Body-centred cubic crystal

FIGURE 4.8 Energy bands formed from ns and np atomic orbitals for (a) a body-centred cubic crystal and (b) a crystal of diamond structure, depicting filled levels for 4iVelectrons. 

T(hxJrky.Jr z) for this atom is 180° when h- -k- -l is odd.) Therefore, reflections from planes having A+ +1 odd are not fotlnd in the diffraction pattern of a-iron. On the other hand, all planes such as 110, 200, 310, and 211 which have h+k+I even give strong reflections, because all the atoms lie on these planes. (In other words, the phase angle for the centre atom is 0° when h -rk- l is even.) It is important to note that this is true not only for body-centred cubic crystals but for a l other body-centred crystals, whatever their symmetry. 

An interactive version of a body-centred cubic crystal... 

Carbon steels exist in three stable crystalline phases ferrite has a body-centred cubic crystal, austenite has a face-centred cubic crystal, and cementite has an orthorhombic crystal. Pearllte is a mixture of ferrite and cementite arranged in parallel plates. The phase diagram shows how the... 

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]. 

Fig. 93. (a) Face centred cubic crystal (b) Body centred cubic crystal (c) Hexagonal closed packed crystal. 

We begin by looking at the smallest scale of controllable structural feature - the way in which the atoms in the metals are packed together to give either a crystalline or a glassy (amorphous) structure. Table 2.2 lists the crystal structures of the pure metals at room temperature. In nearly every case the metal atoms pack into the simple crystal structures of face-centred cubic (f.c.c.), body-centred cubic (b.c.c.) or close-packed hexagonal (c.p.h.). 

Crystal structure Martensite (body centred cubic) austenite (face centred cubic)... 

Mono- or single-crystal materials are undoubtedly the most straightforward to handle conceptually, however, and we start our consideration of electrochemistry by examining some simple substances to show how the surface structure follows immediately from the bulk structure we will need this information in chapter 2, since modern single-crystal studies have shed considerable light on the mechanism of many prototypical electrochemical reactions. The great majority of electrode materials are either elemental metals or metal alloys, most of which have a face-centred or body-centred cubic structure, or one based on a hexagonal close-packed array of atoms. 

Their normal crystal structure, at ambient conditions, corresponds to the body-centred cubic cI2-W-type structure. At very low temperatures, the close-packed hexagonal hP2-Mg-type structure has been observed for Li and Na, while for Rb and Cs the face-centred cubic close-packed cF4-Cu-type structure is known at high pressure. No polymorphic transformation has been reported for potassium. 

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...

The first attempt to calculate realistic wave functions for electrons in metals is that of Wigner and Seitz (1933). These authors pointed out that space in a body-or face-centred cubic crystal could be divided into polyhedra surrounding each atom, that these polyhedra could be replaced without large error by spheres of radius r0, so that for the lowest state one has to find spherically symmetrical solutions of the Schrodinger equation (6) subject to the boundary condition that... 

Fig. 126. Powder patterns of simple, body-centred, and face-centred cubic crystals.

Crystalline solids consist of periodically repeating arrays of atoms, ions or molecules. Many catalytic metals adopt cubic close-packed (also called face-centred cubic) (Co, Ni, Cu, Pd, Ag, Pt) or hexagonal close-packed (Ti, Co, Zn) structures. Others (e.g. Fe, W) adopt the slightly less efficiently packed body-centred cubic structure. The different crystal faces which are possible are conveniently described in terms of their Miller indices. It is customary to describe the geometry of a crystal in terms of its unit cell. This is a parallelepiped of characteristic shape which generates the crystal lattice when many of them are packed together. 

Iron has a body-centred cubic lattice (see Figure 5.16) with a unit cell side of 286 pm. Calculate the number of iron atoms per cm2 of surface for each of the Fe(100), Fe(110) and Fe(lll) crystal faces. Nitrogen adsorbs dissociatively on the Fe(100) surface and the LEED pattern is that of a C(2 x 2) adsorbed layer. Assuming saturation of this layer, calculate the number of adsorbed nitrogen atoms per cm2 of surface. 

As noted earlier, A depends on the symmetry of the ligands surrounding a transition metal ion. The relationships expressed in eqs (2.7), (2.8) and (2.9) for crystal field splittings in octahedral, tetrahedral, body-centred cubic and dodecahedral coordinations are summarized in eq. (2.26)... 

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