Chapter 9 - 1

ISSUES TO ADDRESS...

• Phase diagrams in ceramic systems

Chapter 9: Phase Diagrams

• Application of phase diagram

• Phase diagram and microstructure evolution

• Fe – C system phase diagram

• Other phase diagrams: peritectic and eutectoid

Chapter 9 -

• What type of phase diagram is this?

Binary eutectic phase diagram

• How many components and what are they?

Two (2) components: sucrose and water

• How many single phase that can be present

and what are they?

Three (3): Liquid, Ice (solid), and Sucrose (solid)

• What is the melting point of sucrose?

About 180C

• What is the roughly the eutectic temperature?

About -16C

• Write down eutectic reaction and the

composition for each of the phase

involved?

L Sucrose + Ice

composition for each phase involved:

CL ~ 62wt% sucrose

Csucrose = 100 wt% sucrose

Cice = 0 wt% sucrose

Class Exercise Sucrose-water

phase diagram

Chapter 9 -

• For a system with 80wt% of sucrose at 20C

– How many phases and what are they?

Two(2): Liquid and sucrose

– The composition for each phase

Liquid phase composition: ~66wt% sucrose

Sucrose phase composition: ~100wt%

sucrose

– The relative amount (or weight fraction) of

each phase

Liquid phase relative amount/weight fraction

Sucrose phase relative amount/weight fraction

Class Exercise Sucrose-water

phase diagram

%8.58588.066100

80100

LW

%2.41412.066100

6680

SucroseW

What about the same system but at -80C (80 below 0C)?

Two phases: ice (Cice=0wt% sucrose) & sucrose (Csucrose=100wt% sucrose),

Relative amount: Wice=(100-80)/(100-0)=20%, Wsucrose=80%

Chapter 9 - 4

• Co < 2 wt% Sn

Adapted from Fig. 9.11,

Callister 7e.

Microstructure Evolution

in Eutectic Systems: I

0

L + a

200

T(°C)

Co , wt% Sn 10

2

20 Co

300

100

L

a

30

a + b

400

(room T solubility limit)

TE

(Pb-Sn System)

a L

L: Co wt% Sn

a: Co wt% Sn

1. One component rich

composition.

a: start with homogeneous liquid.

b: a-phase solids with liquid.

Compositions and mass fractions

can be found via tie lines and lever

rule.

c: a-phase solid solution only.

Net result: polycrystalline a solid.

Cooling for this composition yields

similar microstructure to that

obtained in a binary isomorphous

system

a

b

c

Chapter 9 - 5

• ~2 wt% Sn < Co < 18.3 wt% Sn

Adapted from Fig. 9.12,

Callister 7e.

Microstructure Evolution

in Eutectic Systems: II

Pb-Sn

system

L + a

200

T(°C)

, wt% Sn 10

18.3

20 0 Co

300

100

L

a

30

a + b

400

(sol. limit at TE)

TE

2 (sol. limit at T room )

L

a

L: Co wt% Sn

a b

a: Co wt% Sn

2. One-component rich but cooling to

a + b coexistence two phase region.

d: homogeneous liquid.

e: a + L phase (same as previous but at

different compositions and mass fractions).

f: all a-phase solid solution.

g: a + b phase (passing through solvus line

leads to exceeding solubility limit and b

phase precipitates out).

Net result: polycrystalline a-solid with fine

b crystals or “b precipitates”.

d

f

e

g

Chapter 9 - 6

• Co = CE

Eutectic reaction/transformation: L(61.9wt%Sn) a(18.3wt%Sn)+b(97.8%Ag)

• Upon cooling forms Eutectic or lamellar/layered microstructure:

--closely spaced alternating layers (lamellae) of a and b crystals.

Adapted from Fig. 9.13,

Callister 7e.

Microstructure Evolution

in Eutectic Systems: III

Adapted from Fig. 9.14, Callister 7e.

160 m

Pb-Sn eutectic microstructure

Pb-Sn

system

L b

a b

200

T(°C)

C, wt% Sn

20 60 80 100 0

300

100

L

a b

L + a

183°C

40

TE

18.3

a: 18.3 wt%Sn

97.8

b: 97.8 wt% Sn

CE 61.9

L: Co wt% Sn

h

i

cool

heat

Chapter 9 - 7

Lamellar Eutectic Structure

Adapted from Figs. 9.14 & 9.15, Callister

7e.

L

Sn

Pb

b

a Pb rich

Sn rich

In order to achieve larger homogeneous

regions, longer diffusion lengths are

required, which is not easy

Lamellar structure forms because relatively

short diffusion lengths at lower

temperature (small D and )

a

b

Dt

Chapter 9 - 8

• 18.3 wt% Sn < Co < 61.9 wt% Sn

• Result: a crystals and an eutectic microstructure

Microstructure Evolution

in Eutectic Systems: IV

18.3 61.9

S R

97.8

S R

primary a

eutectic a

eutectic b

WL = (1- W a ) = 50 wt%

C a = 18.3 wt% Sn

CL = 61.9 wt% Sn S

R + S W a = = 50 wt%

• Just above TE : L + a

• Just below TE : a+b

C a = 18.3 wt% Sn

C b = 97.8 wt% Sn S

R + S W a = = 73 wt%

W b = 27 wt% Adapted from Fig. 9.16,

Callister 7e.

Pb-Sn

system L + b 200

T(°C)

Co, wt% Sn

20 60 80 100 0

300

100

L

a b

L + a

40

a + b

TE

L: Co wt% Sn L a L a

Pb-Sn System

Chapter 9 - 9

Other Features in Phase Diagrams -

Intermediate Solid Solutions Intermediate solid solutions (intermediate phases): Solid solutions

that do not extend to pure components in the phase diagram.

Cu-Zn

Terminal solid

solutions: a and h.

Intermediate solid

solutions: b, g, d and e.

Tie lines and lever rule can

be used to determine

compositions and wt% of

phases.

e.g. at 800oC with 70 wt%

Zn

CL = 78 wt% Zn

Cg = 67 wt% Zn

Chapter 9 - 10

Other Features in Phase Diagrams

- Intermetallic Compounds

Mg2Pb

Note: intermetallic compounds often form a discrete line in

composition – also called line compounds

Adapted from

Fig. 9.20, Callister 7e.

Chapter 9 -

• Peritectic - liquid + solid 1 solid 2

S1 + L S2

11

Other Features in Phase Diagrams

Eutectoid & Peritectic Transformation

• Eutectic - liquid in equilibrium with two solids

L a + b

cool

heat

• Eutectoid - solid phase in equation with two solid

phases

S2 S1+S3

Chapter 9 - 12

Eutectoid & Peritectic

Cu-Zn Phase diagram

Adapted from

Fig. 9.21, Callister 7e.

Peritectic transition g + L d cool

heat

Eutectoid transition d g + e cool

heat

Chapter 9 - 13

Ceramic phase diagrams

Al2O3-Cr2O3 MgO-Al2O3

Chapter 9 - 14

TVR Tuscan Speed 6, high-performance sports

car with an austempered ductile iron crankshaft.

The world's first bridge made of iron

in 1779. The entire structure is

made of cast iron. (near Broseley,

UK)

Iron-Carbon System structural material

Ferrite Magnets

Chapter 9 - 15

Iron-Carbon System

The Akashi Kaikyo bridge, a 3-span 2-

hinged truss-stiffened suspension bridge.

completed in 1998. It connects Kobe with

Awaji Island. It is the world's longest

suspension bridge, with a span between

the towers of 1.9 km.

Millau Viaduct in France, the

highest bridge in the world.

Golden Gate Bridge

Steel bridges

Chapter 9 - 16

Classification Scheme of Ferrous Alloys

• Iron Pure ion contains less than 0.008wt% C

• Steel

0.008-2.14 wt% C, in practice,<1.0 wt% C

• Cast Iron

2.14-6.70 wt% C, in practice, <4.5 wt% C

Chapter 9 - 17

• Iron-carbon (Fe-C) system is the most important

binary system due to the versatile uses of the iron-

based structural alloys.

• This phase diagram is important in understanding the

equilibrium structure, and in the design of heat

treatment process of iron alloys.

• The most important part of the phase diagram is the

region below 6.7 w% carbon. All practical iron-carbon

alloys contain C below 6.7 w%. This part is of the

phase diagram is thus the most analyzed part of the

iron carbon phase diagram.

• C is an interstitial element in Fe matrix.

Iron-Carbon System

Chapter 9 -

18

Iron-Carbon (Fe-C) Phase Diagram

• 2 important reactions

-Eutectoid reaction (B):

-Eutectic reaction (A):

L(4.3wt%C) g(2.2wt%C) + Fe3C(6.7wt%C)

Adapted from Fig. 9.24,Callister 7e.

Fe

3C

(ce

me

ntite

)

1600

1400

1200

1000

800

600

400 0 1 2 3 4 5 6 6.7

L

g

(austenite)

g +L

g +Fe3C

a +Fe3C

L+Fe3C

d

(Fe) Co, wt% C

1148°C

T(°C)

a

ferrite

727°C = T eutectoid

A

S R

4.30

Result: Pearlite = alternating layers of a and Fe3C phases

120 m

(Adapted from Fig. 9.27, Callister 7e.)

g g

g g

R S

0.76

C e

ute

cto

id

B

Fe3C (cementite-hard)

a (ferrite-soft)

g (0.76wt%C) a(0.022wt%C)+Fe3C(6.7wt%C)

Ca m

ax=

0.0

22

Chapter 9 - 19

Ferrite (90x) or a-Fe

Almost pure BCC-structured

Fe with very little C (<0.02wt%)

dissolved in it; Exists at RT

Austenite (x325) or g-Fe

FCC-structured Fe with C

solubility up to ~2%. Exist at >727C

Not stable at RT and will

transform to other phase(s)

upon cooling Relatively soft

Chapter 9 - 20

Eutectoid Microstructure

in Fe-Fe3C system:

Pearlite

Pearl-microscope picture

colonies

(X500)

Mechanically, pearlite has properties intermediate between the soft,

ductile ferrite (a-Fe) and the hard, brittle cementite (Fe3C).

Chapter 9 - 21

g 3.947.5100

g 5.7 W

g7.5100 022.07.6

022.04.0

100x

CFe

3

3

aW

gx

gSR

RW CFe

b) the amount of Fe3C and α in

grams that forms per 100 g of

that steel

a) The composition for each phase (in wt% C) Ca = 0.022 wt% C;

CFe C = 6.70 wt% C

3

Fe

3C

(ce

me

ntite

)

1600

1400

1200

1000

800

600

400 0 1 2 3 4 5 6 6.7

L

g (austenite)

g +L

g + Fe3C

a + Fe3C

L+Fe3C

d

Co , wt% C

1148°C

T(°C)

727°C

CO

R S

CFe C 3

Ca

For a 99.6 wt% Fe-0.40 wt% C steel at a temperature just below

the eutectoid temperature (727C), determine the following

a

ferrite

Chapter 9 - 22

• Phase diagrams help understand change in microstructure

during phase change

• Common types of phase diagram:

• Binary isomorphous

• Binary eutectic

• Other: eutectoid, peritectic…

• Use the same principles to read and understand phase

diagrams in other systems such as ceramics

• Fe-C (or more precisely, Fe-Fe3C) is one the most important

phase diagrams

Summary

Chapter 9 -

Homework

• Read chapter 9 and give a statement

confirming reading

• Calister 8ed, 9.1, 9.11, one additional

problem, 9.37

23

Chapter 9 -

Calister 8ed 9.1

9.1 Consider the sugar–water phase diagram of Figure 9.1.

(a) How much sugar will dissolve in 1500 g water at 90C

(194F)?

(b) If the saturated liquid solution in part (a) is cooled to 20C

(68F), some of the sugar will precipitate out as a solid. What

will be the composition of the saturated liquid solution (in wt%

sugar) at 20C?

(c) How much of the solid sugar will come out of solution upon

cooling to 20C?

24

Chapter 9 -

Calister 8ed, 9.11

9.11 A copper-nickel alloy of composition 70 wt% Ni-30 wt%

Cu is slowly heated from a temperature of 1300C.

(a) At what temperature does the first liquid phase form?

(b) What is the composition of this liquid phase?

(c) At what temperature does complete melting of the alloy

occur?

(d) What is the composition of the last solid remaining prior to

complete melting?

25

Chapter 9 -

Homework

26

http://www.aluminium.matter.org.uk/content/html/eng/

default.asp?catid=79&pageid=196589346

L+Si

(Al)+Si

L+(Al)

Al Si

• What type of phase diagram is it?

• How many components? What are they?

• What are the phases that can be present

in the phase diagram?

• What are the phase regions (or phase

fields)?

• What is eutectic temperature?

• Write down the eutectic reaction and

the rough composition (in wt% Si)

for each of the phase involved in the

eutectic reaction?

• What are the phases, their approximate

composition (in wt% Si) and relative

amount (weight fraction) for the following

systems under equilibrium

• C0=20 wt% Si, at ~400K

• C0=20 wt% Si, at just above eutectic

temperature?

Chapter 9 -

Calister 8ed, 9.37

For a 30 wt% Zn-70 wt% Cu alloy, make

schematic sketches of the microstructure

that would be observed for conditions of

very slow cooling at the following

temperatures: 1100C (2010F), 950C (1740F),

900C (1650F), and 700C (1290F). Label all

phases and indicate their approximate

compositions.

27