Unit cells structures

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

Fig. 16.5 Partial structure of CU-9 showing a polyhedral Cu-O-P chain that wraps around the salt lattice, see text. The former is constructed by sharing corner oxygen atoms of alternating square planar CUO4 and tetrahedral P2O7 units. The salt lattice adopts the NaCI core in which each cubical unit is made of 1 /8 of the unit cell structure of the NaCI lattice. Alternating cubical units are highlighted for clarity.

Figure 1.1 Typical unit cell structures of elemental metals or alloys.

Figure 6.33 Unit cell structure of YBa2Cu307 superconductor. Reprinted, by permission, from Sheahan, T. P., Introduction to High-Temperature Superconductivity, p. 5. Copyright 1993 by Plenum Press.

Figure 7.17 Crystal unit cell structure of Bi and the orientation of the (longitudinal) and (transverse) phonon motions. Reproduced from Ref. [42] with permission from Nature Publishing Group.

Among binary (i.e., two-element) ionic compounds, six simple types of unit cell structures are commonly encountered, although many more exist ... 

The atomic form factor accounts for the internal structure of the different atoms or molecules. It will also be different for X-rays and neutrons, since the former probe the electron distribution of the target, while the latter interact with the nuclei of the atoms. Therefore, the analysis of the positions of the reflexes indicates mainly the lattice constants and angles. The intensity of the reflexes contains mainly information about the atomic configuration within an unit cell (structure factor) and the scattering behavior of the single atoms (form factor). 

There are very many unit cell structures if we consider all the atoms or ions in the crystal. However, if we focus on just one atom or ion, we can reduce the number to just 14 primitive cells. Three of these, the simple cubic, face-centered cubic (fee), and body-centered cubic (bcc) unit cells, are shown in Figure 9-2. The lattice points, represented by small spheres in the drawings, correspond to the centers of the atoms, ions, or molecules occupying the lattice. 

Fig. 10. Definition of unit cell structures for closely packed chromophores. This figure illustrates the problem of packing chromophores at high loading. Both shape (nuclear repulsive interactions) and electronic electrostatic interactions come into play and can be treated using the insights from this simple diagram...

Once dehydrated, the microfibrils are practically without functionality in ordinary food processing and preparation operations, because the inert microcrystallites are difficult for water to penetrate. The polymorphs, cellulose I and II (Blackwell, 1982 Coffey el al., 1995), are differentiated by their molecular orientation, hydrogen-bonding patterns, and unit-cell structure. Cellulose I is the natural orientation cellulose II results from NaOH treatment under tension of cellulose I with 18-45% alkali (mercerization). The I—II transition is irreversible. Mercerization strengthens the fibers and improves their lustre and affinity for dyes (Sisson, 1943). Sewing thread was relatively pure mercerized cotton until the advent of synthetic polymer fibers. 

Fig. 14. Unit cell structure for an integrated image sensor. [From M. Matsumura, H. Hayama, Y. Nara, and K. Ishibashi, Amorphous silicon image sensor IC. IEEE Electron Devices Lett., 1980 IEEE.]...

The evidence from wide angle x-ray scattering (WAXS), differential scanning calorimetry (DSC), and IR spectroscopy (IR) shows that both polymers crystallize separately according to their own unit cell structure. The WAXS diffraction lines of each component are present in the blends no new bands appear (12,13,14). By DSC one observes the melting peaks corresponding to each polymer (Figure 1), and IR shows the typical characteristic crystalline bands of the pure polymers in the blends. The IR spectra of the blend can essentially be accounted for as the sum of the spectra of the components. 

The study of the intensity of WAXS diffraction peaks for this purpose is not useful because of the closeness of the diffraction lines of both polymers because of their similar unit cell structures. An overlapping of the peaks occurs and the patterns cannot be efficiently resolved into the... 

Fig. 9. Unit cell structures of metals, (a) Face centred cubic (f.c.c.) (b) body centred cubic (b.c.c.) and (c) hexagonal close packed (h.c.p.).

In proudite, CuPb7.5Bi9.33(S,Se)22, also described by Mumme cannizzarite-like H layers two octahedra thick (cf. one octahedron thick in junoite) are similarly stepped by one octahedron after every 5 H subcells (2 in junoite). Between the steps, deformed (100) galena-like ribbons (again cannizzarite-like), about 6 4T subceUs broad, are enclosed. Although some details of this large unit cell structure pose problems, the basic structural principles appear to be well established. 

Figure 6 Crystal structure of /3-alumina and sodium sites in the conduction plane (a) unit cell structure (b) site model of conduction plane. (Reprinted from Ref. 76 1978, with permission from Elsevier)...

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