Symmetry, atomic arrangements

The diffraction pattern consists of a small number of spots whose symmetry of arrangement is that of the surface grid of atoms (see Fig. IV-10). The pattern is due primarily to the first layer of atoms because of the small penetrating power of the low-energy electrons (or, in HEED, because of the grazing angle of incidence used) there may, however, be weak indications of scattering from a second or third layer. 

In this case, the transition structure must have symmetry, with the two F atoms arranged axially and the H atoms being equatorial. In fact, the transition structure is the lowest energy compound that satisfies this symmetry criteria. 

Crystals A crystal may be defined as a solid composed of atoms arranged in an orderly, repetitive array. The interatomic distances in a ciyst of any definite material are constant and are characteristic of that material. Because the pattern or arrangement of the atoms is repeated in all directions, there are definite restrictions on the lands or symmetry that crystals can possess. 

Fig. 5. Schematic representation of arrays of carbon nanotubes with a common tubule axial direction in the (a) tetragonal, (b) hexagonal I, and (c) hexagonal II arrangements. The reference nanotube is generated using a planar ring of twelve carbon atoms arranged in six pairs with the symmetry [16,17,30].

The first was not the structure of brookite. The second, however, had the same space-group symmetry as brookite (Ft,6), and the predicted dimensions of the unit of structure agreed within 0.5% with those observed. Structure factors calculated for over fifty forms with the use of the predicted values of the nine parameters determining the atomic arrangement accounted satisfactorily for the observed intensities of reflections on rotation photographs. This extensive agreement is so striking as to permit the structure proposed for brookite (shown in Fig. 3) to be accepted with confidence. 

Our investigation of zunyite has shown the cubic unit of structure with a0 = 13.82 A to contain four molecules of composition Al Sifi OH, F)18Cl and to have the space-group symmetry T%, and has led to the formulation of a detailed atomic arrangement. 

The Si (100 surface reconstructs by forming dimers of (2x1) symmetry, which arrange themselves into parallel rows. It is now well established that these dimers buckle to form the higher-order p(2x2) and c(2x4) reconstructions. This buckling is due to a transfer of an electron from the lower to the upper atom of the dimer, which opens up a gap between the occupied and unoccupied states. At room temperatures or above, the buckled dimers oscillate in time, and therefore appear symmetric under... 

X-ray Diffraction Structural characterization of single crystal samples can reveal both the atomic arrangement and the composition of a sample. The unit cell size and symmetry alone can quickly establish whether a crystal is a known material or a new phase. A detailed discussion of X-ray diffraction studies of the known superconductors is the topic of another chapter in this book. 

GdNi crystallizes in the orthorhombic CrB type of structure (space group Cmcm). The Gd atoms are located on the 4c sites with point symmetry mm (0, yGd % 0.14, ). The Ni atoms also occupy the 4c sites with yNi 0.43 (see e.g. Buschow (1980)). It is interesting to note that among the RNi compounds there exists a second type of orthorhombic structure. Only the compounds with R from La to Gd crystallize in the CrB type. The compounds with R from Dy to Tm and Y show the less symmetric FeB type with space group Pnma (see e.g. Burzo et al. (1990)). As reported by Blanco et al. (1992) TbNi crystallizes in a monoclinic intermediate structure. Figure 26 shows the orthorhombic unit cell and the atomic arrangement of the CrB type of structure. (The shown orthorhombic cell is not the... 

With respect to the atomic arrangements of the surfaces, the adsorption of cyclohexane occurs very similarly on (111) and (110) planes, in the former case as a nondissociative complex of symmetry C3v as is often the case, the results on the (100) face [of Pt(100)] are qualitatively different. On Ni the (111) face is less reactive for cyclohexane dehydrogenation than the stepped and kinked [5(111) X (110)] plane. 

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