Bravais lattice type

The unit cell and the Bravais lattice type for IM-5 were obtained from tilt series of SAED patterns such as that shown in Figure 2 (a = 14.3 A, b = 57.4 A, c - 20.1 A with... 

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... 

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... 

L. C. Andrews and H. J. Bernstein, Acta Crystallogr., Sect. A, 44,1009 (1988). Lattices and Reduced Cells as Points in 6-Space and Selection of Bravais Lattice Type by Projections. 

Figure 6.14 The 14 Bravais lattice types. The symbols are defined as follows primitive (P), face centered (F), body centered (I), side centered (C).

A9.5 (i) The Bravais lattice type is F since the diflfaction indices are all even or all odd. 

Note. The Hermann-Mauguin space group notation for any particular crystal comprises two parts. The first part identifies the Bravais lattice type into which the crystal belongs and the second part identifies the total symmetry of the array of atoms in the crystal and therefore also the crystal system. In the second part that identifies the symmetry, only those symmetry elements are included in the symbol that are necessary to describe the space group uniquely. The remainders are being omitted since they follow, as a necessary consequence. 

The magnitudes of a, b, and c can be calculated, depending on the Bravais lattice type. Table III hsts the appropriate equations for determination of unit cell dimensions based on the hkl) indices. 

A fairly simple but sometimes effective symbolism has been given by Pearson. It allows the formal characteristics of crystal structures to be summarized. The Pearson symbol consists of a small letter for the crystal system (anorthic, monoclinic, orthorhombic, tetrahedral, hexagonal or trigonal, cubic), a capital letter for the Bravais lattice type (/, 5, /, R or F) and the number of atoms in the unit cell (e.g., aP% for CaPj). 

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