Orientation azimuthal

Frederick B G, Power J R, Cole R J, Perry C C, Chen Q, Flaq S, Bertrams T, Richardson N V and Weightman P 1998 Adsorbate azimuthal orientation from reflectance anisotropy spectroscopy P/rys. Rev. Lett. 80 4490-3... 

The hybrid orbital has cylindrical symmetry, and accordingly the introduction of d character and f character in the axial bond itself does not lead to an interaction dependent on the relative azimuthal orientation of the two groups. 

Figure 16.2 (a) Model of molecular arrangement (shaded circle) with respect to the Au(lll) surface (open small circle). The diagonal slash indicates the azimuthal orientation of the plane defined bytheC-C-C backbone ofthe all trans-hydrocarbon chain. 

Figure 1.10 UHV-STM images of HtB-HBC adsorption on Cu l 1 0 showing the correlation between the orientation of the adsorbate lattice vectors and the local rotation of the molecule away from its high symmetry azimuthal orientation atop a copper atom.

Introducing two-dimensional unit vectors for azimuthal orientations of adsorbed molecules... 

An inference of fundamental importance follows from Eqs. (2.3.9) and (2.3.11) When long axes of nonpolar molecules deviate from the surface-normal direction slightly enough, their azimuthal orientational behavior is accounted for by much the same Hamiltonian as that for a two-dimensional dipole system. Indeed, at sin<9 1 the main nonlocal contribution to Eq. (2.3.9) is provided by a term quadratic in which contains the interaction tensor V 2 (r) of much the same structure as dipole-dipole interaction tensor 2B3 > 0, B4 < 0, only differing in values 2B3 and B4. For dipole-dipole interactions, 2B3 = D = flic (p is the dipole moment) and B4 = -3D, whereas, e.g., purely quadrupole-quadrupole interactions are characterized by 2B3 = 3U, B4 = - SU (see Table 2.2). Evidently, it is for this reason that the dipole model applied to the system CO/NaCl(100), with rather small values 0(6 25°), provided an adequate picture for the ground-state orientational structure.81 A contradiction arose only in the estimation of the temperature Tc of the observed orientational phase transition For the experimental value Tc = 25 K to be reproduced, the dipole moment should have been set n = 1.3D, which is ten times as large as the corresponding value n in a gas phase. Section 2.4 will be devoted to a detailed consideration of orientational states and excitation spectra of a model system on a square lattice described by relations (2.3.9)-(2.3.11). 

Figure 2.26 Model of packing of chains in form III of iP4MP according to space group /4x, 33. tS3 jwo eqUivaient unit cells characterized by chains having opposite azimuthal orientations indicating possible packing in different microdomains of crystal are shown.

Similar frustration has been evidenced for the crystal structure of isotactic poly(2-vinylpyridine)150 161 (Figure 2.28). Also in this case three independent threefold helices are included in the trigonal unit cell and the frustration is related to a different azimuthal orientation of the chains due to the different interactions between the chains.160 Two chains (chains A in Figure 2.28) maximize their interactions at the expense of the third one (chain B). 

Frustration and symmetry breaking are two different but related concepts. Frustration implies symmetry breaking because it occurs when three isochiral threefold chains having different azimuthal orientations, hence not related by any element of symmetry, are packed in a trigonal lattice. The symmetry breaking is probably a more general concept because it has been found even in the case of orthorhombic and tetragonal unit cells.33,146,149... 

In a bulk SmC material the tilt angle 0 is fixed, but the director is free to take up any azimuthal orientation, defining a tilt cone of degenerate azimuthal... 

Quantitative determination of the local adsorption structure of carbonate on Ag(llO) has been done by Kittel etal. [110]. They have found that the carbonate species is essentially planar and adsorbs almost parallel to the surface at the off-atop site with respect to the outermost layer Ag atom. The C—Ag layer spacing was 0.264 0.009 nm, with a well-defined azimuthal orientation. This geometry is understood best in terms of the added-row model proposed by Guo and Madix. This model assumes that additional Ag atoms lie adjacent to the carbonate, such that the... 

FIGURE 3.2. (a) Chemical structure of octanethiol. (b) A constant current STM image of octanethiol SAM on Au(l 11). Au reconstruction is lifted and alkanethiols adopt commensurate crystalline lattice characteriized by a c(4 x 2) superlattice of a (a/3 x V3)R30°. (c) Model of commensuration condition between alkanethiol monolayer (large circles) and bulk-terminated Au surface (small circles). Diagonal slash in large circles represents azimuthal orientation of plane defined by all-trans hydrocarbon chain. (Reprint with permission from Ref.25 G. E. Poirier, Chem. Rev., 97, 1117-1127 (1997). Copyright 1997 American Chemical Society.)... 

Fig. 15 a M-[7]H forms at 95% of the saturated monolayer CW-rotated pinwheels (top, left) while CCW-rotated pinwheels are observed via STM for P-[7H] (top, right) [44]. At full ML opposite tilt angles of cloverleaf clusters with respect to the adlattice are observed (bottom). Images 10 nm x 10 nm. Reprinted with permission from Wiley, b Model for the M-[7]H cloverleaf structure obtained from MMC. Minimal repulsion is achieved for certain relative azimuthal orientations... 

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