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CENG151 Introduction to Materials Science and Selection Phase Diagrams Homework Solutions 2007.
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Transcript of CENG151 Introduction to Materials Science and Selection Phase Diagrams Homework Solutions 2007.
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CENG151 Introduction to Materials Science and Selection
Phase DiagramsHomework Solutions
2007
![Page 2: CENG151 Introduction to Materials Science and Selection Phase Diagrams Homework Solutions 2007.](https://reader035.fdocuments.net/reader035/viewer/2022062515/56649d245503460f949fab7f/html5/thumbnails/2.jpg)
Homework Problem: 9.3
Calculate the degrees of freedom for a 50:50 copper-nickel alloy at:
(a) 1400˚C where it exists as a single, liquid phase.
(b) 1300˚C where it exists as a two-phase mixture of liquid and solid solution.
(c) 1200˚C where it exists as a single, solid-solution phase.
Assume a constant pressure of 1 atm above the alloy in each case.
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Solution 9.3
Using Gibbs Phase Rule:
F = C – P + 1
= 2 – 1 + 1
= 2
(b) F = 2 – 2 + 1 = 2
(c) F = 2 – 1 + 1 = 2
a
b
c
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Homework Problem: 9.5
Apply the Gibbs phase rule to a sketch of the MgO-Al2O3 phase diagram.(Figure 9-26)
Find out for each phase compartment the degrees of freedom.
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Solution 9.5
F=1-2+1=0
(F=2-2+1=1)
F=2-1+1=2
F=2-2+1=1
F=2-2+1=1
F=2-1+1=2
F=2-1+1=2
F=1-2+1=0
![Page 6: CENG151 Introduction to Materials Science and Selection Phase Diagrams Homework Solutions 2007.](https://reader035.fdocuments.net/reader035/viewer/2022062515/56649d245503460f949fab7f/html5/thumbnails/6.jpg)
Homework Problem 9.8
Describe qualitatively the microstructural development that will occur upon slow cooling of a melt composed of 50wt% Al and 50wt% Si (see Figure 9-13)
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Solution 9.8
The first solid to precipitate is a solid solution, , near 1045˚C. At the eutectic temperature (577˚C), the remaining liquid solidifies leaving a two-phase microstructure of solid solutions α and .
Phase change
Phase change
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Homework Problem 9.12
Describe qualitatively the microstructural development that will occur upon slow cooling of an alloy with equal parts (by weight) of aluminum and phase (Al2Cu) (see Figure 9-27)
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Solution 9.12
Equal parts of Al and is about 26.25wt% Cu.
The first solid to precipitate is near 570˚C. At the eutectic temperature (548.2˚C), the remaining liquid solidifies leaving a two-phase microstructure of solid solutions and .
Phase change
Phase change
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Homework Problem 9.18
Calculate the amount of each phase present in 1 kg of a 50 wt% Pb – 50 wt% Sn solder alloy at the following temperatures. (See Figure 9-16)
(a)300˚C
(b)200˚C
(c)100˚C
(d)0˚C
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Solution 9.18
(a) In the single (L) region:
(b) Two phases exist (α-Pb + L):
kgmkgmL 0,1
gkg
kgkgxx
xxm
gkg
kgkgxx
xxm
PbL
LPb
PbL
PbL
111111.0
11854
50541
889889.0
11854
18501
![Page 12: CENG151 Introduction to Materials Science and Selection Phase Diagrams Homework Solutions 2007.](https://reader035.fdocuments.net/reader035/viewer/2022062515/56649d245503460f949fab7f/html5/thumbnails/12.jpg)
Solution 9.18 (cont.)
gkg
kgkgxx
xxm
gkg
kgkgxx
xxm
PbSn
PbSn
PbSn
SnPb
479479.0
1599
5501
521521.0
1599
50991
(c) Two phases exist (α-Pb + -Sn):
(d) Two phases exist (α-Pb + α-Sn):
gkg
kgkgxx
xxm
gkg
kgkgxx
xxm
PbSn
PbSn
PbSn
SnPb
495495.0
11100
1501
505505.0
11100
501001
![Page 13: CENG151 Introduction to Materials Science and Selection Phase Diagrams Homework Solutions 2007.](https://reader035.fdocuments.net/reader035/viewer/2022062515/56649d245503460f949fab7f/html5/thumbnails/13.jpg)
Homework Problem 9.23
Calculate the amount of proeutectoid α present at the grain boundaries in 1 kg of a common 1020 structural steel (0.20wt% C). (See Figure 9-19)
728˚C
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Solution 9.23
In effect, we need to calculate the equilibrium amount of ferrite at 728˚C.
=760g
kgkgm 76.0102.077.0
20.077.0
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End of Homework Solutions
Thank You!