 | Hansen K. Statistical physics of nanoparticles in the gas phase. - Dordrecht: Springer, 2013. - xi, 282 p.: ill. - (Springer series on atomic, optical, and plasma physics; 73). - Ind.: p.275-282. - ISBN 978-94-007-5838-4; ISSN 1615-5653
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1 Introduction ................................................. 1
1.1 Basic Thermodynamic Concepts ............................ 3
1.2 Ensembles ............................................... 8
1.3 The Microcanonical Ensemble ............................. 8
1.4 The Level Density ....................................... 9
1.5 Temperature and Boltzmann Factor ....................... 12
1.6 The Canonical Ensemble ................................. 16
1.7 Mean Values in the Canonical Ensemble .................. 19
1.8 The Grand Canonical Ensemble ........................... 21
1.9 Exercises .............................................. 23
2 The Relation Between Classical and Quantum Statistics ....... 27
2.1 Fermi and Bose Statistics of Independent Particles ..... 30
2.2 Classical Phase Space .................................. 32
2.3 A Few Elementary and Useful Results from Classical
Statistical Mechanics .................................. 34
2.4 Quantum Corrections to Interatomic Potentials .......... 36
2.5 Example 1: The Harmonic Oscillator ..................... 38
2.6 Example 2: A Free Particle ............................. 40
2.7 Example 3: A Particle in the Gravitational Field ....... 41
2.8 Exercises .............................................. 44
3 Microcanonical Temperature .................................. 45
3.1 Definition ............................................. 45
3.2 Finite Size Heat Bath .................................. 48
3.3 Level Densities and Partition Functions ................ 53
3.4 Exercises .............................................. 58
4 Thermal Properties of Vibrations ............................ 59
4.1 Normal Modes ........................................... 59
4.2 Thermal Properties of Harmonic Oscillators ............. 65
4.3 Debye Particles ........................................ 68
4.4 Degenerate Oscillators ................................. 72
4.5 The Beyer-Swinehart Algorithm .......................... 74
4.6 Vibrational Level Densities from Canonical Quantities .. 77
4.7 Other Computational Schemes ............................ 78
4.8 Level Densities from Bulk Properties ................... 78
4.9 Exercises .............................................. 80
5 Rate Constants for Emission of Atoms, Electrons and
Photons ..................................................... 83
5.1 Atomic Evaporation ..................................... 84
5.2 Electron Emission ...................................... 94
5.3 Photon Emission ........................................ 96
5.4 Photon Emission from a Metal Particle ................. 101
5.5 Kinetic Energy Release in Unimolecular Reactions ...... 102
5.6 Exercises ............................................. 110
6 The Evaporative Ensemble ................................... 113
6.1 Decay of Isolated Particles ........................... 113
6.2 Abundances, Small Particles ........................... 122
6.3 Evaporation of Large Standard Particles ............... 130
6.4 Rates for Large Particles; General Case ............... 133
6.5 Large Particle Abundances ............................. 141
6.6 Metastable Decay Fractions ............................ 142
6.7 Exercises ............................................. 145
7 Abundance Distributions; Large Scale Features .............. 147
7.1 Liquid Drop Energies .................................. 147
7.2 The Partition Functions ............................... 151
7.3 Thermal and Chemical Equilibrium ...................... 155
7.4 Polymerization ........................................ 158
7.5 The Smoluchowski Equation ............................. 161
7.6 The Aggregation Equation .............................. 164
7.7 Supersaturated Gases and the Critical Size ............ 170
7.8 Exercises ............................................. 173
8 Molecular Dynamics and Monte Carlo Simulations ............. 175
8.1 Basics of Molecular Dynamics Simulations .............. 177
8.2 Temperature in MD Simulations ......................... 179
8.3 Monte Carlo Simulations ............................... 186
8.4 Random Number Generation .............................. 190
8.5 Simulated Annealing ................................... 194
8.6 Exercises ............................................. 198
9 Thermal Excitation of Valence Electrons .................... 201
9.1 Electron Number Fluctuations in the Grand Canonical
Ensemble .............................................. 205
9.2 Thermal Electronic Properties in the Microcanonical
Ensemble .............................................. 206
9.3 The Odd-Even Effect ................................... 207
9.4 Canonical Properties of the Equidistant Spectrum ...... 209
9.5 High Energy Level Density of the Equidistant
Spectram .............................................. 214
9.6 Numerical Methods ..................................... 217
9.7 Electronic Shell Structure ............................ 222
9.8 An Excursion into Bose-Einstein Statistics ............ 225
9.9 Exercises ............................................. 227
10 He Droplets ................................................ 229
10.1 The Excitation Spectrum ............................... 232
10.2 Ripplon Thermal Properties ............................ 234
10.3 Molecular Beam Temperatures ........................... 240
10.4 Phonon Level Density .................................. 241
10.5 Thermal Properties of the Combined Excitation
Spectrum .............................................. 244
10.6 Exercises ............................................. 245
11 Melting and Freezing ....................................... 247
11.1 Surface Melting and Melting Point Depression .......... 249
11.2 Measurements of Heat Capacities as Signatures of
Melting ............................................... 252
11.3 The Lindemann Index ................................... 253
11.4 A Simple Model of Melting ............................. 255
11.5 Exercises ............................................. 261
Appendix A Additional Reading ................................ 263
A.l General Statistical Physics ........................... 263
A.2 Classical Mechanics .................................... 264
A.3 Clusters etc ........................................... 264
A.4 Fermionic Degrees of Freedom ........................... 264
A.5 Mathematics and Numerical Methods ...................... 264
Appendix В Constants of Nature and Conversion Factors ........ 267
Appendix С Mathematical Help ................................. 269
С.1 The Euler-Maclaurin Summation Formula ................. 269
C.2 Stirling's Formula and the Г Function ................. 270
C.3 Some Frequently Occurring Integrals ................... 271
Index ......................................................... 275
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