Extended arrays

A more detailed analysis of the results obtained over 10% platinum/ alumina (115) leads to an extended array of parallel, multistep reaction paths, and it was concluded (for 273°C) that an adsorbed species had a chance of reacting via an adsorbed C5 cyclic intermediate of about 0.3, of reacting via a bond shift of about 0.2, and a chance of desorption of about 0.5. One would expect these probabilities to be temperature dependent, but to different extents, so that the nature of the product distributions should also be temperature dependent. 

Initially the q phase was assigned as the nonmolecular form of nitrogen, assuming the cubic gauche structure suggested by Mailhiot as the most likely [324]. However, the value of the band gap and the opaque appearance of the sample are not suited for an extended array of N-N single bonds. As a matter of... 

It is interesting to consider the results of the molecular dynamics simulation showing that the reaction occurs in two stages that could well correspond to the formation of the transparent yellow and to the brownish products. As a whole, the calculations indicate that the final product is a bent polycarbonyl chain with five-membered rings attached and with interconnection between the various chains in a quasi-two-dimensional array. Such a rather extended array is not much different from the suggested structure of the polymer obtained from furan at high pressure [303, 338]. In the molecular dynamics simulation the formation of carbon dioxide molecules is not observed in agreement with the experimental result that CO2 formation only occurs upon intense laser irradiation. 

The availability of integrated circuits paved the way for the next generation ofX-ray inspection system. These units featured a side-shooting fan beam of X-rays incident on an extended array of scintillators optically coupled to photodiodes or phototransistors. The resulting low-level electric currents were then amphfied, integrated, and electronically sampled and digitized. Such systems were under development by ScanRay and Picker in 1977. By 1979, Picker was marketing... 

Fig. 8. Time lapse images of two MMTV arrays visualized with GFP-GR. Time in minutes after addition of 100 nM dexamethasone is indicated. Some arrays become very extended (3-10 pm, B), whereas some cells exhibit a less extended array (< 3 pm, A) (from Ref [68]). Scale bar 1 pm.

All substances, except helium, if cooled sufficiently form a solid phase the vast majority form one or more crystalline phases, where the atoms, molecules, or ions pack together to form a regular repeating array. This book is concerned mostly with the structures of metals, ionic solids, and extended covalent structures structures which do not contain discrete molecules as such, but which comprise extended arrays of atoms or ions. We look at the structure and bonding in these solids, how the properties of a solid depend on its structure, and how the properties can be modified by changes to the structure. 

Section 1.4 introduced the idea of symmetry, both in individual molecules and for extended arrays of molecules, such as are found in crystals. Before going on to discuss three-dimensional lattices and unit cells, it is important to introduce two more symmetry elements these elements involve translation and are only found in the solid state. 

Finally, we consider crystal structures that do not contain any extended arrays of atoms. The example of graphite in the previous section in a way forms a bridge between these structures and the structures with infinite three-dimensional arrays. Many crystals contain small, discrete, covalently bonded molecules that are held together only by weak forces. 

Finally, W02, which has a modified rutile structure 227 exhibits alternate W—W distances of 2.475 and 3.096 A across shared edges of W06 octahedra. Thus, the short distance of 2.475 A which indicates a W—W double bond makes a recognizable dinuclear unit in the infinitely extended array of the metal oxide. 

In Chapter 11 of this edition, the symmetry properties of extended arrays, that is, space group rather than point group symmetry, is treated. In recent years, the use of X-ray crystallography by chemists has increased enormously. No chemist is fully equipped to do research (or read the literature critically) in any field dealing with crystalline compounds, without a general idea of the symmetry conditions that govern the formation of crystalline solids. At least the rudiments of this subject are covered in Chapter 11. 

The most obvious change is the addition of Chapter 11, which deals with the symmetry properties of extended arrays—that is, crystals. My approach may not (or it may) please crystallographic purists I did not have them in mind as I wrote it. I had in mind several generations of students I have taught to use crystallography as a chemist s tool. I have tried to focus on some of the bedrock fundamentals that I have so often noticed are not understood even by students who have learned to do a crystal structure. ... 

It is of particular interest from both NLO and chemical perspectives to understand how the polarizability changes in the evolution from an isolated atom to a molecule, a cluster of atoms or molecules, an extended array, and ultimately the bulk. Intuitively, one would expect that if the effective potential for the electron extends over several atomic sites, the polarizability and nonlinear optical coefficients might be larger. Indeed, the largest NLO coefficients have been found for semiconductors and unsaturated extended organic molecules both of which have highly delocalized electrons (2). 

Now, the above procedure can also be very time-consuming when carrying out calculations on extended arrays of atoms as in crystals and other solids since convergence is often very slow and many iterations are required before the optimisation criterion is satisfied. So, these conventional methods of optimisation also became difficult on large systems. 

The complex between melamine and cyanuric acid (1 1) was reported in the literature in the late 1970s, but it was only in the early 1990s that the contributions from Whitesides and the concept of self-assembly popularized these systems [45]. Whitesides and co-workers reported the formation of tapes (Fig. 11.11), crinkled tapes and cyclic hexamers (rosettes) formed between barbituric acid and N,N -bis(p-substituted phenyl)melamine [46], In this they effectively blocked one face of melamine and, by manipulating substituents at the para position, different structures were obtained. Whiteside s putative suggestion that melamine/cyanuric acid formed an extended array (Fig. 11.12) was confirmed recently by Rao et al. with the crystal structure [47]. Hamilton and coworkers reported the crystal structure of a 5-substituted isophthalic acid derivative, which forms a cyclic aggregate held together with six pairs of hydrogen bonds, which in a way resembles the trimesic acid (Fig. 11.13) [48]. 

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