Unit cells tetragonal

The structure is quite different from that of KCg. Instead of every carbon atom bonded to three other carbon atoms, as in graphite and KC, calcium carbide contains discrete C-i ions with carixm-carbon triple bonds. The structure of CaC2 is similar to the Natl structure, but because Cz is a linear anion (not spherical like Cl") the unit cell of CaCl2 is elongated in one direction making the unit cell tetragonal (see Figure 14.14). This carbide is, hence, ionic. 

Kea.tlte, Keatite has been prepared (65) by the crystallisation of amorphous precipitated silica ia a hydrothermal bomb from dilute alkah hydroxide or carbonate solutions at 380—585°C and 35—120 MPa (345—1180 atm). The stmcture (66) is tetragonal. There are 12 Si02 units ia the unit cell ttg = 745 pm and Cg = 8604 pm the space group is P42. Keatite has a negative volumetric expansion coefficient from 20—550°C. It is unchanged by beating at 1100°C, but is transformed completely to cristobahte ia three hours at 1620°C. 

The a-tetragonal form of boron has a unit cell B qC2 or B qN2 it always has a carbon or nitrogen in the crystal. The cell is centered a single-boron atom is coordinated to four icosahedrons (4Bj2 + 2B). The -tetragonal form has a unit cell of 192 boron atoms but is not, as of this writing, totally defined. 

The crystallographic requirement for tire formation of G-P zones is that the material within the zones shall have an epitaxial relationship with the maUix, and tlrus the eventual precipitate should have a similar unit cell size in one direction as tha maUix. In dre Al-Cu system, the f.c.c. structure of aluminium has a lattice parameter of 0.4014 nm, and the tetragonal CuAl2 compound has lattice parameters a — 0.4872 and b — 0.6063 nm respectively. 

Fig. 8.12. The structure of 0.8% carbon martensite. During the transformation, the carbon atoms put themselves into the interstitial sites shown. To moke room for them the lattice stretches along one cube direction (and contracts slightly along the other two). This produces what is called a face-centred tetragonal unit cell. Note that only a small proportion of the labelled sites actually contain a carbon atom.

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.

Figure 21.2 (a) The tetragonal unit cell of rutile, Ti02- (b) The coordination of Zr in baddeleyite Zr02 the 3 O atoms in the upper plane are each coordinated by 3 Zr atoms in a plane, whereas the 4 lower O atoms are each tetrahedrally coordinated by 4 Zr atoms. 

The magnetic FeaNi system was modeled in a tetragonal symmetry with 4 atoms per unit cell (see Fig. la). The CuZn alloy was also considered to have a tetragonal unit cell, in this case c/a = 1 leads to a CsCl structure, which was shown in Fig. lb. 

Figure 1. Representation of unit cells for (a) FeaNi and (b) CuZn. Corresponding to a tetragonal symmetry in the case of FeaNi (Ni atoms are marked black) and to the LI2 (CuaAu) structure in the case of c/a = 1. CuZn shows also tetragonal symmetry, whereby c/a = 1 corresponds to the B2 structure (black circles represent Cu atoms). In (b) a frozen phonon in [001] direction is indicated for the Zn atom.

The above technique has the practical inconvenience of requiring as many different sets of Tchebyschev coefficients as the unit cell non equivalent sublattices. Furthermore, for non cubic systems, these coefficients depend on the lattice distortion ratios. Namely, for tetragonal lattices different sets of coefficients are required for each value of c/a. This situation has made difficult the implementation of KKR and KKR-CPA calculations for complex lattice structures as, for example, curates. 

The structures of CaC2 and NaN3 (stereo views). Heavy outlines body-centered tetragonal unit cell of CaC2. Dashed line at NaN3 direction of the elongation of the NaCl cell... 

Boron is as unusual in its structures as it is in its chemical behavior. Sixteen boron modifications have been described, but most of them have not been well characterized. Many samples assumed to have consisted only of boron were possibly boron-rich borides (many of which are known, e.g. YB66). An established structure is that of rhombohedral a-B12 (the subscript number designates the number of atoms per unit cell). The crystal structures of three further forms are known, tetragonal -B50, rhombohedral J3-B105 and rhombohedral j3-B 320, but probably boron-rich borides were studied. a-B50 should be formulated B48X2. It consists of B12 icosahedra that are linked by tetrahedrally coordinated X atoms. These atoms are presumably C or N atoms (B, C and N can hardly be distinguished by X-ray diffraction). 

The unit cell is tetragonal, with a = b = 10.7 A (1.07 nm) and c = 16.1 A (1.61 nm). The amylose helix is left-handed, with four D-glucose residues per turn. Both ions are located in a water-like environment. The atoms 0-2, 0-3, and 0-4 from D-glucose residues on adjacent chains coordinate around K+. The R factor is 41%. 

The unit cell is tetragonal, with a symmetry approximating P2i2 2i. The cell dimensions are a = b= 18.87 A (1.887 nm) and c = 7.99 A (799 pm). The helix diameter is 13.3 A (1.33 nm). One ethylenediamine molecule for every two D-glucose residues is indicated. The location of the ethylenediamine molecule in the lattice was discussed. The structure is almost identical to that of the amy-lose-dimethyl sulfoxide complex. 

Electron diffraction by lamellar, single crystals leads to a two-dimensional, tetragonal unit-cell with a = b = 22.9 A (2.29 nm). From X-ray diffraction data obtained from a film of sedimented, lamellar crystals, it was found that the c axis spacing (7.8 A 780 pm) is equivalent to that in 6-fold and 7-fold amylose helices. The true helical diameters of the 1-butanol, isopropyl alcohol, and 1-naphthol complexes were calculated from experimental data. The ratios of 6 7 8 indicated that the 1-naphthol complex has eight D-glucose residues per turn. The diversity of helical orientations in V-amylose crystals was discussed. 

Lamellar, single crystals of cellulose triacetate, precipitated from nitromethane with butyl alcohol, were studied by X-ray and electron diffraction. Only the crystals containing the mother liquor, or moistened with nitromethane, showed rich diffraction details. From stretched and annealed fibers, it was found that the unit cell is tetragonal, with a = fe = 21.15A (2.115 nm), and c = 41.36 A (4.136 nm). 

This polymer crystallizes in three polymorphs. The threefold helical structure packs in a trigonal unit-cell with a = 14.3 A (1.43 nm) and c = 28.7 A (2.87 nm). The 8-fold helical structure occurs in a tetragonal unit-cell with a = 13.8 A (1.38 nm) and c = 78.2 A (7.82 nm). Axial periodicity in both cases is similar [h = 9.6 A (960 pm) and 9.8 A (980 pm), respectively], but the helix twist-angle is different (120 and 45°, respectively). Distribution of the charged side-groups in these helices was discussed. An orthorhombic form, with a twofold helical structure, has a repeat of 18.6 A (1.86 nm). 

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