KEY
SECOND MIDTERM EXAM
Chemistry 465
Professor Buhro
2 April 2009
__________________________________
Signature
__________________________________
Print Name Clearly
ID Number:_______________________
Information. This is a closed-book exam; no books, notes, other students, other student exams,
or any other resource materials may be consulted or examined during the exam period.
Calculators are permitted. Partial credit will be given for partially correct reasoning in support
of incorrect or correct final answers. Additional space for answers is provided at the end of this
exam; please clearly label any answers you place there. Please find “Potentially Useful
Information” attached as the last pages of this exam.
1.
____________________________ (20 pts)
2.
____________________________ (18 pts)
3.
____________________________ (32 pts)
4.
____________________________ (10 pts)
5.
____________________________ (10 pts)
6.
____________________________ (10 pts)
______________________________________________________
Total ____________________________ (100 pts)
1
1. 20 total pts. The compound LiFePO4 has recently emerged as an excellent potential cathode
material for commercial lithium-ion batteries. LiFePO4 exhibits an orthorhombic, olivine
structure built from phosphate tetrahedra and FeO6 octahedra, as shown below. Two
diagrams of the structure are given, in nearly identical crystallographic orientations.
Information for this question was taken from M. S. Islam et al. (Chem. Mater. 2005, 17,
5085) and G. Rousse et al. (Chem. Mater. 2003, 15, 4082).
Li
O
(a) 02 pts. Does LiFePO4 exhibit a layered structure? Yes or No (Please circle one.)
(b) 02 pts. Is this compound electrically conductive? Yes or No (Please circle one.)
(c) 02 pts. Please complete the reaction (chemical equation) below to describe the chargedischarge cycle for a LiFePO4 cathode:
LiFePO4
Li + FePO4
(d) 02 pts. In the reaction above is the battery discharging from right to left or left to right?
(Please circle the correct response.)
(e) 03 pts. Does the oxidation state of any element in LiFePO4 change during the chargedischarge cycle? If so, please name the element and identify the oxidation states that
participate in the cycle.
Yes; Fe(II) and Fe(III)
2
1. Continued
(f) 03 pts. The operating voltage (3.5 V) of the LiFePO4 lithium-ion battery is nearly as high as
that of the Sony cell having a LiCoO2 cathode (3.7 V). Please explain why the LiFePO4
cathode is able to provide a comparably high operating voltage.
The operating voltage is largely determined by the energy at the top of the
valence band of the cathode material, in this case FePO4. This energy is
determined by the oxygen atoms in the phosphate ions. Thus, the phosphate
material behaves as a pseudo-oxide in its electronic structure.
(g) 03 pts. The lithium-ion conductivity in LiFePO4 is highly anisotropic, occurring
preferentially along the [010] direction of the crystal structure. Please describe the structural
nature of the ion-conduction pathways in LiFePO4.
The ions conduct through the [010] tunnels evident in the crystal structure.
(h) 03 pts. Please identify another ion-conducting solid that has ion-conduction pathways of a
similar nature. Write your answer on the line below.
Na--alumina
3
2. 18 total pts. (a) 10 pts. Please consider the hypothetical crystal structures represented below,
each of which is based on a tetragonal unit cell. For each, please circle the reflections that
are systematically absent.
100
100
010
010
001
001
200
200
020
020
002
002
M
100
100
010
010
X
001
001
200
200
020
020
002
002
M
100
010
z
X
001
y
200
020
x
002
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2. Continued
(b) 08 pts. Imagine two compounds that exhibit zinc-blende structures, MX, and M’X’. The
formula weight of the MX compound is only half the formula weight of M’X’. However, the
two compounds exhibit an identical lattice parameter a. Please circle every incorrect
statement below:
i)
The XRD patterns of MX and M’X’ exhibit the same systematic absences (having
the same hkl indices).
ii)
The XRD patterns of the two compounds are indistinguishable.
iii)
M’X’ scatters x-rays more efficiently than does MX.
iv)
The ratio of the intensities of the 111 reflections in M’X’ vs. MX equals the ratio of
the intensities for every matching hkl pair of reflections in M’X’ and MX.
v)
Although the XRD patterns of MX and M’X’ exhibit the same hkl reflections, those
for the lighter MX compound are shifted to higher 2 values.
vi)
Although the XRD patterns of MX and M’X’ exhibit the same hkl reflections, those
for the lighter MX compound are shifted to lower 2 values.
vii) Every reflection present in the pattern of MX is also present in M’X’.
viii) Some of the strong reflections in the XRD pattern of MX may be barely visible in
the pattern of M’X’.
3. 32 total pts. (a) 10 pts. Please label each region on the AB phase diagram below, and
provide the component composition, identity(ies) and composition(s) of the phase(s) present,
and the phase composition at point p.
At point p:
Component composition:
L
A s.s.
+L
26% A and 74% B
___________________________________
B s.s.
+L
T
A s.s.
A s.s.
+
B s.s.
Composition(s) of phase(s) present:
B s.s.: 35% A and 65% B
___________________________________
p
L: 19% A and 81% B
___________________________________
B s.s.
Phase composition:
50% B s.s. and 50% L
___________________________________
A
B
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3. Continued. Now please consider the Ti–B phase diagram shown below and provide the
requested information:
l
A
C
i
j
k
H
m
D
E
n
B
F
G
(b) 08 pts. Please identify the regions marked “A – H”.
A
TiB2 s.s. + L
E
TiB s.s. + -Ti
B
TiB2 s.s. + L
F
TiB + Ti3B4
C
TiB s.s. + L
G
TiB2 s.s. + Ti3B4
D
TiB s.s. + -Ti s.s.
H
TiB2 s.s. + -B s.s.
[1 pt. each correct
answer; “s.s.” may be
omitted]
(c) 06 pts. Please identify the points marked “i – n”.
i (1540 oC)
eutectic
l (3225 oC)
incongruent mp
or peritectic
o
k (~2200 C) incongruent mp
or peritectic
congruent mp
m (2080 oC) eutectic
j (~2160 oC)
n (884 oC)
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solid-solid phase
transition
[1 pt. each correct
answer]
(d) 04 pts. Please identify all line compounds on the Ti–B phase diagram. If none are present,
give “none” as your answer.
Ti3B4
(e) 04 pts. Please identify all phases on the diagram that are shown to have a lower temperature
limit of stability. If no such phases are present, give “none” as your answer.
Liquid and -Ti [2 pts. each]
4. 10 total pts. Imagine a hypothetical two-dimensional universe (a “Flatland”) in which the
structure of NaCl would be that shown below, having Na+ and Cl– ions arranged within a
plane and having a square lattice with equal separations between nearest neighbors in the x
and y directions. Consider calculation of the Madelung constant A for this hypothetical
structure. Please write the first six (6) terms of the infinite series that converges (ultimately)
to the Madelung constant for the two-dimensional NaCl crystal. Hint: you may wish to
choose a unit cell.
+
–
+
–
+
–
+
–
–
+
–
+
–
+
–
+
+
–
+
–
+
–
+
–
–
+
–
+
–
+
–
+
+
–
+
–
+
–
+
–
–
+
–
+
–
+
–
+
+
–
+
–
+
–
+
–
–
+
–
+
–
+
–
+
4
4
2

8
5

4 4
4
 
2 3 2 2
(2 pts. each correct term; -2 pts. for incorrect signs; -2
pts. if A terms not factored correctly)
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5. 10 total pts. A large section from the Fe–C phase diagram is shown below. Prior to the
1800s, the furnaces used by blacksmiths (iron weapon and tool makers) could not achieve the
high temperatures used by modern steelmakers. This limited their ability to prepare ironcarbon alloys.
(a) 04 pts. Please assume that the maximum temperature accessible in the early furnaces was
1200 °C. What is the range of Fe–C alloy compositions that could be prepared, directly from
the furnace, by the early blacksmiths?
The compositional range is approximately 3.8-4.7 wt % C.
(b) 03 pts. Could these early blacksmiths make steel directly from the furnace? Please explain
your answer in one or two sentences.
No, the early blacksmiths could not make steel directly. Steelmaking requires
melt-processing through the austenite region of the phase diagram (wt % C  2.06),
which requires then-unachievable melt temperatures of around 1400 °C or above.
(c) 03 pts. If not steel, what is the conventional name for the Fe–C alloys the early blacksmiths
could make directly?
Cast iron
8
6. 10 total pts. CaO may be dissolved in ZrO2 to form a solid solution. This question concerns
the mechanism of solid-solution formation. If the ZrO2:CaO system forms an interstitial
solid solution, then the formula may be given as Zr1-xCa2xO2 (with some Ca2+ ions in
interstitial positions). However, if the ZrO2:CaO system forms a substitutional solid solution
with vacancies, then the formula may be given as Zr1-xCaxO2-x (with some O2– vacancies).
The mechanisms of solid-solution formation may often be determined by density
measurements. Please consider the ZrO2:CaO solid solution with x = 0.25. Assume that the
ZrO2 lattice parameters are unchanged upon dissolution of CaO. (This is not a valid
assumption, but is a good approximation for this problem.) Therefore, assume the solid
solution has a cubic unit cell with a = 5.123 Å = 5.123  10-8 cm. There are 4 formula units
in the unit cell (Z = 4). (That means, for pure ZrO2 the content of the unit cell is Zr4O8, for
example.)
The density experimentally measured for the ZrO2:CaO solid solution with x = 0.25 is 5.18
g/cm3. Which solid solution mechanism is most consistent with this result? Please show
appropriate calculations in support of your answer.
Hints: Atomic masses; Zr = 91.22 amu, Ca = 40.08 amu, O = 16.00 amu. Avogadro’s
number = 6.022  1023.
If the interstitial mechanism applies:
Formula weight of Zr1-xCa2xO2 =
0.75(91.22 amu) + 0.50(40.08 amu) + 2(16.00 amu) = 120.46 amu
(2 pts.)
d = 4(120.46 amu)(6.022  1023 amu/g)–1(5.123 10–8 cm)–3 = 5.95 g/cm3
(2pts.)
If the vacancy mechanism applies:
Formula weight of Zr1-xCaxO2-x =
0.75(91.22 amu) + 0.25(40.08 amu) + 1.75(16.00 amu) = 106.44 amu
d = 4(106.44 amu)(6.022  1023 amu/g)–1(5.123 10–8 cm)–3 = 5.26 g/cm3
(2 pts.)
(2 pts.)
The second density calculated is very close to the experimental density of 5.18
g/cm3; consequently, the solid solution forms by the vacancy mechanism (2 pts.).
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