Crystal faces, cluster model

In order to compare the electronic properties of the (001), (010) and (100) faces three clusters have been selected each one modelling one specific face of the M0O3 crystal, these clusters contain the same number of oxygen and molybdenum atoms , A2 and C4 for... 

In heterogeneous catalysis, the catalyst often exists in clusters spread over a porous carrier. Experimentally, it is well established that reactivity and selectivity of heterogeneous reactions change enormously with cluster size. Thus, theoretical studies on clusters are particularly important to establish a basis for the determination of their optimal size and geometry. Cluster models are also important for studying the chemistry and reactivity of perfect crystal faces and the associated adsorption and desorption processes in heterogeneous catalysis (Bauschlicher et al, 1987). 

In the present work, the interaction of the ethylene molecule with the (100) surfaces of platinum, palladium and nickel is studied using the cluster model approach. All these metals have a face centered cubic crystal structure. The three metal surfaces are modelled by a two-layer M9(5,4) cluster of C4V symmetry, as shown in Fig. 6, where the numbers inside brackets indicate the number of metal atoms in the first and second layer respectively. In the three metal clusters, all the metal atoms are described by the large LANL2DZ basis set. This basis set treats the outer 18 electrons of platinum, palladium and nickel atoms with a double zeta basis set and treats all the remainder electrons with the effective core potential of Hay and Wadt... 

Figure 1. Cluster geometry and local region of the nickel cluster used to model the (111) crystal face of nickel. The three layer, 62-atom cluster, consists of a surface layer of 28 atoms, a second layer of 17 atoms and a third layer of 17 atoms. Embedding theory is used to reduce the Nig2 cluster to a 26 atom model depicted as shaded atoms. Atoms surrounding the four central atoms in the surface layer and those surrounding the one central atom in the second layer are described by effective...

Modeling of CsyHaopW] and C66H72[NV] clusters was carried out. We got similar qualitative results for both clusters, so here we presents detailed results only for C33H3o[NV]. Structural, electronic and spin characteristics of diamond nanoclusters with the surface completely saturated with hydrogen were considered elsewhere [8,9]. We analyze a role of the free (111) surface on the above mentioned characteristics. The cluster CsyMsoCNV] was built on the basis of C33H36[NV] cluster by removal of six H atoms on a (111) crystal face (see Fig. 1). 

Figure 2 The (a) mass- and (b) surface-averaged distribution of atoms on the (111) and (100) crystal faces and on the edges and corner sites of a cubo-octahedral cluster model. (From Ref. 4.) Mass-averaged and surface-averaged distributions are based on calculations using cubo-octahedron cluster model and represent number of different crystallographic planes divided by the (a) mass or (b) the surface area of the cluster (at the corresponding particle size). Hence (e- -c) in (a) represents edge and kink positions and (100) (111) the normal cubic crystal planes.

For very small metallic particles, or clusters, crystal faces have no meaning. It is better to define surface structure with the notation introduced by Van Hardeveld and Hartog. They consider the coordination number i of a surface atom and the coordination number j of a surface active site, which was called as coordination model. Surface atom is denoted by Cj when it has i nearest neighbors. The active site is denoted by By when it has j nearest neighbors. Examples of C4, Ce and C7 atoms are shown in Fig. 2.8. Several active sites, B4, B5, Be and B7 are shown in Fig. 2.9. 

Another problem, which can be treated by using cluster models, is the study of the influence produced by various structural surface inhomogeneities (fractures, steps, protruding faces, etc.) upon the energy spectrum of the crystal. This is of special importance in the description of the phenomena that involve highly dispersed particles. 

For metal surfaces we show, in Figure 1(a), a cluster model for CO on the Cu(lOO) surface. The cluster shown has 9 Cu atoms in the first layer, 16 in the second layer and 9 in the third layer. The CO is placed on an atop site directly above the central first layer Cu atom, and with its molecular axis perpendicular to the surface. The metal-metal distances and bond angles are taken for a (100) face of the face centered cubic, fee, Cu crystal and any relaxation or reconstruction of the surface atoms from perfect bulk geometry is neglected. Furthermore, the cluster is not embedded because it is not easy to describe the chemical influence of surrounding atoms not directly included in the cluster. One way to include the effect of the remainder of the crystal has been used by Whitten... 

To examine the effective interaction of urea with specific surfaces of KCl, an approach similar to surface docking developed to predict the influence of additives on the crystal morphology has been employed [21-27], The basis of this approach is to analyze the effect of additives on the individual crystal faces, which are cleaved from a crystal. If the additive has a preferred interaction on a special face, the growth of this face will be slower. As a result, the other fast-growing surfaces will disappear, and eventually, the slow-growing surface will control the morphology. In this way, the additive influences the morphology of crystals. For simulations of surfaces of crystalline solids, slab, and cluster models are nevertheless by far more popular because they are feasible from the computational point of view [28]. However, the cluster models came under scrutiny due to their finite size representation. Slab models rather mimic the infinite surface of solids and are considered to be a better approach than the cluster models. In this study, a conventional array of these alkali... 

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

Model structures using octahedral Co(Ni) indicate that all bonding between the four extending orbitals on each lOlO face must be through adjacent positions (cis) on the Co(Ni). Trans bonding is possible for some configurations with larger clusters of Mo or stacked crystals. As the concern is with the Type I Co(Ni)-Mo-S site, discussions here will concentrate on cis attachment. 

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