Body centered cubic packing

S. Martinengo, G. Ciani, A. Sironi, and P. Chini, Analogues of Metallic Lattices in Rhodium Carbonyl Cluster Chemistry. Synthesis and X-ray Structure of the [Rh15 ( i-CO)14(CO)13]3 and [Rh14((j,-CO)15(CO)9]4 Anions Showing a Stepwise Hexagonal Close-Packed/Body-Centered Cubic Interconversion, J. Am. Chem. Soc. 100,7096-7098 (1979). 

Minimum thermodynamically stable configuration Hexagonally packed sheets just touching Random close packing Body-centered cubic packing Face-centered cubic/hexagonal close packed... 

Face-centered cubic Hexagonal close-packed Body-centered cubic ... 

Structural evidence for the intercalation of K, Rb, and Cs in the saturated phase M6C60 indicates that all these solids have non-close-packed body-centered cubic structures as that shown schematically in Fig. 4.52, in which each Ceo is surrounded by 24 alkali metal atoms and each metal atom is in a distorted tetrahedral hole formed by four C o molecules. 

A photonic crystal can be created by templating the crystalline packing of colloidal particles. For a close-packed, body-centered cubic arrangement of 100-nm spherical particles, what volume fraction is occupied by the particles Calculate the most intense reflected wavelength from this photonic crystal. 

Ti Hexagonal closest packed Body-centered cubic above 882 °C... 

As with other related rare-earth metals, gadolinium is silvery white, has a metallic luster, and is malleable and ductile. At room temperature, gadolinium crystallizes in the hexagonal, close-packed alpha form. Upon heating to 1235oG, alpha gadolinium transforms into the beta form, which has a body-centered cubic structure. 

Eig. 1. SoHd—Hquid phase diagram for ( ndashrule ) He and (—) He where bcc = body-centered cubic, fee = face-centered cubic, and hep = hexagonal close-packed (53). To convert MPa to psi, multiply by 145. 

Properties. Thallium is grayish white, heavy, and soft. When freshly cut, it has a metallic luster that quickly dulls to a bluish gray tinge like that of lead. A heavy oxide cmst forms on the metal surface when in contact with air for several days. The metal has a close-packed hexagonal lattice below 230°C, at which point it is transformed to a body-centered cubic lattice. At high pressures, thallium transforms to a face-centered cubic form. The triple point between the three phases is at 110°C and 3000 MPa (30 kbar). The physical properties of thallium are summarized in Table 1. 

It is well known that the 0 of a metal depends on the surface crystallographic orientation.6,65,66 In particular, it is well established that 0 increases with the surface atomic density as a consequence of an increase in the surface potential M. More specifically, for metals crystallizing in the face-centered cubic (fee) system, 0 increases in the sequence (110) <(100) <(111) for those crystallizing in the body-centered cubic (bcc) system, in the sequence (111) < (100) <(110) and for the hexagonal close-packed (hep) system, (1120) < (1010) < (0001). 

FIGURE 5.32 The body-centered cubic (bcc) structure. This structure is not packed as closely as the others that we have illustrated. It is less common among metals than the close-packed structures. Some ionic structures are based on this model. 

The density of copper is 8.93 g-cm 3 and its atomic radius is 128 pm. Is the metal (a) close-packed or (b) body-centered cubic ... 

Self-Test 5.5A The atomic radius of silver is 144 pm and its density is 10.5 g-cm 3. Is the structure close-packed or body-centered cubic ... 

Self-Test 5.5B The atomic radius of iron is 124 pm and its density is 7.87 g-cm-3. Is this density consistent with a close-packed or a body-centered cubic structure ... 

The symbols Al, A2, and A3 represent the three simple metal structures cubic closest packed, body centered, and hexagonal closest packed, respectively. 

Phase Type in Struk-turbericht Character Atoms per unit cell (mini mum) 0 B2 and Z,20 body- centered cubic 2 /3-Mn A13 complex cubic 20 7 D81, 82, 83 84 complex cubic 52 e hexagonal close packed, c/a <(8/3) 2 ... 

The morphology of the ABA-type linear block copolymers is strongly influenced by the volume fraction of the two components. For example, in PS-EB-PS-type block copolymer as the volume fraction of PS is increased, the shape of the dispersed PS phase changes from spherical (comprising body-centered cubic spheres of PS dispersed in continuous soft phase) to cylindrical form (hexagonal packed cylinders of PS) [10,133,134]. When the volume fraction of the two phases... 

The most important metals for catalysis are those of the groups VIII and I-B of the periodic system. Three crystal structures are important, face-centered cubic (fee Ni, Cu, Rh, Pd, Ag, Ir, Pt, Au), hexagonally dose-packed (hep Co, Ru, Os) and body-centered cubic (bcc Fe). Figure 5.1 shows the unit cell for each of these structures. Note that the unit cells contain 4, 2, and 6 atoms for the fee, bcc, and hep structure, respectively. Many other structures, however, exist when considering more complex materials such as oxides, sulfides etc, which we shall not treat here. Before discussing the surfaces that the metals expose, we mention a few general properties. 

Figure 5.1. Unit cells of the face-centered cubic (fee), body-centered cubic (bcc), and hexagonally closed packed (hep) lattices.

Draw the simple (111), (100), and (110) surfaces of face-centered cubic metals, the (110) and (100) surfaces of body-centered cubic metals, and the (001) surface of an hexagonally-dosed packed surface. 

The term crystal structure in essence covers all of the descriptive information, such as the crystal system, the space lattice, the symmetry class, the space group and the lattice parameters pertaining to the crystal under reference. Most metals are found to have relatively simple crystal structures body centered cubic (bcc), face centered cubic (fee) and hexagonal close packed (eph) structures. The majority of the metals exhibit one of these three crystal structures at room temperature. However, some metals do exhibit more complex crystal structures. 

For additional symbols of further packings cf. [38, 156], T (triangular) refers to hexagonal layers, Q to layers with a periodic pattern of squares. The packing Qs yields a primitive cubic lattice (Fig. 2.4), Qf a body-centered cubic lattice (cf. Fig. 14.3, p. 153). Sometimes the symbols are set as superscripts without the angular brackets, for example Ti[Ca03]c. 

This bismuth-III structure is also observed for antimony from 10 to 28 GPa and for bismuth from 2.8 to 8 GPa. At even higher pressures antimony and bismuth adopt the body-centered cubic packing of spheres which is typical for metals. Bi-III has a peculiar incommensurate composite crystal structure. It can be described by two intergrown partial structures that are not compatible metrically with one another (Fig. 11.11). The partial structure 1 consists of square antiprisms which share faces along c and which are connected by tetrahedral building blocks. The partial structure 2 forms linear chains of atoms that run along c in the midst of the square antiprisms. In addition, to compensate for the... 

Germanium forms the same kinds of modifications as silicon at similar conditions (Fig. 12.4). Tin, however, does not exhibit this diversity )3-tin transforms to a body-centered cubic packing of spheres at 45 GPa. Lead already adopts a cubic closest-packing of spheres at ambient pressure. 

The space filling in the body-centered cubic packing of spheres is less than in the closest packings, but the difference is moderate. The fraction of space filled amounts to ns/3 = 0.6802 or 68.02 %. The reduction of the coordination number from 12 to 8 seems to be more serious however, the difference is actually not so serious because in addition to the 8 directly adjacent spheres every sphere has 6 further neighbors that are only 15.5 % more distant (Fig. 14.3). The coordination number can be designated by 8 + 6. 

Corresponding to its inferior space filling, the body-centered cubic packing of spheres is less frequent among the element structures. None the less, 15 elements crystallize with this structure. As tungsten is one of them, the term tungsten type is sometimes used for this kind of packing. 

Unit cell of the body-centered cubic packing of spheres and the coordination around one sphere... 

Structures Derived of Body-centered Cubic Packing (CsCl Type)... 

Disordered alloys may form when two metals are mixed if both have body-centered cubic structures and if their atomic radii do not differ by much (e.g. K and Rb). The formation of ordered alloys, however, is usually favored at higher temperatures the tendency towards disordered structures increases. Such an arrangement can even be adopted if metals are combined which do not crystallize with body-centered cubic packings themselves, on condition of the appropriate composition. /J-Brass (CuZn) is an example below 300 °C it has a CsCl structure, but between 300 °C and 500 °C a A type transformation takes place resulting in a disordered alloy with a body-centered cubic structure. 

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