1. CENG151 Introduction to Materials Science and Selection Phase Diagrams Homework Solutions 2007

2. 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.

3. 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

4. Homework Problem: 9.5 Apply the Gibbs phase rule to a sketch of the MgO-Al 2 O 3 phase diagram. (Figure 9-26) Find out for each phase compartment the degrees of freedom.

5. Solution 9.5 F=1-2+1=0 (F=2-2+1=1) F=2-1+1=2 F=2-2+1=1 F=2-1+1=2 F=1-2+1=0

6. 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)

7. 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

8. 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 (Al 2 Cu) (see Figure 9-27)

9. 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   

10. 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

11. Solution 9.18 (a) In the single (L) region: (b) Two phases exist ( α-Pb + L) :

12. Solution 9.18 (cont.) (c) Two phases exist ( α-Pb +  -Sn) : (d) Two phases exist ( α-Pb + α-Sn) :

13. 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

14. Solution 9.23 In effect, we need to calculate the equilibrium amount of ferrite at 728˚C. =760g

15. End of Homework Solutions Thank You!