Phase Diagrams - Kasetsart Universitypirun.ku.ac.th/~fengppt/213211/Handouts/16-Phase...

Spring 2004

Kasetsart University

Dr.Peerapong Triyacharoen Department of Materials Engineering

213211: Phase Diagrams

212

• When we combine two elements...what equilibrium state do we get?

• In particular, if we specify...--a composition (e.g., wt%Cu - wt%Ni), and--a temperature (T)

then...How many phases do we get?What is the composition of each phase?How much of each phase do we get?

Phase BPhase A

Nickel atomCopper atom

Phase Diagrams




213

• Solubility Limit:Max concentration forwhich only a solutionoccurs.

• Ex: Phase Diagram:Water-Sugar SystemQuestion: What is the

solubility limit at 20°C?Answer: 65wt% sugar.

If Co < 65wt% sugar: syrupIf Co > 65wt% sugar: syrup + sugar.

• Solubility limit increases with T:e.g., if T = 100°C, solubility limit = 80wt% sugar.

Pu

re

Su

ga

r

Te

mp

era

ture

(°C

)

0 20 40 60 80 100Co=Composition (wt% sugar)

L (liquid solution

i.e., syrup)

Solubility Limit L

(liquid)

+ S

(solid sugar)

65

20

40

60

80

100

Pu

re

Wa

ter

The Solubility Limit

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• Components:The elements or compounds which are mixed initially

(e.g., Al and Cu)• Phases:

The physically and chemically distinct material regionsthat result (e.g., α and β).

Aluminum-CopperAlloy

α (darker phase)

β (lighter phase)

Component and Phase




215

Phase Diagrams• Tell us about phases as function of T, Co, P. Phase Diagram for Cu-Ni system at constant Pressure

• 2 phases: L (liquid) α (FCC solid solution)

• 3 phase fields: L L + α α

wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

1500

1600T(°C)

L (liquid)

α (FCC solid solution)

L + αliquidus

solidus

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216

Construction of Phase Diagram




217

Phase Diagram for Pure Iron (Fe)

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Phase Diagrams: # and types of phases• Rule 1: If we know T and Co, then we know:

--the # and types of phases present.

• Examples:

wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

1500

1600T(°C)

L (liquid)

α (FCC solid solution)

L + α

liquidus

solidus

A(1100,60)

B(1

25

0,3

5) Cu-Ni

phasediagram

A(1100, 60): 1 phase: α

B(1250, 35): 2 phases: L + α




219

Phase Diagrams: composition of phase• Rule 2: If we know T and Co, then we know:

--the composition of each phase.

• Examples:

wt% Ni20

1200

1300

T(°C)

L (liquid)

α (solid)L + α

liquidus

solidus

30 40 50

TAA

DTD

TBB

tie line

L + α

433532CoCL Cα

Cu-Ni system

At TA:

Only Liquid (L) CL = Co ( = 35wt% Ni)

At TB:

Both α and L CL = Cliquidus ( = 32wt% Ni here)

Cα = Csolidus ( = 43wt% Ni here)

At TD:

Only Solid (α) Cα = Co ( = 35wt% Ni)

Co = 35wt%Ni

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220

Phase Diagrams: weight fraction of phase• Rule 3: If we know T and Co, then we know:

--the amount of each phase (given in wt%).Cu-Ni

system• Examples:

At TB: Both α and L

At TA: Only Liquid (L)

WL = 100wt%, Wα = 0At TD: Only Solid (α)

WL = 0, Wα = 100wt%

Co = 35wt%Ni

WL = SR + S

Wα = RR + S

=

43 − 3543 − 32

= 73wt %

= 27wt%wt% Ni

20

1200

1300

T(°C)

L (liquid)

α (solid)

L + α

liquidus

solidus

30 40 50

TAA

DTD

TBB

tie line

L + α

433532CoCL Cα

R S




221

Ex: Cooling in a Cu-Ni Binary• Phase diagram:

Cu-Ni system.• System is:

--binaryi.e., 2 components:Cu and Ni.

--isomorphousi.e., completesolubility of onecomponent inanother; α phasefield extends from0 to 100wt% Ni.

wt% Ni20

1200

1300

30 40 501100

L (liquid)

α (solid)

L + α

L + α

T(°C)

A

D

B

35Co

L: 35wt%Ni

α: 46wt%Ni

C

E

L: 35wt%Ni

464332

24

35

36α: 43wt%Ni

L: 32wt%Ni

L: 24wt%Ni

α: 36wt%Ni

• ConsiderCo = 35wt%Ni.

Cu-Nisystem

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222

Nonequilibrium Alloy




223

Cored vs. Equilibrium Phase• Cα changes as we solidify.• Cu-Ni case:

• Fast rate of cooling:Cored structure

• Slow rate of cooling:Equilibrium structure

First α to solidify has Cα = 46wt%Ni.Last α to solidify has Cα = 35wt%Ni.

First α to solidfy: 46wt%Ni

Uniform Cα:

35wt%Ni

Last α to solidfy: < 35wt%Ni

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Binary Eutectic Systems2 components has a special composition

with a min. melting T.

• 3 single phase regions (L, α, β) • Limited solubility: α: mostly Cu β: mostly Ni • TE: No liquid below TE

• CE: Min. melting T

composition

Ex.: Cu-Ag system L (liquid)

α L + α L+β β

α + β

Co, wt% Ag 20 40 60 80 100 0

200

1200 T(°C)

400

600

800

1000

CE

TE 8.0 71.9 91.2 779°C

Cu-Ag system




225

Ex: Pb-Sn Eutectic System (I)• For a 40wt%Sn-60wt%Pb alloy at 150°C, find...

--the phases present:α + β

--the compositions ofthe phases:

Pb-Sn system

L + α L+β

α + β

200

T(°C)

18.3

Co, wt% Sn 20 40 60 80 100 0

Co

300

100

β

L (liquid)

α 183°C 61.9 97.8

150

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226

Ex: Pb-Sn Eutectic System (II)• For a 40wt%Sn-60wt%Pb alloy at 150°C, find...

--the phases present: α + β--the compositions of

the phases:Cα = 11wt%SnCβ = 99wt%Sn

--the relative amountsof each phase:

W α = 59 88

= 67 wt %

W β = 29 88

= 33 wt %

Pb-Sn system

L + α L+β

α + β

200

T(°C)

18.3

Co, wt% Sn 20 40 60 80 100 0

Co

300

100

L (liquid)

α 183°C 61.9 97.8

150

11 99

R S

β




227

Microstructures in Eutectic System (I)

L + α200

T(°C)

Co, wt% Sn10

2

200Co

300

100

L

α

30

L: Cowt%Sn

αL

α: Cowt%Sn

α + β

400

(room T solubility limit)

TE(Pb-Sn System)

• Co < 2wt%Sn• Result:

--polycrystal of α grains.

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228

Microstructures in Eutectic System (II)• 2wt%Sn < Co < 18.3wt%Sn• Result:

--α polycrystal with fineβ crystals.

α: Cowt%SnL + α

200

T(°C)

Co, wt% Sn10

18.3

200Co

300

100

L

α

30

L: Cowt%Sn

α + β

400

(sol. limit at TE)

TE

2(sol. limit at Troom)

Lα

αβPb-Sn

system




229

Microstructures in Eutectic System (III)

L + α200

T(°C)

Co, wt% Sn

20 400

300

100

L

α

60

L: C owt%Sn

α + β

TE

α: 18.3wt%Sn

β

080 100

L + β

CE18.3 97.861.9

183°C

β: 97.8wt%Sn

160µm

Micrograph of Pb-Sn eutectic microstructure

• Co = CE• Result: Eutectic microstructure

--alternating layers of α and β crystals.

Pb-Snsystem

Spring 2004




230

L + α200

T(°C)

Co, wt% Sn

20 400

300

100

L

α

60

L: Cowt%Sn

α + β

TEβ

080 100

L + β

Co18.3 61.9

Lα

Lα

primary α

97.8

S

S

RR

eutectic αeutectic β

Pb-Snsystem

• 18.3wt%Sn < Co < 61.9wt%Sn• Result: α crystals and a eutectic microstructure

• Just above TE:

WL = (1-Wα) =50wt%

Cα = 18.3wt%Sn

CL = 61.9wt%SnS

R + SWα = =50wt%

• Just below TE:Cα = 18.3wt%Sn

Cβ = 97.8wt%SnS

R + SWα = =73wt%

Wβ = 27wt%

Microstructures in Eutectic System (IV)




231

Hypoeutectic & HypereutecticT(°C)

(Pb-Sn System)

L + α200

Co, wt% Sn20 400

300

100

L

α

60

α + β

TE β

080 100

L + β

18.361.9

97.8

Cohypoeutectic

Cohypereutectic

eutectic

hypereutectic: (illustration only)

160µm

eutectic: Co=61.9wt%Sn

175µm

β

ββ

ββ

β

α

α

α

αα

α

hypoeutectic: Co=50wt%Sn

eutectic micro-constituent

Spring 2004




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Peritectic System

Liquid+ solid 1 new solid 2cooling

heating




233

Microstructures in Peritectic System

Spring 2004




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Three-Phase Invariant Reaction (I)

2 1 solidsolidLiquid heating

cooling

+⎯⎯ ⎯←⎯⎯ →⎯

solid 1 + solid 2

L(1) Eutectic reaction

3 2 1 solidsolidSolid heating

cooling

+⎯⎯ ⎯←⎯⎯ →⎯

solid 2 + solid 3

(2) Eutectoid reaction

2 1 solidnewSolidLiquid heating

cooling

⎯⎯ ⎯←⎯⎯ →⎯

+Liquid + Solid 1

new solid 2

(3) Peritectic reaction




235

Three-Phase Invariant Reaction (II)

2 1 solidliquidLiquid heating

cooling

+⎯⎯ ⎯←⎯⎯ →⎯

liquid 2 + solid

L 1(5) Monotectic reaction

Solid 1 + Solid 2

new solid 3

(4) Peritectoid reaction

321 solidnewSolidSolid heating

cooling

⎯⎯⎯ ⎯←

⎯⎯⎯ →⎯+

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236

Ex: Cu-Zn System




237

Iron-Carbon (Fe-C) Phase Diagram

Spring 2004




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Microstructure of Eutectoid Steel




239

Hypo- & Hypereutectiod Steels

Phase Diagrams - Kasetsart Universitypirun.ku.ac.th/~fengppt/213211/Handouts/16-Phase...

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