Metal Surface Electron Physics (eBook)

Front Cover 1
Metal Surface Electron Physics 2
Copyright Page 3
Contents 4
Preface 8
Part I: Classical Description of Metal Surface 10
Chapter 1. The geometry of metal crystals and surfaces 12
1.1 Bravais lattices and metal structures 12
1.2 Unit cell 13
1.3 Crystallographic notations 16
1.4 Some features of the geometrical structure 19
1.5 Two-dimensional lattices 22
1.6 Notations of the real surface structure 25
Chapter 2. The surface of real metals 28
2.1 General remarks 28
2.2 Lattice relaxation and reconstruction of surfaces 30
2.3 Vibrations of surface atoms and the Debye temperature 36
Chapter 3. Thermodynamics of the surface of crystal 42
3.1 Basicnotions 42
3.2 Equilibrium shape of crystalline particles 45
3.3 Thermodynamics of microscopic single crystals 50
3.4 Surface energy, surface tension and surface stress 54
Part II: Quantum Theory of Metal Surface 60
Chapter 4. Electrons in metals 62
4.1 Sommerfeld’s model 62
4.2 Infinite and finite potential well 67
4.3 Jellium model and electrons near metal surface 71
4.4 Electron gas in the Hartree-Fock approximation 74
4.5 Exchange and correlation energy 77
4.6 Fermi hole and the origin of image force 78
4.7 Stability of jellium 80
4.8 Surface energy of semi-infinite free-electron gas 82
Chapter 5. Electron density functional theory 86
5.1 Thomas-Fermi method and its extensions 87
5.2 Hohenberg-Kohn theory 89
5.3 Kohn-Sham equations 91
Chapter 6. Electron gas near the metal surface 94
6.1 Thomas-Fermi electron density profile 94
6.2 Self-consistent Lang-Kohn method 97
6.3 Effective potential 98
6.4 The local density of states 100
Chapter 7. Sum rules and rigorous theorems for jellium surface 104
7.1 The phase-shift sum rules 104
7.2 Budd-Vannimenus theorems 106
7.3 The virial theorem 109
Chapter 8. Surface energy and surface stress 112
8.1 Surface energy components 112
8.2 Surface energy of jellium 113
8.3 Reintroduction of the discrete lattice of ions 116
8.4 Variational treatment of lattice effects 121
8.5 Structureless pseudopotential model 124
8.6 Surface stress 128
Chapter 9. Work function 132
9.1 The definitions 132
9.2 Work function of semi-infinite jellium 133
9.3 Discrete-lattice corrections to the work function 137
Chapter 10. Work function of simple metals: relation between theory and experiment 140
10.1 Jellium part of the work function – a role of the correlation energy . 140
10.2 Work function of the ‘real’ metal bounded by the flat surface 142
10.3 Face-dependent part of work function 143
10.4 Polycrystalline and face-dependent work functions 144
10.5 Relation between theory and experiment 146
Chapter 11. Variational electron density profiles: trial functions 150
11.1 Introduction 150
11.2 Conditions satisfied by various exact electron density profiles 152
11.3 Examples of the trial electron density profiles 153
11.4 Smoluchowski’s density profile and different contributions to the energy 155
Chapter 12. Image potential and image plane 162
12.1 Limitations of the classical picture . Image plane position 162
12.2 Linear response of electron system to static perturbing charges 166
12.3 Response of metal surface to a perturbing charge 168
12.4 The exchange (Fermi) hole near the metal surface 170
12.5 Origin of the image potential 174
Chapter 13. Metal surface in a strong external electric field 180
13.1 Electrostatic field at the surface 180
13.2 Linear and non-linear contributions to the response 186
13.3 Effect of the ionic lattice 188
13.4 Field induced relaxation and field evaporation 190
Chapter 14. Alloy surfaces 196
14.1 The Vegard law and the volume of formation of an alloy 196
14.2 Semi-empirical theory of alloy formation 198
14.3 Surface properties of alkali metal alloys 201
14.4 Work function of ordered alloys 203
14.5 Surface segregation 207
Chapter 15. Quantum size effect and small metallic particles 212
15.1 The notion of size effect 212
15.2 The non-oscillatory QSE 213
15.3 Oscillatory quantum size effect 215
15.4 Small metallic particles 222
15.5 Magic numbers 227
Part III: Metal Surface in Contact with Other Bodies 230
Chapter 16. Adsorption of alkali atoms on metal surface 232
16.1 Introduction 232
16.2 Work function changes due to alkali metal adsorption . Classical picture 233
16.3 Density-functional calculations 236
16.4 Relation between theory and experiment 246
16.5 Sum rules for a metal with an adlayer 249
16.6 Analytical density profiles for jellium-alkali adlayer system 251
Chapter 17. Adhesion between metal surfaces 254
17.1 General considerations 254
17.2 Adhesion of semi-infinite metallic slabs 256
17.3 Exact relations for bimetallic interfaces 262
17.4 The force between metal surfaces at small separations 265
Chapter 18. Universal scaling of binding energies 272
18.1 Scaling of adhesive binding energies 272
18.2 Universal binding energy curves 275
Appendices 282
Appendix A. 282
A.1 Fundamental constants 282
A.2 Atomic units 282
A.3 The quantities characteristic for the electron gas and screening 284
Appendix B. Planar average of the potential difference ?v(r) 286
Appendix C. Surface correlation energy for the Ceperley-Alder parameterization 290
Appendix D. Linear potential approximation for a metal surface 292
Appendix E. Finite linear potential model 296
References 298
Index 308