Structure cubic closest-packed

Figure 5.15 Anion-centered polyhedron (rhombic dodecahedron) found in the cubic closest-packed structure (a) oriented with respect to cubic axes, the c axis is vertical (b) oriented with [111] vertical (c) cation positions occupied in the sodium chloride, NaCl, structure and (id) cation positions occupied in the zinc blende (sphalerite) cubic ZnS structure.

The 17 rare-earth metals are known to adopt five crystalline forms. At room temperature, nine exist in the hexagonal closest packed structure, four in the double c-axis hep (dhep) structure, two in the cubic closest packed structure and one in each of the body-centered cubic packed and rhombic (Sm-type) structures, as listed in Table 18.1.1. This distribution changes with temperature and pressure as many of the elements go through a number of structural phase transitions. All of the crystal structures, with the exception of bep, are closest packed, which can be defined by the stacking sequence of the layers of close-packed atoms, and are labeled in Fig. 18.1.1. 

Silver crystallizes in a cubic closest packed structure. The radius of a silver atom is 1.44 A (144 pm). Calculate the density of solid silver. 

Calcium has a cubic closest packed structure as a solid. Assuming that calcium has an atomic radius of 197 pm, calculate the density of solid calcium. 

What fraction of the total volume of a cubic closest packed structure is occupied by atoms (Hint Vsp lt.rg = ynr3.) What fraction of the total volume of a simple cubic structure is occupied by atoms Compare the answers. 

The synthesis of macroscopic amounts of buckybail led to the study of many interesting properties of this molecule which continue unabated as this hook goes to press. The molecule is nearly spherical, and while the molecules tbemsdvcs pack nicely in a cubic closest packed structure, each molecule has essentially the free rotation of a ball bearing, and because of this disorder the structure could not be determined at room temperature. Being nearly spherical and ladcing bond polarities... 

Pure, sublimed buckminsterfullerene condenses in a regular face-centered cubic (= cubic closest packed) structure. Complications may occur through the presence of other fullcrcnc impurities or crystallization from a variety of solvents. Sec Hawkins, J. M. Lewis, T. A. Loren, S. D. Meyer, A. Heath, J. R. Saykally, R. J. Hollander, F. J. J. Chem. Soc., Chem. Commun. 1991,175-716, Guo. Y. Kurasawa, N. Goddard, W. A., HI Nature 1991, S5l, 464-467. 

In fact, trigonal holes are so small that they are never occupied in binary ionic compounds. Whether the tetrahedral or octahedral holes in a given binary ionic solid are occupied depends mainly on the relative sizes of the anion and cation. For example, in zinc sulfide the ions (ionic radius = 180 pm) are arranged in a cubic closest packed structure with the smaller ions (ionic radius = 70 pm) in the tetrahedral holes. The locations of the tetrahedral holes in the face-centered cubic unit cell of the ccp structure are shown in Fig. 10.36(a). Note from this figure that there are eight tetrahedral holes in the unit cell. Also recall from the discussion in Section 10.4 that there are four net spheres in the face-centered cubic unit cell. Thus there are twice as many tetrahedral holes as packed anions in the closest packed structure. Zinc sulfide must have the same number of S ions and Zn ions to achieve electrical neutrality. Thus in the zinc sulfide structure only half the tetrahedral holes contain Zn ions, as shown in Fig. 10.36(c). 

A certain form of lead has a cubic closest packed structure with an edge length of 492 pm. Calculate the value of the atomic radius and the density of lead. 

A similar trend exists for the halogens. The structure of crystalline iodine is shown in Figure 13.9. The ratios r2/r for crystalline CI2 (s), Br2 (s), and I2 (s) are 1.68, 1.46, and 1.29, respectively. Although each of the halogens is classified as a nonmetal, the percent metallic character increases down the series. Iodine is the most metallic of the group, a fact that is supported by its grayish color as a solid and its metallic reflectance. In fact, iodine can even adopt a distorted cubic closest-packed structure similar to many metallic solids when it is crystallized at high pressure. 

It has been found by experiment (Appendix IV) that eveiy crystal consists of atoms arranged in a three-dimensional pattern that repeats itself regularly. In a crystal of copper all of the atoms are alike, and they are arranged in the way shown in Figures 2-3 and 2-4. This is a way in which spheres of uniform size may be packed together to occupy the smallest volume. This structure, called the cubic closest-packed structure, was assigned to the copper crystal by W. L. Bragg in 1913. 

Similarly, for a cubic crystal the unit of structure can be taken as a cube, which when reproduced in parallel orientation would fill space to produce a cubic lattice, as shown in Figure 2-6. The unit of structure could be described, for a cubic crystal, by giving the value of the edge of the unit, a, and the values of the coordinates x, y, and z for each atom, as fractions of the edge of the unit. Thus, for the cubic closest-packed structure, represented by metallic copper, the unit of structure is cubic, with edge a = V2 X 255 pm, and with four atoms per unit, with coordinates jc = 0, y = 0. z = 0 jf = 0, y = i, z = x = i, y = 0, z = i and jr=i, y = i, z = 0, as shown in Figure 2-7. Often these coordinates are written without giving the symbols jc, y, and z it is then said that there are four copper atoms in the unit, at 0, 0, 0 0, i, i i, 0, i i, i, 0. These are called the coordinates of the atoms in the unit cube. 

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