Metal Surface Electron Physics 0080426751

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

I Classical Description of Metal Surface				1
1	The geometry of metal crystals and surfaces			3
	1.1	Bravais lattices and metal structures . . .	. . . . . . . . . . . . . . . .	3
	1.2	. . . . . . . . . . . . . . . . . . . .	. . . . . . . . . . . . . . .
	1.3	Crystallographic notations . . . . . . . . . .	. . . . . . . . . . . . . . .	7
	1.4	Some features of the geometrical structure	. . . . . . . . . . . . . . . .	10
	1.5	Two-dimensional lattices . . . . . . . . . . .	. . . . . . . . . . . . . . .	13
	1.6	Notations of the real surface structure . .	. . . . . . . . . . . . . . . .	16
2	The surface of real metals			19
	2.1	General remarks . . . . . . . . . . . . . . .	. . . . . . . . . . . . . . .	19
	2.2	Lattice relaxation and reconstruction of surfaces . . . . . . . . . . . .		21
	2.3	Vibrations of surface atoms and the	temperature . . . . . . . .	27
3 Thermodynamics of the surface of crystal				33
	3.1	Basicnotions . . . . . . . . . . . . . . . . .	. . . . . . . . . . . . . . .	33
	3.2	Equilibrium shape of crystalline particles	. . . . . . . . . . . . . . . .	36
	3.3	Thermodynamics of microscopic single crystals . . . . . . . . . . . . .		41
	3.4	Surface energy, surface tension and surface stress . . . . . . . . . . . .		45
	Quantum Theory of Metal Surface			51
4	Electrons in metals			53
	4.1	model . . . . . . . . . . . . .	. . . . . . . . . . . . . . .	53
	4.2	Infinite and finite potential well . . . . . . .	. . . . . . . . . . . . . . .	58
	4.3	Jellium model and electrons near metal surface . . . . . . . . . . . . .		62
	4.4	Electron gas in the Hartree-Fock approximation . . . . . . . . . . . . .		65
	4.5	Exchange and correlation energy . . . . . .	. . . . . . . . . . . . . . .	68
	4.6	Fermi hole and the origin of image force .	. . . . . . . . . . . . . . . .	69
	4.7	Stability of jellium . . . . . . . . . . . . . .	. . . . . . . . . . . . . . .	71
	4.8	Surface energy of semi-infinite free-electron gas . . . . . . . . . . . . .		73

...

111

5	Electron density functional theory		77
	5.1	Thomas-Fermi method and its extensions . . . . . . . . . . . . . . . .	78
	5.2	Hohenberg-Kohn theory . . . . . . . . . . . . . . . . . . . . . . . . . .	80
	5.3	Kohn-Sham equations . . . . . . . . . . . . . . . . . . . . . . . . . . .	82
6 Electron gas near the metal surface			85
	6.1	Thomas-Fermi electron density profile . . . . . . . . . . . . . . . . . .	85
	6.2	Self-consistent Lang-Kohn method . . . . . . . . . . . . . . . . . . . .	88
	6.3	Effective potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	89
	6.4	The local density of states . . . . . . . . . . . . . . . . . . . . . . . . .	91
7	Sum rules and rigorous theorems for jellium surface		95
	7.1	The phase-shift sum rules . . . . . . . . . . . . . . . . . . . . . . . . .	95
	7.2	Budd-Vannimenus theorems . . . . . . . . . . . . . . . . . . . . . . . .	97
	7.3	The virial theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	100
8 Surface energy and surface stress			103
	8.1	Surface energy components . . . . . . . . . . . . . . . . . . . . . . . .	103
	8.2	Surface energy of jellium . . . . . . . . . . . . . . . . . . . . . . . . . .	104
	8.3	Reintroduction of the discrete lattice of ions . . . . . . . . . . . . . . .	107
	8.4	Variational treatment of lattice effects . . . . . . . . . . . . . . . . . .	112
	8.5	Structureless pseudopotential model . . . . . . . . . . . . . . . . . . .	115
	8.6	Surface stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	119
9	Work function		123
	9.1	The definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	123
	9.2	Work function of semi-infinite jellium . . . . . . . . . . . . . . . . . . .	124
	9.3	Discrete-lattice corrections to the work function . . . . . . . . . . . . .	128
10 Work function of simple metals: relation between theory and
	experiment		131
	10.1 Jellium part of the work function .a role of the correlation energy . .		131
	10.2 Work function of the metal bounded by the flat surface . . . . .		133
	10.3 Face-dependent part of work function . . . . . . . . . . . . . . . . . .		134
	10.4 Polycrystalline and face-dependent work functions . . . . . . . . . . .		135
	10.5 Relation between theory and experiment . . . . . . . . . . . . . . . . .		137
11 Variational electron density profiles: trial functions			141
	11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		141
	11.2 Conditions satisfied by various exact electron density profiles . . . . .		143
	11.3 Examples of the trial electron density profiles . . . . . . . . . . . . . .		144
	11.4 Smoluchowski’sdensity profile and different contributions to
		the energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	146

iv

Image potential and image plane			153
12.1	Limitations of the classical picture. Image plane position . . . . . . . .		153
12.2	Linear response of electron system to static perturbing charges . . . .		157
12.3 Response of metal surface to a perturbing charge . . .		. . . . . . . . .	159
12.4 The exchange (Fermi) hole near the metal surface . . .		. . . . . . . . .	161
12.5	Origin of the image potential . . . . . . . . . . . . . . .	. . . . . . . .	165
13 Metal surface in a strong external electric field			171
13.1	Electrostatic field at the surface . . . . . . . . . . . . . .	. . . . . . . .	171
13.2	Linear and non-linear contributions to the response . .	. . . . . . . . .	177
13.3	Effect of the ionic lattice . . . . . . . . . . . . . . . . . .	. . . . . . . .	179
13.4	Field induced relaxation and field evaporation . . . . .	. . . . . . . . .	181
14 Alloy surfaces			187
14.1	The Vegard law and the volume of formation of an alloy . . . . . . . .		187
14.2	Semi-empirical theory of alloy formation . . . . . . . .	. . . . . . . . .	189
14.3	Surface properties of alkali metal alloys . . . . . . . .	. . . . . . . . .	192
14.4 Work function of ordered alloys . . . . . . . . . . . . . .		. . . . . . . .	194
14.5	Surface segregation . . . . . . . . . . . . . . . . . . . . .	. . . . . . . .	198
15 Quantum size effect and small metallic particles			203
15.1	The notion of size effect . . . . . . . . . . . . . . . . . .	. . . . . . . .	203
15.2	The non-oscillatory QSE . . . . . . . . . . . . . . . . . .	. . . . . . . .	204
15.3	Oscillatory quantum size effect . . . . . . . . . . . . . .	. . . . . . . .	206
15.4 Small metallic particles . . . . . . . . . . . . . . . . . .		. . . . . . . .	213
15.5	Magic numbers . . . . . . . . . . . . . . . . . . . . . . .	. . . . . . . .	218
Metal Surface in Contact with Other Bodies			221
16 Adsorption of alkali atoms on metal surface			223
16.1	Introduction . . . . . . . . . . . . . . . . . . . . . . . . .	. . . . . . . .	223
16.2 Work function changes due to alkali metal adsorption. Classical
	picture . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. . . . . . . .	224
16.3	Density-functional calculations . . . . . . . . . . . . . .	. . . . . . . .	227
	16.3.1 The model of . . . . . . . . .	. . . . . . . . .	227
	16.3.2 The adsorption of single alkali atoms on metallic substrate . .		232
16.4	Relation between theory and experiment . . . . . . . .	. . . . . . . . .	237
16.5	Sum rules for a metal with an adlayer . . . . . . . . .	. . . . . . . . .	240
	16.5.1 Phase-shift sum rule. . . . . . . . . . . . . . . . .	. . . . . . . .	240
	16.5.2 Budd-Vannimenus theorem for a	system . . . . .	241
16.6 Analytical density profiles for jellium-alkali adlayer system . . . . . . .			242

V

17.4 The force between metal surfaces at small separations

18 Universal scaling of binding energies

17.3 Exact relations for bimetallic interfaces

17 Adhesion between metal surfaces

245

17.1General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

17.2Adhesion of semi-infinite metallic slabs . . . . . . . . . . . . . . . . . . 247

. . . . . . . . . . . . . . . . . 253

. . . . . . . . . 256

263

18.1Scaling of adhesive binding energies . . . . . . . . . . . . . . . . . . . 263

18.2Universal binding energy curves . . . . . . . . . . . . . . . . . . . . . . 266

Appendices

A	Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . .	273
A . l		273
A.2	Atomic units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	273
A.3	The quantities characteristic for the electron gas and screening . . . .	275
B Planar average of the potential difference		277
C Surface correlation energy for the Ceperley-Alder		281
parameterization
D Linear potential approximation for a metal surface		283
E Finite linear potential model		287
References		289
Index		299

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