Crystal lattice cubic closest packe

The crystal structure of NaCl is cubic (isometric) with one type of ion in a face-centered lattice (cubic closest packing. Sections 2-4 and 2-5) with origin at 0, 0, 0 in the cubic unit cell, and the other ion on a face-centered lattice with origin at 0, 0, i (or i, 0, 0 or 0, 0), as shown in Figure 6-19. 

Figure 7.1 Three common crystal lattices adopted by elements (a) body-centred cubic packing, (b) cubic closest packed (or face-centred cubic) and (c) hexagonal closest packed...

Similarly, for a cubic crystal the unit of structure can be taken as a cube, which when reproduced in parallel orientation would fill space to produce a cubic lattice, as shown in Figure 2-6. The unit of structure could be described, for a cubic crystal, by giving the value of the edge of the unit, a, and the values of the coordinates x, y, and z for each atom, as fractions of the edge of the unit. Thus, for the cubic closest-packed structure, represented by metallic copper, the unit of structure is cubic, with edge a = V2 X 255 pm, and with four atoms per unit, with coordinates jc = 0, y = 0. z = 0 jf = 0, y = i, z = x = i, y = 0, z = i and jr=i, y = i, z = 0, as shown in Figure 2-7. Often these coordinates are written without giving the symbols jc, y, and z it is then said that there are four copper atoms in the unit, at 0, 0, 0 0, i, i i, 0, i i, i, 0. These are called the coordinates of the atoms in the unit cube. 

Some crystal lattices can also be depicted as closest-packed structures, including the hexagonal closest-packing structure (not cubic) and the cubic closest-packing structure (which has a face-centered cubic unit cell). 

The bonding and crystal structure of alumina account for its physical properties. The small Al ions and small ions form a very stable ionic lattice. The crystal has a cubic closest packed structure of 0 ions, with Al ions occupying octahedral holes. Alumina is a very hard material and is often used as an abrasive. It is also resistant to heat (mp 2020 °C) and is used in linings for high-temperature furnaces and as a catalyst support in industrial chemical processes. Aluminum oxide is relatively unreactive except at very high temperatures. Its stability at high temperatures classifies it as a refractory material. 

There has been some interest in the alkali metal fullerides, M C6o(s), because at low temperatures, some of these compounds become superconducting. The alkali metal fullerides are ionic crystals comprising ions and Cgo" ions. The value of n can be deduced from the crystal structure. If M C6q consists of a cubic closest packed array of fulleride ions, with ions occupying all the octahedral and tetrahedral holes in the fulleride lattice, then what is the value of n and what is the empirical formula of the fulleride ... 

Iron is a metal with a body-centered cubic lattice. The three low-index planes used in the present study are shown in Fig. 1. The Fe(IIO) plane is the closest-packed iron surface with only six-coordinated (C ) atoms exposed. The Fe(lOO) plane is less closely packed and only has four-coordinated (C4) atoms in its surface. The Fe(l 11) plane was the most open surface studied and has both C4 and seven-coordinated (C7) atoms exposed. Three approximately circular iron specimens were cut from a high-purity (4iV) single-crystal rod and diamond polished, the final dimensions being ap-ivoximately 6 mm diameter and 1 mm thickness. 

The body-centred cubic crystal is not close-packed. The slip systems with the closest packed directions and planes in this lattice are of the type 110 (111) (figure 6.15). With two slip directions per plane and six different slip planes, twelve slip systems result. As summarised in table 6.2, slip is also possible on other crystallographic planes that are only slightly more difficult to activate [55]. 

We can describe the structures of metals as the closest packing of spheres, first discussed in Section 11.11. Elemental metals generally crystallize in one of the basic types of crystal lattices, including face-centered cubic, body-centered cubic, and hexagonal closest packed. The crystal structure of a metal may change, however, as a function of temperature and pressure. Table 23.2 lists the crystal structures for the 3d transition metals at attnospheric pressure. 

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