Face-centered cubic array

In an ionic solid, the coordination number means the number of ions of opposite charge immediately surrounding a specific ion. In the rock-salt structure, the coordination numbers of the cations and the anions are both 6, and the structure overall is described as having (6,6)-coordination. In this notation, the first number is the cation coordination number and the second is that of the anion. The rock-salt structure is found for a number of other minerals having ions of the same charge number, including KBr, Rbl, MgO, CaO, and AgCl. It is common whenever the cations and anions have very different radii, in which case the smaller cations can fit into the octahedral holes in a face-centered cubic array of anions. The radius ratio, p (rho), which is defined as... 

Three views of the hexagonal layers contained within a face-centered cubic array, (a) A view perpendicular to the hexagonal layers, with all but one atom removed from the top layer. (Z>) A side view showing an outline of the cube and atoms from three successive layers of the cubic array, (c) The same side view, with two hexagonal layers screened for emphasis. 

For many 1 1 ionic crystais such as NaCi, the most stabie arrangement is a face-centered cubic array of anions with the cations packed into the hoies between the anions. This structure appears in Figure 11-32. In addition to... 

Cations occupies octahedral holes of a face centered cubic array of anions... 

The porous membrane templates described above do exhibit three-dimensionality, but with limited interconnectedness between the discrete tubelike structures. Porous structures with more integrated pore—solid architectures can be designed using templates assembled from discrete solid objects or su-pramolecular structures. One class of such structures are three-dimensionally ordered macroporous (or 3-DOM) solids, which are a class of inverse opal structures. The design of 3-DOM structures is based on the initial formation of a colloidal crystal composed of monodisperse polymer or silica spheres assembled in a close-packed arrangement. The interconnected void spaces of the template, 26 vol % for a face-centered-cubic array, are subsequently infiltrated with the desired material. 

The easiest way is to take a face-centered cubic array (Fig. 4.14c). and by removing I... 

In 1991, scientists at AT T Bell Laboratories discovered a new class of high-temperature superconductors based on fullerene, the allotrope of carbon that contains Cgo molecules (Sections 10.10 and 19.6). Called "buckyballs," after the architect R. Buckminster Fuller, these soccer ball-shaped Cgo molecules react with potassium to give K3C6o- This stable crystalline solid contains a face-centered cubic array of buckyballs, with K+ ions in the cavities between the Cgo molecules (Figure 21.16). At room temperature, K3Q,o is a metallic conductor, but it becomes a superconductor at 18 K. The rubidium fulleride, Rb C o, and a rubidium— thallium-Cfio compound of unknown stoichiometry have higher Tc values of 30 K and 45M8 K, respectively. 

Figure 5 Spinel structure, AB2O4, composed of eight octants of alternating AO4 tetrahedra and B2O4 cubes. The four oxygen atoms have the same orientation in all octants and therefore build up a face-centered cubic lattice of 32 ions. The four A octants contain four A ions while the four B octants contain 16 B ions. The unit cell is completed by a surrounding face-centered cubic array of 14 A ions. These are shared with adjacent unit cells and comprise the remaining four A ions required for the stoichiometry AgBi6032...

The structure of the compound CaF2 can be described as a face-centered cubic array of Ca2+ ions with the F ions in all the tetrahedral holes. This gives the required 1 2 ratio of Ca2+ and F ions. This structure is called the fluorite structure [see Fig. 16.41(d)] and is also observed in the compounds SrF2, BaCl2, PbF2, and CdF2, among others. 

One could follow a similar practice and construct a similar hexagonal sandwich with two layers (B, Q of fiHer, but a cuImc cell of higher symmetry can be constructed the second system is thus charact ized as cubic closest packed. The relation between the cubic unit cell (which is identical to the face-centered cubic cell we have already seen) is not easy to visualize unless one is quite familiar with this system. The easiest way is to take a face-centered cubic array (Fig. 4.14c). and by removing... 

The Ca " ions in fluorite are in a face-centered cubic arrangement. This lattice has, in addition to the octahedral holes mentioned earlier, holes that are tetrahedrally coordinated. The tetrahedral holes of the fee structure are occupied by F ions in fluorite. Each F" ion is tetrahedrally coordinated to Ca " ions. Figure 27.10(a) also shows that the Ca " ion on the top face is connected to four F ions below it it is similarly connected to four F ions (not shown) lying above it. The coordination of the Ca " ion is eight, and the fluorite structure is described as having 8-4 coordination. Fluorite may be considered as a face-centered cubic array of Ca " ions interpenetrated by a simple cubic array of F ions. 

Figure 18. The unrelaxed structure of the (100) surface of galena. Both Pb and S are equally arranged in a face-centered cubic array across the siuface. Perpendicular to the surface plane, the surface can be seen to be built up from stacks of charge neutral atomic planes. The sitrface is type 1 and electrostatically stable (see Fig. 3).

For most applications Equation (8.24) may be adequate since the advantages of more complex models have not been extensively verified. The porosities for body-center cubic array (BCC) and face-center cubic array (FCC) are in the range of 0.3-0.25 and 0.2, respectively (Figure 8.5). 

Nickel atoms form a face-centered cubic array (fee). In fact, using a simpler notation, we can describe the crystalline array of nickel only with the coordinates... 

In the sohd state, the units form a crystalline structure and pack together in a face-centered cubic array. This material is called and Table 13.4 lists some of its properties. 

The parameter a is the ratio of the conductivity of the dispersed phase to that of the continuous phase. Meredith and Tobias extended this result to higher-order terms. Zuzovsky and Brenner used a multipole expansion technique to calculate the effective conductivity of simple cubic, body-centered cubic, and face-centered cubic arrays of spheres. Their technique allowed for fourfold symmetry in the arrays, while those of previous authors did not. McPhe-dran and McKenzie and McKenzie, McPhedran, and Derrick extended Rayleigh s method for calculating the conductivities of lattices of spheres. Their method includes the effects of multipoles of arbitrarily high order specifically, their equation gives the numerical value of the / -order term referred to by Zuzovsky and Brenner. Sangani and Acrivos also used a fourfold potential to calculate effective conductivities of simple cubic, body-centered cubic, and face-centered cubic lattices to 0(/ ). They corrected a numerical slip in the work of Zuzovsky and Brenner. Their equation is... 

Buckminsterfullerene C,jq crystallizes in a face-centered cubic array. If potassium atoms fill all the tetrahedral and octahedral holes, what is the formula of the resulting compound ... 

Solid CaC2 can be regarded as a face-centered cubic array of Ca ions with the C2 ions in the octahedral holes, as shown in the figure in the margin. 

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