CENG151 Introduction to Materials Science and Selection

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CENG151 Introduction to Materials
Science and Selection

• Phase Diagrams
• Homework Solutions
• 2007

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Homework Problem 9.3

• Calculate the degrees of freedom for a 5050
  copper-nickel alloy at
• 1400C where it exists as a single, liquid phase.
• 1300C where it exists as a two-phase mixture of
  liquid and solid solution.
• 1200C 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
• F 2 2 1 2
• 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
F1-210
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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 1045C. At the eutectic
  temperature (577C), the remaining liquid
  solidifies leaving a two-phase microstructure of
  solid solutions a 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
Phase change

• Equal parts of Al and ? is about 26.25wt Cu.
• The first solid to precipitate is ? near 570C.
  At the eutectic temperature (548.2C), the
  remaining liquid solidifies leaving a two-phase
  microstructure of solid solutions ? and ?.

?
?
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)
• 300C
• 200C
• 100C
• 0C

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Solution 9.18

• (a) In the single (L) region
• (b) Two phases exist (a-Pb L)

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Solution 9.18 (cont.)
(c) Two phases exist (a-Pb ?-Sn)
(d) Two phases exist (a-Pb a-Sn)
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Homework Problem 9.23

• Calculate the amount of proeutectoid a present
  at the grain boundaries in 1 kg of a common 1020
  structural steel (0.20wt C). (See Figure 9-19)

728C
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Solution 9.23

• In effect, we need to calculate the equilibrium
  amount of ferrite at 728C.
• 760g

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End of Homework Solutions

• Thank You!