Tetragonal cell

A face-centred cubic cell (having a unit edge a0), compressed along an axis, when the reduction corresponds to a face-centred tetragonal cell with a c a ratio... 

Figure 3.12. A face-centred cubic cell (edge ac) can be described in terms of a body-centred tetragonal cell with a da ratio having the value - 2 (a, = ac yfl /2, ct = ac). By a convenient compression along the c axis, the body-centred tetragonal cell can be transformed into a body-centred cubic cell.

Nevertheless it may be observed that, in some specific cases, reference to a pseudo-face-centred tetragonal cell may be useful, for instance to compare the structure under examination with a face-centred cubic structure. 

The In cell may be considered a distortion of the Cu type, face-centred cubic, cell. The unconventional face-centred tetragonal cell (equivalent to the tI2 cell), corresponds to a = aJY = 459.8, c = c = 494.7 and c /a = 1.076. Protactinium has a similar structure, which however with a c/a value lower than one, can be considered a distortion of the body-centred cubic structure. 

This is apparent from Fig. 3.12 where the relation between a small tetragonal cell (tP2 or tI2) and a larger (nearly cubic) cell is shown. The large cell has ac = 280.4 2= 396.5pm and c = c = 367.3. It is similar to a Cu-type cell, slightly compressed (c/a = 0.926) and in which the atoms placed in the centre of the side... 

It is also possible to compare the three structures in terms of 44 net layer stacking (along the c direction of the tetragonal cells). See Figs. 7.42,7.43 and, for NbAs, Fig. 7.27. 

Xenon Difluoride. XeF2 mw 169.30 colorl linear cryst with a body-centered tetragonal cell structure, possessing a nauseating odor mp 129.03 0.05° d 4.32g/cc. V sol in liq anhydr HF moderately sol in w. Prepn is by reacting two moles of Xe with one mole of fluorine in a Ni or Monel vessel at 400°, quenching the reaction at RT, and isolating the product by vac sublimation. Ref 2 lists nine other techniques for the prepn of the difluoride. The pure compd is stable and can be kept indefinitely in Ni or Monel containers... 

Note that a tetragonal cell with an axial ratio of I is cubic, and thii chart at this position can therefore be used for cubic crystals. 

Figure 4.5. (a) A projection of the cubic cell on one face for gray tin. (b) A projection along c0 of the tetragonal cell for white tin. 

Figure 4.7. (a) A projection on one face of two cells of a face-centered cubic cell. The projection of the body-centered tetragonal cells is shown by dashed lines. Open and black circles show different heights in the cell, (b) The body-centered tetragonal cell. 

Figure 7.4. A projection along c0 of the atoms in the tetragonal cell of B5H9. Boron atoms are the smaller circles. The centers of the four B atoms in the square base of the pyramidal molecules are at 0 (and 100) and 50 giving a body-centered cell.

Biin is tetragonal with two molecules per unit cell, a = 5.015 and c = 4.781 A. The face-centered tetragonal cell shown in Figure 9.6 has In at comers and in the centers of the top and bottom faces. The Bi atoms are displaced from the center of side faces. Two Bi in opposite... 

Figure 9.6. The distorted face-centered tetragonal cell of Biin is shown. Bi atoms are the larger circles.

The CuA12 tetragonal crystal structure, D j, 14/m cm is found for many AM2 type intermetallic and boride compounds (see Table 9.6). The tetragonal cell has four molecules per unit cell, a = 6.067 and... 

Figure 10.6. The tetragonal cell of stishovite, Si02, isolated SiC>6 octahedra are...

Figure 11.8. A projection along an aQ axis of the tetragonal cell of urea. The carbon atoms at 50 and 0 form a body-centered tetragonal cell.

Tetrakis(hydroxymethyl)methane, [C(CH20H)4, also known as pen-taerythritol], is one of the simpler substitution products of methane for which structures have been determined. The tetragonal cell contains two molecules, S4,14, a0 6.083, c0 = 6.726 A. The structure shown in Figure 11.10 is body centered, 3 2PTOT(t). At higher temperatures, between 179.5 and 260.5°C, this body-centered structure is transformed to a face-centered cubic structure. The cubic cell (a0 = 8.963 A at 230°C) contains four molecules. It has been proposed that at the higher temperature the molecules achieve a statistical orientation that makes them effectively spherical crystallographically. The notation is 3P. 

When subjected to high temperatures and pressures, polymorphs have been prepared for some of the difluorides. These all have distorted variants of the fluorite structure, with cubic, or pseudocubic, tetragonal cells. Manganese difluoride has been most studied (28-30) and similar polymorphism reported for cobalt and zinc difluorides (30). Recently, palladium and silver difluorides have been shown to behave in a similar way forming cubic metastable phases (31). In all cases there is a decrease in volume for the structure change. 

However, all these syntheses have resulted in intractable powder samples, which were either poorly crystalline, or for which unit-cell dimensions were not obtained from the powder data. The tetragonal cell reported for rhenium tetrafluoride (80) is based on 20 powder lines and may not represent the correct crystal symmetry. 

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