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Chemical Engineering 378
Science of Materials Engineering
Lecture 19Phase Equilibrium
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Spiritual Thought
“I Testify that bad days come to an end, that faith always triumphs, and that heavenly promises are always kept.”
-Jeffery R. Holland
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Materials Roadmap3
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Phase Equilibria: Solubility Limit
Question: What is thesolubility limit for sugar in water at 20°C?
Answer: 65 wt% sugar.At 20°C, if C < 65 wt% sugar: syrupAt 20°C, if C > 65 wt% sugar:
syrup + sugar
65
• Solubility Limit:
Maximum concentration forwhich only a single phase solution exists.
Sugar/Water Phase Diagram
Suga
r
Tem
pera
ture
(°C
)
0 20 40 60 80 100C = Composition (wt% sugar)
L
(liquid solution i.e., syrup)
Solubility Limit L
(liquid) +
S
(solid sugar)20
40
60
80
100
Wat
er
Adapted from Fig. 9.1, Callister & Rethwisch 10e.
• Solution – solid, liquid, or gas solutions, single phase• Mixture – more than one phase
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• Components:
The elements or compounds which are present in the alloy(e.g., Al and Cu)
• Phases:
The physically and chemically distinct material regionsthat form (e.g., α and β).
Aluminum-CopperAlloy
Components and Phases
α (darker phase)
β (lighter phase)
Adapted from chapter-opening photograph, Chapter 9, Callister, Materials Science & Engineering: An Introduction, 3e.
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70 80 1006040200
Tem
pera
ture
(°C
)
C = Composition (wt% sugar)
L
(liquid solution i.e., syrup)
20
100
40
60
80
0
L
(liquid) +
S
(solid sugar)
Effect of Temperature & Composition
• Altering T can change # of phases: path A to B.• Altering C can change # of phases: path B to D.
water-sugarsystem
Fig. 9.1, Callister & Rethwisch 10e.
D (100°C,C = 90)2 phases
B (100°C,C = 70)1 phase
A (20°C,C = 70)2 phases
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Criteria for Solid Solubility
CrystalStructure
electroneg r (nm)
Ni FCC 1.9 0.1246Cu FCC 1.8 0.1278
• Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume –Rothery rules) suggesting high mutual solubility.
Simple system (e.g., Ni-Cu solution)
• Ni and Cu are totally soluble in one another for all proportions.
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Phase Diagrams• Indicate phases as a function of T, C, and P. • For this course:
- binary systems: just 2 components.- independent variables: T and C (P = 1 atm is almost always used).
PhaseDiagramfor Cu-Nisystem
Fig. 9.3(a), Callister & Rethwisch 10e.(Adapted from Phase Diagrams of BinaryNickel Alloys, P. Nash, Editor, 1991. Reprintedby permission of ASM International, MaterialsPark, OH.)
• 2 phases:L (liquid)α (FCC solid solution)
• 3 different phase fields: LL + αα
wt% Ni20 40 60 80 10001000
1100
1200
1300
1400
1500
1600T(°C)
L (liquid)
α
(FCC solid
solution)
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Cu-Niphase
diagram
Isomorphous Binary Phase Diagram
• Phase diagram:Cu-Ni system.
• System is:
Fig. 9.3(a), Callister & Rethwisch 10e.(Adapted from Phase Diagrams of BinaryNickel Alloys, P. Nash, Editor, 1991. Reprintedby permission of ASM International, MaterialsPark, OH.)
-- binaryi.e., 2 components:Cu and Ni.
-- isomorphousi.e., completesolubility of onecomponent inanother; α phasefield extends from0 to 100 wt% Ni.
wt% Ni20 40 60 80 10001000
1100
1200
1300
1400
1500
1600T(°C)
L (liquid)
α
(FCC solid
solution)
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wt% Ni20 40 60 80 10001000
1100
1200
1300
1400
1500
1600T(°C)
L (liquid)
α
(FCC solidsolution)
Cu-Niphase
diagram
10Phase Diagrams:Determination of phase(s) present
• Rule 1: If we know T and Co, then we know:-- which phase(s) is (are) present.
• Examples:A(1100°C, 60 wt% Ni):
1 phase: α
B(1250°C, 35 wt% Ni): 2 phases: L + α
B(1
250º
C,3
5)A(1100ºC,60)
Fig. 9.3(a), Callister & Rethwisch 10e.(Adapted from Phase Diagrams of BinaryNickel Alloys, P. Nash, Editor, 1991. Reprintedby permission of ASM International, MaterialsPark, OH.)
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wt% Ni20
1200
1300
T(°C)
L (liquid)
α(solid)
30 40 50
Cu-Ni system
Phase Diagrams:Determination of phase compositions
• Rule 2: If we know T and C0, then we can determine:-- the composition of each phase.
• Examples:
TAA
35C0
32CL
At TA = 1320°C: Only Liquid (L) present CL = C0 ( = 35 wt% Ni)
At TB = 1250°C: Both α and L presentCL = Cliquidus ( = 32 wt% Ni) Cα = Csolidus ( = 43 wt% Ni)
At TD = 1190°C: Only Solid (α) presentCα = C0 ( = 35 wt% Ni)
Consider C0 = 35 wt% Ni
DTD
tie line
4Cα
3
Fig. 9.3(b), Callister & Rethwisch 10e.(Adapted from Phase Diagrams of BinaryNickel Alloys, P. Nash, Editor, 1991. Reprintedby permission of ASM International, MaterialsPark, OH.)
BTB
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• Rule 3: If we know T and C0, then can determine:-- the weight fraction of each phase.
• Examples:
At TA : Only Liquid (L) present WL = 1.00, Wα = 0
At TD : Only Solid (α ) present WL = 0, Wα = 1.00
Phase Diagrams:Determination of phase weight fractions
wt% Ni20
1200
1300
T(°C)
L (liquid)
α(solid)
30 40 50
Cu-Ni system
TAA
35C0
32CL
BTB
DTD
tie line
4Cα3
R S
At TB : Both α and L present
= 0.27
WL =S
R + S
Wα =R
R + S
Consider C0 = 35 wt% Ni
Fig. 9.3(b), Callister & Rethwisch 10e.(Adapted from Phase Diagrams of BinaryNickel Alloys, P. Nash, Editor, 1991. Reprintedby permission of ASM International, MaterialsPark, OH.)
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• Tie line – connects the phases in equilibrium with each other – also sometimes called an isotherm
The Lever Rule
What fraction of each phase?Think of the tie line as a lever (teeter-totter)
ML Mα
R S
wt% Ni20
1200
1300
T(°C)
L (liquid)
α(solid)
30 40 50
BTB
tie line
C0CL Cα
SR
Adapted from Fig. 9.3(b), Callister & Rethwisch 10e.
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wt% Ni20
1200
1300
30 40 50110 0
L (liquid)
α(solid)
T(°C)
A
35C0
L: 35 wt%NiCu-Ni
system
• Phase diagram:Cu-Ni system.
Adapted from Fig. 9.4, Callister & Rethwisch 10e.
• Consider microstucturalchanges that accompany the cooling of a
C0 = 35 wt% Ni alloy
Ex: Cooling of a Cu-Ni Alloy
46354332
α: 43 wt% Ni L: 32 wt% Ni
Bα: 46 wt% NiL: 35 wt% Ni
C
EL: 24 wt% Ni
α: 36 wt% Ni
24 36D
α: 35 wt% Ni
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• Slow rate of cooling:Equilibrium structure
• Fast rate of cooling:Cored structure
First α to solidify:46 wt% NiLast α to solidify:< 35 wt% Ni
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• Cα changes as we solidify.• Cu-Ni case: First α to solidify has Cα = 46 wt% Ni.
Last α to solidify has Cα = 35 wt% Ni.
Cored vs Equilibrium Structures
Uniform Cα:35 wt% Ni
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Mechanical Properties: Cu-Ni System
• Effect of solid solution strengthening on:
-- Tensile strength (TS) -- Ductility (%EL)
Adapted from Fig. 9.6(a), Callister & Rethwisch 10e.
Tens
ile S
treng
th (M
Pa)
Composition, wt% NiCu Ni0 20 40 60 80 100200
300
400
TS for pure Ni
TS for pure Cu
Elon
gatio
n (%
EL)
Composition, wt% NiCu Ni0 20 40 60 80 10020
30
40
50
60
%EL for pure Ni
%EL for pure Cu
Adapted from Fig. 9.6(b), Callister & Rethwisch 10e.
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2 componentshas a special compositionwith a min. melting T.
Fig. 9.7, Callister & Rethwisch 10e [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.].
Binary-Eutectic Systems
• 3 single phase regions (L, α, β)
• Limited solubility: α: mostly Cu β: mostly Ag
• TE : No liquid below TE
: Composition at temperature TE
• CE
Ex.: Cu-Ag systemCu-Agsystem
L (liquid)
α L + αL+ββ
α + β
C, wt% Ag20 40 60 80 1000
200
1200T(°C)
400
600
800
1000
CE
TE 8.0 71.9 91.2779°C
cooling
heating
• Eutectic reaction
L(CE) α(CαE) + α(CαE)
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L + α
L+β
α + β
200
T(°C)
18.3
C, wt% Sn20 60 80 1000
300
100
L (liquid)
α183°C
61.9 97.8
β
• For a 40 wt% Sn-60 wt% Pb alloy at 150°C, determine:
-- the phases presentPb-Snsystem
EX 1: Pb-Sn Eutectic System
Answer: α + β-- the phase compositions
-- the relative amountof each phase
150
40C0
11Cα
99Cβ
SR
Answer: Cα = 11 wt% SnCβ = 99 wt% Sn
Wα=Cβ - C0Cβ - Cα
= 99 - 4099 - 11 = 59
88 = 0.67
SR+S =
Wβ=C0 - CαCβ - Cα
=RR+S
= 2988
= 0.33= 40 - 1199 - 11
Answer:
Fig. 9.8, Callister & Rethwisch 10e.[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]
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Answer: Cα = 17 wt% Sn-- the phase compositions
L+β
α + β
200
T(°C)
C, wt% Sn20 60 80 1000
300
100
L (liquid)
α β
L + α
183°C
• For a 40 wt% Sn-60 wt% Pb alloy at 220°C, determine:
-- the phases present:Pb-Snsystem
EX 2: Pb-Sn Eutectic System
-- the relative amountof each phase
Wα =CL - C0
CL - Cα=
46 - 4046 - 17
=629 = 0.21
WL =C0 - Cα
CL - Cα=
2329 = 0.79
40C0
46CL
17Cα
220SR
Answer: α + L
CL = 46 wt% Sn
Answer:
Fig. 9.8, Callister & Rethwisch 10e.[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]
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• For alloys for which C0 < 2 wt% Sn
• Result: at room temperature
-- polycrystalline with grains of α phase having composition C0
Microstructural Developments in Eutectic Systems I
0
L+ α200
T(°C)
C, wt% Sn10
2
20C0
300
100
L
α
30
α+β
400
(room T solubility limit)
TE(Pb-SnSystem)
αL
L: C0 wt% Sn
α: C0 wt% Sn
Fig. 9.11, Callister & Rethwisch 10e.
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• For alloys for which 2 wt% Sn < C0 < 18.3 wt% Sn
• Result: at temperatures in α + β range-- polycrystalline with α grainsand small β-phase particles
Fig. 9.12, Callister & Rethwisch 10e.
Microstructural Developments in Eutectic Systems II
Pb-Snsystem
L + α
200
T(°C)
C, wt% Sn10
18.3
200C0
300
100
L
α
30
α+ β
400
(sol. limit at TE)
TE
2(sol. limit at Troom)
Lα
L: C0 wt% Sn
αβ
α: C0 wt% Sn
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• For alloy of composition C0 = CE• Result: Eutectic microstructure (lamellar structure)
-- alternating layers (lamellae) of α and β phases.
Fig. 9.13, Callister & Rethwisch 10e.
Microstructural Developments in Eutectic Systems III
Fig. 9.14, Callister & Rethwisch 10e. (From Metals Handbook, 9th edition, Vol. 9,Metallography and Microstructures, 1985.Reproduced by permission of ASM International, Materials Park, OH.)
160μm
Micrograph of Pb-Sn eutectic microstructure
Pb-Snsystem
L+β
α + β
200
T(°C)
C, wt% Sn20 60 80 1000
300
100
L
α β
L + α
183°C
40
TE
18.3
α: 18.3 wt%Sn
97.8
β: 97.8 wt% Sn
CE61.9
L: C0 wt% Sn
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Lamellar Eutectic Structure
Figs. 9.14 & 9.15, Callister & Rethwisch 10e.(Fig. 9.14 from Metals Handbook, 9th edition, Vol. 9, Metallography and Microstructures, 1985. Reproduced by permission of ASM International, Materials Park, OH.)