Bulk Crystal Structures

Corundum AI2O3, FejOj, CrjOj, VjOj, TijOj 

The spinel structure is a cubic structure with one-half of the octahedral and one-eighth of the tetrahedral sites in an fee oxygen lattice being occupied. In the normal spinel, one type of metal sits on the octahedral site and another metal ion on the tetrahedral sites giving a stoichiometry of Me(I)Me(II)204, for example, MgAl204. On the other hand, in the inverse spinel structure, only one type of metal with 

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Sinkler, W., Bengu, E., Marks, L. D. (1998), Appheation of Direet Methods to Dynamical Electron Diffraction Data for Solving Bulk Crystal Structures", Acta Cryst. A54, 591-605. 

As an example, Fig. 4.4 shows another view of the Cu surface that highlights where the plane of the surface is relative to the bulk crystal structure. The orientation of this plane can be defined by stating the direction of a vector normal to the plane.1 From Fig. 4.4, you can see that one valid choice for this vector would be [0,0,1]. Another valid choice would be [0,0,2], or [0,0,7], and so on, since all of these vectors are parallel. 

Multilayers condensed upon the ordered monolayers maintained the same orientation and packing as found in the monolayers. Thus, the monolayer structure determines the growth orientation and the surface structure of the growing organic crystal. This phenomenon is called pseudomorphism and as a result the surface structures of the growing organic crystals do not correspond to planes in the reported bulk crystal structures. The exception appears to be n-octane on the Ag(l 11) surface that is deposited with the (lOl) orientation of its bulk crystal structure. 

Cyclohexane forms a (9 X 9) surface structure on the Ag(l 11) crystal face and a (j j) surface structure on the Pt(l 11) crystal face at around 200 K. This latter surface structure corresponds to the (001) surface orientation of the monoclinic bulk crystal structure of the molecule. On heating the platinum crystal face to 450 K a ( ) surface structure forms that is identical to the surface structure formed by cyclohexene monolayers at the same temperature. It appears that cyclohexane dehydrogenates at elevated temperatures on platinum to form the same species or that of cyclohexene. 

The surface structures observed for the multilayer deposits of the phthalocyanines on both substrate faces, Cu(l 11) and Cu(lOO), were not those of any plane in the bulk crystal structure of the phthalocyanines. 

Generally, LEED experiments are conducted on specified faces of single crystals. When this is done, the diffraction pattern produced consists of a series of spots with a location, shape, and intensity that can be interpreted in terms of the surface structure. We focus attention on what can be learned from the location and shape of the spots since the study of intensity is beyond the scope of this book. It is generally assumed that the surface examined by LEED is an extension of an already-known bulk crystal structure. The correctness of this assumption can be tested, and results are often expressed in terms of modifications of the three-dimensional structure at the surface. Before we turn to the LEED patterns below, we must first figure out how they are read. 

The bulk crystal structure of the samples was determined by XRD (Rigaku D-max B) using a filtered Cu Ka radiation. Surface structure and composition were monitored by XPS (Perkin-Elmer PHI 5400). The N2 BET surface area and CO chemisorption were measured in a constant-volume adsorption apparatus. For the latter, two successive isotherms separated by evacuation were obtained at RT for a sample and the difference extrapolated to zero pressure was taken as chemisorbed CO. 

Here f and f2 represent the bond strength of the Cd-X bond, dictated by bulk crystal structure, and that between the surface Cd and the probably adsorbed, polysulfide species from solution, resp. The larger fj, the more likely it is that the photogenerated hole,h+, will react with the polysulfide species, i.e. the lower the probability of self-oxidation. 

Let us start with the simple case of an ideal crystal with one atom per unit cell that is cut along a plane, and assume that the surface does not change. The resulting surface structure can then be described by specifying the bulk crystal structure and the relative orientation of the cutting plane. This ideal surface structure is called the substrate structure. The orientation of the cutting plane and thus of the surface is commonly notated by use of the so-called Miller indices. 

Cadmium clusters have been treated by Baetzold (47) using EH and CNDO calculations. With atomic valence electron configuration 4dl05s25p, the clusters are calculated to be weakly stable. Linear geometry is more stable than symmetric three-dimensional geometries or even the bulk crystal structure for small Cd clusters. Poor stability is a consequence of the closed atomic 5s shell in Cd. Unstable antisymmetric 5s molecular orbitals are filled in the small clusters, but the amount of bonding by 5p orbitals increases with size. This leads to the trend of increasing stability with size as observed in Table VIII. Compari-... 

If the 10 point groups allowed are arranged in nonredundant patterns allowed by the five 2D Bravais lattices, 17 unique two-dimensional space groups, called plane groups, are obtained (Fedorov, 1891a). Surface structures are usually referred to the underlying bulk crystal structure. For example, translation between lattice points on the crystal lattice plane beneath and parallel to the surface (termed the substrate) can be described by an equation identical to Eq 1.10 ... 

This brings the discussion of the changes in the solid full circle. Spiltover hydrogen can exchange with the surface. It may react with and replace methoxyls with hydroxyls. It may be incorporated into the bulk with a change in the bulk crystal structure. Bulk reduction may occur. The species spilling over may react only with the surface, with coke, or with other sorbed species. In addition, spillover may promote or inhibit reaction on the surface. 

Total energy calculations of sufficient precision would be able to determine the energetically favorable adsorption site. Such calculations are still much more difficult than the calculation of orbital energy levels and vibrational frequencies. Values of the Ni-Ni bond distance were chosen to correspond to the bulk crystal structure. In the DV-LCAO calculations the C-O and C-Ni bond distances were... 

Fig. 2. Connected polyhedra representation of the bulk crystal structures of...

The bulk crystal structures of many oxides are discussed at length in Refs. 9 and 19. Our interest here is in determining the geometric structure of various surfaces that can exist on bulk oxide crystals. 

A good example of these principles is the rocksalt structure we will consider MgO to be specific. In the bulk crystal structure, both cations and anions have six nearest-neighbor ligands in an octahedral configuration this is the ideal... 

This section summarizes the present stage of our knowledge on clean oxide surfaces, obtained from numerical works. It is presented according to the oxide bulk crystal structures, with special emphasis on those oxides which have been more thoroughly studied. 

Cr203 has the same bulk crystal structure as a-Al203, namely corundum. Of its several low Miller index surfaces only one, (0001), has been employed for adsorbate structural determinations so far. To overcome sample charging problems a thin film has been utilised for these studies, rather than a single crystal. The surface structure of this (0001) oriented thin film has been investigated by LEED-IV [112]. Simulations of the experimental data evidence a chromium terminated surface with large vertical interlayer relaxations, reaching down five or six layers. 

Naturally chiral surfaces can be created from achiral crystalline materials. The bulk structures of many crystalline materials such as metals are highly symmetric, contain one or more mirror symmetry elements and thus, are not chiral. Although it may seem counterintuitive, such achiral bulk structures can, nonetheless, expose surfaces with chiral atomic structures. These are planes whose normals do not lie in one of the bulk mirror planes. The classification of the symmetry of surfaces of a variety of bulk crystal structures has recently been reviewed by Jenkins et al. and they have identified all planes in those crystal structures that are chiral [9,10]. As a simple example consider the two surfaces illustrated in Fig. 4.1. These are the two enantiomers of the (643) surfaces of a face centered cubic lattice. 

Bakaev s computer simulations [4-7] of oxide surfaces suggest that even in the case of oxides having a well defined bulk crystal structure, the degree of the surface disorder may be larger than it is generally believed. 

Using the first peak of each pair of doublets, the peaks are indexed to a rectangular in-plane unit cell with dimensions a = 5.99 k,b = 7.66 A, and y = 90.0°. For 2, a similar in-plane unit cell was found with a = 5.98 k,b = 7.64 A, and y = 90.0°. There are two molecules per unit cell similar to the pentacene bulk crystal structure... 

This shows that the question of nonreactivity is much more closely related to the bulk crystal structure than previously assumed. 

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