Simple crystal structures

Simple crystal structures Simple crystal structures are composed of atoms that are positioned on the edges of the unit cell. 

Knowing the lattice is usually not sufficient to reconstruct the crystal structure. A knowledge of the vectors (a, b, c) does not specify the positions of the atoms within the unit cell. The positions of the atoms withm the unit cell is given by a set of vectors i., = 1, 2, 3... u where n is the number of atoms in the unit cell. The set of vectors, x., is called the basis. For simple elemental structures, the unit cell may contain only one atom. The lattice sites in this case can be chosen to correspond to the atomic sites, and no basis exists. 

This structure is called close packed because the number of atoms per unit volume is quite large compared with other simple crystal structures. 

In compound materials - in the ceramic sodium chloride, for instance - there are two (sometimes more) species of atoms, packed together. The crystal structures of such compounds can still be simple. Figure 5.8(a) shows that the ceramics NaCl, KCl and MgO, for example, also form a cubic structure. Naturally, when two species of atoms are not in the ratio 1 1, as in compounds like the nuclear fuel UO2 (a ceramic too) the structure is more complicated (it is shown in Fig. 5.8(b)), although this, too, has a cubic unit cell. 

We begin by looking at the smallest scale of controllable structural feature - the way in which the atoms in the metals are packed together to give either a crystalline or a glassy (amorphous) structure. Table 2.2 lists the crystal structures of the pure metals at room temperature. In nearly every case the metal atoms pack into the simple crystal structures of face-centred cubic (f.c.c.), body-centred cubic (b.c.c.) or close-packed hexagonal (c.p.h.). 

We will be looking at kinetics in Chapter 6. But before we can do this we need to know what we mean by driving forces and how we calculate them. In this chapter we show that driving forces can be expressed in terms of simple thermodynamic quantities, and we illustrate this by calculating driving forces for some typical processes like solidification, changes in crystal structure, and precipitate coarsening. 

How is the binding specificity of the heterodimer achieved compared with the specificity of Mat a2 alone The crystal structure rules out the simple model that the contacts made between the Mat a2 homeodomain and DNA are altered as a result of heterodimerization. The contacts between the Mat o2 homeodomain and DNA in the heterodimer complex are virtually indistinguishable from those seen in the structure of the Mat o2 monomer bound to DNA. However, there are at least two significant factors that may account for the increased specificity of the heterodimer. First, the Mat al homeodomain makes significant contacts with the DNA, and the heterodimeric complex will therefore bind more tightly to sites that provide the contacts required by both partners. Second, site-directed mutagenesis experiments have shown that the protein-protein interactions involving the... 

Most materials scientists at an early stage in their university courses learn some elementary aspects of what is still miscalled strength of materials . This field incorporates elementary treatments of problems such as the elastic response of beams to continuous or localised loading, the distribution of torque across a shaft under torsion, or the elastic stresses in the components of a simple girder. Materials come into it only insofar as the specific elastic properties of a particular metal or timber determine the numerical values for some of the symbols in the algebraic treatment. This kind of simple theory is an example of continuum mechanics, and its derivation does not require any knowledge of the crystal structure or crystal properties of simple materials or of the microstructure of more complex materials. The specific aim is to design simple structures that will not exceed their elastic limit under load. 

The materials shown and described above were generally prepared from the nucleophilic phenoxide or alkoxide and the appropriate bromide. The syntheses of a variety of such compounds were detailed in a report which appeared in 1977. In the same report, complex stability and complexation kinetics are reported. Other, detailed studies, of a similar nature have recently appeared" . Vogtle and his collaborators have also demonstrated that solid complexes can be formed even from simple polyethylene glycol ethers . Crystal structures of such species are also available... 

Generally the name of a compound should correspond to the most stable tautomer (76AHCS1, p. 5). This is often problematic when several tautomers have similar stabilities, but is a simple and reasonable rule whose violation could lead to naming phenol as cyclohexadienone. Different types of tautomerism use different types of nomenclature. For instance, in the case of annular tautomers both are named, e.g., 4(5)-methylimidazole, while for functional tautomerism, usually the name of an individual tautomer is used because to name all would be cumbersome. In the case of crystal structures, the name should reflect the tautomer actually found therefore, 3-nitropyrazole should be named as such (97JPOC637) and not as 3(5)-nitropyrazole. 

In a previous work we showed that we could reproduce qualitativlely the LMTO-CPA results for the Fe-Co system within a simple spin polarized canonical band model. The structural properties of the Fe-Co alloy can thus be explained from the filling of the d-band. In that work we presented the results in canonical units and we could of course not do any quantitative comparisons. To proceed that work we have here done calculations based on the virtual crystal approximation (VGA). In this approximation each atom in the alloy has the same surrounding neighbours, it is thus not possible to distinguish between random and ordered alloys, but one may analyze the energy difference between different crystal structures. 

If we look at the mechanistic and crystallographic aspects of the operation of polycomponent electrodes, we see that the incorporation of electroactive species such as lithium into a crystalline electrode can occur in two basic ways. In the examples discussed above, and in which complete equilibrium is assumed, the introduction of the guest species can either involve a simple change in the composition of an existing phase by solid solution, or it can result in the formation of new phases with different crystal structures from that of the initial host material. When the identity and/or amounts of phases present in the electrode change, the process is described as a reconstitution reaction. That is, the microstructure is reconstituted. 

Whereas in many metals with relatively simple and isotropic crystal structures the parameter / has values between 0.5 and 1, it can have much more extreme values in materials in which the mobile species move through much less isotropic structures with 1-D or two-dimensional (2-D) channels, as is often the case with insertion reaction electrode materials. As a result, radiotracer experiments can provide misleading information about self-diffusion kinetics in such cases. 

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