicrystals516

19.5.1 3-D Penrose tilings517

19.5.2 Indexing icosahedral quasicrystal diffraction patterns519

19.5.3 Icosahedral quasicrystal diffraction patterns and quasilattice constants521

19.5.4 3-D Penrose tiles：stacking，decoration，and quasilattice constants522

19.5.5 3-D Penrose tiles：projection method524

19.6 Multiple twinning and icosahedral glass models525

19.7 Microscopic observations of quasicrystal morphologies526

19.8 Chapter summary528

19.9 Historical notes528

19.10 Selected problems530

20 Metallic structures Ⅳ：amorphous metals531

20.1 Introductory comments531

20.2 Order in amorphous and nanocrystalline alloys532

20.3 Atomic positions in amorphous alloys535

20.4 Atomic volume，packing，and bonding in amorphous solids536

20.4.1 DRPHS model537

20.4.2 Binding in clusters：crystalline and icosahedral short-range order539

20.4.3 Icosahedral short-range order models539

20.5 Amorphous metal synthesis540

20.6 Thermodynamic and kinetic criteria for glass formation542

20.7 Examples of amorphous metal alloy systems543

20.7.1 Metal-metalloid systems544

20.7.2 Rare earth-transition metal systems545

20.7.3 Early transition metal-late transition metal systems546

20.7.4 Multi-component nanocomposite systems546

20.7.5 Multi-component bulk amorphous systems548

20.8 X-ray scattering in amorphous materials550

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

20.10 Mossbauer spectroscopy557

20.11 Chapter summary558

20.12 Historical notes558

20.13 Selected problems560

21 Ceramic structures Ⅰ：basic structure prototypes561

21.1 Introductory remarks561

21.2 Ionic radii562

21.3 Bonding energetics in ionic structures565

21.4 Rules for packing and connectivity in ionic crystals566

21.4.1 Pauling’s rules for ionic structures566

21.4.2 Radius ratio rules for ionic compounds567

21.5 Oxides of iron570

21.6 Halide salt structures：CsCl，NaCl，and CaF2571

21.7 Close-packed sulfide and oxide structures：ZnS and Al2O3574

21.8 Perovskite and spinel structures577

21.8.1 Perovskites：ABO3577

21.8.2 Spinels：AB2O4580

21.9 Non-cubic close-packed structures：NiAs，CdI2，and TiO2584

21.10 Layered structures585

21.10.1 Magnetoplumbite phases586

21.10.2 Aurivillius phases586

21.10.3 Ruddlesden-Popper phases588

21.10.4 Tungsten bronzes589

21.10.5 Titanium carbosulfide591

21.11 Additional remarks591

21.12 Point defects in ceramics592

21.13 Chapter summary594

21.14 Historical notes594

21.15 Selected problems596

22 Ceramic structures Ⅱ：high-temperature superconductors597

22.1 Introductory remarks about superconductivity597

22.2 High-temperature superconductors：nomenclature598

22.3 Perovskite-based high-temperature superconductors599

22.3.1 Single-layer perovskite high-temperature superconductors599

22.3.2 Triple-layer perovskite-based high-temperature superconductors601

22.4 BSCCO，TBCCO，HBCCO，and ACBCCO HTSC layered structures606

22.4.1 The BSCCO double-layer high-temperature superconductors606

22.4.2 The TBCCO double-layer high-temperature superconductors608

22.4.3 The TBCCO single-layer high-temperature superconductors611

22.4.4 The HBCCO high-temperature superconductors613

22.4.5 The ACBCCO high-temperature superconductors615

22.4.6 Rutheno-cuprate high-temperature superconductors615

22.4.7 Infinite-layer high-temperature superconductors616

22.5 Chapter summary616

22.6 Historical notes617

22.7 Selected problems619

23 Ceramic structures Ⅲ：terrestrial and extraterrestrial minerals620

23.1 Classification of minerals620

23.2 Silicates overview622

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 tetrahedra633

23.2.5 Sheets of tetrahedra，phyllosilicates634

23.2.6 Networks of tetrahedra，tectosilicates635

23.2.7 Random networks of tetrahedra：silicate glasses639

23.2.8 Mesoporous silicates641

23.2.9 Sol-gel synthesis of silicate nanostructures642

23.3 Magnetic minerals on Mars and their biogenic origins643

23.3.1 Hydroxides646

23.3.2 Sulfates649

23.4 Chapter summary650

23.5 Historical notes651

23.6 Selected problems652

24 Molecular solids and biological materials653

24.1 Introductory remarks653

24.2 Simple molecular crystals：ice，dry ice，benzene，the clathrates，and self-assembled structures654

24.2.1 Solid H2O：ice654

24.2.2 Solid CO2：dry ice656

24.2.3 Hydrocarbon crystals657

24.2.4 Clathrates658

24.2.5 Amphiphiles and micelles659

24.3 Polymers660

24.3.1 Polymer classification661

24.3.2 Polymerization reactions and products662

24.3.3 Polymer chains：spatial configurations664

24.3.4 Copolymers and self-assembly666

24.3.5 Conducting and superconducting polymers668

24.3.6 Polymeric derivatives of fullerenes670

24.4 Biological macromolecules671

24.4.1 DNA and RNA671

24.4.2 Virus structures674

24.5 Fullerene-based molecular solids677

24.5.1 Fullerites679

24.5.2 Fullerides681

24.5.3 Carbon nanotubes681

24.6 Chapter summary685

24.7 Historical notes685

24.8 Selected problems687

References688

Index716