Circles hexagonal

Fig. 4. (a) Coverage as deduced from a LEED pattern as a liinclion of dq>osition time crosses, nx2 structure solid circles, hexagonal structure, (b) Model of the 10x2 structure (letters a-d). One half of the unit mesh is shown with the correct relative size of Yb and Mo atoms. (By courtesy of Prof E. Bauer, Physikalisches Institut, Univ, Clausthal, 3392 Clausthal-Zellerfeld, Germany). 

The two Kekule structures for benzene have the same arrangement of atoms but differ m the placement of electrons Thus they are resonance forms and neither one by Itself correctly describes the bonding m the actual molecule As a hybrid of the two Kekule structures benzene is often represented by a hexagon containing an inscribed circle... 

The circle m a hexagon symbol was first suggested by the British chemist Sir Robert Robinson to represent what he called the aromatic sextet —the six delocalized TT electrons of the three double bonds Robinson s symbol is a convenient time saving shorthand device but Kekule type formulas are better for counting and keeping track of electrons especially m chemical reactions... 

If we consider the /k part of the chain of the circle, the number of hexagons can be put and nj for the outer and inner circle of the upper (or lower) hexagonal chain (see Fig. 6), respectively. Each upper and lower hexagonal chain contains -t- 2(/ i / 2)... 

Fig. 6. Part of the elongated torus here, 2. sad L are the number of the hexagons along the inner circle, outer circle, and height of the torus, respectively this figure is for the case of i = 12, = 6, and L =. ...

A diffraction pattern of a single MWCNT (Fig. 1) contains in general two types of reflexions (i) a row of sharp oo.l (/ = even) reflexions perpendicular to the direction of the tube axis, (ii) graphite-like reflexions of the type ho.o (and hh.o) which are situated in most cases on somewhat deformed hexagons inscribed in circles with radii gho.o (or hh.o)-... 

It may also be represented as a hexagon with a circle in the middle. The circle is a symbol of the n cloud encircling the benzene ring. The delocalized electrons associated with the benzene ring impart very special properties to aromatic hydrocarbons. They have chemical properties of single-bond compounds such as paraffin hydrocarbons and doublebond compounds such as olefins, as well as many properties of their own. 

Scheme 10.8 Biosynthesis of epothilone. Individual PKS domains are represented as circles and individual NRPS domains as hexagons. Acyl carrier proteins (ACPs) and thiola-tion domains (T) are posttranslationally modified by a phos-phopantetheinyl group to which the biosynthetic intermediates are covalently bound throughout the chain assembly. The thioesterase domain (TE) cyclizes the fully assembled carbon chain to give the 16-membered lactone. Following dehydration of Cl 2—Cl 3 to give epothilones C and D, the final step in epothilone biosynthesis is the epoxidation of the C12=C13 double bond by the cytochrome P450 enzyme P450epol<. KS ketosyn-thase KS(Y) active-site tyrosine mutant of KS AT acyltransfer-ase C condensation domain A adenylation domain ...

Figure 2. The brucite structure of Ni(OH), (a) hexagonal brucite layer, in which the small circles are the Ni atoms and the large circles the O atoms and alternate O atoms are below and above the plane of the Ni atoms (b) stacking of the planes showing the orientation of the O-H bonds.

A line structure (introduced in Section C) represents a chain of carbon atoms as a zigzag line. The end of each short line in the zigzag represents a carbon atom. Because carbon nearly always has a valence of 4 in organic compounds, we do not need to show the C—H bonds. We just fill in the correct number of hydrogen atoms mentally, as we see for methylbutane (6), isoprene (7), and propyne (8). As explained in Section 2.7, a benzene ring is represented by a circle inside a hexagon, and we need to remember that one hydrogen atom is attached to each carbon atom. 

A methyl group may be shown in a structural representation as CH3 or Me, and similar pseudo-elemental symbols are used for ethyl, propyl and butyl side chains. It is cortrmon to represent a phenyl group as either Ph or as a hexagon with a circle irtscribed within it. This circle is meant to represent electron density that lies above and beneath the main plane of the molecule. However, when faced with... 

Although the above structures satisfy the molecular formula, double bonds do not in reality exist in aromatic compounds. Thus, aromatic rings are usually depicted by a hexagon with a circle in it. It is understood that a hydrogen is at each corner. 

FIG. 23 Surface pressure vs. area/molecule isotherms at 300 K from molecular dynamics simulations of Karaborni et al. (Refs. 362-365). All are for hydrocarbon chains with carboxylate-like head groups, (a) (filled squares) A 20-carbon chain, (b) (filled circles) A 16-carbon chain with a square simulation box the curve is shifted 5 A to the right, (c) (open squares) A 16-carbon chain with a nonsquare box with dimensions in the ratio xly = (3/4) to fit a hexagonal lattice the curve is shifted 5 A to the right. (Reproduced with permission from Ref. 365. Copyright 1993 American Chemical Society.)... 

Fig. 35.—Diagrammatic Representation of the Topologies of the Areas Representing the Sweet (Circle) and Bitter (Hexagon) Modalities. ...

Fig. 2. CO conversions at 363 K in the dry condition (open points) and 353 K in the wet condition (filled points) over lOOmg and 50 mg of Aa/CeOi catal) containing 0.95 wt% Au prepared at different calcination temperatures (373 K (circle), 473 K(square), 573 K(triangle up), 673 K (triangle down), 773 K (diamond), 873 K (hexagon)). The reactants of 100 ml/min, 1 vol% CO and 1 vol% O2 in He, were fed to the catalyst.

Fig. 1.3 The hexagonal array of water molecules in ice I. Even at low temperatures the hydrogen atoms (smaller circles) are randomly ordered... 

The heat transfer data discussed above refer only to the average behavior of a vial of a given type which is surrounded by other vials in a hexagonal packing array of vials. We now consider intervial variations in heat transfer in a set of nominally equivalent vials and variations in heat transfer arising from variations in the position of the vial in the array. An experiment demonstrating such variations is described by Figure 35. Each circle represents a vial placed on a temperature-controlled shelf in a small laboratory freeze dryer. The vials contained pure... 

Figure 2.15 High-resolution STM image (a) [30] and AFM image (b) [49] of the alumina film on Ni3AI(l 1 1). The high-symmetry sites marked by triangles (circles) and the hexagons correspond to the network and dot structure, respectively.

Figure 6.1 Atomically resolved STM image of a thin Al203 film on NiAI(l 1 0), taken at 4 K with U = 500mV, /=1 nA (58Ax40A). All atoms exhibit a quasi-hexagonal coordination, where the three characteristic directions are marked with arrows. The unit cell was determined from the repetition of atoms. Here, gray-filled circles mark the most prominent atomic features,...

Because of its great stability, the six-membered ring of carbon atoms persists in most reactions. For simplicity, the ring is sometimes represented as a hexagon, each corner of which is assumed to be occupied by a carbon atom with a hydrogen atom attached (unless some other atom is explicitly indicated at that point). The delocalized electrons are indicated by a circle within the hexagon. The following representations illustrate these rules ... 

Fig. 1. Oxygen abundances as a function of the activity index, Rx, derived from X-ray data (left-hand panels) and the excitation temperature Texc (right-hand panels). The bottom panels show the difference between [O/Fe] yielded by the OI triplet at about 7774 A and the [OI] A6300 line. Filled circles RS CVn binaries ([2] and [3]), filled squares field subgiants [3], filled triangles Pleiades stars, open triangles Hyades stars, open circles, squares and hexagons disk dwarfs. The source of the literature data for the open cluster and Galactic disk stars can be found in [4].

Fig. 1 Atomic arrangement of X (open circles) and T (filled circles) in projection for (a) hexagonal close-packing of X with T occupying half the octahedral holes (positions of the other half being indicated by crosses), and (b) the FeS2—m type structure, where the X—X pairs are emphasized by connecting bars...

---