Coincident structures

The physical origin of this structural flexibility of the FeO overlayer is still unclear, the more so since no clear trend is observable in the sequence of lattice parameters of the coincidence structures. The FeO(l 11) phase forming up to coverages of 2-3 ML is clearly stabilized by the interactions with the Pt substrate since FeO is thermodynamically metastable with respect to the higher iron oxides [106,114], FeO has the rock salt structure and the (111) plane yields a polar surface with a high surface energy [115], which requires stabilization by internal reconstruction or external compensation. The structural relaxation observed in the form of the reduced Fe—O... 

Figure 6.13 Left panel Large-scale (left) and atomic resolution (right) STM images of epitaxial FeO(l 1 1) films on Pt(l 1 1). Four different coincidence structures 1—4 are formed sequentially as the coverage increases. They exhibit different contrasts in the large-scale images as indicated by the numbers. Right panel Rigid model of the four FeO(l 1 1)...

At low adsorbate coverages the surface structure of the deposited metal is determined by the substrate periodicity. Thus, under these conditions the adsorbate-substrate interaction is predominant. At higher coverages the adsorbate may continue to follow the substrate periodicity or form coincidence structures with new periodicities that are unrelated to the substrate periodicity. The ordering geometry of large-radius metallic adatoms (especially K, Rb and Cs) shows relatively little dependence on the substrate lattice they tend to form hexagonal close-packed layers on any metal... 

Figure 9.17b schematically represents a cross-sectional view of the surface of a solid and represents the topmost layer of atoms by shaded circles. The open circles represent molecules in an ordered pattern on the solid substrate. Since the adsorbed molecules are ordered, their structure on the surface is characterized by what is called a supernet. Suppose we define <50 as the characteristic spacing of the substrate and 8S the equivalent quantity for the supernet. Then the two arrangements in Figure 9.17b are described by the ratios 5/60 = 4/1 and 8s/80 = 4/3. Building on the notion of reciprocal distances as developed in the discussion of Figure 9.15, it follows that the adsorbed layer with 8/80 = 4/1 should produce spots with a separation that is 1/4 that of the substrate. Likewise, for the case when 8s/80 = 4/3, a pattern of spots with a separation that is 3/4 that of the substrate is predicted. Thus, if the substrate produces spots at, say, 0 and 1, extra spots would be expected at 1/4, 2/4, and 3/4 for the 6/60 = 4 case, and at 3/4, 6/4, and 9/4 when 8s/80 = 4/3. The cases illustrated here are called coincident structures since the two patterns coincide periodically. When there is no correlation between two structures, they are said to be incoherent. 

Those interested can examine the notes by Rovida and Pratesi, Huber and Oudar, and Orent and Hansen.Thus although O2 or NO can produce an apparent c(2 x 6) overlayer on Ru(lOTO) at 750 °C, Orent and Hansenpoint out that the overlayers do not account for the stability of the coincident structures, for the fact that transition from simple to coincident lattice was irreversible, or for the activation energy necessary to form these structures. For these reasons Orent and Hansen favour reconstructions, an example of which is shown in Figure 5, which is taken from a catalytic study of the NO + O2 reaction on a Ru(lOTO) surface. 

To illustrate some of these problems, we consider a general (3x1) difEraction pattern along the direction of trebled surface spacings. Let us imagine a coincidence structure in which an adsorbed layer of equally spaced identical atoms (x) rests upon a substrate (O). A simplest possible structure is given below. One dimension is all we need to consider (m = 3). We assume n =. ... 

KBr(OOl) revealing atomic/molecular corrugation on each surface, (b) Schematic diagram of a ( x 3) coincidence structure assumed for Ceo molecular layers on KBr(OOl). 

Structural noise is sometimes called a "correlated" one because signals reflected by structural heterogeneities and forming structural noise, repeat the form of the initial pulse, have the same spectral composition. Energy spectrum of the structural noise to an approximation of constant coincides with energy spectrum of the signal ... 

The FCC structure is illustrated in figure Al.3.2. Metallic elements such as calcium, nickel, and copper fonu in the FCC structure, as well as some of the inert gases. The conventional unit cell of the FCC structure is cubic with the lengdi of the edge given by the lattice parameter, a. There are four atoms in the conventional cell. In the primitive unit cell, there is only one atom. This atom coincides with the lattice pomts. The lattice vectors for the primitive cell are given by... 

Time-of-flight mass spectrometers have been used as detectors in a wider variety of experiments tlian any other mass spectrometer. This is especially true of spectroscopic applications, many of which are discussed in this encyclopedia. Unlike the other instruments described in this chapter, the TOP mass spectrometer is usually used for one purpose, to acquire the mass spectrum of a compound. They caimot generally be used for the kinds of ion-molecule chemistry discussed in this chapter, or structural characterization experiments such as collision-induced dissociation. Plowever, they are easily used as detectors for spectroscopic applications such as multi-photoionization (for the spectroscopy of molecular excited states) [38], zero kinetic energy electron spectroscopy [39] (ZEKE, for the precise measurement of ionization energies) and comcidence measurements (such as photoelectron-photoion coincidence spectroscopy [40] for the measurement of ion fragmentation breakdown diagrams). 

A number of other software packages are available to predict NMR spectra. The use of large NMR spectral databases is the most popular approach it utilizes assigned chemical structures. In an advanced approach, parameters such as solvent information can be used to refine the accuracy of the prediction. A typical application works with tables of experimental chemical shifts from experimental NMR spectra. Each shift value is assigned to a specific structural fragment. The query structure is dissected into fragments that are compared with the fragments in the database. For each coincidence, the experimental chemical shift from the database is used to compose the final set of chemical shifts for the... 

Provided that these structures contnbute equally the resonance picture coincides with the MO treat ment in assigning one third of a positive charge (+ 0 33) to each of the indicated carbons... 

The polyions postulated in solution all have known structural analogues in crystalline borate salts. Investigations of the Raman (66) and B nmr (67) spectra of borate solutions have confirmed the presence of three of these species the triborate (3), B202(0H) 4, tetraborate (4), [B40 (0H) 4], and pentaborate (5) B O (OH) 4, polyanions. Skeletal stmctures were assigned based on coincidences between the solution spectra and those soHd borates for which definitive stmctural data are available (52). These same ions have been postulated to be present in alkah metal borate glasses as well. 

While the smooth substrate considered in the preceding section is sufficiently reahstic for many applications, the crystallographic structure of the substrate needs to be taken into account for more realistic models. The essential complications due to lack of transverse symmetry can be dehneated by the following two-dimensional structured-wall model an ideal gas confined in a periodic square-well potential field (see Fig. 3). The two-dimensional lamella remains rectangular with variable dimensions Sy. and Sy and is therefore not subject to shear stresses. The boundaries of the lamella coinciding with the x and y axes are anchored. From Eqs. (2) and (10) one has... 

The matrix distribution is assumed to correspond to an equilibrium distribution of spheres. The structure of the matrix follows from the common OZ equation coinciding with Eq. (21)... 

Archer, owing to very unfortunate coincidences, had mistaken acid potassium tartrate for the acetylamino acid. Goldfarb et al. prepared authentic 5-acetylamino-2-thiophenecarboxylic acid, mp 230 232°C (methyl ester, mp 171-171.5°C ethyl ester, mp 161°C), through reduction of 5-nitro-2-thiophenecarboxylic acid with Raney nickel in acetic anhydride and proved the structure by Raney nickel desulfurization to 8-aminovaleric acid. They also confirmed that the acid mp 272-273°C (methyl ester, mp 135-136°C ethyl ester, mp 116-117°C) is 4-acetylamino-2-thiophenecar boxy lie acid as originally stated by Steinkopf and Miiller. The statement of Tirouflet and Chane that the acid obtained upon reduction and acetylation of 5-nitro-2-thiophenecarboxylic acid melts at 272°C must result from some mistake as they give the correct melting point for the methyl ester. 

All components have one or more natural frequencies that can be excited by an energy source that coincides with, or is in close proximity to, that frequency. The result is a substantial increase in the amplitude of the natural frequency vibration component, which is referred to as resonance. Higher levels of input energy can cause catastrophic, near instantaneous failure of the machine or structure. The base frequency referred to in a vibration analysis that includes vibrations that are harmonics of the primary frequency. 

While most stationary machine components move during normal operation, they are not always resonant. Some degree of flexing or movement is common in most stationary machine-trains and structural members. The amount of movement depends on the spring constant or stiffness of the member. However, when an energy source coincides and couples with the natural frequency of a structure, excessive and extremely destructive vibration amplitudes result. 

Figure 7.6 The structure of dichlorocarbene. Electrostatic potential maps show how the positive region (blue) coincides with the empty p orbital in both dichlorocarbene and a carbocation (CH3+). The negative region (red) in the dichlorocarbene map coincides with the lone-pair electrons.

Figure 8.2 The structure of a secondary vinylic carbocation. The cationic carbon atom is sp-hybridized and has a vacant p orbital perpendicular to the plane of the tt bond orbitals. Only one R group is attached to the positively charged carbon rather than two, as in a secondary alkyl carbocation. The electrostatic potential map shows that the most positive (blue) regions coincide with lobes of the vacant p orbital and are perpendicular to the most negative (red) regions associated with the ir bond.

There are two main differences between the structure of the NH4NbOF4 chains and that of the Rb5Nb30Fi8 chains. The first difference is, that in the case ofRbjNbjOFu neighboring octahedrons along the chain are rotated by 7t/4 relative to one another (the rotation axis coincides with z-axis), as shown in Fig. 31. The second difference is that in the NbOF4 complexes, the niobium atoms are all shifted in the same direction, forming a polar structure. 

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