Face-centered cubic unit

Three types of unit cells. In each case, there is an atom at each of the eight corners of the cube. In the body-centered cubic unit cell, there is an additional atom in the center of the cube. In the face-centered cubic unit cell, there is an atom in the center of each of the six faces. 

Lead (atomic radius = 0.181 nm) crystallizes with a face-centered cubic unit cell. What is the length of a side of the cell ... 

In the LiCl structure shown in Figure 9.18, the chloride ions form a face-centered cubic unit cell 0.513 nm on an edge. The ionic radius of Cl- is 0.181 nm. 

FIGURE 5.43 Hie zinc-blende (sphalerite) structure, rhe tour zinc ions (pink) form a tetrahedron within a face-centered cubic unit cell composed of sulfide ions (vellow).The zinc ions occupy half the tetrahedral holes between the sulfide ions, and the parts or the unit cell occupied by zinc ions are shaded blue. The detail shows how each zinc ion is surrounded by four sulfide ions each sulfide ion is similarly surrounded by four zinc ions. 

Krypton crystallizes with a face-centered cubic unit cell of edge 559 pm. (a) What is the density of solid krypton (b) What is the atomic radius of krypton (c) What is the volume of one krypton atom (d) What percentage of the unit cell is empty space if each atom is treated as a hard sphere ... 

The high-temperature contribution of vibrational modes to the molar heat capacity of a solid at constant volume is R for each mode of vibrational motion. Hence, for an atomic solid, the molar heat capacity at constant volume is approximately 3/. (a) The specific heat capacity of a certain atomic solid is 0.392 J-K 1 -g. The chloride of this element (XC12) is 52.7% chlorine by mass. Identify the element, (b) This element crystallizes in a face-centered cubic unit cell and its atomic radius is 128 pm. What is the density of this atomic solid ... 

For a face-centered cubic unit cell, the diagonal of a face is the hypotenuse of a right triangle and equals 4r where r is the radius of an Ir atom. From the Pythagorean Theorem,... 

A face-centered cubic unit cell contains 4 atoms ... 

The sodium chloride structure, AX systems. Cubic Fm3m (Space Group 225) The sodium chloride or rock salt, NaCl, structure has a simple face-centered cubic unit cell (Figure 8) with alternating cations-anions along the three cubic axes. 

FIGURE 5.27 The relation of the dimensions of a face-centered cubic unit cell to the radius, r, of the spheres. The spheres are in contact along a face diagonal. Four unit cells are shown here. 

Both calcium and strontium crystallize in face-centered cubic unit cells. Determine which metal is more dense, calcium or strontium, given that their radii are 197 pm and 215 pm, respectively. The molar mass of Ca is 40.08 g-mol 1 and that of Sr is 87.62 g-mol (See Section 5.10.)... 

Cubic closest-packing uses a face-centered cubic unit cell. Looking at any one face of the cube head-on shows that the face atoms touch the corner atoms along the diagonal... 

Nickel has a face-centered cubic unit cell with a length of 352.4 pm along an edge. What is the density of nickel in g/cm3 ... 

FIGURE 10.24 The unit cell of NaCl in both (a) a skeletal view and (b) a space-filling view in which one face of the unit cell is viewed head-on. The larger chloride anions adopt a face-centered cubic unit cell, with the smaller sodium cations fitting into the holes between adjacent anions. 

Sodium hydride, NaH, crystallizes in a face-centered cubic unit cell similar to that of NaCl (Figure 10.24). How many Na+ ions touch each H ion, and how many H- ions touch each Na+ ion ... 

Silver metal crystallizes in a face-centered cubic unit cell with an edge length of 408 pm. The molar mass of silver is 107.9 g/mol, and its density is 10.50 g/cm3. Use these data to calculate a value for Avogadro s number. 

A ceramic work of art is constructed by hand and formed into a predetermined shape. A crystalline solid grows to a assume a predetermined shape. Aluminum atoms always pack into a face-centered cubic unit. 

The mixed-metal oxide spinel, MgA fTt, is one of the most important inorganic materials. The structure of spinel can be regarded as a ccp structure of O2-anions with Mg2+ ions orderly occupying /8 of the tetrahedral interstices, and Al3+ ions orderly occupying half of the octahedral interstices the remainder 7/x tetrahedral interstices and half octahedral interstices are unoccupied. The sites of the three kinds of ions in the face-centered cubic unit cell are displayed in Fig. 9.6.29. 

A metastable crystalline phase of carbon atoms, consisting of a face-centered cubic unit cell with a parameter of 0.3563 nm, was found in either thin films or nanoparticles [18]. 

The fluorite structure has been described in terms of a face-centered-cubic unit cell containing four units of M02. Table I lists the lattice parameters for these substances. 

Figure 1.5. The rocksalt (halite) face-centered-cubic unit cell, with lattice parameter a.

The aba arrangement has the hexagonal unit cell shown in Fig. 16.14, and the resulting structure is called the hexagonal closest packed (hep) structure. The abc arrangement has a face-centered cubic unit cell, as shown in Fig. 16.15 on page 779, and the resulting structure is called the cubic closest packed (ccp) structure. Note that in the hep structure the spheres in every other layer occupy the same vertical position (ababab. . . ), while in the ccp structure the spheres in every fourth layer occupy the same vertical position (abcabca. . . ). A characteristic of both structures is that each sphere has 12 equivalent nearest... 

Knowing the net number of spheres (atoms) in a particular unit cell is important for many applications involving solids. To illustrate the procedure for finding the net number of spheres in a unit cell, let s consider a face-centered cubic unit cell (Fig. 16.17). Note that this unit cell is defined by the centers of the spheres on the cube s corners. Thus 8 cubes share a given sphere, so j of this sphere lies inside each unit cell. Since a cube has 8 corners, there are 8 X pieces, or enough to put together 1 whole sphere. The spheres at the center of each face are shared by 2 unit cells, so of each lies inside a particular unit cell. Since the cube has 6 faces, we have 6 X f pieces, or enough to construct 3 whole spheres. Thus the net number of spheres in a face-centered cubic unit cell is... 

The net number of spheres in a face-centered cubic unit cell, (a) Note that the sphere on a corner of the colored cell is shared with 7 other unit cells. Thus l of such a sphere lies within a given unit cell. Since there are 8 corners in a cube, there are 8 of these pieces, the equivalent of 1 net sphere, (b) The sphere on the center of each face is shared by two unit cells, and thus each unit cell has of each of these types of spheres. There are 6 of these spheres, yielding 3 net spheres, (c) Thus the face-centered cubic unit cell contains 4 net spheres. 

Since the net number of atoms in a face-centered cubic unit cell is 4, there are 4 silver atoms in a volume of 6.74 X 10-23 cm3. Therefore... 

Before we consider specific compounds, we need to consider the locations and relative numbers of tetrahedral and octahedral holes in the closest packed structures. The location of the tetrahedral holes in the face-centered cubic unit cell of the ccp structure is shown in Fig. 16.41(a). Note from this figure that there are eight tetrahedral holes in the unit cell. Recall from the discussion in Section 16.4 that there are four net spheres in the face-centered cubic unit cell. Thus there are twice as many tetrahedral holes as there are packed spheres in the closest packed structure. 

The location of the octahedral holes in the face-centered cubic unit cell is shown in Fig. 16.42(a). The easiest octahedral hole to find in this structure is the one at the center of the cube. Note that this hole is surrounded by six spheres, as is required to form an octahedron. Since the remaining octahedral holes are shared with other unit cells, they are more difficult to visualize. However, it can be shown that the number of octahedral holes in the ccp structure is the same as the number of packed spheres. 

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