Ordered arrays

McConnell et al. [196] and Andelman and co-workers have predicted [197,198] an ordered array of liquid domains in the gas-liquid coexistence regime caused by the dipole moment difference between the phases. These superstructures were observed in monolayers of dipalmitoyl phosphatidylcholine monolayers [170]. 

Transmission electron microscopy (tern) is used to analyze the stmcture of crystals, such as distinguishing between amorphous siUcon dioxide and crystalline quartz. The technique is based on the phenomenon that crystalline materials are ordered arrays that scatter waves coherently. A crystalline material diffracts a beam in such a way that discrete spots can be detected on a photographic plate, whereas an amorphous substrate produces diffuse rings. Tern is also used in an imaging mode to produce images of substrate grain stmctures. Tern requires samples that are very thin (10—50 nm) sections, and is a destmctive as well as time-consuming method of analysis. 

Chemicals exist as gases, liquids or solids. Solids have definite shapes and volume and are held together by strong intermolecular and interatomic forces. For many substances, these forces are strong enough to maintain the atoms in definite ordered arrays, called crystals. Solids with little or no crystal structure are termed amorphous. 

Of particular importance to carbon nanotube physics are the many possible symmetries or geometries that can be realized on a cylindrical surface in carbon nanotubes without the introduction of strain. For ID systems on a cylindrical surface, translational symmetry with a screw axis could affect the electronic structure and related properties. The exotic electronic properties of ID carbon nanotubes are seen to arise predominately from intralayer interactions, rather than from interlayer interactions between multilayers within a single carbon nanotube or between two different nanotubes. Since the symmetry of a single nanotube is essential for understanding the basic physics of carbon nanotubes, most of this article focuses on the symmetry properties of single layer nanotubes, with a brief discussion also provided for two-layer nanotubes and an ordered array of similar nanotubes. 

When we study a solid that does not have the characteristic lustrous appearance of a metal, we find that the conductivity is extremely low. This includes the solids we have called ionic solids sodium chloride, sodium nitrate, silver nitrate, and silver chloride. It includes, as well, the molecular crystals, such as ice. This solid, shown in Figure 5-3, is made up of molecules (such as exist in the gas phase) regularly packed in an orderly array. These poor conductors differ widely from the metals in almost every property. Thus electrical conductivity furnishes the key to one of the most fundamental classification schemes for substances. 

A microscopic, ordered array of nucleic acids, proteins, small molecules, cells or other substances that enables parallel analysis of complex biochemical samples. 

A crystalline solid is a solid in which the atoms, ions, or molecules lie in an orderly array (Fig. 5.16). A crystalline solid has long-range order. An amorphous solid is one in which the atoms, ions, or molecules lie in a random jumble, as in butter, rubber, and glass (Fig. 5.17). An amorphous solid has a structure like that of a frozen instant in the life of a liquid, with only short-range order. Crystalline solids typically have flat, well-defined planar surfaces called crystal faces, which lie at definite angles to one another. These faces are formed by orderly layers of atoms (Box 5.1). Amorphous solids do not have well-defined faces unless they have been molded or cut. 

In this part of the chapter, we begin with molecular solids and distinguish them from network solids. Then we examine metallic solids, which, if consisting of a single element, are built from identical atoms stacked together in orderly arrays. The structures of ionic solids are based on the same kinds of arrays but are complicated by the need to take into account the presence of ions of opposite charges and different sizes. 

One type of material that has transformed electronic displays is neither a solid nor a liquid, but something intermediate between the two. Liquid crystals are substances that flow like viscous liquids, but their molecules lie in a moderately orderly array, like those in a crystal. They are examples of a mesophase, an intermediate state of matter with the fluidity of a liquid and some of the molecular order of a solid. Liquid crystalline materials are finding many applications in the electronics industry because they are responsive to changes in temperature and electric fields. 

FIGURE 7.5 A representation of the arrangement of molecules in (a) a liquid and (b) a solid. When the liquid freezes, the molecules lie in an ordered array consequently there is a decrease in the disorder of the system (a drop in entropy). The entropy rises again when the solid melts. 

That is, S —> 0 as T - 0. The perfect crystal part of this statement of the third law refers to a substance in which all the atoms are in a perfectly orderly array, and so there is no positional disorder. The T— 0 part of the statement implies the absence of thermal motion-—thermal disorder vanishes as the temperature approaches zero. As the temperature of a substance is raised from zero, more orientations become available to the molecules and their thermal disorder increases. Thus we can expect the entropy of any substance to he greater than zero above T = 0. 

Molecular-level characterization of surface composition and stmcture can be obtained through a variety of electron and ion spectroscopies. The two-dimensional stmcture of surfaces and ordered arrays formed by adsorbates is revealed by low-energy electron drfiraction... 

Douglas and coworkers were the first one that described a bottom-up approach based on S-layers as templates for the formation of perfectly ordered arrays of nanoparticles [128]. The S-layer lattice was used primarily to generate a nanometric lithographic mask for the subsequent deposition of metals. In this approach a thin Ta-W film was deposited... 

The hypothetical metal jellium consists of an ordered array of positively charged metal ions surrounded by a structureless sea of electrons that behaves as a free electron gas (Fig. 6.13). 

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