This book proposes two simple quantum mechanical models for the analytical description of metal surfaces and nanoparticles. It gives an ostensive picture of the forces acting in a metal surface and deduces analytical formulae for the description of their physical properties. This book explains the relation between near-surface stress and familiar surface parameters. The concept of the separation of the three-dimensional body into three one-dimensional subsystems was applied. The content is of interest to all those working in the field of surface physics.
Author(s): Wolfgang Gräfe
Publisher: Springer
Year: 2015
Language: English
Pages: 100
Preface
Acknowledgments
Contents
Nomenclature
1 Introduction
Abstract
1.1 Electrocapillarity of Liquids
1.2 Surface Free Energy and Surface Stress of Solids
1.3 The Estance or the Surface Stress-Charge Coefficient
1.4 Experimental Data in the Literature
1.5 State of the Theoretical Knowledge
1.6 The Aim of the Following Text
References
2 The Model of Kronig and Penney
Abstract
2.1 The Density of the Electron Energy Levels n(E)
2.2 Remarks
Reference
3 Tamm's Electronic Surface States
Abstract
Reference
4 The Extension of the Kronig--Penney Model by Binding Forces
Abstract
5 The Separation of the Semi-infinite Model and the Calculation of the Surface Parameters for the Three-Dimensional body at T = 0 K (Regula Falsi of Surface Theory)
Abstract
5.1 The Separability of the Chemical Potential
5.2 The Separability of the Fermi Distribution Function
5.3 The Calculation of Surface Energy, Surface Stress, and Surface Charge at T = 0 K (Regula Falsi of Surface Theory)
References
6 The Surface Parameters for the Semi-infinite Three-Dimensional Body at Arbitrary Temperature
Abstract
6.1 Discussion
References
7 The Surface Free Energy varphi and the Point of Zero Charge Determined for the Semi-infinite Model
Abstract
7.1 Electron Transitions from the Bulk into the Surface and the Contribution to the Surface Free Energy varphi Tr
7.2 The Point of Zero Charge (PZC) and the Fermi Level Shift
7.3 The Contribution of the Electrostatic Repulsion Between the Electrons in the Surface Bands to the Surface Energy
Reference
8 A Model with a Limited Number of Potential Wells
Abstract
8.1 Modeling a Nanoparticle and a Solid Surface
8.2 The Energy of the Electrons in the Bulk and in the Surface Bands
8.3 Calculation of the Surface Parameters
8.3.1 The Surface Energy \varvec{\varphi}^{\rm{ESB}} of the Electrons in a Surface Band of a Nanocube
8.3.2 Calculation of the Surface Free Energy \varvec{\varphi} in a Nanocube
8.3.3 Calculation of the Surface Stress for a Nanocube and a Plate-like Body
8.4 Remarks
8.5 The Surface Charge Densities and the Point of Zero Charge in a Nanocube
Reference
9 Surface Stress-Charge Coefficient (Estance)
Abstract
10 Regard to the Spin in the Foregoing Texts
Abstract
11 Detailed Calculation of the Convolution Integrals
Abstract
References
12 Comparison of the Results for the Semi-infinite and the Limited Body
Abstract
12.1 The Semi-infinite Body
12.1.1 Surface States
12.1.2 Density Distribution of the Energy Levels
12.1.3 Remark
12.1.4 Surface Free Energy
12.2 The Limited Body
12.2.1 Surface States
12.2.2 Density Distribution of the Energy Levels
12.2.3 Surface Free Energy of a Nanocube
12.2.4 Surface Free Energy of a Plate-like Body
12.3 Summary
13 Calculation of Surface Stress and Herring's Formula
Abstract
13.1 Conclusions
References
14 Miscellaneous and Open Questions
Abstract
14.1 The Scientific Ambition of this Book
14.2 Own Results
14.2.1 Semi-infinitely Extended Body at 300 K
14.2.2 Nanocube of 10 x 10 x 10 Potential Wells at 0 K
14.3 Support for the Presented Theory
14.4 Fatigue Limit
14.5 Surface Stress and Young's Modulus
14.6 Electrocapillarity
14.7 The Minimum of the Surface Free Energy
14.8 Fermi Level/Chemcal Potential
14.9 The Influence of the Number of Atoms on the Results
References
Index
