Crystal space lattice structure

The color variations of a nonmetallic mineral are often the result of ionic trace impurities in the crystal space lattice structure. Since the impurities vary from sample to sample, the color may vary. Some nonmetallic minerals have no color and are referred to as colorless. This variability in color, which can sometimes be extreme, means that color is one of the least useful properties for identifying nonmetallic minerals even though it is probably the most obvious. The origin of a mineral s color can be explained by three types of electronic transitions in the crystalline solids. 

Recently, the structure of liquid crystals has been studied by van der Lingen and by E. Huckel, by the method of X-ray analysis. No evidence of any space-lattice structure, which is regarded as the criterion of a true crystal, was revealed in the first X-radiograms but on further investigation of -azoxyanisole in the liquid crystal form a pattern of faint horizontal lines was obtained. This might be interpreted as due to diffraction of the X-rays from parallel layers of lamellar molecules. 

The theoretical density, p, expressed in kg.m of a crystal having a number Z of entities with atomic (or molecular) molar mass M, expressed in kg.mol , placed in a space lattice structure having a unit cell of volume Y, expressed in m is given by the following equation, where AT, is Avogadro s number (i.e., 6.0221367 x 10 mol ) ... 

It is often difficult to represent inorganic compounds with the usual structure models because these structures are based on complex crystals space groups), aggregates, or metal lattices. Therefore, these compounds are represented by individual polyhedral coordination of the ligands such as the octahedron or tetrahedron Figure 2-124d). 

Returning to the observed values for these cesium salts, plotted as dark circles in Fig. 57, we must conclude that the position of the experimental points—nearer the diagonal than any salt of Rb, K, or Na—does not indicate anything unusual about the aqueous solution of the cesium salts, but merely arises from the fact that these cesium salts happen to crystallize in a more compact lattice structure, with less void space between the ions. We cannot make a similar remark about the points for the lithium salts, which lie astride the diagonal the interpretation of these values will be discussed later. 

The result is that Factor III of 2.2.6. given above imposes further symmetry restrictions on the 32 point groups and we obtain a total of 231 space groups. We do not intend to delve further into this aspect of lattice contributions to crystal structure of solids, and the factors which cause them to vary in form. It is sufficient to know that they exist. Having covered the essential parts of lattice structure, we will elucidate how one goes about determining the structure for a given solid. 

One of the concepts in use to specify crystal structures the space lattice or Bravais lattice. There are in all fourteen possible space (or Bravais) lattices. 

Space lattices and crystal systems provide only a partial description of the crystal structure of a crystalline material. If the structure is to be fully specified, it is also necessary to take into account the symmetry elements and ultimately determine the pertinent space group. There are in all two hundred and thirty space groups. When the space group as well as the interatomic distances are known, the crystal structure is completely determined. 

The term crystal structure in essence covers all of the descriptive information, such as the crystal system, the space lattice, the symmetry class, the space group and the lattice parameters pertaining to the crystal under reference. Most metals are found to have relatively simple crystal structures body centered cubic (bcc), face centered cubic (fee) and hexagonal close packed (eph) structures. The majority of the metals exhibit one of these three crystal structures at room temperature. However, some metals do exhibit more complex crystal structures. 

Our description of atomic packing leads naturally into crystal structures. While some of the simpler structures are used by metals, these structures can be employed by heteronuclear structures, as well. We have already discussed FCC and HCP, but there are 12 other types of crystal structures, for a total of 14 space lattices or Bravais lattices. These 14 space lattices belong to more general classifications called crystal systems, of which there are seven. 

Only fourteen space lattices, called Bravais lattices, are possible for the seven crystal systems (Fig. 328). Designations are P (primitive), / (body-centered), F (face-centered),34 C pace-centered in one set of laces), and R (rhombohedral) Thus our monoclinic structure P2Jc belongs to the monoclinic crystal system and has a primitive Bravais lattice. 

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