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Surface Physics in Tribology
Published in Bharat Bhushan, Handbook of Micro/Nano Tribology, 2020
John Ferrante, Phillip B. Abel
The initial and classic solutions of the Kohn—Sham equations for surfaces and interfaces were accomplished by Lang and Kohn (1970) for the free surface and Ferrante and Smith for interfaces (Ferrante and Smith, 1985; Smith and Ferrante, 1986). The calculations were simplified by using the jellium model to represent the ionic charge. In the jellium model the ionic charge is smeared into a uniform distribution. Both sets of authors introduced the effects of discreteness on the ionic contribution through perturbation theory for the electron—ion interaction and through lattice sums for the ion—ion interaction. The jellium model is only expected to give reasonable results for the densest packed planes of simple metals.
Surface Electronic Structure
Published in M. Prutton, Electronic Properties of Surfaces, 2018
An atom at the surface is in an environment midway between the bulk and the isolated atom, and this is reflected in the ‘local density of states’, which is the charge density of electrons at a particular energy. The local density of states at a surface is made up of the tails of bulk wavefunctions, as well as an extra type of solution of the Schrödinger equation—surface states—which are wavefunctions localised at the surface (Forstmann 1978). Surface states are greatly influenced by the surface atomic structure, and play an important role in the reconstruction of semiconductors (Appelbaum and Hamann 1975) (but probably not metals). Surface states occur both on semiconductor and metal surfaces, but on semiconductors they sometimes have the character of dangling bonds (Appelbaum and Hamann 1973)—chemical bonds which are cut when the surface is made. The interpretation of the electronic structure in terms of local chemical bonds works quite well on semiconductor and insulator surfaces, but is not so useful for metals whose valence orbitals are less directional, and whose bonding is not covalent. As in the bulk metals, where the free-electron model is useful, the surface of jellium, in which the atomic potentials are smeared out into a uniform positive background, provides a useful starting point for understanding the surface electronic structure of metals like Na and Al (Lang 1973). In the transition metals where the d electrons dominate the bonding, the tight-binding (lcao) method provides a useful starting point (Friedel 1973). The change in the local density of states at the surface of transition metals can, in fact, lead to changes in magnetism, with the possibility of reduced magnetism at the surface of ferromagnets (Liebermann et al 1970) or ferromagnetism at the surface of paramagnets (Akoh and Tasaki 1978).
Basics of Resonance
Published in Banshi Dhar Gupta, Anand Mohan Shrivastav, Sruthi Prasood Usha, Optical Sensors for Biomedical Diagnostics and Environmental Monitoring, 2017
Banshi Dhar Gupta, Anand Mohan Shrivastav, Sruthi Prasood Usha
Before understanding the physics of SPR, it is necessary to understand plasmons and SPs. Plasmons are the quantum of wave-like excitations in the plasmonic systems where the electrons/ions interact with each other through Coulomb interactions. It can be found in metals, highly doped semiconductors, ionic gases, etc. In metals, the Coulomb interaction between the free electrons and the positive-charge background takes place which is discussed as the Jellium model. When an electric field is applied on metal at a point, the local free electron density is reduced due to Coulomb repulsion resulting in an increased positive-charge background at the same point. An increase in positive-charge background attracts the free electrons again because of Coulomb attraction. Due to the attraction of free electrons to the positive-charge background, the local negative charge increases and a restoring force in terms of Coulomb repulsion produces, because of which the free electrons start repulsing. This process of repulsion–attraction continues and results in a longitudinal oscillation of free electrons. These oscillations are termed as plasma oscillations and the quanta of these oscillations are called as plasmons. The plasma oscillation can be visualized as the wave propagation in water. If we drop a small particle in calm water, a longitudinal wave is produced which propagates away from its origin which is similar to the propagation of the plasma waves (Gupta et al. 2015). The frequency of plasmons, ωp, is expressed as ωp=Ne2ε0m where N, e, ε0, and m correspond to the electron density, charge of an electron, electric permittivity of vacuum, and the mass of a free electron, respectively.
The geometry, electronic and magnetic properties of VLi n (n = 2–13) clusters using the first-principles and PSO method
Published in Molecular Physics, 2020
Haitao Liu, Haibin Cao, Xiuhua Cui, Haiming Duan, Qun Jing, Qian Wang
In this paper, we obtained the ground-state structure of the VLin (n = 2–13) clusters by particle swarm optimisation algorithm software CALYPSO [40–43]. When n ≥ 3, the ground-state structure of VLin clusters prefers the three-dimensional configuration and a cage structure appears from VLi8. According to the stability analysed: After the cage structure appeared, the stability of the cluster is better. the ground-state structure of VLi6,8,12 clusters had good stability. VLi12 is considered a magic cluster. The magnetic properties are analysed. When n = 2–6, the change of magnetic moment shows oscillation. In the Vlin (n = 8–13) cluster, the magnetic moment decreases from 5 to 0 µB. Among them, VLi12 has a magnetic moment of 1 µB. The molecular orbital was observed in the Gaussian09 software package [56] and the molecular orbital composition of VLi12 cluster was analysed by multiwfn software [59]. The electronic structure conforms to the Jellium model. Analysed by AdNDP method [58] found that V participates in all localised and delocalised bonds in spin-up and spin-down molecular and there are all delocalised bonds in β-spin.
C/N/O centred metal clusters: super valence bonding and magic structure with 26 valence electrons
Published in Molecular Physics, 2020
Jianling Tang, Cairong Zhang, Hongshan Chen
The physical and chemical properties of clusters differ from those of the bulk and exhibit strong dependence on size and composition. One of the most exciting developments in the field of clusters is that chosen cluster can mimic the chemical behaviours of a group of atoms in the periodic table. This idea offers the prospect of a new dimension of the periodic table formed by stable clusters called superatoms. And it offers the potential to create novel materials with tailored properties by using clusters as building units [1–4]. The electron counting rules are central to the understanding of superatoms, and they play an important part in designing these new species. The simplest electron counting rules are the octet rule and 18-electron rule; they correspond to the closed s2p6 and s2p6d10 electronic configurations of noble gas atoms. For simple metal clusters, the Jellium model is very successful in understanding their stabilities and properties [5–9]. This model assumes a uniform background of positive charge for the atomic nuclei and the core electrons, and the valence electrons from the individual atoms are treated nearly free and move in this potential. This leads to the Jellium shells of 1S21P61D102S21F142P6 … , and the shell closure gives the series of magic numbers 2, 8, 18, 20, 34, 40 … . (In this paper we use the uppercase S, P, D to denote the Jellium orbitals, and the lowercase s, p, d for atomic orbitals). The well-known example of Al13, with 39 valence electrons, needs one extra electron to close the 2P6 shells and behaves as a halogen atom [10–13]. While the Jellium model works very well for pure metal clusters, the scope of application of the Jellium model and modification of the theory to account for nonmetal doped metal clusters are still illusive.