Cubic close-packed lattice

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. 

Consider a metallic element that crystallizes in a cubic close-packed lattice. The edge length of the unit cell is 408 pm. If close-packed layers are deposited on a flat surface to a depth (of metal) of 0.125 mm, how many close-packed layers are present ... 

The ratio d3a of the lattice constants is a direct measure of the deviation of the lattice from a perfect cubic close-packed lattice, which is it measures the layeredness of the lattice. An ideal ccp lattice has a d3a ratio of 1.633, whereas a pure layered lattice with no transition metal in the lithium layer has a... 

A distinct dihydride phase is the strongest confirmation of the magnitude of the influence of hydrogen on the metal systems. As the metal is exposed to hydrogen gas, spontaneous uptake occurs within the metal lattice. This concentration is usually very small but can have strong influence on the mechanical properties, a phenomenon known as embrittlement. With further increase of hydrogen, the metal lattice transforms to a cubic close packed lattice with... 

Both the hexagonal close-packed and cubic close-packed lattices have the same 74 percent filling of space by spheres in contact [see Problem 10.1(d)], and the two lattices also have the same coordination number, which is 12. 

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. 

In addition, the smaller size of Al + and its lack of crystal field stabilization energy permits the stability of tetrahedral coordination of A13+ to approach that of octahedral. In Cr +, tetrahedral coordination is much less stable. Therefore, a series of aluminas are known based upon a cubic close-packed lattice of oxide ions in which some A13+ occupies tetrahedral holes (87, 88). All catalytically important aluminas... 

The unit cell for a cubic close-packed lattice is the fee unit cell. For this cell, the relation between the radius of the atom r and the unit cell edge length a is... 

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... 

X-ray diffraction patterns of face-centred cubic and body-centred cubic metals is shown in Pig. 18. It might be mentioned at this stage that X-ray examination has shown why it is that there is a definite contraction in volume and increase in density when a-iron changes to y-iron at the Ac3 point (900° C.), at which there is a change of arrangement of the iron atoms from that of the rather loosely packed body-centred cubic lattice of the a-iron to that of the cubic close-packed lattice of the y-iron. It should also be noted that the face-centred cubic... 

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. 

Rearrange the top layer so that each sphere fits over an octahedral hole formed by the lower two layers. Displace all three layers horizontally from each other. Position another sphere of the same size on top so that it forms a fourth layer above a sphere in the bottom layer. You have now formed four layers of a cubic close-packed lattice. Additional layers would pack a,b,c,a,b,c,a,b,c,... 

The layers of a cubic close-packed lattice actually form what unit cell ... 

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 cubic close-packed lattice is identical to Ihe lattice having a face-centered cubic unit cell. To see this, you take portions of four layers from the cubic close-packed array (Figure 11.39, left). When these are placed together, they form a cube, as shown in Figure 11.39, right. 

Figure 2.19. Illustrations of the locations of interstitial sites within (a) fee, (b) bcc, and (c) hep unit cells. The positions of black spheres are the cubic close-packed lattice positions, whereas red and blue indicate octahedral and tetrahedral interstitial positions, respectively.

Interactions between second and farther neighbors were calculated in detail by Kihara and Koba. It was shown, however, that the stability of the cubic close-packed lattice does not follow from the additive potential... 

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. 

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