Problemas Askeland Cap 9

9
Solid Solutions and Phase Equilibrium

9–15 The unary phase diagram for SiO2 is shown in Figure 9–3(c). Locate the triple point
where solid, liquid, and vapor coexist and give the temperature and the type of solid
present. What do the other “triple” points indicate?
Solution: (a) The solid-liquid-vapor triple point occurs at 1713 C; the solid phase present at this point is b-cristobalite.(b) The other triple points describe the equilibrium between two solids and a
vapor phase.
9–34 Based on Hume-Rothery’s conditions, which of the following systems would be
expected to display unlimited solid solubility? Explain.
(a) Au–Ag
(e) Mo–Ta
Solution: (a) rAu
rAg
¢r

(b) Al–Cu
(f) Nb–W
1.442
1.445
0.2%

(c) Al–Au
(g) Mg–Zn
v
v

1
1

FCC
FCC
Yes

(b) rAl
rCu¢r

1.432 v
1.278 v
10.7%

3
1

FCC
FCC
No

(c) rAl
rAu
¢r

1.432
1.442
0.7%

v
v

3
1

FCC
FCC
No

(d) rU
rW
¢r

1.38
1.371
0.7%

v
v

4
4

(d) U–W
(h) Mg–Cd

Ortho
FCC
No

99

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The Science and Engineering of Materials

Instructor’s Solution Manual

(e) rMo
rTa
¢r

1.363 v
1.43 v
4.7%

4
5

BCC
BCC
No

(f) rNb
rW
¢r1.426
1.371
3.9%

v
v

4
4

BCC
BCC
Yes

(g) rMg
rZn
¢r

1.604 v
1.332 v
17%

2
2

HCP
HCP
No

(h) rMg
rCd
¢r

1.604 v
1.490 v
7.1%

2
2

HCP
HCP
Yes

The Au – Ag, Mo – Ta, and Mg – Cd systems have the required radius ratio, the
same crystal structures, and the same valences. Each of these might be
expected to display complete solid solubility. [TheAu – Ag and Mo – Ta do
have isomorphous phase diagrams. In addition, the Mg – Cd alloys all solidify
like isomorphous alloys; however a number of solid state phase transformations complicate the diagram.]
9–35 Suppose 1 at% of the following elements is added to copper (forming a separate
alloy with each element) without exceeding the solubility limit. Which one would be
expected to give thehigher strength alloy? Is any of the alloying elements expected
to have unlimited solid solubility in copper?
(a) Au

(b) Mn

(c) Sr

Solution: For copper: rCu

(d) Si

(e) Co

1.278 Å
rCu

rAu

1.442

¢r

(b) Mn: r

1.12

¢r

12.4%

Different structure.

(c) Sr: r

2.151

¢r

68.3%

Highest Strength

(d) Si: r

1.176

¢r

8.0%

Differentstructure.

(e) Co: r

1.253

¢r

2.0%

Different structure.

rCu

12.8%

May be Unlimited
Solubility.

(a) Au: r

The Cu – Sr alloy would be expected to be strongest (largest size difference).
The Cu – Au alloy satisfies Hume-Rothery’s conditions and might be expected
to display complete solid solubility — in fact it freezes like an isomorphous
series of alloys, but a number ofsolid state transformations occur at lower
temperatures.
9–36 Suppose 1 at% of the following elements is added to aluminum (forming a separate
alloy with each element) without exceeding the solubility limit. Which one would be
expected to give the least reduction in electrical conductivity? Is any of the alloy
elements expected to have unlimited solid solubility in aluminum?
(a) Li

(b) Ba(c) Be

(d) Cd

(e) Ga

CHAPTER 9
Solution: For aluminum: r

Solid Solutions and Phase Equilibrium

101

1.432 Å (FCC structure with valence of 3)

(a) Li: r

1.519

¢r

(b) Ba: r

2.176

¢r

(c) Be: r

1.143

¢r

(d) Cd: r

1.49

¢r

(e) Ga: r

1.218

6.1%

¢r

BCC

valence

1

52.0%

BCC

valence

2

20.2%

HCP

valence

24.1%

HCP

valence

2

14.9%

Orthorhombic

valence

3

The cadmium would be expected to give the smallest reduction in electrical
conductivity, since the Cd atoms are most similar in size to the aluminum
atoms.
None are expected to have unlimited solid solubility, due either to difference
in valence, atomic radius or crystal structure.
9–37 Which of the following oxides is...