Problem Set 12
Due: Wednesday, May 2, 2012 <5:00PM
outside B-013
E-344
Spring 2012
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On the solution set you submit, please:
Staple multiple pages together; and legibly (e.g. print) write your name and 5-digit ID number.
Papers without this information will be awarded zero credit.
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Final, Fall 2011:
1. The adjacent Figure 1A illustrates a so-called Jominy
test. A steel rod 0.5 inches in diameter and 2 inches long
is heated until its temperature is uniformly at 1000 oC. At
time t=0, room-temperature water is sprayed on one end.
In the configuration shown, insulation forces the heat flow
to be one dimensional. The Rockwell C hardness as a
function of distance from the quenched end after cooling
is given for several steels in figure 1B.
A copy of the C-rich portion of the Fe-Fe3C phase
diagram is given on the next page.
A. (6 pts) Assuming the thermal properties of all the
steels in Fig. 1B are essentially the same, sketch a welllabeled plot of temperature as a function of distance from
the quenched end for time t=0, t =infinity, and two
intermediate times. (No calculations are required).
B. (4 pts) Consider a sample of plain-carbon 1040 steel
with a composition of Fe-0.4 wt% C. At the quenched
end of the rod, the microstructure is almost 100% martensite. What would a likely microstructure be at the far
end of the rod to be in order for the hardness to be so different at HRC<20? Briefly explain why these
differences in microsctructure occur.
C. (4 pts) Suppose after cooling, the 1040 steel rod is sliced into sections each 1/4 " thick with the section cut
perpendicular to the long axis of the rod. What is the average composition of each slice? Briefly explain your
answer.
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1A.
_____/6
1B.
_____/4
1C.
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2A.
_____/2
2B.
_____/2
2C.
_____/2
2D.
_____/4
2E.
_____/4
2F.
_____/4
2G.
_____/4
3A.
_____/4
3B.
_____/4
3C.
_____/4
3D.
_____/4
3E.
_____/4
4A.
_____/4
4B.
_____/4
4C.
_____/4
4D.
_____/4
5A.
_____/2
8.
_____/3
5B.
_____/2
9.
_____/3
5C.
_____/2
10.
_____/3
5D.
_____/2
11.
_____/3
5E.
_____/3
12.
_____/3
6A.
_____/4
13.
_____/3
6B.
_____/4
14.
_____/3
6C.
_____/4
15.
_____/3
6D.
_____/4
16.
_____/3
7A.
_____/3
17.
_____/3
7B.
_____/3
18.
_____/3
7C.
_____/3
19.
_____/3
7D.
_____/3
7E.
_____/3
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total:
___________/150
Constants:
h = 6.626x10-34 Jsec
kB = 8.617x10-5 eV/K
1 eV = 1.6x10-19 J
c = 3x108 m/sec
R = 8.3144 J/mole-K
2. The Al-rich end of the Al-Cu phase diagram is given below.
A. (2 pts) What is the melting temperature of pure aluminum?
B. (2 pts) Identify the eutectic composition
C. (2 pts) Identify the eutectic temperature
A sample of Al - 33.0 wt% Cu was cooled from T=600 oC to 545 oC and then
quenched to room temperature. The resulting microstructure is depicted by
the adjacent micrograph. The  phase has dark contrast. The  phase (CuAl2)
has bright contrast.
D. (4 pts) What is the composition of each of the two phases?
E. (4 pts) How much of each phase is present?
F. (4 pts) On a well-labeled plot of composition versus distance, sketch the composition (in wt% Cu) as a
function of distance along the line A-B. No calculations are required.
G. (4 pts) The alternating lines in the micrograph correspond to alternating plates (lamellae) of  and  where
the lamellae are coming out of the plane of the paper in this 2-D section of a 3-D structure. If the cooling rate
from 600 oC to 545 oC is increased, the spacing between the lamellae will decrease. Using concepts of
diffusion, briefly explain why.
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3. Ni is sometimes used in electrical applications where a higher resistivity is required, such as in the heating
elements in a furnace. Its electrical resistivity at room temperature is 6.99 x 10-8 -m. Its melting temperature
is 1453 oC.
A. (4 pts) Suppose the heating element of a particular furnace is a wire with a diameter of 2 mm and a length of
2 m. Calculate the room-temperature resistance of this wire.
B. (4 pts) For a different furnace application the diameter of the wire must be reduced to 1 mm. At room
temperature, it is thus pulled through a series of dies (a die is a metal block with a small hole in it) until its final
diameter is reduced by plastic deformation from 2 mm to 1 mm. Describe how (goes up, down, or stays the
same) the resistance changes as a consequence of the cold-drawing process.
C. (4 pts) If electrical current is now passed through the wire so it is heated to 1000 oC and held there, how will
the resistance change? Briefly explain why.
D. (4 pts) After operating at T=1000 oC for one hour, the furnace is cooled to room temperature. Is the
resistance higher, lower, or the same as it was immediately after the cold drawing process (part B)? Briefly
explain your answer.
E. (4 pts) To improve the oxidation resistance of the wire, nickel is often alloyed with chromium (Cr) to form
an alloy known as Nichrome (Ni -20 wt% Cr). The electrical resistivity of pure Cr at room temperature is 12.5
x 10-8 -m. Assuming Cr dissolves in Ni as a substitutional alloying element, predict the electrical resistivity
of Nichrome.
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4. Germanium is a group IV semiconductor with a bandgap of 0.661 eV.
A. (4 pts) Sketch a well-labeled energy-band diagram characteristic of Ge.
B. (4 pts) Visible light has wavelengths ranging from 350 nm (blue) to 750 nm (red). If a piece of solid
germanium is exposed to white light containing all wavelengths of the visible spectrum, determine the range of
visible wavelengths that will be transmitted by the germanium. Be quantitative.
C. (4 pts) Arsenic (As) is often used to dope germanium. Suppose a Ge single crystal is doped to a level of
1018 As atoms/cm3. Use a well-labeled energy-band diagram to explain why the As doping changes the
electrical conductivity of the Ge.
D. (4 pts) Suppose pure Ge is doped to a a level of 1018 Si atoms/cm3. How will such Si doping affect the Ge
conductivity? Briefly explain.
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5. Stress-strain data for a series of aluminum alloys are described in the figure below.
A) (2 pts) Which of these four alloys has the highest tensile strength?
B) (2 pts) Which is most brittle?
C) (2 pts) Which would you expect to have the lowest fracture toughness?
D) (6 pts) For the 7020-T6 alloy, determine the:
(i) yield stress
(ii) the tensile stress
(iii) the elongation to failure
E) (3 pts) Why do each of the four alloys have an additional designation (e.g. O or T6) after the four-digit
designation of composition?
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6. A. (4 pts) Sketch the current (I)-voltage (V) relationship of a rod of Copper (Cu) metal and a rod of pure
silicon (Si) with same geometry.
B. (4 pts) On the same figure, sketch the I-V curve for an identical rod of Si that is doped with Phosphorus (P)
to 1018 P/cm3. Briefly explain why there is a difference relative to the pure Si.
C. (4 pts) When the pure Si rod is heated from 300 K to 600 K, the conductivity increases. However, the
conductivity of the Cu rod decreases when similarly heated. Explain why.
D. (4 pts) A Si crystal doped with P is joined to a Si crystal doped with boron (B). When an increasing AC
voltage is applied, current begins to flow first in one direction and not in the other. In which direction does the
current flow first? Briefly explain why.
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7. Suppose a cube of pure solid silicon (Si) with an edge length of 1 cm is cleaved by brittle fracture to create
two identical pieces 1 cm x 1 cm x 0.5 cm in size.
A. ( 3 pts) Show that the volume of the two pieces after cleaving is the same as the volume before cleaving.
B. (3 pts) Show that the total surface area after cleaving is greater than that before cleaving.
C. (3 pts) Develop a brief argument why the total energy of the two pieces after cleaving is greater than that of
the one piece before cleaving.
D. (3 pts) Suppose the cleaving process is performed in a very high vacuum (no air). After cleaving the two
pieces are brought back together, precisely aligned along the cleavage face, and heated to 0.8 of the melting
temperature of Si for one hour. What do you expect will happen? Why?
E. (3 pts) Suppose the cleaving process is performed in air. After cleaving the two pieces are brought back
together, precisely aligned along the cleavage face, and heated to 0.8 of the melting temperature of Si for one
hour. What do you expect will happen? Why?
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In the following multiple-choice problems, circle the one answer which BEST completes the sentence. 3 points
per problem. No partial credit.
8. Metals and alloys can be shaped by:
a. casting;
b. rolling;
c. forging;
d. extrusion;
e. all of the above.
9. An amorphous material:
a. has atoms arranged periodically on a lattice;
b. exhibits long-ranged translational order;
c. has the structure of a liquid but the mechanical properties of a solid;
d. all of the above;
e. none of the above.
10. When mixed with water, cement hardens due to:
(a) the water chemically reacts with various components in the cement;
(b) the water evaporates leaving solid cement;
(c) the viscosity decreases until the cement becomes too hard to deform;
(d) water converts the cement into concrete;
(e) none of the above.
11. Viscosity
(a) decreases with decreasing temperature;
(b) is an important property in the deformation processing of a metal;
(c) is independent of compositions;
(d) all the above;
(e) none of the above.
12. A hydrogel:
a. is a crosslinked polymer designed primarily to interact with organic solvents;
b. is a crosslinked polymer designed primarily to interact with water;
c. dissolves in water;
d. all of the above;
e. none of the above.
13. A thermoset polymer such as epoxy:
a. cannot be recycled by heating above the material's melting point;
b. can be thought of as a highly crosslinked polymer;
c. is typically formed by the reaction of two or more different components;
d. all of the above.
e. none of the above.
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14. The glass transition temperature of polystyrene is about 110 oC.
Relative to a sample at 120 oC, at room temperature polystyrene is:
a.
b.
c.
d.
e.
orders of magnitude more viscous;
slightly more viscous;
equally as viscous;
less viscous;
none of the above.
15. Thermoplastic polymers such as polyethylene can be melted relatively easily, because:
a. they are highly crosslinked by a curing agent;
b. the bonds between molecules are primarily covalent;
c. the monomer units are short;
d. the intermolecular bonds are relatively weak secondary bonds;
e. none of the above.
16. Fracture toughness (KIC) is a measure of a material's:
a. ability to elastically deform;
b. corrosion resistance;
c. resistance to brittle failure;
d. tensile strength;
e. none of the above.
17. Consider a cold-worked metal that has been annealed at a temperature just below its melting point for 1
hour. Relative to the initial hardness, the annealed hardness would:
a. be greater;
b. be the same;
c. be less;
d. depend on degree of doping;
e. none of the above.
18. The diffusivity of one element through another:
a.
b.
c.
d.
e.
decreases with increasing temperature;
does not depend on temperature;
increases with increasing temperature;
can increase or decrease with temperature depending on whether the solvent is solid or liquid;
none of the above.
19. Failure by creep can occur under conditions of:
a. cyclic or repeated loading;
b. rapid loading at low temperature until brittle failure occurs;
c. constant loading at a temperature below Tg.
d. all of the above;
e. none of the above.
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