• Ex: Phase Diagram: Water-Sugar System

Pure

Sugar

Tem

pera

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

Pure

W

ate

r

THE SOLUBILITY LIMIT

• Components: The elements or compounds which are mixed initially (e.g., Al and Cu)• Phases: The physically and chemically distinct material regions that result (e.g., and ).

Aluminum-CopperAlloy

(darker phase)

(lighter phase)

COMPONENTS AND PHASES

• Changing T can change # of phases: path A to B. • Changing Co can change # of phases: path B to D.

• water- sugar system

70 80 1006040200

Tem

pe

ratu

re (

°C)

Co=Composition (wt% sugar)

L (liquid solution

i.e., syrup)

A(70,20) 2 phases

B(100,70) 1 phase

20

100

D(100,90) 2 phases

40

60

80

0

L (liquid)

+ S

(solid sugar)

EFFECT OF T & COMPOSITION (Co)

• Tell us about phases as function of T, Co, P.

PHASE DIAGRAMS

• For this course: --binary systems: just 2 components. --independent variables: T and Co (P = 1atm is always used).

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

• 3 phase fields: L L +

wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

1500

1600T(°C)

L (liquid)

(FCC solid solution)

• PHASE DIAGRAM FOR Cu-Ni SYSTEM

• Rule 1: If we know T and Co, then we know: --the # and types of phases present.

wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

1500

1600T(°C)

L (liquid)

(FCC solid solution)

L +

liquidus

solid

us

A(1100,60)

B(1

250,3

5) Cu-Ni

phasediagram

PHASE DIAGRAMS: # and types of phases

• Rule 2: If we know T and Co, then we know: --the composition of each phase.

wt% Ni20

1200

1300

T(°C)

L (liquid)

(solid)L +

liquidus

solidus

30 40 50

TAA

DTD

TBB

tie line

L +

433532CoCL C

Cu-Ni system

PHASE DIAGRAMS: composition of phases

• Rule 3: If we know T and Co, then we know: --the amount of each phase (given in wt%).

Cu-Nisystem

• Examples:

wt% Ni

20

1200

1300

T(°C)

L (liquid)

(solid)

L +

liquidus

solidus

30 40 50

TAA

DTD

TBB

tie line

L +

433532CoCL C

R S

PHASE DIAGRAMS: weight fractions of phases

• Sum of weight fractions:

• Combine above equations:

WL W 1

RR S

W Co CLC CL

SR S

WLC Co

C CL

• A geometric interpretation:

CoR S

WWL

CL C

moment equilibrium:

1 Wsolving gives Lever Rule

WLR WS

THE LEVER RULE: A PROOF

• Phase diagram: Cu-Ni system.

• System is: --binary i.e., 2 components: Cu and Ni. --isomorphous i.e., complete solubility of one component in another; phase field extends from 0 to 100wt% Ni.

wt% Ni20

1200

1300

30 40 501100

L (liquid)

(solid)

L +

L +

T(°C)

A

D

B

35Co

L: 35wt%Ni

: 46wt%Ni

C

E

L: 35wt%Ni

464332

24

35

36: 43wt%Ni

L: 32wt%Ni

L: 24wt%Ni

: 36wt%Ni

• Consider Co = 35wt%Ni.

Cu-Nisystem

EX: COOLING IN A Cu-Ni BINARY

• Effect of solid solution strengthening on:--Tensile strength (TS) --Ductility (%EL,%AR)

--Peak as a function of Co --Min. as a function of Co

MECHANICAL PROPERTIES: Cu-Ni System

Elo

ng

ati

on

(%

EL)

Composition, wt%NiCu Ni0 20 40 60 80 10020

30

40

50

60

%EL for pure Ni

%EL for pure Cu

Ten

sile

Str

en

gth

(M

Pa)

Composition, wt%NiCu Ni0 20 40 60 80 100

200

300

400

TS for pure Ni

TS for pure Cu

2 componentshas a special compositionwith a min. melting T.

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

• CE: Min. melting T

composition

Ex.: Cu-Ag system L (liquid)

L + L+

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-Agsystem

BINARY-EUTECTIC SYSTEMS

L + 200

T(°C)

Co, wt% Sn10

2

200Co

300

100

L

30

L: Cowt%Sn

L

: Cowt%Sn

+

400

(room T solubility limit)

TE(Pb-Sn System)

• Co < 2wt%Sn• Result: --polycrystal of grains.

MICROSTRUCTURESIN EUTECTIC SYSTEMS-I

• 2wt%Sn < Co < 18.3wt%Sn• Result: -- polycrystal with fine crystals.

: Cowt%SnL +

200

T(°C)

Co, wt% Sn10

18.3

200Co

300

100

L

30

L: Cowt%Sn

+

400

(sol. limit at TE)

TE

2(sol. limit at Troom)

L

Pb-Snsystem

MICROSTRUCTURESIN EUTECTIC SYSTEMS-II

L + 200

T(°C)

Co, wt% Sn

20 400

300

100

L

60

L: Cowt%Sn

+

TE

: 18.3wt%Sn

080 100

L +

CE18.3 97.861.9

183°C

: 97.8wt%Sn160m

Micrograph of Pb-Sn eutectic microstructure

• Co = CE • Result: Eutectic microstructure --alternating layers of and crystals.

Pb-Snsystem

MICROSTRUCTURESIN EUTECTIC SYSTEMS-III

L + 200

T(°C)

Co, wt% Sn

20 400

300

100

L

60

L: Cowt%Sn

+

TE

080 100

L +

Co18.3 61.9

L

L

primary

97.8

SS

RR

eutectic eutectic

Pb-Snsystem

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

• Just above TE:

WL = (1-W) =50wt%

C = 18.3wt%Sn

CL = 61.9wt%SnS

R + SW = =50wt%

• Just below TE:C = 18.3wt%Sn

C = 97.8wt%SnS

R + SW = =73wt%

W = 27wt%

MICROSTRUCTURESIN EUTECTIC SYSTEMS-IV

T(°C)

(Pb-Sn System)

L + 200

Co, wt% Sn20 400

300

100

L

60

+

TE

080 100

L +

18.361.9

97.8

Cohypoeutectic

Cohypereutectic

eutectic

hypereutectic: (illustration only)

160m

eutectic: Co=61.9wt%Sn

175m

hypoeutectic: Co=50wt%Sn

eutectic micro-constituent

HYPOEUTECTIC & HYPEREUTECTIC

INTERMEDIATE PHASES

INTERMEDIATE COMPOUND

H2O – NaCl PHASE DIAGRAM

Result: Pearlite = alternating layers of and Fe3C phases.

120m

• 2 important points

-Eutectic (A):

-Eutectoid (B): L Fe3C

Fe3C

Fe3C

(cem

enti

te)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

austenite)

+L

+Fe3C

+Fe3C

L+Fe3C

(Fe) Co, wt% C0.77 4.30

727°C = Teutectoid

1148°C

T(°C)

A

B

SR

R S

Fe3C (cementite-hard)(ferrite-soft)

C

eu

tecto

id

IRON-CARBON (Fe-C) PHASE DIAGRAM

HYPOEUTECTOID STEEL

(Fe-C System)

Co

Fe3C

(cem

enti

te)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

austenite)

+L

+Fe3C

+Fe3C

L+Fe3C

Co, wt% C0.7

7

727°C

1148°C

T(°C)

R S

r s

w =s/(r+s)w =(1-w)

w =S/(R+S)wFe3C =(1-w)

wpearlite = w

pearlite

100m Hypoeutectoid steel

(Fe-C System)

Co

Fe3C

(cem

enti

te)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

austenite)

+L

+Fe3C

+Fe3C

L+Fe3C

Co, wt% C0.7

71148°C

T(°C)

R S

s

wFe3C =r/(r+s)w =(1-wFe3C)

w =S/(R+S)wFe3C =(1-w)

wpearlite = wpearlite

60m Hypereutectoid steel

r

Fe3C

HYPEREUTECTOID STEEL