3. Tetragonal tin (Sn) has a unit cell with lattice constants a = b = 5.82 Å and c = 3.17 Å, and interaxial angles a = ẞ= y = 90°. a. Make a perspective drawing of the unit cell of tetragonal Sn. Do not draw in any Sn atoms, just lattice points. b. Outline the planes (011) and (011) in your drawing from part (a). c. What direction is common to the (011) and (011) planes in tetragonal tin? d. Calculate the angle between the [011] and [011] directions in tetragonal tin.

Outline a two-dimensional unit cell for the pattern shown here. If the black squares are labeled A and the white squares are B, what is the simplest formula for a compound based on this pattern?

8.75 Using pentagons, draw arrangements that demonstrate low packing efficiency and higher packing efficiency.

Why is the C 60form of carbon called buckminsterfullerene?

8.98 If you know the density of material and the length of the edge of its cubic Iattice, how would you determine if it is face-centered cubic, body-centered cubic, or simple cubic Would you have to look up any information?

The density of polonium metal is 9.2 g/cm3. If the extended lattice of polonium exhibits a simple cubic unit cell, estimate the atomic radius of polonium.

The radius of tungsten is 137 pm and the density is 19.3 g/cm3. Does elemental tungsten have a face-centered cubic structure or a body-centered cubic structure?

Phase diagrams for materials that have allotropes can be more complicated than those shown in the chapter. Use the phase diagram for carbon given here to answer the following questions. (a) How many triple points are present and what phases are in equilibrium for each? (b) Is there a single point where all four phases are in equilibrium? (c) Which is more stable at high pressures, diamond or graphite? (d) Which is the stable phase of carbon at room temperature and 1 atmosphere pressure?

CaTiO3, a perovskite, has the structure below. (a) If the density of the solid is 4.10 g/cm3, what is the length of a side of the unit cell? (b) Calculate the radius of the Ti4+ ion in the center of the unit cell. How well does your calculation agree with a literature value of 75 pm? Unit cell of the perovskite CaTiO3 A sample of perovskite, iO3 FIGURE 7.11 Relative sizes of some common ions. Rodii are given in picometers (1 pm 1 1012 m). (Data taken from J. Emsley, The Elements, Clarendon Press, Oxford, 1998, 3rd edition.)

What is the relationship between the structures of buckminsterfullerene and carbon nanotubes?