Page 380 - Materials Science and Engineering An Introduction

352 • Chapter 9 / Phase Diagrams

9.38 For a lead–tin alloy of composition 80 wt% Sn– composition of the alloy, and then compare this
20 wt% Pb and at 180 C (355 F), do the following: estimate with the composition given in the legend
(a) Determine the mass fractions of the a and b of Figure 9.17. Make the following assumptions:
phases. (1) The area fraction of each phase and micro-
constituent in the photomicrograph is equal to its
(b) Determine the mass fractions of primary b volume fraction; (2) the densities of the a and b
and eutectic microconstituents. phases and the eutectic structure are 11.2, 7.3, and
3
(c) Determine the mass fraction of eutectic b. 8.7 g/cm , respectively; and (3) this photomicro-
graph represents the equilibrium microstructure
9.39 The microstructure of a copper–silver alloy at at 180 C (355 F).
775 C (1425 F) consists of primary a and eutec-
tic structures. If the mass fractions of these two 9.46 The room-temperature tensile strengths of pure
microconstituents are 0.73 and 0.27, respectively, copper and pure silver are 209 and 125 MPa, re-
determine the composition of the alloy. spectively.
9.40 A magnesium–lead alloy is cooled from 600 C to (a) Make a schematic graph of the room-temper-
450 C and is found to consist of primary Mg 2 Pb ature tensile strength versus composition for all
and eutectic microconstituents. If the mass frac- compositions between pure copper and pure silver.
tion of the eutectic microconstituent is 0.28, deter- (Hint: You may want to consult Sections 9.10 and
mine the alloy composition. 9.11, as well as Equation 9.24 in Problem 9.79.)
9.41 Consider a hypothetical eutectic phase diagram (b) On this same graph, schematically plot tensile
for metals A and B that is similar to that for the strength versus composition at 600 C.
lead–tin system (Figure 9.8). Assume that: (l) a (c) Explain the shapes of these two curves as well
and b phases exist at the A and B extremes of the as any differences between them.
phase diagram, respectively; (2) the eutectic com-
position is 36 wt% A–64 wt% B; and (3) the com- Equilibrium Diagrams Having Intermediate
position of the a phase at the eutectic temperature Phases or Compounds
is 88 wt% A–12 wt% B. Determine the composi-
tion of an alloy that will yield primary b and total 9.47 Two intermetallic compounds, A 3 B and AB 3 , ex-
b mass fractions of 0.367 and 0.768, respectively. ist for elements A and B. If the compositions for
9.42 For a 64 wt% Zn–36 wt% Cu alloy, make sche- A 3 B and AB 3 are 91.0 wt% A–9.0 wt% B and 53.0
wt% A–47.0 wt% B, respectively, and element A
matic sketches of the microstructure that would is zirconium, identify element B.
be observed for conditions of very slow cooling at
the following temperatures: 900 C (1650 F), 820 C 9.48 An intermetallic compound is found in the alu-
(1510 F), 750 C (1380 F), and 600 C (1100 F). minum–zirconium system that has a composition
Label all phases and indicate their approximate of 22.8 wt% Al–77.2 wt% Zr. Specify the formula
compositions. for this compound.
9.43 For a 76 wt% Pb–24 wt% Mg alloy, make sche- 9.49 An intermetallic compound is found in the gold–
matic sketches of the microstructure that would titanium system that has a composition of 58.0
be observed for conditions of very slow cooling wt% Au–42.0 wt% Ti. Specify the formula for this
at the following temperatures: 575 C (1070 F), compound.
500 C (930 F), 450 C (840 F), and 300 C (570 F). 9.50 Specify the liquidus, solidus, and solvus tempera-
Label all phases and indicate their approximate tures for the following alloys:
compositions. (a) 30 wt% Ni–70 wt% Cu
9.44 For a 52 wt% Zn–48 wt% Cu alloy, make sche-
matic sketches of the microstructure that would (b) 5 wt% Ag–95 wt% Cu
be observed for conditions of very slow cooling at (c) 20 wt% Zn–80 wt% Cu
the following temperatures: 950 C (1740 F), 860 C (d) 30 wt% Pb–70 wt% Mg
(1580 F), 800 C (1470 F), and 600 C (1100 F).
Label all phases and indicate their approximate (e) 3 wt% C–97 wt% Fe
compositions.
Congruent Phase Transformations
9.45 On the basis of the photomicrograph (i.e., the
relative amounts of the microconstituents) for Eutectoid and Peritectic Reactions
the lead–tin alloy shown in Figure 9.17 and the 9.51 What is the principal difference between congru-
Pb–Sn phase diagram (Figure 9.8), estimate the ent and incongruent phase transformations?