Metal body-centred cubic

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...

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.). 

When Li metal is cold-worked it transforms from body-centred cubic to cubic close-packed in which each atom is surrounded by 12 others in twinned cuboctahedral coordination below 78 K the stable crystalline modification is hexagonal dose-packed in which each lithium atom has 12 nearest neighbours in the form of a cuboctahedron. This very high coordination... 

The selection of materials for high-temperature applications is discussed by Day (1979). At low temperatures, less than 10°C, metals that are normally ductile can fail in a brittle manner. Serious disasters have occurred through the failure of welded carbon steel vessels at low temperatures. The phenomenon of brittle failure is associated with the crystalline structure of metals. Metals with a body-centred-cubic (bcc) lattice are more liable to brittle failure than those with a face-centred-cubic (fee) or hexagonal lattice. For low-temperature equipment, such as cryogenic plant and liquefied-gas storages, austenitic stainless steel (fee) or aluminium alloys (hex) should be specified see Wigley (1978). 

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. 

The atomic structure of the nuclei of metal deposits, which have the simplest form since they involve only one atomic species, appear to be quite different from those of the bulk metals. The structures of metals fall mainly into three classes. In the face-centred cubic and the hexagonal structures each atom has 12 co-ordination with six neighbours in the plane. The repeat patterns obtained by laying one plane over another in the closest fit have two alternative arrangements. In the hexagonal structure the repeat pattern is A-B-A-B etc., whereas in the face-centred cubic structure the repeat pattern is A-B-C-A-B-C. In the body-centred cubic structure in which each atom is eight co-ordinated, the repeat pattern is A-B-A-B. (See Figure 1.4.)... 

According to the Frank-Kasper definition, the coordination number is unambiguously 12 in the hexagonal close-packed metals and assumes the value 14 in a body-centred cubic metal. Generally in several complex metallic structures this definition yields reasonable values such as 14, even when the nearest-neighbour definition would give 1 or 2. 

The cell can be described as formed by two superimposed slightly distorted body-centred cubic subcells of the metal atoms. The O atom is surrounded by a slightly compressed Ta atom octahedron. 

Another contribution is represented by an investigation of a cubic thallium cluster phase of the Bergmann type Na13(TlA.Cdi A.)27 (0.24 < x <0.33) (Li and Corbett 2004). For this phase too the body centred cubic structure (space group Im 3, a = 1587-1599 pm) may be described in terms of multiple endo-hedral concentric shells of atoms around the cell positions 0, 0, 0, and 14,14,14. The subsequent shells in every unit are an icosahedron (formed by mixed Cd-Tl atoms), a pentagonal dodecahedron (20 Na atoms), a larger icosahedron (12 Cd atoms) these are surrounded by a truncated icosahedron (60 mixed Cd-Tl atoms) and then by a 24 vertices Na polyhedron. Every atom in the last two shells is shared with those of like shells in adjacent units. A view of the unit cell is shown in Fig. 4.38. According to Li and Corbett (2004), it may be described as an electron-poor Zintl phase. A systematic description of condensed metal clusters was reported by Simon (1981). 

The body-centred cubic W-type structure. The W-type structure is another important structure of metallic elements it is common to a number of metals Li, Na, K, Rb, Ba, Cs, Eu, Cr, Mo, Y Ta, W, etc. (as the only room temperature stable form), Be, Ca, Sr, several rare earth elements, Th, etc. (as a high-temperature form) and a and 8 Fe forms. The data relevant to the prototype are reported in the following. 

Random substitutional models are used for phases such as the gas phase or simple metallic liquid and solid solutions where components can mix on any atial position which is available to the phase. For example, in a simple body-centred cubic phase any of the components could occupy any of the atomic sites which define the cubic structure as shown below (Fig. 5.1). 

Metals generally have face-centred cubic (fee), body-centred cubic (bee) or hexagonal structures. The simplest is fee. In the bee structure, if the central atom is different, the lattice is known as a CsCl (cesium chloride) structure. A bee structure can be considered as two interpenetrating cubic lattices. These are shown schematically in figure 1.3. In catalysis, nanoscopic metallic particles supported on ceramic supports or carbon are employed in many catalytic applications as we show in chapter 5. Increasingly, a combination of two metals (bimetallic) or alloys of two or more metals with special properties are used for specific catalytic applications. 

Some metals do not adopt a close-packed structure but have a slightly less efficient packing method this is the body-centred cubic structure (bcc), shown in Figure 1.8. (Unlike the previous diagrams, the positions of the atoms are now represented here—and in subsequent diagrams—by small spheres which do not touch this is merely a device to open up the structure and allow it to be seen more clearly—the whole question of atom and ion size is discussed in Section 1.6.4.) In this structure an atom in the middle of a cube is surrounded by eight identical and equidistant atoms at the corners of the cube—... 

The distance along any side of the body-centred cubic lattice as shown in Figure 7.1(a) is equal to twice the metallic radius of the atom, 2rM. The distance between the centre of the atom in the centre of the unit cell and the centre of any atom at the cube corner is 31/3/ m. The distance between the centres of two atoms at the centres of adjacent cubes is 2rM. This means that any atom in the body- centred cubic arrangement is coordinated by eight atoms at the 1 cube corners with a distance 3l/3rM, and six more atoms in the centres of the six adjacent cubes with a distance 2rM. The extra six atoms contributing to the coordination number of body-centred atoms are 100 x (2rM - 3,/3rM)/(3I/3rM) = 15.5% further away from the central atom than the eight nearest neighbours. 

With such high coordination numbers it is quite clear that there can be no possibility of covalency, because there are insufficient numbers of electrons. The difficulty is shown in the case of metallic lithium, with its body-centred cubic structure and coordination number of 14. Each lithium atom has one valency electron and for each atom to participate in 14 covalent bonds is quite impossible. 

The weakness of the covalent bond in dilithium is understandable in terms of the low effective nuclear charge, which allows the 2s orbital to be very diffuse. The addition of an electron to the lithium atom is exothermic only to the extent of 59.8 kJ mol-1, which indicates the weakness of the attraction for the extra electron. By comparison, the exother-micity of electron attachment to the fluorine atom is 333 kJ mol-1. The diffuseness of the 2s orbital of lithium is indicated by the large bond length (267 pm) in the dilithium molecule. The metal exists in the form of a body-centred cubic lattice in which the radius of the lithium atoms is 152 pm again a very high value, indicative of the low cohesiveness of the metallic structure. The metallic lattice is preferred to the diatomic molecule as the more stable state of lithium. 

The majority of elemental substances, and a large number of compounds, have metallic properties (see Section 3.3). Metallic elemental substances are characterised by three-dimensional structures with high coordination numbers. For example, Na(s) has a body-centred cubic (bcc) structure in which each atom is surrounded by eight others at the corners of a cube, each at a distance of 371.6pm from the atom at the centre. The Na atom also has six next-nearest neighbours in the form of an octahedron, with Na-Na distances of 429.1pm. A fragment of this lattice is shown in Fig. 7.14. These distances may be compared with the Na-Na bond length of 307.6 pm in the Na2 molecule, which can be studied in the gas phase by vaporisation of sodium metal. 

Fig. 7.14. Part of body-centred cubic (bcc) metallic lattice, showing its relationship to the CsCl ionic lattice with cubic eight-coordination of each atom.

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. 

In body-centred cubic coordination, the eight ligands surrounding a transition metal ion lie at the vertices of a cube (cf. fig. 2.6a.). In one type of dodecahedral coordination site found in the ideal perovskite structure (cf. fig. 9.3), the 12 nearest-neighbour anions lie at the vertices of a cuboctahedron illustrated in fig. 2.6b. The relative energies of the eg and t2g orbital groups in these two cen-trosymmetric coordinations are identical to those of the e and t2 orbital groups... 

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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