Chapter 18

Explain the difference between cubic closest-packed and hexagonal closest- packed arrangements of identical spheres.

Is it possible to have a closest-packed crystal lattice with four different repeating layers, \(abcdabcd\)...?

Which unit cell has the greater packing efficiency, simple cubic or body- centered cubic?

The unit cell in iron metal is either fec or bec, depending on temperature (see Sample Exercise 18.1 ). Are the fcc and the bcc forms of iron allotropes? Explain your answer.

At low temperatures, the unit cell of calcium metal is found to be fec. At higher temperatures, the unit cell of calcium metal is bec. What might be a reason for this temperature dependence?

Europium is a lanthanide element that is used in the phosphors in fluorescent lamps. Metallic Eu forms bcc unit cells with an edge length of \(240.6 \mathrm{pm}\) Use this information to calculate the radius of a europium atom.

Nickel has an fcc unit cell with an edge length of \(350.7 \mathrm{pm}\). Use this information to calculate the radius of a nickel atom.

What is the length of an edge of the unit cell when barium (atomic radius \(222 \mathrm{pm}\) ) crystallizes in a crystal lattice of bcc unit cells?

What is the length of an edge of the unit cell when aluminum (atomic radius \(143 \mathrm{pm}\) ) crystallizes in a crystal lattice of fcc unit cells?

A crystalline form of copper has a density of \(8.95 \mathrm{g} / \mathrm{cm}^{3} .\) If the radius of copper atoms is \(127.8 \mathrm{pm},\) is the copper unit cell (a) simple cubic, (b) body-centered cubic, or (c) face-centered cubic?

A crystalline form of molybdenum has a density of \(10.28 \mathrm{g} / \mathrm{cm}^{3}\) at a temperature at which the radius of a molybdenum atom is \(139 \mathrm{pm}\). Which unit cell is consistent with these data: (a) simple cubic, (b) body-centered cubic, or (c) face-centered cubic?

Is there a difference between a solid solution and a homogeneous alloy?

White gold was originally developed to give the appearance of platinum. One formulation of white gold contains \(25 \%\) nickel and \(75 \%\) gold. Which is more malleable, white gold or pure gold?

Explain why an alloy that is \(28 \%\) Cu and \(72 \%\) Ag melts at a lower temperature than the melting points of either Cu or \(\mathrm{Ag}\)

Is it possible for an alloy to be both substitutional and interstitial?

The nibs on some fountain pens were made from an alloy called Osmiroid that contains osmium and iridium. Using only the periodic table as a guide, do you expect osmium and iridium to form a substitutional or an interstitial alloy?

The unit cell of an intermetallic compound consists of a face-centered cube that has an atom of element X at each corner and an atom of element \(Y\) at the center of each face. a. What is the formula of the compound? b. What would be the formula if the positions of the two elements were reversed in the unit cell?

The bec unit cell of an intermetallic compound has atoms of element \(A\) at the corners of the unit cell and an atom of element \(\mathrm{B}\) at the center of the unit cell. a. What is the formula of the compound? b. What would be the formula if the positions of the two elements were reversed in the unit cell?

Vanadium and carbon form vanadium carbide, an interstitial alloy. Given the atomic radii of \(\mathrm{V}(135 \mathrm{pm})\) and \(\mathrm{C}(77 \mathrm{pm}),\) which holes in a cubic closest-packed array of vanadium atoms do you think the carbon atoms are more likely to occupy-octahedral or tetrahedral?

Dental fillings are mixtures of several alloys, including one made of silver and tin. Silver \((r=144 \mathrm{pm})\) and \(\operatorname{tin}(r=140 \mathrm{pm})\) both crystallize in an fcc unit cell. Is this alloy likely to be a substitutional alloy or an interstitial alloy?

Surfaces Plasma nitriding is a process for embedding nitrogen atoms in the surfaces of metals that hardens the surfaces and makes them more corrosion resistant. Do the nitrogen atoms in the nitrided surface of a sample of cubic closest-packed iron fit in the octahedral holes of the crystal lattice? (Assume that the atomic radii of \(\mathrm{N}\) and \(\mathrm{Fe}\) are \(75\) and \(126 \mathrm{pm}\), respectively.)

A number of crystalline transition metals (including titanium, zirconium, and hafnium) can store hydrogen as metal hydrides for use as fuel in a hydrogen- powered vehicle. Are the H atoms (radius \(37 \mathrm{pm}\) ) more likely to be in the tetrahedral or octahedral holes of these three metals whose atomic radii are \(147,160,\) and \(159 \mathrm{pm},\) respectively?

An interstitial alloy is prepared from metals \(\mathrm{A}\) and \(\mathrm{B}\), where \(\mathrm{B}\) has the smaller atomic radius. The unit cell of metal \(\mathrm{A}\) is fec. What is the formula of the alloy if \(\mathrm{B}\) occupies (a) all of the octahedral holes; (b) half of the octahedral holes; (c) half of the tetrahedral holes?

An interstitial alloy with a fcc unit cell contains one atom of B for every five atoms of host element A. What fraction of the octahedral holes is occupied in this alloy?

If the unit cell of an interstitial alloy of vanadium and carbon has the same edge length as the unit cell of vanadium, will the alloy have a greater density than vanadium?

How does the sea-of-electrons model (Chapter 4 ) explain the high electrical conductivity of gold?

How does band theory explain the high electrical conductivity of mercury?

The melting and boiling points of sodium metal are much lower than those of sodium chloride. What does this difference reveal about the relative strengths of metallic bonds and ionic bonds of the alkali metals?

Which metal do you expect to have the higher melting point- Al or Na? Explain your answer.

Some scientists believe that the solid hydrogen that forms at very low temperatures and high pressures may conduct electricity. Is this hypothesis supported by band theory?

Would you expect solid helium to conduct electricity?

Which groups in the periodic table contain metals with filled valence bands?

Insulators are materials that do not conduct electricity; conductors are substances that allow electricity to flow through them easily. Rank the following in order of increasing band gap: semiconductor, insulator, and conductor.

Why is it important to keep phosphorus out of silicon chips during their manufacture?

How might doping of silicon with germanium affect the conductivity of silicon?

Antimony (Sb) combines with sulfur to form the semiconductor compound \(\mathrm{Sb}_{2} \mathrm{S}_{3} .\) In which group of the periodic table might you find elements for doping \(\mathrm{Sb}_{2} \mathrm{S}_{3}\) to form a p-type semiconductor?

In which group of the periodic table might you find elements for doping \(\mathrm{Sb}_{2} \mathrm{S}_{3}\) to form an \(\mathrm{n}\) -type semiconductor?

The nitride ceramics AIN, GaN, and InN are all semiconductors used in the microelectronics industry. Their band gaps are \(580.6,322.1,\) and \(192.9 \mathrm{kJ} / \mathrm{mol},\) respectively. Which, if any, of these energies correspond to radiation in the visible region of the spectrum?

Molecules of \(\mathrm{S}_{8}\) are not flat octagons- -why?

Selenium exists either as \(\mathrm{Se}_{8}\) rings or in a structure with helical chains of Se atoms. Are these two structures of selenium allotropes? Explain your answer.

Ice is a molecular solid. However, theory predicts that, under high pressure, ice (solid \(\mathrm{H}_{2} \mathrm{O}\) ) becomes an ionic compound composed of \(\mathrm{H}^{+}\) and \(\mathrm{O}^{2-}\) ions. The proposed unit cell for ice under these conditions is a bec unit cell of oxygen ions with hydrogen ions in holes. a. How many \(\mathrm{H}^{+}\) and \(\mathrm{O}^{2-}\) ions are in each unit cell? b. Draw a Lewis structure for "ionic" ice.

Kurt Vonnegut's novel Cat's Cradle describes an imaginary, high-pressure form of ice called "ice nine." Assuming ice nine has a cubic closest-packed arrangement of oxygen atoms with hydrogen atoms in the appropriate holes, what type of hole will accommodate the H atoms?

A chemical reaction between \(\mathrm{H}_{2} \mathrm{S}_{4}\) and \(\mathrm{S}_{2} \mathrm{Cl}_{2}\) produces cyclic \(S_{6} .\) What are the bond angles in \(S_{6} ?\)

Crystals of both \(\mathrm{LiCl}\) and $$\mathrm{KCl}$$ have the rock salt structure. In the unit cell of \(\mathrm{LiCl}\), adjacent $$\mathrm{Cl}^{-}$$ ions touch each other. In $$\mathrm{KCl}$$ they don't. Why?

Can $$\mathrm{CaCl}_{2}$$ have the rock salt structure?

In the crystals of ionic compounds, how do the relative sizes of the ions influence the location of the smaller ions?

Instead of describing the unit cell of \(\mathrm{NaCl}\) as a fcc array of \(\mathrm{Cl}^{-}\) ions with \(\mathrm{Na}^{+}\) ions in octahedral holes, might we describe it as an fcc array of \(\mathrm{Na}^{+}\) ions with \(\mathrm{Cl}^{-}\) ions in octahedral holes? Explain why or why not.

Why isn't crystalline sodium chloride considered a network solid? Why isn't sodium chloride considered an alloy of sodium and chlorine?

As the cation-anion radius ratio increases for an ionic compound with the rock salt crystal structure, is the calculated density more likely to be greater than or less than the measured value?

As the cation-anion radius ratio increases for an ionic compound with the rock salt crystal structure, is the length of the edge of the unit cell calculated from ionic radii likely to be greater than or less than the observed edge length?