DeutschesFachbuch.de : Phase Transitions of Simple Systems Springer Series in Atomic, Optical, and Plasma Physics 42 Von Boris M. Smirnov, Stephen R. Berry

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Contents
Introduction 1
Part I Thermodynamics of Ensembles of Classical Particles
1 Excitations in Simple Atomic Ensembles 7
1.1 Thermodynamics and Dynamics of Particle Ensembles 7
1.2 Interaction of Inert Gas Atoms 9
1.3 Similarity Law for Simple Atomic Ensembles 13
1.4 Evolution of Particle Ensembles 13
1.5 Voids as Elementary Configurational Excitations 17
2 Structures of Ensembles of Interacting Particles 21
2.1 Close-Packed Structures 21
2.2 Shells in Close-Packed Structures 24
2.3 Lennard-Jones Crystal 27
2.4 Morse Crystal 29
2.5 Surface Energy of Lennard-Jones and Morse Crystals 30
2.6 Solid and Liquid Inert Gases Near the Triple Point 33
3 Thermodynamics of Dense Gases and Liquids 39
3.1 Equation of State for an Ensemble of Randomly Distributed Particles 39
3.2 Equilibrium of Gas and Condensed States 42
3.3 Liquid Surface Parameters 45
3.4 Peculiarities of Similarity for Inert Gases 47
3.5 Scaling Law for Molecular Systems 48
4 Clusters with Short-Range Interaction 51
4.1 Configurations of Solid Clusters with Pairwise Atomic Interactions 51
4.2 Peculiarities of Close-Packed Clusters with Short-Range Interaction 53
4.3 Constructing fcc-Clusters with Short-Range Interaction 54
4.4 Growth of fcc-Clusters with Short-Range Atomic Interaction 56
4.5 Regular Clusters of Close-Packed Structures 59
4.6 Icosahedral Clusters 64
4.7 Competition of Icosahedral and Close-Packed Structures 67
5 Ensembles of Classical Particles with Repulsion 75
5.1 Thermodynamics of Ensembles of Repelling Particles 75
5.2 A System of Hard Spheres 77
5.3 Colloid Suspensions as Systems of Repelling Particles 80
5.4 Virial Theorem and Instability of Crystal Structure 82
5.5 Phase Transition for an Ensemble of Repelling Atoms 88
5.6 Phase Transitions in Inert Gases under High Pressure 90
5.7 Structures of an Ensemble of Repelling Particles at Low Temperatures 94
Part II Configurational Excitations and Aggregate States of Ensembles of Cl...
6 Configurational Excitation and Voids in Ensembles of Bound Classical Atoms...
6.1 Separation of Thermal and Configurational Degrees of Freedom of Clusters...
6.2 Lattice Model for the Order-Disorder Phase Transition 100
6.3 Chemical Equilibria and Phase Transitions 102
6.4 Internal Voids in a System of Identical Particles 105
6.5 Void Formation in Two Dimensions 109
6.6 The Cell Model for Disk Particles 113
6.7 Peculiarities of Configurational Excitation for Bulk Atomic Systems 115
6.8 Two-State Approximation for Aggregate States 117
7 Configurational Cluster Excitation with Pairwise Interactions 121
7.1 Peculiarities of Configurational Excitation of Clusters 121
7.2 Structural Phase Transition in a Solid Cluster 127
7.3 Configurational Excitation of the Icosahedral Cluster of 13 Atoms 131
7.4 The Cluster as a Microcanonical Ensemble of Bound Atoms 134
7.5 The Cluster as a Canonical Ensemble of Bound Atoms 137
7.6 Configurational Excitation of the Icosahedral Cluster of 55 Atoms 140
7.7 Character of Configuration Transitions in Clusters 146
8 Phase Transitions in Macroscopic Systems of Atoms 149
8.1 Configurational Excitation of a Solid 149
8.2 Modified Lattice Model for Configurational Excitation 151
8.3 Parameters of Voids for Liquid Inert Gases 153
8.4 Voids in a Macroscopic System of Bound Atoms 157
8.5 Criterion of Existence of the Liquid State 157
8.6 Freezing Points for Bulk Inert Gases 160
8.7 General Liquid Properties 161
9 Melting of Clusters and Bulk Atomic Ensembles 163
9.1 Entanglement of Thermal and Configurational Excitations in Clusters 163
9.2 Parameters of Melting 165
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Index
AAggregate state 1, 7, 8, 17, 19, 39, 52, 75-77, 79, 81, 83, 85, 86, 90, 91, 93, 94, ...
Aggregate state of clusters 172
Anharmonicity parameter 135, 140, 200
Arrhenius law 8, 161, 204
BBerry parameter 165
Bimodal energy distribution 136
Boiling point 42, 43, 45, 49, 50
CCanonical ensemble 134, 140, 180, 187, 188, 195
Cell model 113-115, 202, 204
Chemical potential 217-226, 228
Clausius-Clapeyron equation 34, 42, 91, 208
Close-packed crystal structures 3
Coexistence of aggregate states or phases 133, 137, 141, 163, 165, 167, 172, 179
Configuration cluster temperature 137
Configurational entropy 105, 191
Configurational excitation 15, 18, 19, 51, 99 ff, 121 ff
Coordination number 44, 79, 84-86, 87, 93, 94, 211
Critical phenomenon 40
Critical point 40-42, 46, 47, 50, 92, 160
Critical radius 218
Cuboctahedral cluster 56, 61, 68
DDebye frequency 130
Debye temperature 122, 159, 160, 227
Density of random packing 78
Diffusion coefficient of vacancies 203, 204
Disk model 115, 203, 204
Disks in rhombic box 109, 110
Diffusion of voids 4, 200, 201, 229
Dividing surface 222-224
Domain structure 79, 87
Drift velocity of voids 219, 223, 228
DSD (diamond-square-diamond) transitions 146
Dulong Petit formula or law 122, 138, 160, 165, 196
Dusty plasma 75, 85, 86, 94, 225, 229, 230
EEB (edge-bridging) transitions 146
Effective cluster temperatures 125
Einstein relation 220
Ensemble of repelling particles 75, 76, 78, 79, 82, 85, 89, 94, 95, 203, 211
Entropy of configurational excitation 106
Equation of state 39-42, 83, 179
Equilibrium constant 118, 133, 184
Etters-Kaeberer parameter 165
Exchange interaction 1, 2, 10-12, 76, 80, 90
FFace-centered cubic (fcc) structure 3, 12, 22-24, 26, 28, 29, 30, 32, 35, 53, 54, 63...
Floaters 144, 184
Frenkel model 147
Fluid, fluidity 79, 81, 89, 170, 173, 174, 199, 231
Freezing limit 160, 199, 227, 232
Freezing point 81, 158, 160, 199, 227
Fusion energy 36, 44, 50, 89, 118, 136, 139, 140, 156, 158, 165, 185
GGas equation of state 39, 40
Gibbs phase rule 172, 179
Gibbs thermodynamical potential, Gibbs free energy 7, 84, 199, 220, 225
Glass temperature 207
Glassy state 4, 7, 8, 19, 79, 161, 199, 207-211, 213-215
Growth of grains 218, 219
Growth of nucleus 224, 225
Growth of thin films 218
HHard balls or spheres 22, 76-80, 87, 94
Hard disk model 115, 204
Hard sphere model 76-82, 86, 91, 94, 95, 109, 211, 213
Heat capacity 102, 103, 128-131, 136-139, 142, 144, 145, 165, 190, 192-198, 226, 227,...
Heat capacity of cluster 128-131, 136-139, 142, 144, 145, 165, 190, 192-198
Heat-induced glassy transition 209
Hexagonal cluster 24, 59, 61-63
Hexagonal structure 21-25, 28, 59, 61-63, 70, 71, 76, 77, 82, 87, 90, 93, 94, 109-111...
Hierarchy of times 105, 147
IIcosahedral cluster 16, 64-69, 71-74, 123, 130, 131
Instability of a superheated solid 200
Interaction potential 9-14, 21, 23, 26, 27, 29-33, 35, 37, 42, 47, 48, 51, 53, 54, 65...
Interfacial interaction 81
Ionization equilibrium 102-104, 184
LLattice model 100-102, 116, 127, 149-152
Lennard-Jones crystal 28, 30, 32, 63
Lennard-Jones interaction potential and cluster 9, 14, 19, 27, 29-32, 35, 37, 42, 67-...
Lindemann criterion 165, 166
Lindemann parameter 166
Long-range interaction 10, 11, 21, 22, 26, 27, 35, 58, 61, 69
Local thermal equilibrium 19, 197
Loose random packing 78
MMagic numbers 52, 54, 57, 58, 62, 74, 94, 167, 169
Mean square of atom displacement 166, 167
Melting point 7, 34, 36, 42, 43, 45, 50, 52, 90, 92, 102, 108, 118, 119, 167-169, 171...
Microcanonical ensemble 122, 134, 180, 192, 193, 198
Miller indices 23
Mixture of cluster structures 72
Modified lattice model 151, 153
Morse interaction potential 29, 30, 32, 33, 35, 69, 73, 74, 128
NNearest neighbors 3, 13, 16, 17, 21, 22, 24-35, 37, 41, 44, 45, 53-57, 59, 61, 64-70...
Non-nearest neighbors 21, 22, 27, 28, 30, 74
Nucleation phenomenon 10, 218, 219, 225
O
Octahedral cluster 59, 61
Order-disorder phase transition 92, 101-105, 116, 149
Ostwald ripening 218
PPacking density 78, 79, 87, 89, 93, 202
Packing parameter 77-79, 81, 82, 89, 94, 110-115, 203, 204, 211-213
Pairwise interaction 1-4, 21, 51, 59, 87, 93, 127, 131, 160, 174, 208
Partition function 104, 105, 108, 113, 114, 118, 128, 129, 150, 151, 153, 154, 156, 1...
Phase, phase transition 1-6, 7-9, 19, 36, 39, 43, 46-48, 50, 79, 81, 82, 84-86, 88-92...
Phase diagram 39, 40, 46, 47, 79-82, 92, 211
Planes of fcc structure 26
Potential energy surface (PES) 2, 8, 12-17, 51, 91, 99, 100, 116, 121, 122, 124, 132,...
Principle of detailed balance 186, 205
RRepelling colloid particles 81
Repulsive interaction of particles 2, 11, 75, 76, 84, 85, 90, 204
Restructuring of chemical bonds 215
Root mean square of the bond length fluctuation 166
SSaddle-crossing dynamics 14, 18, 105, 121
Saddle points 14, 16, 17, 116, 123, 124, 142
Saturated vapor pressure 42, 43, 49, 152, 208-210
S-bend of caloric curve 193
Scaling law 12, 13, 33, 35, 37, 40, 41, 43, 47-49, 88, 105, 117, 153
Self-diffusion coefficient 201
Short-range interaction 10, 13, 16, 22, 28, 33, 35, 37, 43, 44, 48, 53, 55, 57, 58, 6...
Single-atom transitions 123
Solid (cluster) temperature 125
Specific free energy 158
Specific surface energy 30-32, 46, 54, 58, 61, 67, 73, 74
Stacking instability 77, 87, 93
Statistical weight of voids 108
Stishov statement 92
Strain energy 28, 30
Structural phase transition 127
Structures of close packing 22, 23, 28, 59, 89
Sublimation energy 21, 24, 27, 29, 35, 153, 208
Surface energy 30-32, 46, 53, 54, 58, 60, 61, 67, 72-74, 218
Surface tension 35, 45, 46, 54, 218
Suspension with PMMA (polymetilmethacrylate) particles 80
Symmetry of fcc structure 23
Symmetry of hexagonal structure 23
TTransition temperature 103, 128-130, 209
Truncated Lennard-Jones potential 35, 67, 69
Truncated octahedral structure 61
Twinning 71
Two-dimensional cell model 202
Two-state approach 117, 119, 136, 173
Types of fee-clusters 55
VVan der Waals equation 40-42, 47, 48
Virial theorem 82, 83, 85, 86
Void formation 105, 144, 151, 152, 154, 156-158, 202, 213
Void model 44, 153
WWigner-Seits radius 45
YYukawa interaction potential 85, 86, 94
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