Page 379 - Materials Science and Engineering An Introduction

Questions and Problems • 351

gion. If the mass fraction of each phase is 0.5, The following table gives the approximate densi-
then estimate ties of the various metals at the alloy temperatures:
(a) the temperature of the alloy
3
Metal Temperature ( C) Density (g/cm )
(b) the compositions of the two phases in weight Cu 600 8.68
percent
Mg 425 1.68
(c) the compositions of the two phases in atom
percent Pb 100 11.27
Pb 425 10.96
9.23 A copper–silver alloy is heated to 900 C and is
found to consist of a and liquid phases. If the mass Sn 100 7.29
fraction of the liquid phase is 0.68, determine Zn 600 6.67
(a) the composition of both phases, in both weight
percent and atom percent, and Development of Microstructure
in Isomorphous Alloys
(b) the composition of the alloy, in both weight
percent and atom percent 9.30 (a) Briefly describe the phenomenon of coring
and why it occurs.
9.24 For alloys of two hypothetical metals A and B,
there exist an a, A-rich phase and a b, B-rich phase. (b) Cite one undesirable consequence of coring.
From the mass fractions of both phases for two dif-
ferent alloys provided in the following table (which Mechanical Properties of Isomorphous Alloys
are at the same temperature), determine the com- 9.31 It is desirable to produce a copper–nickel alloy
position of the phase boundary (or solubility limit) that has a minimum non-cold-worked tensile
for both a and b phases at this temperature. strength of 380 MPa (55,000 psi) and a ductility of
at least 45%EL. Is such an alloy possible? If so,
Alloy Fraction Fraction what must be its composition? If this is not pos-
Composition A Phase B Phase sible, then explain why.
70 wt% A–30 wt% B 0.78 0.22 Binary Eutectic Systems
35 wt% A–65 wt% B 0.36 0.64
9.32 A 60 wt% Pb–40 wt% Mg alloy is rapidly
9.25 A hypothetical A–B alloy of composition 40 quenched to room temperature from an elevated
wt% B–60 wt% A at some temperature is found temperature in such a way that the high-tempera-
to consist of mass fractions of 0.66 and 0.34 for the ture microstructure is preserved. This microstruc-
a and b phases, respectively. If the composition of ture is found to consist of the a phase and Mg 2 Pb,
the a phase is 13 wt% B–87 wt% A, what is the having respective mass fractions of 0.42 and 0.58.
composition of the b phase? Determine the approximate temperature from
which the alloy was quenched.
9.26 Is it possible to have a copper–silver alloy of
composition 20 wt% Ag–80 wt% Cu that, at equi- Development of Microstructure in Eutectic Alloys
librium, consists of a and liquid phases having Briefly explain why, upon solidification, an alloy
mass fractions W a 0.80 and W L 0.20? If so, 9.33
what will be the approximate temperature of the of eutectic composition forms a microstructure con-
alloy? If such an alloy is not possible, explain why. sisting of alternating layers of the two solid phases.
9.27 For 5.7 kg of a magnesium–lead alloy of com- 9.34 What is the difference between a phase and a
position 50 wt% Pb–50 wt% Mg, is it possible, microconstituent?
at equilibrium, to have a and Mg 2 Pb phases with 9.35 Plot the mass fraction of phases present versus
respective masses of 5.13 and 0.57 kg? If so, what temperature for a 40 wt% Sn–60 wt% Pb alloy as
will be the approximate temperature of the alloy? it is slowly cooled from 250 C to 150 C.
If such an alloy is not possible, then explain why. 9.36 Is it possible to have a magnesium–lead alloy in
9.28 Derive Equations 9.6a and 9.7a, which may be which the mass fractions of primary a and total a
used to convert mass fraction to volume fraction, are 0.60 and 0.85, respectively, at 460 C (860 F)?
and vice versa. Why or why not?

9.29 Determine the relative amounts (in terms of 9.37 For 2.8 kg of a lead–tin alloy, is it possible to have
volume fractions) of the phases for the alloys and the masses of primary b and total b of 2.21 and 2.53
temperatures given in Problems 9.10a, b, and d. kg, respectively, at 180 C (355 F)? Why or why not?