BY

PHASE DIAGRAM

BY

ENGR. MS TAYYABA BANO

Cu-Ni System

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

• 3 phase fields: 1400

1500

1600T(°C)

L (liquid)

• 3 phase fields:

L

L + α

α

wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

α (FCC solid solution)

L +

αliquidus

solidus

• Rule 1: If we know T and Co, then we know:

the # and types of phases present# and types of phases present# and types of phases present# and types of phases present.

• Examples:

1500

1600T(°C)

L (liquid)

liquidus

(1250,35) Cu-Ni

phase

A(1100, 60): 1 phase: α

PHASE DIAGRAMS: # and types of phases

wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

α

(FCC solid solution)

L +

α

liquidus

solidus

A(1100,60)B(1250,35)

phase

diagramB(1250, 35): 2 phases: L + α

Rule 2: If we know T and Co, then we

know: the composition of each phase.

• Examples:

1300

T(°C)

L (liquid) liquidu

s

solidu

s

TAA

TBB

tie line

L + α

Cu-Ni

system

At TA:

Only Liquid (L) C = C ( = 35wt% Ni)

Co = 35wt%Ni

PHASE DIAGRAMS: composition of phases

wt% Ni

20

1200

α

(solid)L + α

solidu

s

30 40 50

DTD

TBB

433532CoCL Cα

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)

Rule 3: If we know T and Co, then we know:

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

system• Examples:

At TA: Only Liquid (L)

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

Co = 35wt%Ni

1300

T(°C)

L (liquid) liquidu

s

solidu

s

TAA

TBB

tie line

L + α

PHASE DIAGRAMS: weight fractions of phases

At TB: Both α and L

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

WL = S

R +S

Wα = R

R +S

%733243

35430 wtCC

CC

L

=−−=

−−=

α

α

= 27wt%

wt% Ni

20

1200α

(solid)L +

α

solidu

s

30 40 50

DTD

TBB

433532CoCL Cα

R S

%27wtCC

CC

L

o =−−=

α

α

• Sum of weight fractions:

• Conservation of mass (Ni):

• Combine above equations:

WL + Wα = 1

Co = WLCL + WαCα

= R

R +S Wα =

Co −CLCα −CL

= S

R+ SWL

= Cα −CoCα −CL

THE LEVER RULE: A PROOF

R S Cα −CLR SCα CL

• A geometric interpretation:

Co

R S

WαWL

CL Cα moment equilibrium:

1−Wαsolving gives Lever Rule

WLR = WαS

• Phase diagram:• Phase diagram:• Phase diagram:• Phase diagram:

CuCuCuCu----Ni system.Ni system.Ni system.Ni system.

• System is:• System is:• System is:• System is:

--------binarybinarybinarybinaryi.e.i.e.i.e.i.e., 2 components:, 2 components:, 2 components:, 2 components:

Cu and Ni.Cu and Ni.Cu and Ni.Cu and Ni.

--------isomorphousisomorphousisomorphousisomorphous

1300

L (liquid)

L +

α

T(°C)

A

D

B

L: 35wt%Ni

α: 46wt%NiC

L: 35wt%Ni

46

4332

24

35

L: 32wt%Ni

Cu-Ni

system

COOLING IN A Cu-Ni BINARY

--------isomorphousisomorphousisomorphousisomorphousi.e., completei.e., completei.e., completei.e., complete

solubility of onesolubility of onesolubility of onesolubility of one

component incomponent incomponent incomponent in

another; another; another; another; αααα phasephasephasephase

field extends fromfield extends fromfield extends fromfield extends from

0 to 100wt% Ni.0 to 100wt% Ni.0 to 100wt% Ni.0 to 100wt% Ni.

wt% Ni20

1200

30 40 501100

α (solid)

L +

αD

35Co

E

24 36

α: 43wt%Ni

L: 32wt%Ni

L: 24wt%Ni

α: 36wt%Ni

• Consider

Co = 35wt%Ni.

2 componentshas a special composition

with a min. melting T.

• 3 single phase regions

(L, α, β) • Limited solubility:

α: mostly Cu

Ex.: Cu-Ag system

L (liquid)

α L + α L+β β

1200 T(°C)

800

1000

TE 779°C

Cu-Ag

system

BINARY-EUTECTIC SYSTEMS

α: mostly Cu

β: mostly Ni

• TE: No liquid below TE

• CE: Min. melting T

composition

L+β β

α + β

Co, wt% Ag 20 40 60 80 100 0

200

400

600

800

CE

TE 8.0 71.9 91.2 779°C

L (liquid)

α L + α L+β β

120 0 T(°C)

800

1000

TE 8.0 71.9 91.2 779°C

α + β

Co, wt% Ag 20 40 60 80 100 0

200

400

600

CE

IRON-CARBON/ SYSTEM/ PHASE DIAGRAMPHASE DIAGRAM

• 2 important points

-Eutectic (A):

-Eutectoid (B):

L⇒ γ +Fe3C

γ ⇒ α +Fe3C

C (cementite)

1600

1400

1200

1000

800

L

γ (austenite)

γ+L

γ+Fe3Cα+γ

L+Fe3C

δ

727°C = Teutectoid

1148°C

T(°C)

A

B

SR

γ γγγ

α

IRON-CARBON (Fe-C) PHASE DIAGRAM

Result: Pearlite = alternating layers of α and Fe3C phases.

120µm

Fe3C (cementite)

800

600

4000 1 2 3 4 5 6 6.7

α+Fe3C

+γ

(Fe) Co, wt% C0.77 4.30

727°C = TeutectoidBR S

Fe3C (cementite-hard)

α (ferrite-soft)

αCeutectoid

DEVELOPMENT OF MICROSTRUCTURESDEVELOPMENT OF MICROSTRUCTURES

� Austenite precipitates Fe3C at Eutectoid Transformation Temperature (727°C).

γγγγ αααα + Fe3C Cooling

Heating

� When cooled slowly, forms Pearlite, which is a micro-contituent made of ferrite (αααα) and Cementite (Fe3C),

Heating

HYPOEUTECTOID STEEL

(Fe-C System)

C (cementite)

1600

1400

1200

1000

L

γ (austenite)

γ+L

γ+Fe3C

L+Fe3C

δ

1148°C

T(°C)

γ γγγ

γγγ γ

α

Adapted from

Fig. 9.27,Callister6e. (Fig. 9.27 courtesy Republic Steel Corporation.)

Co

Fe3C (cementite)

800

600

4000 1 2 3 4 5 6 6.7

α+Fe3C

Co, wt% C0.77

727°C

R Sαγγ γ

γ r s

wα =s/(r+s)wγ =(1-wα)

wα =S/(R+S)wFe3C =(1-wα)

wpearlite = wγ

ααα

αα

α pearlite

100µm Hypoeutectoid steel

HYPOHYPO--EUTECTOIDEUTECTOID

“Proeutectoid” means it formed ABOVE or BEFORE the Eutectoid Temperature!

How to calculate the relative amounts of proeutectoid

phase (α or Fe3C) and pearlite?Eutectoid ,0.76% CEutectoid ,0.76% C

2.14

HypoEutectoidHyperEutectoid

2.14

� Fraction of pearlite:

74.0

022.0'

022.076.0

022.0' −=−−=

+= CoCo

UT

TWp 74.0022.076.0

=−

=+

=UT

Wp

� Fraction of Proeutectoid :

74.0

'76.0

022.076.0

'76.0 CoCo

UT

UW

−=−−=

+=α

� Fraction of pearlite: (for Hypereutectoid alloys)

94.5

'170.6

76.070.6

'170.6 CC

XV

XWp

−=−−=

+=

94.576.070.6XVWp =

−=

+=

� Fraction proeutectoid cementite: (Hypereutectoid)

76.0'176.0'1 −=−== CCVW

94.576.070.63 =−

=+

=XV

W CFe

(Fe-C System)

C (cementite)

1600

1400

1200

1000

L

γ (austenite)

γ+L

γ+Fe3C

L+Fe3C

δ

1148°C

T(°C)

γ γγγ

γγγ γ

Fe3C

HYPEREUTECTOID STEEL

Co

Fe3C (cementite)

800

600

4000 1 2 3 4 5 6 6.7

α+Fe3C

Co, wt% C0.77

R Sαs

wFe3C =r/(r+s)wγ =(1-wFe3C)

wα =S/(R+S)wFe3C =(1-wα)

wpearlite = wγpearlite

60µm Hypereutectoid steel

r

γγγ γ

Fe3C

HYPERHYPER--EUTECTOIDEUTECTOID

“Proeutectoid” means it formed ABOVE or BEFORE the Eutectoid Temperature!

THANK YOU