Relaxation, Rumpling, and Reconstruction

A different mechanism that includes bond rotation rather than bond length changes has been proposed for more covalently bonded oxides [18]. 

We note that reconstruction is not hmited to the first surface layer. In particular, in ionic crystals and semiconductors, it may reach up to 10 layers into the bulk. This is different from metals where screening limits reconstruction to the first few layers. 

Polar type 3 surfaces are unstable due to the diverging electrostatic energy caused by the finite dipole moment in all building blocks. However, there are several examples of naturally occurring minerals that expose polar surfaces, for example, MgO(lll) and NiO(lll) or ZnO(OOOl). The mechanisms that lead to stabilization of polar surfaces necessarily involve charge modifications of the surface layers. There are several ways to achieve the charge modifications of polar surfaces [20]  

Strong surface relaxation may reduce or compensate the excess surface charge. The stoichiometry of the surface may change in order to provide charge compensation. This can be achieved, for example, by the formation of an ordered array of vacancies and is generally known as surface reconstruction. 

The charge state of the surface may be changed by adsorption of atoms or ions on the surface. As polar oxide surfaces are highly reactive, adsorption of gases from the residual background, even under ultrahigh-vacuum (UHV) conditions, can take place on a very short time scale. 

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Bulk Chemical Potential and Stoichiometric Surfaces Generating Slab Models Relaxation, Rumpling and Reconstruction... 

We will make some preliminary remarks concerning the designation of the surfaces, their polar or non-polar character and their structural distortions - relaxation, rumpling and reconstruction. 

Fig. 2.4. Relaxation, rumpling and reconstruction effects. In the first two cases, the surface cell is identical to the projection of the bulk three-dimensional cell but the inter-atomic distances between the surface and the underlying planes are modified. When a reconstruction takes place, the size of the surface cell changes.

The first chapter of the book summarizes classical approaches, introduces the concept of ionicity, and describes the mixed iono-covalent character of the oxygen cation bond in bulk materials. The next three chapters focus on the characteristics of the atomic structure (relaxation, rumpling and reconstruction effects), the electronic structure (band width, gap width, etc.) and the excitations of clean surfaces. Metal-oxide interfaces are considered in the fifth chapter with special emphasis on the microscopic interfacial interactions responsible for adhesion. The last chapter develops the concepts underlying acid-base reactions on oxide surfaces, which are used in catalysis, in adhesion science, and in colloid physics, and discusses their applicability to the adsorption of hydroxyl groups. A comprehensive list of references is included. 

In Figs. 2.1 and 2.3, the atoms located in the outer layer, the ad-atoms or the ad-vacancies have been represented at positions defined by the bulk three-dimensional lattice. However, the bond-breaking process in the surface formation induces forces which push the atoms out of their bulk positions. When a two-dimensional periodicity is kept in the surface layers, the structural distortions are called relaxations, rumplings or reconstructions (Fig. 2.4). 

The shape of the density of states reveals the peculiarities of the hybridization between anion and cation orbitals, which depend upon three parameters the values of the resonance integrals the coordination number of the surface atoms and the energy separation between the relevant atomic levels. In the absence of relaxation, rumpling or reconstructions, the resonance integrals have the same values as in the bulk. The surface atom coordination numbers and the level separation, on the other hand, are smaller than in the bulk and they decrease as the surface becomes more open. We will first discuss how these modifications are reflected in the gross features of the local densities of states at the surface and, more specifically, in their second moments. Then we will focus on the details of the band shapes and on the possible occurrence of localized states in the gap. 

Through the formation of surfaces, bonds are broken and the above-addressed relaxations, rumpling, or reconstruction phenomena affect the interatomic potentials and bonding characteristics. The surface electronic structure is modified with respect to the bulk. In the following, we will address a few topics connected with surface electronic structure of some selected oxides. 

Figure 15.7 Schematic representation of (a) relaxation, (b) rumpling, and (c) reconstruction.

Fig. 1 shows the rocksalt lattice [15]. We will discuss MgO and NiO as limiting cases of oxides, one containing a simple metal ion and the other one a transition metal ion. The (100) surface of such a material represents a non-polar surface, the (111) surface represents a polar oxide surface. Since the lattice constants are very similar for both oxides (MgO 4.21 A, NiO 4.17 A) [15], we expect the surface structures to be similar. The non-polar surface exhibits a nearly bulk terminated surface as shown in Fig. 2a and it is very similar for both materials. We have put together information from FEED [16-21] and STM [22-25] analysis. There is very small interlayer relaxation and only a small rumpling of the surface atoms, whereby the larger anions move outwards and the small cations very slightly inward. A completely different situation is encountered for the polar (111) surfaces. Due to the divergent surface potential [13] on an ideally, bulk terminated polar surface, the surfaee reconstructs and exhibits a so... 

This surface stress coefficient can be manipulated by controlling the ambience (template material, composite glassy matrix, glue, gel, or gas) of the nanowire and depends on surface reconstruction, see Ref. [11] for details. In addition to surface relaxation, surface rumpling is another important issue for discussion. For... 

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