Crystallization terminology

The simple forms on the right-hand sides are obtained directly in the special cases where u y =0. Note that C] +C2 is twice the mean curvature and c,C2 is the Gaussian curvature in differential geometry. In liquid crystal terminology, C -f C2 is splay and —c Cj is saddle splay. The sign of the curvatures has been defined such that c, -f- C2 is positive for a sphere or cylinder. 

As the membrane is in the fluid state of matter (i.e. smectic A in liquid crystal terminology), it cannot withstand shear in its plane. Moreover, the solubility of the double chain phospholipids is extremely low. Therefore, there is practically no exchange of material between membrane and solution. This fact, together with the small compressibility of the membrane, implies that for almost all phenomena the membrane can be considered as locally incompressible. 

So, by the 1990s, Professor Rao had been active in several of the major aspects which, together, were beginning to define materials chemistry crystal defects, phase transitions, novel methods of synthesis. Yet, although he has been president of the Materials Research Society of India, he does not call himself a materials chemist but remains a famous solid-state chemist. As with many new conceptual categories, use of the new terminology has developed sluggishly. 

In the previous sections, we have seen how computer simulations have contributed to our understanding of the microscopic structure of liquid crystals. By applying periodic boundary conditions preferably at constant pressure, a bulk fluid can be simulated free from any surface interactions. However, the surface properties of liquid crystals are significant in technological applications such as electro-optic displays. Liquid crystals also show a number of interesting features at surfaces which are not seen in the bulk phase and are of fundamental interest. In this final section, we describe recent simulations designed to study the interfacial properties of liquid crystals at various types of interface. First, however, it is appropriate to introduce some necessary terminology. 

At this point, you may find that the subject of symmetry in a crysted structure to be confusing. However, by studying the terminology carefully in Table 2-2, one can begin to sort out the various lattice structures and the symbols used to delineate them. All of the crystal systems can be described by use of either Schoenflies or Hermaim-Mauguin S5mbols, coupled with the use of the proper geometrical symbols. 

Hikosaka presented a chain sliding diffusion theory and formulated the topological nature in nucleation theory [14,15]. We will define chain sliding diffusion as self-diffusion of a polymer chain molecule along its chain axis in some anisotropic potential field as seen within a nucleus, a crystal or the interface between the crystalline and the isotropic phases . The terminology of diffusion derives from the effect of chain sliding diffusion, which could be successfully formulated as a diffusion coefficient in our kinetic theory. 

Since this review is oriented towards chemists who may have very little familiarity with semiconductors, Sect. 2 attempts to provide some brief useful background not otherwise readily found in one place (much more detailed exposition can be found in textbooks such as the excellent one by Yu and Cardona [15]). It begins in Sect. 2.1 with a concise introduction to some basics aspects of semiconductors relevant to understanding terminology encountered in the literature on NMR of semiconductors. The four crystal structures adopted by the majority of important semiconductors will be summarized in Sect. 2.2, and the various methods of making semiconductors will be outlined in Sect. 2.3. 

The author was supported by the Ferroelectric Liquid Crystal Materials Research Center (National Science Foundation MRSEC award No. DMR-9809555) during the writing of this chapter. The author thanks Professors Tom Lubensky, Leo Radzihovsky, and Joseph Gal for helpful discussions around the issue of terminology for reflection symmetry breaking, and especially Professor Noel Clark for his help on this and many other banana-phase issues. The author also thanks Dr. Renfan Shao for the photomicrographs shown in Figures 8.32 and 8.33. 

To simplify terminology of axial systems, gzz is defined to be g(l (the g-value observed with the symmetry axis of Cu + parallel to the applied field), and gxx (= gyy) is defined to be gA (the g-value observed with the symmetry axis perpendicular to the applied field). An elongated z-axis (depicted in Figure 11 for Cu(H20)5 +) results in gjj > gj. For axially symmetric Cu + rigidly bound in a crystal, the g-value can then vary between the minimum (gj.) and maximum (g(,), depending on orientation of the crystal within the magnetic field. However, for axial Cu + bound in a powdered clay sample, all possible orientations, and therefore all g-values between gA and gj are represented in the "powder" spectrum. Therefore, electron spin resonance occurs only for field values, H, between Hjj and H, where ... 

The type 1-3 terminology to distinguish different Cu protein active sites remains extremely useful. Sub-groupings are appearing however in all three categories particularly in the case of the binuclear (EPR inactive) type 3 centers. Thus, in the recently determined X-ray crystal structure of ascorbate oxidase the type 3 and type 2 centers are present as a single trimer unit [. A discrete binuclear type 3 center is, however, retained in hemocyanin [6]. 

Terminology relating to molecular conformation within polymer crystals... 

The recommendations embodied in this document are concerned with the terminology relating to the structure of crystalline polymers and the process of macromolecular crystallization. The document is limited to systems exhibiting crystallinity in the classical sense of three-dimensionally periodic regularity. The recommendations deal primarily with crystal structures that are comprised of essentially rectilinear, parallel-packed polymer chains, and secondarily, with those composed of so-called globular macromolecules. Since the latter are biological in nature, they are not covered in detail here. In general, macromolecular systems with mesophases are also omitted, but crystalline polymers with conformational disorder are included. 

TERMINOLOGY RELATING TO MOLECULAR CONFORMATION WITHIN POLYMER CRYSTALS [9,10]... 

Fig. 34. Examples of side-group polymer liquid crystals I - mesogenic group, II - spacer, III - backbone. The terminology side-group is used for (a), side-on fixed is used for (b), end-on fixed for (c) and side-chain for (d).

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