10 Dispersion Strengthening and Eutectic Phase Diagrams 10–22
A hypothetical phase diagram diagram is shown in Figure 10–32. (a) Are any intermetallic intermetallic compounds present? If so, identify them and determine whether they are stoichiometric or nonstoichiometric. (b) Identify the solid solutions present in the system. Is either material A or B allotropic? Explain. (c) Identify the three-phase reactions by writing down the temperature, the reaction in equation form, the composition of each phase in the reaction, and the name of the reaction.
Solution: (a) u non-stoichiometric intermetallic compound. (b) a, h, g, and b; material B is allotropic, existing in three different forms at different temperatures (c) 1100° 1100°C:
g L
900° 900°C: L1 680° 680°C: L 600° 600°C: 300° 300°C:
10–23
S
S
S
b;
L2 a;
a b;
ab b
S
S
u;
u h;
peri perittect ectic; ic;
L: 82% B g: 97% B
monotectic; L1: 28% B L 2: 50% B eutectic; peri perite tect ctoi oid; d; eutectoid;
b: 90% B a: 5% B
L: 60% B a: 5% B
b: 90% B
a: 5% B b: 80% B
u: 37% B
b: 90% B u: 40% B
h: 95% B
The Cu–Zn phase diagram is shown in Figure 10–33. (a) Are any intermetallic compounds present? If so, identify them and determine whether they are stoichiometric or nonstoichiometric. (b) Identify the solid solutions present in the system. (c) Identify the three-phase reactions by writing down the temperature, the reaction in equation form, and the name of the reaction.
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Solution: (a) b, b, g, d, e: all nonstoichiometric. (b) a, u
10–24
(c) 900°C:
a L
S
b;
peritectic
830°C:
b L
S
g;
peritectic
700°C:
g L
S
d;
peritectic
600°C:
d L
S
550°C:
d
420°C:
e L
250°C:
b¿
S
S
peritectic
g e;
eutectoid
S
u;
peritectic
a g;
eutectoid
A portion of the Al–Cu phase diagram is shown in Figure 10 –34. (a) Determine the formula for the u compound. (b) Identify the three-phase reaction by writing down the temperature, the reaction in equation form, the composition of each phase in the reaction, and the name of the reaction. 54 g 63.54 g/mol
Solution: (a) u at 54% Cu; (b) 548°C; L
10–25
e;
S
54 63.54 46 26.981 a u;
33 at% Cu;
CuAl2
eutectic; L: 33.2% Cu, a: 5.65% Cu,
u: 52.5% Cu.
The Al–Li phase diagram is shown in Figure 10 –35. (a) Are any intermetallic compounds present? If so, identify them and determine whether they are stoichiometric or nonstoichiometric. Determine the formula for each compound. (b) Identify the three-phase reactions by writing down the temperature, the reaction in equation form, the composition of each phase in the reaction, and the name of the reaction.
Solution: (a) b is non-stoichiometric @ 21 wt% Li: at% Li
21 g 6.94 g/mol 21 6.94 79 26.981
100% 50 at% Li ∴ AlLi
100% 66.7% Li ∴ AlLi2
g, is stoichiometric @ 34 wt% Li: at% Li (b) 600°C: L
34 g 6.94 g/mol 34 6.94 66 26.981 S
ab
eutectic
L: 9.9% Li
a: 4% Li 510°C: b L
S
g
peritectic
b: 20.4% Li
b: 25% Li L: 47% Li
170°C: L
10–26
S
g a 1 Li 2
eutectic
L: 98% Li g: 34% Li
g: 34% Li
a 1 Li 2 : 99% Li
An intermetallic compound is found for 10 wt% Si in the Cu –Si phase diagram. Determine the formula for the compound.
Solution:
at% Si
10 g 28.08 g/mol 10 28.08 90 63.54
0.20
or
SiCu4
CHAPTER 10 10–27
Dispersion Strengthening and Eutect ic Phase Diagrams
Using the phase rule, predict and explain how many solid phases will form in an eutectic reaction in a ternary (three-component) phase diagram, assuming that the pressure is fixed.
Solution:
F C P 1
At the eutectic, F 0, C 3 Therefore, L S a b g 10–30
113
03P1
or
P4
and 3 solid phases form.
Consider a Pb–15% Sn alloy. During solidification, determine (a) the composition of the first solid to form, (b) the liquidus temperature, solidus temperature, solvus temperature, and freezing range of the alloy, (c) the amounts and compositions of each phase at 260°C, (d) the amounts and compositions of each phase at 183°C, and (e) the amounts and compositions of each phase at 25 °C.
Solution: (a) 8% Sn (b) liquidus 290°C, solvus 170°C,
solidus 240°C, freezing range 50°C
(c) L: 30% Sn a: 12% Sn; 15 12 % L 100% 17% 30 12 (d) a: 15% Sn
100% a
(e) a: 2% Pb b: 100% Sn 100 15 %a 100 87% 100 2 10–31
%a 83%
%b 13%
Consider an Al–12% Mg alloy (Figure 10 –36). During solidification, determine (a) the composition of the first solid to form, (b) the liquidus temperature, solidus temperature, solvus temperature, and freezing range of the alloy, (c) the amounts and compositions of each phase at 525 °C, (d) the amounts and compositions of each phase at 450°C, and (e) the amounts and compositions of each phase at 25°C.
Solution: (a) 2.5% Mg (b) liquidus 600°C, solvus 400°C,
solidus 470°C, freezing range 130°C
(c) L: 26% Mg a: 7% Mg; 26 12 %a 100% 74% 26 7 (d) a: 12% Mg
% L 26%
100% a
(e) a: 1% Mg b: 34% Mg 34 12 %a 100% 67% 34 1
%b 33%
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Instructor’s Solution Manual
Consider a Pb–35% Sn alloy. Determine (a) if the alloy is hypoeutectic or hypereutectic, (b) the composition of the first solid to form during solidification, (c) the amounts and compositions of each phase at 184 °C, (d) the amounts and compositions of each phase at 182°C, (e) the amounts and compositions of each microconstituent at 182°C, and (f) the amounts and compositions of each phase at 25 °C.
Solution: (a) hypoeutectic
(b) 14% Sn
(c) a: 19% Sn L: 61.9% Sn 61.9 35 100% 63% %a 61.9 19 (d) a: 19% Sn b: 97.5% Sn 97.5 35 %a 100% 80% 97.5 19 (e) primary a: 19% Sn eutectic: 61.9% Sn
%b 20%
%primary a 63% %eutectic 37%
(f) a: 2% Sn b: 100% Sn 100 35 100% 66% %a 100 2 10–33
% L 37%
%b 34%
Consider a Pb–70% Sn alloy. Determine (a) if the alloy is hypoeutectic or hypereutectic, (b) the composition of the first solid to form during solidification, (c) the amounts and compositions of each phase at 184 °C, (d) the amounts and compositions of each phase at 182°C, (e) the amounts and compositions of each microconstituent at 182°C, and (f) the amounts and compositions of each phase at 25 °C.
Solution: (a) hypereutectic
(b) 98% Sn
(c) b: 97.5% Sn L: 61.9% Sn 70 61.9 100% 22.8% %b 97.5 61.9 (d) a: 19% Sn b: 97.5% Sn 97.5 70 %a 100% 35% 97.5 19 (e) primary b: 97.5% Sn eutectic: 61.9% Sn
%b 65%
%primary b 22.8% %eutectic 77.2%
b: 100% Sn (f) a: 2% Sn 100 70 100% 30% %a 100 2 10–34
% L 77.2%
%b 70%
Calculate the total % b and the % eutectic microconstituent at room temperature for the following lead-tin alloys: 10% Sn, 20% Sn, 50% Sn, 60% Sn, 80% Sn, and 95% Sn. Using Figure 10–22, plot the strength of the alloys versus the % b and the % eutectic and explain your graphs.
CHAPTER 10
Dispersion Strengthening and Eutect ic Phase Diagrams
Solution:
%b 10% Sn 20% Sn 50% Sn 60% Sn 80% Sn 95% Sn
10 2 99 2 20 2 99 2 50 2 99 2 60 2 99 2 80 2 99 2 95 2 99 2
%eutectic
8.2%
18.6%
49.5%
59.8%
80.4%
95.9%
0% 20 19 61.9 19 50 19 61.9 19 60 19 61.9 19 97.5 80 97.5 61.9 97.5 95 97.5 61.9
2.3%
72.3%
95.6%
49.2%
7.0%
8000
8000
) i s p ( h t g n e r t s e l i s n e T
115
) i s p ( h t g n e r t s e l i s n e T
7000
6000
5000
7000
o H y p
r p e y H
6000
5000
4000 20
40
60 %
10–35
80
100
20
40
60
80
% eutectic
β
Consider an Al–4% Si alloy. (See Figure 10 –23.) Determine (a) if the alloy is hypoeutectic or hypereutectic, (b) the composition of the first solid to form during solidification, (c) the amounts and compositions of each phase at 578 °C, (d) the amounts and compositions of each phase at 576 °C, the amounts and compositions of each microconstituent at 576°C, and (e) the amounts and compositions of each phase at 25°C.
Solution: (a) hypoeutectic (b) 1% Si (c) a: 1.65% Si L: 12.6% Si 12.6 4 %a 78.5% 12.6 1.65 (d) a: 1.65% Si b: 99.83% Si 99.83 4 97.6% %a 99.83 1.65
% L 21.5%
%b 2.4%
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Instructor’s Solution Manual %primary a 78.5% %eutectic 21.5%
(e) primary a: 1.65% Si eutectic: 12.6% Si a: 0% Si 10–36
%a
b: 100% Si
100 4 100 0
96%
%b 4%
Consider a Al–25% Si alloy. (See Figure 10 –23.) Determine (a) if the alloy is hypoeutectic or hypereutectic, (b) the composition of the first solid to form during solidification, (c) the amounts and compositions of each phase at 578 °C, (d) the amounts and compositions of each phase at 576 °C, (e) the amounts and compositions of each microconstituent at 576 °C, and (f) the amounts and compositions of each phase at 25°C.
Solution: (a) hypereutectic (b) 100% Si (c) b: 99.83% Si L: 12.6% Si 99.83 25 % L 85.8% 99.83 12.6
%b 14.2%
(d) a: 1.65% Si b: 99.83% Si 99.83 25 %a 76.2% 99.83 1.65
%primary b 14.2% %eutectic 85.8%
(e) primary b: 99.83% Si eutectic: 12.6% Si (f) a: 0% Si 10–37
100 0
75%
%b 25%
%a 45
98.0 x 98.0 5
or x 56.15% Sn
100
Hypoeutectic
%a 85
100 x 100 1
100
or x 15.85% Si
Hypereutectic
A Pb–Sn alloy contains 23% primary a and 77% eutectic microconstituent. Determine the composition of the alloy.
Solution: 10–40
100 25
An Al–Si alloy contains 85% a and 15% b at 500°C. Determine the composition of the alloy. Is the alloy hypoeutectic or hypereutectic?
Solution: 10–39
%a
b: 100% Si
A Pb–Sn alloy contains 45% a and 55% b at 100°C. Determine the composition of the alloy. Is the alloy hypoeutectic or hypereutectic?
Solution: 10–38
%b 23.8%
%primary a 23
61.9 x 61.9 19
100
or x 52% Sn
An Al–Si alloy contains 15% primary b and 85% eutectic microconstituent. Determine the composition of the alloy.
CHAPTER 10
Solution: 10–41
Dispersion Strengthening and Eutect ic Phase Diagrams
%eutectic 85
100 x 100 12.6
100
117
or x 25.71% Si
Determine the maximum solubility for the following cases. (a) lithium in aluminum (Figure 10 –35), (b) aluminum in magnesium (Figure 10 –37), (c) copper in zinc (Figure 10–33), and (d) carbon in g-iron (Figure 10–38)
Solution: (a) 4% Li dissolves in aluminum (b) 12.7% Al dissolves in magnesium (c) 3% Cu dissolves in zinc (d) 2.11% C dissolves in g-iron 10–42
Determine the maximum solubility for the following cases. (a) (b) (c) (d)
magnesium in aluminum (Figure 10–36), zinc in copper (Figure 10–33), beryllium in copper (Figure 10–33), and Al2O3 in MgO (Figure 10–39)
Solution: (a) 14.9% Mg dissolves in aluminum (b) 40% Zn dissolves in copper (c) 2.5% Be dissolves in copper (d) 18% Al2O3 dissolves in MgO 10–43
Observation of a microstructure shows that there is 28% eutectic and 72% primary b in an Al–Li alloy (Figure 10 –35). (a) Determine the composition of the alloy and whether it is hypoeutectic or hypereutectic. (b) How much a and b are in the eutectic microconstituent?
Solution: (a) 28
20.4 x 20.4 9.9
(b) %aEut 10–44
100
20.4 9.9 20.4 4
or x 17.46% Li
100% 64%
and
Hypereutectic
%bEut 36%
Write the eutectic reaction that occurs, including the compositions of the three phases in equilibrium, and calculate the amount of a and b in the eutectic microconstituent in the Mg –Al system, (Figure 10 –36).
Solution:
L32.3 S a12.7 g40.2
∴ %aEut
40.2 32.3 40.2 12.7
100% 28.7%
and
%gEut 71.3%
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Instructor’s Solution Manual
Calculate the total amount of a and b and the amount of each microconstituent in a Pb–50% Sn alloy at 182°C. What fraction of the total a in the alloy is contained in the eutectic microconstituent?
Solution:
atotal aPrimary
97.5 50 97.5 19 61.9 50 61.9 19
100% 60.5%
bTotal 39.5%
100% 27.7%
Eutectic 72.3%
ain eutectic 60.5 27.7 32.8% f 32.8 60.5 0.54 10–46
Figure 10–40 shows a cooling curve for a Pb –Sn alloy. Determine (a) the pouring temperature, (b) the superheat, (c) the liquidus temperature, (d) the eutectic temperature, (e) the freezing range, (f) the local solidification time, (g) the total solidification time, and (h) the composition of the alloy.
Solution: (a) pouring temperature
360°C
(b) superheat 360 250 110°C (c) liquidus temperature 250°C (d) eutectic temperature 183°C (e) freezing range 250 183 67°C (f) local solidification time 600 110 490 s (g) total solidification time 600 s (h) approximately 32% Sn 10–47
Figure 10–41 shows a cooling curve for an Al –Si alloy. Determine (a) the pouring temperature, (b) the superheat, (c) the liquidus temperature, (d) the eutectic temperature, (e) the freezing range, (f) the local solidification time, (g) the total solidification time, and (h) the composition of the alloy.
Solution: (a) pouring temperature
1150°C
(b) superheat 1150 1000 150°C (c) liquidus temperature 1000°C (d) eutectic temperature 577°C (e) freezing range 1000 577 423°C (f) local solidification time 11.5 1 10.5 min (g) total solidification time 11.5 min (h) approximately 45% Si
CHAPTER 10 10–48
Dispersion Strengthening and Eutect ic Phase Diagrams
119
Draw the cooling curves, including appropriate temperatures, expected for the following Al–Si alloys. (a) Al–4% Si
(b) Al–12.6% Si
(c) Al–25% Si
(d) Al–65% Si
Solution:
780°
630° 577°
T
577°
T
Al – 4% Si
10–49
577°
T
Al – 12.6% Si
t
1200° T
Al – 25% Si
t
577° Al – 65% Si
t
t
Based on the following observations, construct a phase diagram. Element A melts at 850°C and element B melts at 1200°C. Element B has a maximum solubility of 5% in element A, and element A has a maximum solubility of 15% in element B. The number of degrees of freedom from the phase rule is zero when the temperature is 725°C and there is 35% B present. At room temperature 1% B is soluble in A and 7% A is soluble in B.
Solution:
1200 1000 ) C ° ( e r u t a r e p m e T
L
b+L
800
a+L
a
b
600 a+b
400 200
A
5
20
40
60 % B
80 85
B
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Cooling curves are obtained for a series of Cu –Ag alloys, (Figure 10–42). Use this data to produce the Cu–Ag phase diagram. The maximum solubility of Ag in Cu is 7.9% and the maximum solubility of Cu in Ag is 8.8%. The solubilities at room temperature are near zero.
Solution: 0% Ag 8% Ag 20% Ag 50% Ag 71.9% Ag 90% Ag 100% Ag
S S S S S S S
T liq
T sol
1085°C 1030°C 975°C 860°C 780°C 870°C 961°C
950°C 780°C 780°C 780°C 780°C
1100
) 1000 C ° ( e r u t a r 900 e p m e T
L
a+L
a
b+L
800
b a+b
700 Cu
29
40
60
80
Ag
% Ag
10–51
The SiO2 –Al2O3 phase diagram is included in Figure 10 –27(b). A refractory is required to contain molten metal at 1900 °C. (a) Will pure Al 2O3 be a potential candidate? Explain. (b) Will Al2O3 contaminated with 1% SiO 2 be a candidate? Explain.
Solution: (a) Yes. T m 2040°C 1900°C
No liquid will form.
(b) No. Some liquid will form. % L
100 99 100 80
100% 5% L
This liquid will weaken the refractory.
CHAPTER 10 10–66
10–67
10–68
Dispersion Strengthening and Eutect ic Phase Diagrams
121
Consider the ternary phase diagram shown in Figures 10 –30 and 10–31. Determine the liquidus temperature, the first solid to form, and the phases present at room temperature for the following compositions. (a) 30% B –20% C , balance A (c) 60% B –10% C , balance A
(b) 10% B –25% C , balance A
Solution: (a) T Liq
220°C;
b;
agb
(b) T Liq 330°C;
a;
ag
(c) T Liq 390°C;
b;
ab
Consider the ternary phase diagram shown in Figures 10 –30 and 10–31. Determine the liquidus temperature, the first solid to form, and the phases present at room temperature for the following compositions. (a) 5% B –80% C , balance A (c) 30% B –35% C , balance A
(b) 50% B –5% C , balance A
Solution: (a) T Liq
390°C;
g;
ag
(b) T Liq 330°C;
b;
ab
(c) T Liq 290°C;
b;
abg
Consider the liquidus plot in Figure 10 –30. (a) For a constant 20% B, draw a graph showing how the liquidus temperature changes from 20% B –0% C, balance A to 20% B–80% C, balance A, (b) What is the composition of the ternary eutectic in this system? (c) Estimate the temperature at which the ternary eutectic reaction occurs.
Solution:
% A % B %C
T liquidus
80–20–0 70–20–10 60–20–20 50–20–30 40–20–40 30–20–50 20–20–60 10–20–70 0–20–80
390C 355°C 300°C 210°C 150°C 210°C 270°C 320°C 400°C
400
) C ° ( 300 e r u t a r e 200 p m e T 100
L
a+L g+L
B =
0
20
40 %C
60
20% 80
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(b) The composition of the ternary eutectic is about 40% 20% B –40% C , balance A (c) The ternary eutectic temperature is about 150°C 10–69
From the liquidus plot in Figure 10 –30, prepare a graph of liquidus temperature versus percent B for a constant ratio of materials A and C (that is, from pure B to 50% A –50% C on the liquidus plot). Material B melts at 600°C.
Solution:
A
B C
50– 0–50 45–10–45 40–20–40 35–30–35 30–40–30 25–50–25 20–60–20 15–70–15 0–100–0
200°C 180°C 150°C 280°C 330°C 375°C 415°C 485°C 580°C
600 500 ) C ° ( 400 e r u t 300 a r e p m200 e T
L
b + L
a+L
% A = % C
100
0
20
40
60 % B
80
100
