A compound of cadmium, tin, and phosphorus is used in the fabrication of some semiconductors. It crystallizes with cadmium occupying one-fourth of the tetrahedral holes and tin occupying one-fourth of the tetrahedral holes in a closest packed array of phosphide ions. What is the formula of the compound? Explain your answer.

Like ZnS, lead(II) sulfide, PbS (commonly called galena), has a 1:1 empirical formula with a 2+ cation combined with the sulfide anion. Unit cell of PbS Sample of galena Does PbS have the same solid structure as ZnS? If different, how are they different? How is the unit cell of PbS related to its formula?

Which of the following elements reacts with sulfur to form a solid in which the sulfur atoms form a closest packed array with all of the octahedral holes occupied: Li, Na, Be, Ca, or Al?

You are given a small bar of an unknown metal X. You find the density of the metal to be 10.5 g/cm3. An X-ray diffraction experiment measures the edge of the face-centered cubic unit cell as 4.09 (1 = 1010 m). Identify X.

The structures of another class of ceramic, high-temperature superconductors are shown in figures a-d. a. Determine the formula of each of these four superconductors. b. One of the structural features that appears to be essential for high-temperature superconductivity is the presence of planar sheets of copper and oxygen atoms. As the number of sheets in each unit cell increases, the temperature for the onset of superconductivity increases. Order the four structures from lowest to the highest superconducting temperature. c. Assign oxidation states to Cu in each structure assuming Tl exists as Tl3+. The oxidation states of Ca, Ba, and O are assumed to be + 2, + 2, and 2, respectively. d. It also appears that copper must display a mixture of oxidation states for a material to exhibit superconductivity. Explain how this occurs in these materi.als as well as in the superconductor in Exercise 87.

(a) Determining an Atom Radius from Lattice Dimensions: Gold has a face-centered unit cell, and its density is 19.32 g/cm3. Calculate the radius of a gold atom. (b) The Structure of Solid Iron: Iron has a density of 7.8740 g/cm3, and the radius of an iron atom is 126 pm. Verify that solid iron has a body-centered cubic unit cell. (Be sure to note that the atoms in a body-centered cubic unit cell touch along the diagonal across the cell. They do not touch along the edges of the cell.) (Hint: The diagonal distance across the unit cell = edge 3.)

The memory metal, nitinol, is an alloy of nickel and titanium. It is called a memory metal because after being deformed, a piece of nitinol wire will return to its original shape. The structure of nitinol consists of a simple cubic array of Ni atoms and an inner penetrating simple cubic array of Ti atoms. In the extended lattice, a Ti atom is found at the center of a cube of Ni atoms; the reverse is also true. a. Describe the unit cell for nitinol. b. What is the empirical formula of nitinol? c. What are the coordination numbers (number of nearest neighbors) of Ni and Ti in nitinol?

Consider the three types of cubic units cells. (a) Assuming that the spherical atoms or ions in a primitive cubic unit cell just touch along the cubes edges, calculate the percentage of occupied space within the unit cell. (Recall that the volume of a sphere is (4/3)r3, where r is the radius of the sphere.) (b) Compare the percentage of occupied space in the primitive cell (pc) with the bcc and fcc unit cells. Based on this, will a metal in these three forms have the same or different densities? If different, in which is it most dense? In which is it least dense?

Materials containing the elements Y, Ba, Cu, and O that are superconductors (electrical resistance equals zero) at temperatures above that of liquid nitrogen were recently discovered. The structures of these materials are based on the perovskite structure. Were they to have the ideal perovskite structure, the superconductor would have the structure shown in pant (a) of the following figure. a. What is the formula of this ideal perovskite material? b. How is this structure related to the perovskite structure shown in Exercise 85? These materials, however, do not act as superconductors unless they are deficient in oxygen. The structure of the actual superconducting phase appears to be that shown in pan (b) of the figure. c. What is the formula of this material?