Part I. Basic Principles and Fundamental Properties
1. Size Effects on Structure and Morphology of Free
or Supported Nanoparticles
C. Henry ................................................ 3
1.1. Size and Confinement Effects ............................... 3
1.1.1. Introduction ........................................ 3
1.1.2. Fraction of Surface Atoms ........................... 3
1.1.3. Specific Surface Energy and Surface Stress .......... 4
1.1.4. Effect on the Lattice Parameter ..................... 5
1.1.5. Effect on the Phonon Density of States .............. 8
1.2. Nanoparticle Morphology .................................... 8
1.2.1. Equilibrium Shape of a Macroscopic Crystal .......... 8
1.2.2. Equilibrium Shape of Nanometric Crystals ........... 10
1.2.3. Morphology of Supported Particles .................. 17
References 32
2. Structure and Phase Transitions in Nanocrystals
J.-C. Nièpce, L. Pizzagalli ............................ 35
2.1. Introduction .............................................. 35
2.2. Crystalline Phase Transitions in Nanocrystals ............. 39
2.2.1. Phase Transitions and Grain Size Dependence ........ 39
2.2.2. Elementary Thermodynamics of the Grain Size
Dependence of Phase Transitions .................... 40
2.2.3. Influence of the Surface or Interface on
Nanocrystals ....................................... 42
2.2.4. Modification of Transition Barriers ................ 44
2.3. Geometric Evolution of the Lattice in Nanocrystals ........ 46
2.3.1. Grain Size Dependence .............................. 46
2.3.2. Theory ............................................. 47
2.3.3. Influence of the Nanocrystal Surface or Interface
on the Lattice Parameter ........................... 50
2.3.4. Is There a Continuous Variation of the Crystal
State Within Nanocrystals? ......................... 51
References ..................................................... 53
3. Thermodynamics and Solid—Liquid Transitions
P. Labastie, F. Calvo .................................. 55
3.1. Size Dependence of the Solid-Liquid Transition ............ 56
3.1.1. From the Macroscopic to the Nanornetric ............ 56
3.1.2. From Nanoparticles to Molecules .................... 64
3.2. Thermodynamics of Very Small Systems ...................... 67
3.2.1. General Considerations ............................. 67
3.2.2. Non-Equivalence of the Gibbs Ensembles ............. 68
3.2.3. Dynamically Coexisting Phases ...................... 69
3.2.4. Stability of an Isolated Particle. Thermodynamic
Equilibrium ........................................ 73
3.3. Evaporation: Consequences and Observations ................ 74
3.3.1. Statistical Theories of Evaporation ................ 74
3.3.2. Link with the Solid-Liquid Transition. Numerical
Results ............................................ 79
3.3.3. Experimental Investigation of Evaporation .......... 80
3.3.4. Beyond Unimolecular Evaporation .................... 81
3.3.5. Toward the Liquid-Gas Transition ................... 82
References ..................................................... 86
4. Modelling and Simulating the Dynamics of Nano-Objects
A. Pimpinelli .......................................... 89
4.1. Introduction .............................................. 89
4.2. Free Clusters of Atoms. Molecular Dynamics Simulations .... 90
4.3. Evolution of Free and Supported Nanoclusters Toward
Equilibrium. Kinetic Monte Carlo Simulations .............. 93
References ..................................................... 97
Part II Physical and Chemical Properties on the Nanoscale
5. Magnetism in Nanomaterials
D. Givord ............................................. 101
5.1. Introduction ............................................. 101
5.2. Magnetism in Matter ...................................... 102
5.2.1. Magnetic Moment ................................... 102
5.2.2. Magnetic Order .................................... 105
5.2.3. Magnetocrystalline Anisotropy ..................... 108
5.3. Magnetisation Process and Magnetic Materials ............. 110
5.3.1. Energy of the Demagnetising Field. Domains and
Walls ............................................. 111
5.3.2. The Magnetisation Process ......................... 112
5.3.3. Magnetic Materials ................................ 115
5.4. Magnetism in Small Systems ............................... 116
5.4.1. Magnetic Moments in Clusters ...................... 116
5.4.2. Magnetic Order in Nanoparticles ................... 119
5.4.3. Magnetic Anisotropy in Clusters and
Nanoparticles ..................................... 120
5.5. Magnetostatics and Magnetisation Processes in
Nanoparticles ............................................ 121
5.5.1. Single-Domain Magnetic Particles .................. 121
5.5.2. Thermal Activation and Superparamagnetism ......... 122
5.5.3. Coherent Rotation in Nanoparticles ................ 123
5.5.4. From Thermal Activation to the Macroscopic
Tunnel Effect ..................................... 124
5.6. Magnetism in Coupled Nanosystems ......................... 126
5.6.1. Exchange-Coupled Nanocrystals. Ultrasoft
Materials and Enhanced Remanence .................. 126
5.6.2. Coercivity in Nanocomposites ...................... 128
5.6.3. Exchange Bias in Systems of Ferromagnetic
Nanoparticles Coupled with an Antiferromagnetic
Matrix ............................................ 130
References .................................................... 132
6. Electronic Structure in Clusters and Nanoparticles
F. Spiegelman ......................................... 135
6.1. Introduction ............................................. 135
6.2. Liquid-Drop Model ........................................ 139
6.3. Methods for Calculating Electronic Structure ............. 141
6.3.1. Born-Oppenheimer Approximation. Surface
Potential ......................................... 142
6.3.2. Ab Initio Calculation of Electronic Structure ..... 144
6.3.3. Density Functional Theory ......................... 147
6.3.4. Charge Analysis ................................... 149
6.3.5. Approximate and Semi-Empirical Descriptions ....... 150
6.3.6. Energy Bands and Densities of States .............. 152
6.4. Applications to Some Typical Examples .................... 154
6.4.1. Metallic Nanoparticles ............................ 154
6.4.2. Molecular Clusters ................................ 162
6.4.3. Ionic and Ionocovalent Clusters ................... 170
6.4.4. Covalent Systems .................................. 175
6.5. Valence Changes .......................................... 178
6.5.1. Transitions with Size ............................. 178
6.5.2. Transitions with Stoichiometry .................... 179
6.6. Nanotubes ................................................ 182
6.7. Prospects ................................................ 185
References .................................................... 188
7. Optical Properties of Metallic Nanoparticles
F. Vallée ............................................. 197
7.1. Optical Response for Free Clusters and Composite
Materials ................................................ 198
7.2. Optical Response in the Quasi-Static Approximation:
Nanospheres .............................................. 199
7.3. Dielectric Constant of a Metal: Nanometric Size Effect ... 203
7.4. Surface Plasmon Resonance in the Quasi-Static
Approximation: Nanospheres ............................... 207
7.5. Surface Plasmon Resonance: Quantum Effects for Small
Sizes (D < 5 nm) ......................................... 211
7.6. General Case for Nanospheres: The Mie Model .............. 213
7.7. Non-Spherical or Inhomogeneous Nanoparticles in the
Quasi-Static Model ....................................... 216
7.7.1. Shape Effects: Ellipsoids ......................... 216
7.7.2. Structure Effects: Core-Shell System .............. 217
7.8. Optical Response of a Single Metal Nanoparticle .......... 219
7.9. Electromagnetic Field Enhancement: Applications .......... 221
7.9.1. Nonlinear Optical Response ........................ 221
7.9.2. Time-Resolved Spectroscopy ........................ 222
7.9.3. Local Enhancement of Raman Scattering: SERS ....... 223
7.10. Conclusion .............................................. 224
References .................................................... 226
8. Mechanical and Nanomechanical Properties
С. Tromas, M. Verdier, M. Fivel, P. Aubert,
S. Labdi, Z.-Q. Feng, M. Zei, P. Joli ................. 229
8.1. Macroscopic Mechanical Properties ........................ 229
8.1.1. Introduction ...................................... 229
8.1.2. Elastic Properties ................................ 229
8.1.3. Hardness .......................................... 231
8.1.4. Ductility ......................................... 234
8.1.5. Numerical Modelling ............................... 236
8.2. Nanomechanical Properties ................................ 238
8.2.1. Experimentation ................................... 238
8.2.2. Computer Modelling ................................ 254
References .................................................... 265
9. Superplasticity
T. Rouxel ............................................. 269
9.1. Introduction ............................................. 269
9.2. Mechanism ................................................ 270
9.3. Superplastic Nanostructured Materials .................... 276
9.4. Industrial Applications .................................. 277
References .................................................... 280
10. Reactivity of Metal Nanoparticles
J.-C. Bertolini, J.-L. Rousset ........................ 281
10.1.Size Effects ............................................. 282
10.1.1.Structural Properties ............................. 282
10.1.2.Electronic Properties ............................. 286
10.1.3.Reactivity in Chemisorption and Catalysis of
Monometallic Nanoparticles ........................ 288
10.2.Support Effects .......................................... 293
10.3.Alloying Effects ......................................... 295
10.3.1.Effect of Surface Segregation ..................... 296
10.3.2.Geometric Effects ................................. 297
10.3.3.Electronic Effects ................................ 298
10.4.Preparation and Implementation in the Laboratory and
in Industry .............................................. 299
References .................................................... 302
11. Inverse Systems — Nanoporous Solids
J. Patarin, O. Spalla, F. Di Renzo .................... 305
11.1.Introduction ............................................. 305
11.2.Nomenclature: The Main Families of Porous Materials ...... 305
11.3.Zeolites and Related Microporous Solids. Definition and
Structure ................................................ 307
11.4.Ordered Mesoporous Solids ................................ 309
11.5.Disordered Nanoporous Solids ............................. 311
References .................................................... 314
12. Inverse Systems — Confined Fluids: Phase Diagram and
Metastability
E. Charlaix, R. Denoyel ............................. 315
12.1.Displacement of First Order Transitions: Evaporation
and Condensation ......................................... 315
12.1.1.Adsorption Isotherms .............................. 315
12.1.2.Capillary Condensation ............................ 317
12.1.3.Capillary Pressure and the Kelvin Radius .......... 319
12.1.4.Non-Wetting Fluid ................................. 320
12.1.5.Perfectly Wetting Fluid ........................... 320
12.1.6.Hysteresis, Metastability and Nucleation .......... 322
12.2.Melting-Solidification ................................... 325
12.3.Modification of the Critical Temperature ................. 329
12.4.Ultraconfinement: Microporous Materials .................. 331
References .................................................... 334
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