Cubic cell face-centered

Face-centered cubic cell (FCC). Here there is an atom at each comer of the cube and one in the center of each of the six faces of the cube. In this structure, atoms at the comers of the cube do not touch one another they are forced slightly apart Instead, contact occurs along a face diagonal The atom at the center of each face touches atoms at opposite comers of the face. 

Face-centered cubic cell (FCC) A cubic unit cell with atoms at each corner and one at the center of each face, 246 Fahrenheit, Daniel, 8 Fahrenheit temperature scales, 8... 

FIGURE 5.37 The calculation of the net number of atoms in a face-centered cubic cell. 

Buckminsterfullerene is an allotrope of carbon in which the carbon atoms form spheres of 60 atoms each (see Section 14.16). In the pure compound the spheres pack in a cubic close-packed array, (a) The length of a side of the face-centered cubic cell formed by buckminsterfullerene is 142 pm. Use this information to calculate the radius of the buckminsterfullerene molecule treated as a hard sphere, (b) The compound K3C60 is a superconductor at low temperatures. In this compound the K+ ions lie in holes in the C60 face-centered cubic lattice. Considering the radius of the K+ ion and assuming that the radius of Q,0 is the same as for the Cft0 molecule, predict in what type of holes the K ions lie (tetrahedral, octahedral, or both) and indicate what percentage of those holes are filled. 

Simple Cubic, Body-Centered Cubic, and Face-Centered Cubic Cells... 

The formula which relates the radius of an atom (r) to the length of the side (s) of the unit cell for a face-centered cubic cell is 4r = s/2. 

The first preparation of metallic Ac was on the microgram scale and used the metallothermic reduction (Section II,A) of AcClj with K metal vapor (38), which is the same method used by Klemm and Bommer (67) to prepare La metal. The metal produced by this method is mixed with KCl and K metal. X-Ray diffraction revealed that Ac metal was isostructural with P-La, but that the face-centered cubic cell dimension of Ac (5.311 A) was slightly larger than that of La (5.304 A). 

One could follow a similar practice and construct a similar hexagonal sandwich with two layers (B, Q of filler, but a cubic cell of higher symmetry can be. constructed the second system is thus characterized as cubic closest packed. The relation between the cubic unit cell (which is identical to the face-centered cubic cell we <... 

Figure 4.7. (a) A projection on one face of two cells of a face-centered cubic cell. The projection of the body-centered tetragonal cells is shown by dashed lines. Open and black circles show different heights in the cell, (b) The body-centered tetragonal cell. 

Figure 4.20. A projection of the face-centered cubic cell for CO2.

Figure B.l (a) The relationship of a hexagonal cell to trigonal (rhombohedral) cells. (b) the 60° rhombohedral cell related to a face-centered cubic cell.

All silver crystals have the same geometric shape. Therefore, the crystalline shape of a metallic solid is a function of the size of the metal solid atoms and their electron configuration. Each metal has its own geometric crystalline shape. Aluminum atoms pack into a face-centered cubic cell. Iron s solid structure is body-centered cubic. 

PROBLEM 7.4.4. For a monoatomic cubic crystal consisting of spherical atoms packed as close as possible, given the choices of a simple cubic crystal (SCC atom at cell edges only this structure is rarely used in nature, but is found in a-Po), a body-centered cubic crystal (BCC, atom at comers and at center of body), and a face-centered cubic crystal (FCC body at face comers and at face centers), show that the density is largest (or the void volume is smallest) for the FCC structure (see Fig. 7.12). In particular, show that the packing density of spheres is (a) 52% in a simple cubic cell (b) 68% for a body-centered cell (c) 71% for a face-centered cubic cell. 

The other types of cubic cells are the body-centered cubic cell (bcc) and the face-centered cubic cell (fee) (Figure 11.17). A body-centered cubic arrangement differs from a simple cube in that the second layer of spheres fits into the depressions of the first layer and the third layer into the depressions of the second layer (Figure 11.18). The coordination number of each sphere in this stmetnre is 8 (each sphere is in contact with four spheres in the layer above and four spheres in the layer below). In the face-centered cubic cell there are spheres at the center of each of the six faces of the cube, in addition to the eight comer spheres. 

Clearly there is more empty space in the simple cubic and body-centered cubic cells than in the face-centered cubic cell. Closest packing, the most efficient arrangement of spheres, starts with the structure shown in Figure 11.20(a), which we call layer A. Focusing on the only enclosed sphere we see that it has six immediate neighbors in that layer. In the second layer (which we call layer B), spheres are packed into the depressions between the spheres in the first layer so that all the spheres are as close together as possible [Figure 11.20(b)]. 

FIGURE 11.22 The relationship between the edge length (a) and radius (rj of atoms in the simple cubic cell, body-centered cubic cell, and face-centered cubic cell. 

Figure 11.22 summarizes the relationship between the atomic radius r and the edge length a of a simple cubic cell, a body-centered cubic cell, and a face-centered cubic cell. This relationship can be used to determine the atomic radius of a sphere if the density of the crystal is known, as the following example shows. 

When silver crystallizes, it forms face-centered cubic cells. The unit cell edge length is 408.7 pm. Calculate the density of silver. 

Calculate the number of spheres that would be found at the lattice points in the simple cubic, body-centered cubic, and face-centered cubic cells. Assume that the spheres are the same. 

A face-centered cubic cell contains 8 X atoms at the corners of the cell and 6 Y atoms at the faces. What is the empirical formula of the solid ... 

E20.10(b) The fact that the 111 reflection is the third one implies that the cubic lattice is simple, where all indices give reflections. The 111 reflection would be the first reflection in a face-centered cubic cell and would be absent from a body-centered cubic. 

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