Cubic close packing structures

The surface of a single crystal of nickel, showing the regularity of its cubic close-packed structure. 

The differing malleabilities of metals can be traced to their crystal structures. The crystal structure of a metal typically has slip planes, which are planes of atoms that under stress may slip or slide relative to one another. The slip planes of a ccp structure are the close-packed planes, and careful inspection of a unit cell shows that there are eight sets of slip planes in different directions. As a result, metals with cubic close-packed structures, such as copper, are malleable they can be easily bent, flattened, or pounded into shape. In contrast, a hexagonal close-packed structure has only one set of slip planes, and metals with hexagonal close packing, such as zinc or cadmium, tend to be relatively brittle. 

Mercury has a structure obtained by compressing the cubic close packed structure along a three-fold axis, causing the six equatorial distances (3.463 A.) to become greater than the six others (2.999 A.). The values of n are 0.11 and 0.63, respectively, leading to 72(1) = 1.440 A. The increasing weakness of the six longer bonds in the sequence zinc, cadmium, mercury is noteworthy. 

Side and expanded views of hexagonal and cubic close-packed crystal types. In the hexagonal close-packed structure, spheres on both sides of any plane are in the same positions, and the third layer is directly above the first. In the cubic close-packed structure, layers take up three different positions, and the fourth layer is directly above the first. 

In the cubic close-packed structure, the third layer is offset from the other two, but the fourth layer is directly above the first. This arrangement can be labeled ABCABC. 

Structure types have been established. Similar to Al, the M2X3 crystals (M = Ga, In, Tl X = S, Se, Te) are mostly based on M-defect tetrahedral structures, namely W (Ga2S3, In2Se3) and ZB (Ga2Se3, Ga2Te3, In2Te3). At atmospheric pressure, 283 can be present in three modifications. The low-temperature a-form is a cubic close-packed structure of S atoms, where 70% of the In atoms are randomly distributed on octahedral sites and the rest remain on tetrahedral sites. The P-form is related to the spinel structure, and the y-modification is hexagonal. 

Figure 3.11 Cubic close-packed structure of face-centered cubic crystals such as copper as a packing of atom layers (a) a single close-packed layer of copper atoms (b) two identical layers, layer B sits in dimples in layer A (c) three identical layers, layer C sits in dimples in layer B that are not over atoms in layer A. The direction normal to these layers is the cubic [111] direction.

The sequence ABCABC... having a cubic symmetry is shown in Fig. 3.21. It is the cubic (face-centred cubic) close-packed structure, also described as cF4-Cu type structure. 

Figure 3.21. The face-centred cubic close-packed structure (Cu type). On the left a block of eight cells is shown (one cell darkened). On the right a section of the structure is presented it corresponds to a plane perpendicular to the cube diagonal. Notice that the plane is the same presented on the left in Fig. 3.19. The sequence of the layers in this structure is shown in Fig. 3.20 in comparison with other close-packed elemental structures.

Several cubic structures, therefore, in which (besides 0, 0, 0 0, K, M M, 0, M M, M, 0) one or more of the reported coordinate groups are occupied could be considered as filled-up derivatives of the cubic close-packed structures. The NaCl, CaF2, ZnS (sphalerite), AgMgAs and Li3Bi-type structures could, therefore, be included in this family of derivative structures. For this purpose, however, it may be useful to note that the radii of small spheres which fit exactly into tetrahedral and octahedral holes are, respectively, 0.225. and 0.414... if the radius of the close-packed spheres is 1.0. For a given phase pertaining to one of the aforementioned types (NaCl, ZnS, etc.) if the stated dimensional conditions are not fulfilled, alternative descriptions of the structure may be more convenient than the reported derivation schemes. 

The scheme of cluster condensation or cluster fragment condensation leads eventually to structures observed in bulk metals. Particularly through extensive condensation of tetrahedral and octahedral clusters, arrangements closely related to the hexagonal and cubic close-packed structures can be obtained. Condensation also of icosahedral five-fold symmetrical clusters may be related to crystalline and quasicrystalline metallic structures. 

A large number of compounds belong to the NaCl-type structure for instance those given by the alkaline earths with O, S, Se, Te, Po, etc. and nearly all the (partially ionic-covalent and metallic) 1 1 compounds formed by the rare earths and the actinides with N, P, As, Sb, Bi, S, Se, Te, Po. Notice that this structure may also be described as a derivative of the cubic close-packed structure (cF4-Cu type) in... 

Sphalerite and wurtzite structures general remarks. Compounds isostructural with the cubic cF8-ZnS sphalerite include AgSe, A1P, AlAs, AlSb, BAs, GaAs, InAs, BeS, BeSe, BeTe, BePo, CdS, CdSe, CdTe, CdPo, HgS, HgSe, HgTe, etc. The sphalerite structure can be described as a derivative structure of the diamond-type structure. Alternatively, we may describe the same structure as a derivative of the cubic close-packed structure (cF4-Cu type) in which a set of tetrahedral holes has been filled-in. This alternative description would be especially convenient when the atomic diameter ratio of the two species is close to 0.225 see the comments reported in 3.7.3.1. In a similar way the closely related hP4-ZnO... 

As pointed out in the description of the cubic close-packed structure (cF4-Cu type), this structure may be described (especially for certain values of the atomic diameter ratio) as a derivative of the Cu-type structure in which two sets of tetrahedral holes have been filled-in. 

Cristobahte is the third crystaUine sihca form stable at high temperature. It exists between 1,470 to 1,723°C. A metastable form may exist below 1,470°C. Cristobahte has three-layer sequences of Si04. The oxygen atoms of the tetrahedral Si04 have cubic close-packed structure. Cristobahte is found in some volcanic rocks. 

Figure 1.24(c) shows a unit cell of a face-centred cubic structure. If a single atom is placed at each lattice point then this becomes the unit cell of the ccp (cubic close-packed) structure. Find the 100, 110, and the 111 planes and calculate the density of atoms per unit area for each type of plane. (Hint Calculate the area of each plane assuming a cell length a. Decide the fractional contribution made by each atom to the plane.)... 

Cu crystallizes with a cubic close-packed structure. The Bragg angles of the first two reflections in the powder pattern collected using Cu-Ka radiation are 21.6° and 25.15°. Calculate the unit cell length a, and estimate a radius for the Cu atom. 

The 100 and 111 planes are the same as the planes for the cubic-close packed structure in Question 7, Figure 1.63. The only plane that has changed is the 110 (Figure 1.64) which now has two additional atoms. Thus, the relative densities per unit area become ... 

Organic solids have received much attention in the last 10 to 15 years especially because of possible technological applications. Typically important aspects of these solids are superconductivity (of quasi one-dimensional materials), photoconducting properties in relation to commercial photocopying processes and photochemical transformations in the solid state. In organic solids formed by nonpolar molecules, cohesion in the solid state is mainly due to van der Waals forces. Because of the relatively weak nature of the cohesive forces, organic crystals as a class are soft and low melting. Nonpolar aliphatic hydrocarbons tend to crystallize in approximately close-packed structures because of the nondirectional character of van der Waals forces. Methane above 22 K, for example, crystallizes in a cubic close-packed structure where the molecules exhibit considerable rotation. The intermolecular C—C distance is 4.1 A, similar to the van der Waals bonds present in krypton (3.82 A) and xenon (4.0 A). Such close-packed structures are not found in molecular crystals of polar molecules. 

The borohydride Cr(BH4)2-2THF has been prepared from [Cr(OBu )4] and B2H6 (Section 35.3.4.2) and from CrCl3 (p. 725). CrH2 has a cubic close packed structure and in hexagonal close-packed CrH the CrH distance is 1.91 A.281 The hydride [CrH2 P(OMe)3 5] is discussed in Section 35.3.4.1. 

Q Gold crystallizes in a cubic close-packed structure, based on a cube with side a. Given that the density of metallic gold is 19.3 x 103 kg m-3 (density is mass divided by volume) and that a = 4.08 x 10-10 m, find the number of Au atoms per unit cell using the molar mass of 197Au(100%) = 197 g mol-1. Give your answer to 3 sig. figs. 

In the second arrangement, the spheres of the third layer lie in the dips of the second layer that do not lie directly over the atoms of the first layer (Fig. 5.25). If we call this third layer C, the resulting structure has an ABCABC. . . pattern of layers to give a cubic close-packed structure (ccp). The name comes from the fact that the atoms in a ccp structure form a cubic pattern (Fig. 5.26). The coordination number is also 12 each sphere has three nearest neighbors in the layer below, six in its own layer and three in the layer above. Aluminum, copper, silver, and gold are examples of metals that crystallize in this way. 

All noble gases except helium crystallize with cubic close-packed structures at very low temperatures. Find an equation relating the atomic radius to the density of a cubic close-packed solid of given molar mass and apply it to deduce the atomic radii of the noble gases, given the following densities (in g-cm-3) Ne, 1.20 Aq 1.40 Kr, 2.16 Xe, 2.83 Rn, 4.4. 

Metals with bcc structures, like tungsten, are not close packed. Therefore, their densities would be greater if they were to change to a cubic close-packed structure (under pressure, for instance). What would the density of tungsten be if it had a cubic close-packed structure rather than bcc Its actual density is... 

The third layer of spheres can now be placed on top of the second in two ways.These three layers are called A, B and C, the spheres of a layer with the same letter are placed vertically above each other. By placing the third layer vertically above the first and the fourth above the second, a packing ABABA. arises, a so-called hexagonal close-packed structure, abbreviated hep. A second possibility is a packing of the type ABCABC..., a so-called cubic close-packed structure, abbreviated ccp. Both types of packing are shown in figure 4.3. 

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