Unit cell face centered

Fig. 4.6 Crystal structure of Prl2-V. (a) The cubic face-centered unit cell, (b) One cluster Pr4 l4l,2. (c) Hexagonal setting of the structure exhibiting the close relationship to the CdCl2-type of structure.

The way to count the contents of a unit cell for the example of the face-centered unit cell of NaCl 8 Cl- ions in 8 vertices, each of which belongs to 8 adjacent cells makes 8/8 = 1 6 Cl- ions in the centers of 6 faces belonging to two adjacent cells each makes 6/2 = 3. 12 Na+ ions in the centers of 12 edges belonging to 4 cells each makes 12/4 = 3 1 Na+ ion in the cube center, belonging only to this cell. Total 4 Na+ and 4 Cl-ions or four formula units of NaCl (Z = 4). 

The structure of iodine at four different pressures. The outlined face-centered unit cell in the 30-Gpa figure corresponds to that of a (distorted) cubic closest-packing of spheres. At 24.6 GPa four unit cells of the face-centered approximant structure are shown the structure is incommensurately modulated, the atomic positions follow a sine wave with a wave length of 3.89 x c. The amplitude of the wave is exaggerated by a factor of two. Lower left Dependence of the twelve interatomic contact distances on pressure... 

In cubic closest-packing, consideration of the face-centered unit cell is a convenient way to get an impression of the arrangement of the interstices. The octahedral interstices are situated in the center of the unit cell and in the middle of each of its edges [Fig. 17.3(a)], The octahedra share vertices in the three directions parallel to the unit cell edges. They share edges in the directions diagonal to the unit cell faces. There are no face-sharing octahedra. 

Face-centered unit cell of cubic closest-packing ... 

The face-centered unit cell has particles at the corners and one in the center of each face of the cube, but not in the center of the cube itself. 

The structure of iodine at four different pressures. The outlined face-centered unit cell in the 30-Gpa figure corresponds to that of a... 

Figure 11.14. The face-centered unit cell of benzene is shown.

Face-centered unit cell Figure 1.25) contains three additional lattice points located in the middle of each face, which results in a total of four lattice points in a single face-centered unit cell. 

The assumption of randomly distributed interstitial, i.e. uncoordinated, metal ions at position 8 c is discarded. Only the positions 4 a and 4 b, the two fourfold positions of the cubic face-centered unit cell, are considered as possible sites for the two metal atoms. Consequently, the occupancies of these two sites depend on the composition of the cyano compound M [M (CN)e]r H20, more specifically, on the stoichiometric ratio k 1. Positions 4 a and 4 b are both completely occupied only when k = l—l. For all other stoichiometries, the positions assigned to M , C, and N are assumed to have occupancies less than 1, whereas position 4 a is stiU occupied by the complete set of four... 

The results of all the single-crystal investigations carried out so far for compounds M8[M (CN)e]a xTlzO are in good agreement with the postulated properties of the modified model. Position 4 a (0, 0, 0) of the cubic face-centered unit cell is fully occupied by four ions and... 

Because K and Q are isoelectronic, their scattering power to x-rays is very nearly the same, and the face-centered unit cell thus appears to be simple cubic, one-eighth as large. 

The rule for body centering is that the sum of the indices must be even to appear and are absent if the sum is odd. For face-centering the rule is the / A7 values must all be even or all odd to appear, those with mixed indices are absent. A useful summary of the nature of the several types of cubic X-ray patterns is given in Figure 19. Similar absences appear for any body and face-centered unit cell so that by indexing any powder pattern one may be able to tell the lattice type. 

No systematic absences are present for a primitive unit cell. The indices are unmixed (all indices odd or all even otherwise is called mixed ) for a side-centered unit cell showing only the k + l = 2n reflections for the A type h + l = ln for B and h + k = 2n for C. All reflections with mixed indices are missing in a face-centered unit cell, while for a body-centered unit cell all B - - - - / = odd reflections are missing. 

Figure 11.21 Exploded views of (a) a hexagonal close-packed structure and p) a cubic close-packed structure. The arrow is tilted to show the face-centered cubic unit cell more clearly. Note that this arrangement is the same as the face-centered unit cell.

What is a lattice What is a unit cell Describe a simple cubic unit cell. How many net atoms are contained in a simple cubic unit cell How is the radius of the atom related to the cube edge length for a simple cubic unit cell Answer the same questions for the body-centered cubic unit cell and for the face-centered unit cell. 

In certain of the seven crystal systems, the unit cells can contain face- or body-centered building blocks. For the cubic lattice, the body- and face-centered unit cell is shown in Figure 2.7. 

Face-centered unit cell. If we place the third layer of spheres (blue) over the white spaces in layer b (look down and right to Fignie 12.24F), the placement is different from layers a and b (an abcabc.. . pattern) and we obtain cubic closest packing, which is based on the face-centered cubic unit ceU. 

Figure 12.28 Cubic closest packing (face-centered unit cell) of frozen CH4.

Because there are four atoms in a face-centered unit cell having one atom at each lattice point (see Example 11.9), the mass of a silver atom is... 

Nickel has a face-centered unit cell with all atoms at lattice points and an edge length of 352.4 pm. The density of metallic nickel is 8.91 g/cm. What is the mass of a nickel atom From the atomic weight, calculate Avogadro s number. 

In either case, it is easy to show that the ratio of ions in the unit cell is 1 1. The two possible face-centered unit cells are consistent with a 1 1 ion ratio in the formula for the compound. The particular structure, however, depends on the relative sizes of the ions. 

Fig. 11.12 The cubic unit cells. The letter P denotes a primitive unit cell, I a body-centered unit ceU, and F a face-centered unit cell.

Fig. 10.17. Left is the fullerene structure of C 60 and right shows the face-centered unit cell with fullerene structured carbon atoms at the eight corners and at the center of the six faces...

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