Cubic close-packed lattice structure

When the radius ratio of an ionic compound is less than about 0.4, corresponding to cations that are significantly smaller than the anion, the small tetrahedral holes may be occupied. An example is the zinc-blende structure (which is also called the sphalerite structure), named after a form of the mineral ZnS (Fig. 5.43). This structure is based on an expanded cubic close-packed lattice of the big S2 anions, with the small Zn2+ cations occupying half the tetrahedral holes. Each Zn2+ ion is surrounded by four S2 ions, and each S2" ion is surrounded by four Zn2+ ions so the zinc-blende structure has (4,4)-coordination. 

Cubed compound, in PVC siding manufacture, 25 685 Cube lattice, 8 114t Cubic boron nitride, 1 8 4 654 grinding wheels, 1 21 hardness in various scales, l 3t physical properties of, 4 653t Cubic close-packed (CCP) structure, of spinel ferrites, 11 60 Cubic ferrites, 11 55-57 Cubic geometry, for metal coordination numbers, 7 574, 575t. See also Cubic structure Cubic symmetry Cubic silsesquioxanes (CSS), 13 539 Cubic structure, of ferroelectric crystals, 11 94-95, 96 Cubic symmetry, 8 114t Cubitron sol-gel abrasives, 1 7 Cucurbituril inclusion compounds,... 

The relationship between cubic close-packed (ccp) structures and ionic compounds of type B1 is obvious. Interstitial sites with respect to metal positions are at fractional coordinates of the type 00 and equivalent to the ionic sites in Bl. The Madelung constant of Al type metals with interstitially localized free electrons is therefore the same as that of rocksalt structures. It is noted that the interstitial sites define the same face-centred lattice as the metal ions. 

Some ternary and mixed-valency oxides have the spinel structure where metal ions occupy a proportion of tetrahedral and octahedral holes in a cubic close-packed lattice. Examples include M304 with M=Mn,... 

Various schemes have been proposed for the classification of the different alumina structures (Lippens and Steggerda, 1970). One approach was to focus attention on the temperatures at which they are formed, but it is perhaps more logical to look for differences in the oxide lattice. On this basis, one can distinguish broadly between the a-series with hexagonal close-packed lattices (i.e. ABAB...) and the y-series with cubic close-packed lattices (i.e. ABCABC...). Furthermore, there is little doubt that both y- and j/-A1203 have a spinel (MgAl204) type of lattice. The unit cell of spinel is made up of 32 cubic close-packed O2" ions and therefore 21.33 Al3+ ions have to be distributed between a total of 24 possible cationic sites. Differences between the individual members of the y-series are likely to be due to disorder of the lattice and in the distribution of the cations between octahedral and tetrahedral interstices. 

The fluorite structure. Figure 7-9, can be described as having the calcium ions in a cubic close-packed lattice, with eight fluoride ions surrounding each one and occupying all of the tetrahedral holes. An alternative description of the same structure, shown in... 

FIGURE 7-9 Fluorite and Antifluorite Crystal Structures, (a) Fluorite shown as Ca in a cubic close-packed lattice, each surrounded by eight F in the tetrahedral holes. 

The similar organization energies of the hep and ccp lattices make their intergrowth easy in mesoporous materials synthesized from both simple surfactant and copolymer surfactant. Intergrowth with cubic close-packed (ccp) structure was typically observed... 

A The halite structure consists of a cubic close-packed lattice where all octahedral holes are filled. However, the tetrahedral holes which are generated by a cubic close-packed array of spheres (Chapter 1) will be empty. There are a number of available holes, for example... 

Some ternary and mixed-valency oxides have the spinel structure where metal ions occupy a proportion of tetrahedral and octahedral holes in a cubic close-packed lattice (see Topic G5). Examples include M304 with M=Mn, Fe, Co. The distribution of M2+ and M3+ ions between the tetrahedral and octahedral sites shows the influence of ligand field stabilization energies (see Topic H2). In Fe304, Fe2+ (3d6) has an octahedral preference whereas Fe3+ (3d5) has none, and this... 

D20.6 In a face-centered cubic close-packed lattice, there is an octahedral hole in the center. The rock-salt structure can be thought of as being derived from an fee structure of Cl ions in which Na+ ions have filled the octahedral holes. 

On the other hand, the metallic structures of [RuioN(CO)24] (Fig. 1), [Rhi4N2(CO)25] (Fig. 1), and [Rh2gN4(CO)4iHx]( / - (Fig. 8), whose metallic frameworks are slightly distorted fragments of the cubic close packed lattice ccp), should be considered. In both the ruthenium and the giant 28-metal rhodium compounds, the interstitial nitrides are within oh cavities in [Rhi4N2(CO)2s]... 

FIGURE 7.9 Fluorite and Antifluorite Crystal Structures, (a) Fluorite shown as Ca + in a cubic close-packed lattice, each surrounded by eight F" in the tetrahedral holes, (b) Fluorite shown as F in a simple cubic array, with Ca + in alternate body centers. Solid lines enclose the cubes containing Ca + ions. If the positive and negative ion positions are reversed, as in LijO, the structure is known as antifluorite. 

Aoki and Williams (1979) pointed out that the NaCl defect structure is stable in the approximate composition range 0.33 x 0.45. They inferred that in the cubic close-packed lattice built up of atoms of radius r, the octahedral holes will just contain... 

We have already noted that the formation of liquids and solids at low temperatures is due to intermolecular attractions. Solid state Ne forms a cubic close-packed lattice each atom is surrounded by 12 nearest neighbors at a distance of 316 pm, about 2% longer than the 7 m distance obtained experimentally by molecular beam studies. The crystal structure of methane at 35 K is also cubic close packed with twelve nearest neighbors at R(C---C) = 416 pm [10] or about 3% longer than the distance of 402 pm. These results indicate that information about the van der Waals radii of atoms may be obtained from the distances... 

The structures of spinels, A B2 4, are determined not only by the radius of the ions involved but also by the crystal field stabilization energies of the cations that occupy octahedral or tetrahedral holes in the cubic close-packed lattice of oxide ions. These structures offer an opportunity to combine a knowledge of crystal field theory obtained in earlier chapters with the knowledge of solid-state structures covered in this chapter. 

Curium metal exists in two modifications, a double hexagonal close-packed (dhcp) structure (a-lanthanum type) and a high-temperature cubic close-packed (fee) structure. Using Cm, the dhcp form was found to have lattice constants a = 3.496(3)andc = 11.331(5) A, giving a calculated density of 13.5 gem and a metallic radius of 1.74 A [27,97]. In a recent pressure study, slightly less accurate lattice constants were obtained (yielding a calculated density of 13.8 g cm ) but did establish that the dhcp phase was stable at least to 6.5 GPa [162]. 

Figure 29.1 Crystal structures of ZnS. (a) Zinc blende, consisting of two, interpenetrating, cep lattices of Zn and S atoms displaced with respect to each other so that the atoms of each achieve 4-coordination (Zn-S = 235 pm) by occupying tetrahedral sites of the other lattice. The face-centred cube, characteristic of the cep lattice, can be seen — in this case composed of S atoms, but an extended diagram would reveal the same arrangement of Zn atoms. Note that if all the atoms of this structure were C, the structure would be that of diamond (p. 275). (b) Wurtzite. As with zinc blende, tetrahedral coordination of both Zn and S is achieved (Zn-S = 236 pm) but this time the interpenetrating lattices are hexagonal, rather than cubic, close-packed.

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. 

The layered oxides LiNiOj and LiCoOj also have the 3R form AbC(a)BcA(b)CaB. In this structure, the oxygen lattice considered alone has cubic close packing ACBACB (or equivalently ABCABC). As a result, these compounds are closely related to cubic compounds. To visualise the structure of LiNiOj or LiCoOj, for example, start from cubic NiO or CoO (AbCaBcAbCaB), and replace every second layer of Ni or Co by Li. In the case of Ni this replacement may be incomplete, and the Li layers may contain residual Ni (Dahn, von Sacken and Michal, 1990b). 

---