Cubic body-centred structure

From Fig. 3.11, it can be seen that by increasing the chromium content while maintaining a limited amount of nickel-equivalent elements, first mixed martensite-ferrite structures are produced and then fully ferritic. This is 6-ferrite, that is a body-centred cubic structure stable at all temperatures. Relative to martensite it is soft, but it is also usually brittle. For this latter reason, usage has in the main been in small section form. This and some other disadvantages are offset for some purposes by attractive corrosion resistance or physical properties. 

Structure Although massive chromium has a body-centred cubic structure, electrodeposited chromium can exist as two primary modifications, i.e. a-(b.c.c.) and (c.p.h.). The precise conditions under which these forms of chromium can be deposited are not known with certainty. Muro" showed that at 40°C and 2-0-22 A/dm the deposit was essentially a-chromium but small amounts of 0- and 7- were present, while Koch and Hein observed... 

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 for instance to O Keeffe, however, this definition may lead to some difficulties. The value 14 for the body-centred cubic structure, higher than that of closest packing, does not seem entirely reasonable the difficulty becomes more acute in a structure such as that of diamond for which a very high value, 16, is computed according to the mentioned definition. 

WoWj/2 the body-centred cubic structure of W (1 atom in 0, 0, 0 and 1 atom in A, A, /) corresponds to a sequence of type 1 and type 4 square nets at the heights 0 and A, respectively. Note, however, that for a fall description of the structure, either in the hexagonal or the tetragonal case, the inter-layer distance must be taken into account not only in terms of the fractional coordinates (that is, the c/a axial ratio must be considered). For more complex polygonal nets, their symbolic representation and use in the description, for instance, of the Frank-Kasper phases, see Frank and Kasper (1958) and Pearson (1972). 

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 W body-centred cubic structure can be compared with the simple cubic CsCl-type structure (which can be obtained from the W type by an ordered substitution of the atoms) and with the MnCu2Al-type structure ( ordered superstructure of the CsCl type) see Fig. 3.31 and notice the typical eight (cubic) coordination. 

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. 

Body-centred cubic structures and their derivatives, cP2-CsCl (B2), cF16-Fe3Al (D03), cF16-NaTl (B32), cF16-MnCu2Al (Lip. 

A) Face-centred cubic structure of NaCI (B) Body-centred cubic structure... 

Figure 5.1. Simple body-centred cubic structure with random occupation of atoms on all sites.

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—... 

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 resulting phase diagram for diblock copolymers is shown in Fig. 2.40.The theory predicts that microphase separation occurs to a body-centred cubic structure for all compositions except where a direct second-order transition to a lamellar structure is predicted. First-order transitions to hex and lam phases are expected on further lowering the temperature for asymmetric diblocks. 

Not all ionic substances form the same structures. Caesium chloride (CsCl), for example, forms a different structure due to the larger size of the caesium ion compared with that of the sodium ion. This gives rise to the structure shown in Figure 3.16, which is called a body-centred cubic structure. Each caesium ion is surrounded by eight chloride ions and, in turn, each chloride ion is surrounded by eight caesium ions. 

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. 

For lithium with a body-centred cubic structure (CN 8) with 8 nearest neighbours at 3.032 A and 6 more at a slightly larger distance of 3.502 A one calculates with a total bond order of 1, a bond order of n = 0.111 and n = 0.018 for both categories with rx — 1.220 A (comp. Li2 r — 1.33 A, but for a nearly pure s bond). 

The body-centred cubic structure consists of spheres of diameter 2Rq filled with the hydrophobic paraffinic chains of lipopeptides and assembled on a body centred cubic lattice of side a, while the space between the spheres is occupied by the hydrophilic peptidic chains and the water. 

The figures 1 and 2 illustrate such a behaviour in the case of the lamellar and hexagonal structures of Ci8K2 nd of the body-centred cubic structure of C ySar o respectively. 

When the a phase, i.e, the primary solid solution, has only a limited range of stability, other intermediate phases are formed. At particular concentrations of the second component a transformation from one crystal structure to another takes place. In a large number of binary systems, e.g. Gu-Au, Cu-Al, Cu-Sn, a transition from the cubic close packed structure of copper to a body centred cubic structure ()3 phase) occurs at a particular concentration. The phase is stable over a particular range of concentration and at higher concentrations is generally converted to the y-phase which has a complex structure, followed by the e and >) phases which are... 

In the p phase, which has a body centred cubic structure, the planes which are the greatest distance apart are the (i 10) planes. For these... 

The structures that have been determined so far include those of the pure, electrically insulating Qo (ref. 5) and the heavily doped KfcCfto (ref. 6). At room temperature, solid forms a face-centred cubic (f.c.c.) lattice with 10.0 A intercluster separ-ation KeCftQ has a body-centred cubic structure, with K. atoms in distorted tetrahedral sites. No superconductivity was observed in that material. Cs6Cso has the same structure. We have found that the superconductor K3Q0 has a f.c.c. structure derived from that of C o by incorporating K ions into all of the octahedral and tetrahedral interstices of the host lattice. 

Among the high-pressure forms of elementary Si there is one with a body-centred cubic structure which is related to the diamond structure in an interesting way. The diamond net is shown in Fig. 3.41(a) viewed along the direction of a C-C bond, the 6-gon layers (distinguished as full and broken lines) being buckled. Alternate atoms of a layer are joined to atoms of the layers above and below by bonds perpendicular to the plane of the paper, as indicated by the pair of circles. Suppose now that the latter bonds are broken and that alternate... 

This group of more than 50 elements, including the 4f and 5f elements, comprises most of the metals. The structure of at least one form of most of these metals is known (Table 29.3), and with few exceptions they crystallize with one or more of three structures. These are the hexagonal and cubic close-packed structures and the body-centred cubic structure. 

The two simplest forms of closest packing, hexagonal and cubic, have already been described in Chapter 4. In Fig. 29.3 we show these in their conventional orientations together with the body-centred cubic structure. Sufficient atoms of adjacent unit cells are depicted to show the full set of nearest neighbours of one... 

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