Tetragonal lattice body-centered

Standard ASTM E157-82a has the Bravais lattices designations as following C - primitive cubic B - body-centered cubic F - face-centered cubic T - primitive tetragonal U - body-centered tetragonal R - rhombohedral H - hexagonal O - primitive orthorhombic P - body-centered orthorhombic Q - base-centered orthorhombic S - face-centered orthorhombic M - primitive monoclinic N - centered monoclinic A - triclinic. 

Standard ASTM E157-82ahasthe Bravais lattices designations as following C — primitive cubic B — body-centered cubic F — face-centered cubic T — primitive tetragonal U—body-centered tetragonal R—rhombohedral H — hexagonal O—primitive orthorhombic P — body-centered orthorhombic Q — base-centered orthorhombic S — face-centered orthorhombic M — primitive monoclinic N — centered monoclinic A — triclinic. 

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

The basic structures of Tl-compounds are tetragonal body centered layer structures with layers normal to the c-axis. The lattice constants are a = 3.8A, and c - 29.4A (for 2212), 35.4A (for 2223), 22A (for 1245) and so on. The common structural features are Tl-O layers sandwiched by Ba-O sheets and blocks of Cu-O layers separated by Ca intermediate layers. The structures differ from each other by the number of Cu-O layers. For example, the number of Cu-O layers in the 2212 phase is two three in 2223 and five in the 1245 structure. A schematic representation of the 1245 structure is shown in Figure 14. The samples are normally prepared from the component oxides in sealed gold tubes to avoid problems with the toxicity and loss of Tl... 

Continuing with our survey of the seven crystal systems, we see that the tetragonal crystal system is similar to the cubic system in that all the interaxial angles are 90°. However, the cell height, characterized by the lattice parameter, c, is not equal to the base, which is square (a = b). There are two types of tetragonal space lattices simple tetragonal, with atoms only at the comers of the unit cell, and body-centered tetragonal, with an additional atom at the center of the unit cell. 

Orthorhombic crystals are similar to both tetragonal and cubic crystals because their coordinate axes are still orthogonal, but now all the lattice parameters are unequal. There are four types of orthorhombic space lattices simple orthorhombic, face-centered orthorhombic, body-centered orthorhombic, and a type we have not yet encountered, base-centered orthorhombic. The first three types are similar to those we have seen for the cubic and tetragonal systems. The base-centered orthorhombic space lattice has a lattice point (atom) at each comer, as well as a lattice point only on the top and bottom faces (called basal faces). All four orthorhombic space lattices are shown in Figure 1.20. 

Eu—G system.—The black dicarbide, EuC2, was prepared by GEBELTand Eick [231] by the reaction of europium metal with graphite (1 2 ratio) in a steel bomb at about 1050° G. The compound has a body-centered tetragonal structure with the lattice parameters a = 4.045 and c 6.645 A. The lattice constants compare reasonably well with SrC2 (a = 4.11, c = 6.68 A). 

Figure 7.9 Energy band structure of YNi2B2C along three different directions of the first Brillouin zone (FBZ) for a body-centered tetragonal lattice.15 T (0,0,0) X (1/2,0,0) M (1/2,1/2,0) and (0,0,1/2). Thus, the line TM is along [110] and Mr is along [001] in the FBZ. (Reprinted wifh permission from the American Chemical Society.)...

There are two kinds of nickel sites in Ni2N as shown in Figure 9.12. One is in the corner of the tetragonal lattice and is planarly coordinated with four nitrogen atoms. The other is at the body center and is linearly... 

The valence electron density of the tetragonal-phase polymer is shown in Fig. 10a [37]. It is evident from the figures that this tetragonal phase should have different in-plane lattice constants (a and b) if the stacking is a simple AA type with a body-centered lattice. It has been reported recently that it is actually the case in this polymer, and the material has a pseudo-tetragonal orthorhombic lattice [38]. 

The rutile structure is tetragonal (see Figure 2.9). That is, it is formed by a cationic framework of a tetragonal body-centered structure with the Ti4+ cation, located in the lattice sites and the O2 anions arranged as a TiOe octahedron connected through opposite edges alongside the c-axis. 

Unit cells are further subclassified as simple cubic/ face-centered cubic, body-centered cubic, base-centered rhombic, etc. but in order to avoid duplication in classification (Exercise 3), certain of the possibilities are left out (for example, face-centered tetragonal, side-centered rhombic), Actually 14 distinct types of space lattice are recognized. A number of cubic unit ceils and one body-centered tetragonal cell... 

The face-centered tetragonal unit cell can be transformed to body-centered tetragonal in which the lattice sites occupied are ... 

X-Ray powder diffraction data of a large number of NF4+ salts are described by various workers. The data (Table I) indicate these salts have a tetragonal lattice. Single crystals of 98.9% pure (NF4)2NiF6 showed that the compound has a body-centered tetragonal cell, space group /4/m (37). The salt is made up of octahedral NiF62- ions and tetrahedral NF4+ cations and has the antifluorite structure. The interatomic N-F distance in the NF4+ tetrahedron is 130-140 pm and the F---F distance is 220 pm. 

Both short and full symbols are used for the space groups. In the latter, both symmetry axes and symmetry planes for each symmetry direction are explicitly designated whereas in the former symmetry axes are suppressed. For example, the short symbol lA/mmm designates a body-centered tetragonal space lattice with three perpendicular mirror planes. One of these mirror planes is also perpendicular to the rotation axis, which is denoted by the slash between the 4 and the first m, while the other two mirror planes are parallel with, or contain, the rotation axis. The full symbol for this space group is lA/m Ijm Ijm 42/n 2i/n 2i/c, which reveals the additional presence of screw axes and a diagonal glide line. 

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