Originally published in 1979, this book discusses how the physical and chemical properties of disordered systems such as liquids, glasses, alloys, amorphous semiconductors, polymer solutions and magnetic materials can be explained by theories based on a variety of mathematical models, including random assemblies of hard spheres, tetrahedrally-bonded networks and lattices of 'spins'. The text describes these models and the various mathematical theories by which the observable properties are derived. Techniques and concepts such as the mean field and coherent approximations, graphical summation, percolation, scaling and the renormalisation group are explained and applied. This book will be of value to anyone with an interest in theoretical and experimental physics.
Author(s): J. M. Ziman
Publisher: Cambridge University Press
Year: 1979
Language: English
Pages: 541
Preface
1 Cellular disorder
1.1 Perfect spatial order
1.2 Substitutional disorder
1.3 Magnetic disorder
1.4 Ice disorder
1.5 Short-range order
1.6 Long-range order
1.7 The range of order and ordered domains
1.8 Spectral disorder
2 Topological disorder
2.1 Atomicity 36
2.2 Disordered linear chains 39
2.3 Physical realizations of one-dimensional systems 43
2.4 Dimensionality and order 47
2.5 Dislocation disorder 51
2.6 .rv1icrocrystalline disorder 56
2.7 Atomic distribution functions 58
2.8 Bond network disorder 64
2.9 Amorphous or paracrystalline? 67
2.10 Statistical geometry of bond networks 72
2.11 The Bernal model of a liquid 77
2.12 Analytical theories of the liquid state 87
2.13 Liquid mixtures 96
2.14 Liquid phases of non-spherical molecules 102
2.15 Gas-like disorder 106
3 Continuum disorder
3.1 Continuum models 108
3.2 Homogeneous random fields 110
3.3 Ga ussian randomness 113
3.4 Statistical topography 118
4 The observation of disorder
4.1 Diffraction experiments and diffraction theory 122
4.2 Neutron diffraction 127
4.3 Structure determination by X-rays 129
4.4 Small-angle scattering 129
4.5 Diffraction by a mixture 133
4.6 Diffraction effects of substitutional disorder 137
4.7 Diffraction and imaging 140
5 Statistical mechanics of substitutional disorder
5.1 Physical problems and mathematical puzzles 142
5.2 Mean field approximation 144
5.3 Short-range order 147
5.4 Cluster methods 151
5.5 The Ising model in one dimension 161
5.6 The one-dimensional Heisenberg model 165
5.7 The Onsager solution of the two-dimensional I sing problem 171
5.8 Ferroelectric models in two dimensions 178
5.9 The spherical model of ferromagnetism 182
5.10 Graphical expansions 187
5.11 Order as a thermodynamic variable 197
5.12 Scaling and renormalization of critical phenomena 200
6 Thermodynamics of topological disorder
6.1 The linear gas-liquid--crystal 209
6.2 The van der Waals approximation 213
6.3 The Percus- Y evick approximation 218
6.4 Perturbation methods 220
6.5 The virial series 223
6.6 Computer sin1ulation methods 226
6.7 Melting 232
6.8 Entropy and free volume 240
7 Macromolecular disorder
Regular solutions
Entropy of macromolecular solutions
Model chains
Random coils
Branching and gel formation
Rubber elasticity
Excluded volume
Random walks on a lattice
Continuum models
Entanglements
8 Excitations on a disordered linear chain
Dynamical, magnetic and electronic excitations
One-dimensional models
Phase-angle representation
Spectral gaps in disordered chains
The spectral density
Local density approximation
Localization of eigenfunctions
9 Excitations on a disordered lattice
9.1 The TBA model
9.2 The Green function formalism
9.3 Propagator and locator expansions
9.4 The coherent potential approximation
9.5 Local environment corrections to CPA
9.6 Spectral bounds and band tails
9.7 Spectral moments and continued fractions
9.8 Off-diagonal disorder
9.9 Anderson localization
9.10 Percolation theory
9.11 Maze conduction
10 Electrons in disordered metals
10.1 The NFE model
10.2 Screened pseudopotentials
10.3 Muffin-tin potentials
10.4 The electron spectrum
10.5 Many-atom scattering
10.6 Scattering operators
10.7 Partial-wave representations
10.8 The coherent-wave approximation
10.9 Cluster scattering
10.10 Transport theory
11 Excitations of a topologically disordered network
11.1 Dynamics of liquids and glasses
11.2 The continuum limit
11.3 Ideal tetrahedral coordination
11.4 Tree models
11.5 The band-gap paradox
12 Dilute and amorphous magnets
12.1 The dilute Ising model
12.2 Dilute Heisenberg magnets
12.3 Amorphous ferromagnets and spin glasses
13 Electrons in 'gases'
13.1 Gas-like disorder
13.2 The metal-insulator transition
13.3 Hopping conduction
13.4 Semi-classical electrons in a random potential
13.5 Spectral tails in a choppy random potential
References
Index
