Structure and dynamics : an atomic view of materials / Martin T. Dove.

Format:

Book

Author/Creator:

Dove, Martin T.

Contributor:

Harry E. Humphreys Book Fund.

Series:

Oxford master series in condensed matter physics

Language:

English

Subjects (All):

Solid state physics.

Matter--Constitution.

Matter.

Matter--Properties.

Physical Description:

xxii, 334 pages : illustrations ; 25 cm.

Place of Publication:

Oxford ; New York : Oxford University Press, 2003.

Summary:

Structure and Dynamics covers the wide range of general principles that govern the behavior of atoms in solids and applies them to the full range of material types known to man. It focuses on the structure of materials at an atomic level and how the atoms vibrate inside solids, bringing these topics together to explore how the atomic principles determine the behavior and properties of materials. Topics discussed include the factors and reciprocal space, the types of atomic bonding, the formalism of atomic vibrations and the theories of phase transitions. The tools of diffraction and spectroscopy in both laboratory and large scale facilities are also covered.

Contents:

1.1 Observations 1

1.2 Length scales and time scales 12

1.3 Tools of the trade 13

2 Structure of materials 18

2.2 Crystal structures of the elements 19

2.3 Crystal structures of some simple inorganic compounds 29

2.4 The perovskite family of crystal structures 35

2.5 Organic crystals 40

2.6 Disordered materials 41

2.7 Glasses and amorphous phases 44

3 Formal description of crystal structures 52

3.2 Crystal structure: lattices, unit cell, and atomic coordinates 53

3.3 Crystal symmetry 1. Point-symmetry operations 61

3.4 Application of the formalism of point groups 66

3.5 Crystal symmetry 2. Translational symmetry and space groups 70

3.6 Breaking the rules: aperiodic structures, incommensurate materials, and quasicrystals 73

4 The reciprocal lattice 78

4.1 The concept of the reciprocal lattice 78

4.3 Non-primitive lattices 82

4.4 The reciprocal lattice as the Fourier transform of the crystal lattice 86

4.5 Reciprocal space and the Brillouin zone 87

5 Atomic bonding in crystals 91

5.1 Bonding and the variety of crystal structures 91

5.2 Thermodynamic preamble: the context of the binding energy 91

5.3 Lattice energy 94

5.4 Models of bonding 96

5.5 Quantum mechanical view of chemical bonding 105

6 Diffraction 117

6.1 Basics of diffraction 117

6.2 Beams of radiation and measurement of diffraction patterns 119

6.3 Basics of the theory of diffraction 129

6.4 Scattering of radiation from a continuous distribution of particles 133

6.5 Diffraction and Fourier analysis 134

6.6 Application: the structure of glasses revealed by neutron scattering 136

6.7 Diffraction from crystalline materials 138

6.8 Effects of symmetry on diffraction patterns 142

6.9 Solution of the phase problem and determination of crystal structure 149

7 Physical properties 156

7.2 First-rank tensors 158

7.3 Second-rank tensors 158

7.4 Third-rank tensors 165

7.5 Fourth-rank tensors 171

7.6 Induced changes in matter tensors 172

8 Lattice dynamics 175

8.1 Why do we need to consider dynamics? 175

8.2 The harmonic approximation 175

8.3 Lattice vibrations of one-dimensional monatomic crystals 176

8.4 Dispersion curves in face-centred cubic materials 183

8.5 Lattice vibrations of crystals with several atoms in the unit cell 189

9 Thermodynamics and lattice dynamics 202

9.1 The quantization of lattice vibrations 202

9.2 Thermodynamic functions for crystals 206

9.3 Atomic displacements 211

10 Experimental methods for measurements of vibrational frequencies 216

10.2 Basic ideas of spectroscopy 217

10.3 Neutron scattering techniques 219

10.4 Inelastic X-ray scattering 228

10.5 Light scattering 228

10.6 Infrared absorption spectroscopy 231

11 Anharmonic interactions 236

11.2 Thermal conductivity 239

11.3 Thermal expansion 241

11.4 Temperature dependence of phonon frequencies 244

12 Displacive phase transitions 247

12.1 Introduction to displacive phase transitions 247

12.2 Quantitative description of displacive phase transitions: the concept of the order parameter 252

12.3 Landau theory of displacive phase transitions 258

12.4 Soft mode theory of displacive phase transitions 263

12.5 Lattice dynamical theory of the low-temperature phase 267

A Real crystals! 274

A.1 Reality against ideality 274

A.2 Point defects 275

A.3 Large-scale imperfections 277

B Fourier analysis 280

B.1 Fourier transforms as the extension of Fourier series 280

B.2 One-dimensional Fourier transform 280

B.3 Some one-dimensional Fourier transforms 281

B.4 Convolution theorem 282

C Schoenflies representation of the point groups 284

C.1 The Schoenflies and International systems 284

C.2 Schoenflies labelling of non-cubic point groups 284

C.3 Schoenflies labelling of the cubic point groups 285

D Rhombohedral, trigonal, and hexagonal unit cells 286

E Space groups 287

E.1 Space group symbols 287

E.2 Defining symmetry 288

E.3 General and special positions 289

E.4 The International Tables of Crystallography 290

E.5 Relating general equivalent positions to actual atomic positions 290

F Lattice energy minimization 292

G Some notes on the variational theorem 293

H Ewald sphere 295

I The Wilson plot 298

J Diffraction from isotropic materials 300

J.1 Basic diffraction equations 300

J.2 Isotropic orientational averages 300

J.3 Pair distribution functions 301

J.4 Reverse Fourier transform 302

J.5 General approach to analysis of diffraction data 303

K Calculation of physical properties 304

K.1 Expansion of the crystal energy 304

K.2 Equilibrium condition and the elastic constant tensor 304

K.3 Piezoelectric and dielectric tensors 305

L Partition function: some key results 307

L.1 The definition and use of the partition function 307

L.2 The free energy 307

L.3 Some results 308

M Lattice sums 310

N Mean-square atomic displacement and temperature factors 311.

Notes:

Includes bibliographical references (pages [326]-329) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Harry E. Humphreys Book Fund.

ISBN:

0198506783

OCLC:

50022684