Lattice types, crystallography

X-ray crystallography has provided the crystal type and lattice dimensions for numerous solids. In this technique, high-energy x-rays strike the crystal and are diffracted in a pattern characteristic of the particular lattice type. Complex mathematical... 

DISLOCATION. In crystallography, a type of lattice imperfection whose existence in metals is postulated in order to account for the phenomenon uf crystal growth and of slip, particularly for the low value of shear stress required lo initiate slip. One section of the crystal adjacent to the slip plane is assumed to contain one mure atomic plane that the section on the opposite side of the slip plane. Motion of the dislocation results in displacement of one of the sections with respect to another. 

Note that this emphasis on the symmetry of the lattices has a profound effect on thinking about structures. Up to now, the lattice type has been characterised by the lattice parameters, the lengths of the lattice vectors and the inter-vector angles. Now, however, it is possible to define a lattice in terms of the symmetry rather than the dimensions. In fact this is the norm in crystallography. As we will see, the crystal system of a phase is allocated in terms of symmetry and not lattice parameters. To pre-empt future chapters somewhat, consider the definition of a monoclinic unit cell in terms of the lattice parameters a b c a = 90°, ft 90°, y = 90° (see Chapter 1). The unit cell may still be regarded as monoclinic (not orthorhombic) even if the angle /I is 90°, provide that the symmetry of the structure complies with that expected of a monoclinic unit cell. 

X-ray crystallography has provided the crystal type and lattice dimensions for numerous solids. In this technique, high-energy x-rays strike the crystal and are diffracted in a pattern characteristic of the particular lattice type. Complex mathematical analysis can convert the diffraction pattern to the actual crystal structure. Advances in computer technology have revolutionized this field in the past few years. Complex structures, formerly requiring months or years to determine, can now be analyzed in short order. Even huge protein and nucleic acid chains can be woiked out by the crystallographer. ... 

X-ray crystallography is a powerful tool with which we can determine the atomic coordinates in crystalline organic compounds. The raw data obtained by four-circle diffractometer include all the information needed to solve the crystal structure. From these data, we can determine the lattice type, the crystal system, and the crystal space group. The reflected intensity X-ray diffraction data are collected with/without several corrections (Lorentz-polarization, absorption, decades, etc.). 

The symbols for plane groups, the Hermann-Mauguin symbol, have been the standard in crystallography. The first place indicates the type of lattice, p indicates primitive, and c indicates centered. The second place indicates the axial symmetry, which has only 5 possible vales, 1-, 2-, 3-, 4-, and 6-fold. For the rest, the letter m indicates a symmetry under a mirror reflection, and the letter g indicates a symmetry with respect to a glide line, that is, one-half of the unit vector translation followed by a mirror reflection. For example, the plane group pAmm means that the surface has fourfold symmetry as well as mirror reflection symmetries through both x and y axes. 

In two dimensions, the equivalents of unit cell and lattice are unit mesh and net, respectively. Crystallography in two dimensions is, obviously, simpler than that in three dimensions, and there are only five types of net (illustrated in Figure 5.15). The choice of unit mesh is arbitrary. The primitive unit mesh (illustrated at the bottom left hand comer of each net) is the smallest possible repeating quadrilateral with lattice points only at the comers. However, it may be appropriate... 

Structures of the CdCl2, Cdl2 and Hgl2 types are often described as layer lattices. The phrase is unfortunate, for the word lattice has a specific meaning in crystallography which is not here applicable. Layer structures is a better term. 

For molecules in the solid state, it is possible that lattice forces may profoundly affect the process of adoption of a particular conformation, and thus the favored conformation of a molecule in the crystalline state is not necessarily the same as that adopted when the molecule is surrounded by a sheath of solvent molecules. Nevertheless, there is a high degree of correlation between the results of X-ray crystallography of alditols and their derivatives (see p. 69) and the conformations adopted by various types of acyclic sugar derivatives in solution. 

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