Chem. 312, Au13
Problem Set 7
Not to be turned in (but important for Midterm Exam II)
1. The alloy CuAu has the ccp/fcc structure. Under certain conditions, this is an ordered
structure, with alternating layers of gold and layers of copper. Under other conditions, the
copper and gold atoms are randomly distributed, so that the odds that any given site in the
solid is occupied by a copper or a gold atom is 50/50. In solid state chemistry terms, these are
two different phases of CuAu (an organic chemist would call them isomers).
(a) Which phase is favored at higher temperatures, and which at lower temperatures? Recall
that equilibria in chemistry are determined by free energies, ΔG. Which phase -- the high
temperature or the low temperature -- has the more favorable enthalpy? Which phase has
the more favorable entropy? Does this make sense based on our intuitive concepts of
bonding and entropy?
(b) Do you think that this is a general principle, that more disordered structures should be
favored at higher temperatures?
2. As mentioned in class and in the text (section 4.8), the principle of isomorphous substitution
states that one cation can substitute for another in a lattice if they have the same charge and
differ in radii by not more than 10-20%. In light of this,
(a) Explain why the olivine minerals on the last problem set (#6) contain varying amounts of
Mg2+ with Fe2+, but not, for instance, Ca2+ with Fe2+ or Li+ with Fe2+.
(b) Most table salt (NaCl) in the U.S. is “iodized,” that is it contains iodide (a necessary
nutrient). Do you think that the iodide ions in table salt are substituted into the NaCl lattice,
or present in separate crystals of NaI or KI? Why or why not?
(c) A few years ago, a person interviewing for a faculty position at UW in the area of
environmental chemistry described a new research project to use the trace radioactive
isotopes of lead and bismuth (Pb and Bi) ions in coral as a way to date when the coral was
formed. When asked why he thought there would be trace lead or bismuth in the corals,
which are mostly CaCO3, he responded that there was a lot of cadmium, so there was likely
to be lead and bismuth as well. What do you think of his answer?
3. Sometimes an impurity ion is incorporated that does not have the same charge as the ions in
the main lattice. I’ve called this non-isomorphous substitution, but the official name is
aliovalent substitution. This occurs to a much smaller extent than isomorphous substitution,
but it still happens. For instance, there is often a little bit of Ca2+ in NaCl. How can a
crystal of NaCl with a little bit of Ca2+ still have no net charge? Give both of the possible
answers.
4. Consider an intrinsic defect in an ionic solid such as LiF or MgO, such as one anion and one
cation missing from their normal lattice positions.
(a) Does this defect make the lattice energy (an enthalpy) more favorable or less favorable?
(b) Is the enthalpic effect of a specific defect larger in LiF or MgO, if all other things are
equal? Explain, and be quantitative if possible.
(c) Is formation of such a defect entropically favorable or unfavorable?
5. Page 172 of the text states that the iron produced in a blast furnace, pig iron, is brittle. Explain
why the impurities in pig iron make it more brittle (less malleable) than pure iron.
6. Look at the paper “Temperature Dependence of Aliovalent-vanadium Doping in LiFePO4
Cathodes” K. Harrison, C. A Bridges, M. P. Paranthaman, C. Segre, J. Katsoudas, V. A.
Maroni, J. C. Idrobo, J. B. Goodenough, and A. Manthiram Chem. Mater. 2013, 25, 768–781.
Problem Set 7, p. 2
Chem. 312, Au13
This journal (Chemistry of Materials) is another of the family of journals from the American
Chemical Society. This is a complicated paper (which I don’t understand all of), but you can
answer the questions below based on just the Abstract, Introduction, and the last paragraph
before the Conclusions.
(a) This is a basic science paper, but it has a long-term technological goal. What is that goal?
(b) LiFePO4 can be thought of as an ionic compound where the counterion is phosphate (PO43–).
But it can also be thought of as a close-packed oxide lattice with Li, Fe, and P cations in the
holes. What are the oxidation states (charges) of the Li, Fe, and P cations? Which kind of hole
does each cation likely occupy? What fraction of each type of hole is filled by a cation?
(c) This compound is called “olivine” in the first line of the Abstract. We discussed olivines in
the last problem set (#6), but their composition was different. Explain why both materials can
be olivines – what is the same about them?
(d) When a battery containing a LiFePO4 cathode is charged, the Li+ is removed from the
cathode (and makes essentially lithium metal at the anode). If all the Li is removed from
LiFePO4, what is the stoichiometry of the material that remains? What oxidation state changes
occur when the cathode is oxidized? When the battery is half charged, what is the
stoichiometry (chemical formula) of the cathode?
(e) The paper discusses aliovalent doping of LiFePO4 with vanadium. The Abstract of the
paper states:
“The compositions of the as-synthesized materials were found to be LiFe1-3x/2Vx□x/2PO4 (0 ≤ x ≤
0.2) with the presence of a small number of lithium vacancies (□) charge-compensated by V4+,
not Fe3+, leading to an average oxidation state of ~3.2+ for vanadium.” I’m not sure how to
read this, what exactly the “□” means. Let’s ignore the “□x/2” for a minute and just consider the
formula LiFe1-3x/2VxPO4. Assuming that the iron is Fe2+, what is the oxidation state of the V in
this compound, based on charge balance? Note that without the □x/2, the answer won’t be +3.2.
(f) Why is LiFe1-3x/2VxPO4 considered aliovalent? Explain how charge balance is maintained
when x vanadium ions are included in the structure.
(g) Read the last paragraph before the Conclusions. Explain based on this paragraph why the
authors want to have aliovalent doping of LiFePO4. Why do they think that this will make a
better battery, in a way that perhaps isomorphous doping with an M3+ cation wouldn’t? Why is
good Li+ mobility important in a lithium battery?
7. Consider the molecular orbital (MO) drawing for H2, drawn at right.
(a) How many atomic orbitals appear in the drawing?
(b) How many molecular orbitals are formed from the atomic orbitals?
In general, what is the relationship between the number of atomic
orbitals and the number of molecular orbitals?
(c) Give MO drawings showing the electrons as appropriate for H2, H2+, and H2- (the last is
not stable). Give the bond order in each case. Which species has the strongest H–H bond?
(Bond order = ½{# electrons in bonding orbitals – # electrons in antibonding orbitals}).
8. In class we have discussed metallic bonding in the d-block elements, which to a first
approximation use the valence s and d orbitals. Aluminum, however, is a p-block
element.
(a) What are the valence orbitals for Al? How many valence electrons does it have?
(b) How filled is the s/p band for Al? Draw a rectangle representing the s/p band,
with shading to indicate how filled it is.
Problem Set 7, p. 3
Chem. 312, Au13
9. Aluminum has the face centered cubic structure. How many nearest neighbors does each Al
atom have? Next to Al in the periodic table is silicon. Elemental Si has the diamond structure
(Wulfsberg pp. 187-8). How many nearest neighbors does each Si have? How would you
describe the bonding in Al and Si? Briefly, why is there this difference?
10. The “width” of a band – the energy difference between the top (antibonding) and the bottom
(bonding) – is related to the strength of the bonding, which in turn is related to their overlap.
We have been lumping the valence s and d bands together for the transition elements, but
they could also be considered separately. In chromium, which has both 4s and 3d valence
orbitals, is the 4s band wider than the 3d band, or vise versa? [Hint: Think back to our
discussion of bonding in transition metal complexes.]
11. (a) Based on your first-hand experience with these materials, which has a larger band gap,
diamond or graphite? Explain. (Both are pure, elemental carbon; graphite is the major
component of pencil “lead.”)
(b) The band gap of a simple material is in many cases roughly related to the average of the
electronegativities of the elements present (see Wulfsberg figure 9.8, p. 335). On this basis,
which should have a higher band gap, AlN or InP?
12. (a) Will doping Ge with Ga lead to an n-doped semiconductor, a p-doped semiconductor, or
neither? (b) What about doping Si into Ge? (c) What about doping P into Ge?
13. Take a quick look at the posted article “Transparent Transistors, Printed on Paper.” This is
really about printing transistors on transparent paper; the transistors themselves don’t look
that transparent. But there is a lot of interest in materials that are transparent and also conduct
electricity. Why is this a difficult combination of properties? Refer to Ellis Figure 7.10,
reproduced as page 12 of the posted “Chem312_Au13 Lecture Figures I_…” file.