Compute the atomic packing factor for the rock salt crystal structure in which $r_{\mathrm{C}} / r_{\mathrm{A}}=0.414$.

Show that the minimum cation-to-anion radius ratio for a coordination number of 4 is 0.225.

Show that the atomic packing factor for HCP is 0.74.

Calculate the fraction of lattice sites that are Schottky defects for cesium chloride at its melting temperature $\left(645^{\circ} \mathrm{C}\right)$. Assume an energy for defect formation of 1.86 eV.

Beryllium oxide ( $\mathrm{BeO})$ may form a crystal structure that consists of an $\mathrm{HCP}$ arrangement of $\mathrm{O}^{2-}$ ions. If the ionic radius of $\mathrm{Be}^{2+}$ is $0.035 \mathrm{~nm}$, then
(a) Which type of interstitial site will the $\mathrm{Be}^{2+}$ ions occupy?
(b) What fraction of these available interstitial sites will be occupied by $\mathrm{Be}^{2+}$ ions?

The zinc blende crystal structure is one that may be generated from close-packed planes of anions. (a) Will the stacking sequence for this structure be FCC or HCP? Why? (b) Will cations fill tetrahedral or octahedral positions? Why? (c) What fraction of the positions will be occupied?

On the basis of ionic charge and ionic radii given, predict crystal structures for the following materials:

(a) CsI

(b) NiO

(c) KI

(d) NiS

Justify your selections.

For a ceramic compound, what are the two characteristics of the component ions that determine the crystal structure?

Which of the cations would you predict to form fluorides having the cesium chloride crystal structure? Justify your choices.

Briefly explain why amorphous polymers are transparent, whereas predominantly crystalline polymers appear opaque or, at best, translucent.

The atomic weight, density, and atomic radius for three hypothetical alloys are listed in the following table. For each, determine whether its crystal structure is FCC, BCC, or simple cubic and then justify your determination.

$$\begin{matrix} & \text{Atomic} & & \text{Atomic}\\ & \text{Weight} & \text{Density} & \text{Radius}\\\text{Alloy} & \mathrm{(g/mol)} & \mathrm{(g/cm^{3)}} & \text{(nm)}\\\text{A} & \text{43.1} & \text{6.40} & \text{0.122}\\ \text{B} & \text{184.4} & \text{12.30} & \text{0.146}\\\text{C} & \text{91.6} & \text{9.60} & \text{0.137}\\\end{matrix}$$

Solve the inequality. Graph your solution. -7r > 49

When the viola section of an orchestra with six members plays together, is the sound 6 times as loud as when a single viola plays? Explain. Is the intensity 6 times what it would be for a single viola? [Hint: The six sound waves are not coherent.]

Write each number in scientific notation. 0.00725