Crystallographic lattice types

The combination of the point lattices constructed on the basis of the crystallographic systems with the possible centring translation results in the 14 so-called Bravais lattice type, illustrated in Fig. 3.4. Substituting (decorating) each lattice... 

Three of the four presumed types of chemical bond that occurs in the solid state have been reduced to the common basis of interaction between opposite charges localized at crystallographic lattice sites, apparently at variance with the pairwise covalency described before. 

Some of the defect equilibria which we have deduced by this type of analysis were not surprising—a parent lattice may dissociate into interstitials and vacancies in conformity with appropriate equilibrium constants defects may associate, again consistent with an equilibrium constant or the lattice may dissolve excess atoms in simple solubility. (When we speak of a solvent or parent lattice we mean the crystallographic lattice, as it would be determined by x-ray analysis, stoichiometri-cally perfect, and free of vacancies or interstitials. We call the process of vacancy and interstitial formation lattice dissociation. Simple solution adds interstitials or fills voids in the parent lattice). 

When these restrictions are not obeyed, no reflections can be obtained from the set of crystallographic planes under consideration, for there will be lattice points lying between the planes and scattering out of phase with those in the planes, resulting in complete cancellation due to destractive interference. By observing experimentally what sets of planes reflect X rays, one can deduce what the restrictions are and thereby deduce the lattice type. 

Since every unit cell in the crystal lattice is identical to all others, it is said that the lattice can be primitive or centered. We already mentioned (Eq. 1.1) that a crystallographic lattice is based on three non-coplanar translations (vectors), thus the presence of lattice centering introduces additional translations that are different from the three basis translations. Properties of various lattices are summarized in Table 1.13 along with the international symbols adopted to differentiate between different lattice types. In a base-centered lattice, there are three different possibilities to select a pair of opposite faces, which is also reflected in Table 1.13. 

High reactivity elements (RE e.g., cerium, yttrium, zirconium, hafnium) are sometimes added to the Fe-Cr-Al matrix these help the formation of the alumina protective layer that is, they speed up the transition from the less to the more stable crystallographic lattices [5,6] and increase its adhesion to the substrate. Secondly this action is assisted by the precipitation of "pegs" made up by fhe oxides of fhe reactive elemenfs (RE), partially immersed both in the substrate and in the scale of continuous superficial oxide [6]. However, fhe same authors state that the formation of fhe pegs is nof vital for the resistance to the scaling off of fhe layers of superficial oxide. It is important to note that its crystallographic type is a-Al203, which is much more effective than the 5, y, or 9 types. 

Pearson symbol - A code for designating crystallographic information, including the crystal system, the lattice type, and the number of atoms per unit cell. 

A unit cell reflects the symmetry of the crystal structure. Thus, an atom at a position (x, y, z) in a unit cell may require the presence of atoms at other positions in order to satisfy the symmetry of the structure. For example, a unit cell with a centre of symmetry will, of necessity, require that an atom at (x,y,z) be paired with an atom at (—x, —y, —z). To avoid long repetitive lists of atom positions in complex structures, crystallographic descriptions usually list only the minimum number of atomic positions which, when combined with the symmetry of the structure, given as the space group, generate all the atom positions in the unit cell. Additionally, the Bravais lattice type and the motif are often specified as well as the number of formula units in the unit cell, written as Z. Thus, in the unit cell of rutile, given above, Z = 2. This means that there are... 

For specifying directions and planes in a crystal, the origin of the crystallographic coordinate system is positioned in a lattice point, and the axes are scaled so that the length of every edge of the unit cell is one. Thus, for non-cubic lattice types, this coordinate system is non-Cartesian. 

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. ... 

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