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Phase Diagrams Binary Eutectoid Systems Iron-Iron-Carbide Phase Diagram Steels and Cast Iron. What is Phase?. The term ‘ phase ’ refers to a separate and identifiable state of matter in which a given substance may exist. Applicable to both crystalline and non-crystalline materials

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what is phase
What is Phase?
  • The term ‘phase’ refers to a separate and identifiable state of matter in which a given substance may exist.
  • Applicable to both crystalline and non-crystalline materials
  • An important refractory oxide silica is able to exist as three crystalline phases, quartz, tridymite and cristobalite, as well as a non-crystalline phase, silica glass, and as molten silica
  • Every pure material is considered to be a phase, so also is every solid, liquid, and gaseous solution
  • For example, the sugar–water syrup solution is one phase, and solid sugar is another
introduction to phase diagram
Introduction to Phase Diagram
  • There is a strong correlation between microstructure and mechanical properties, and the development of microstructure of an alloy is related to the characteristics of its phase diagram
  • It is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium
  • Provides valuable information about melting, casting, crystallization, and other phenomena
issues to address
ISSUES TO ADDRESS...

• 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 B

Phase A

Nickel atom

Copper atom

solubility limit
Solubility Limit
  • At some specific temperature, there is a maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution, which is called as Solubility Limit
  • The addition of solute in excess of this solubility limit results in the formation of another compound that has a distinctly different composition
  • This solubility limit depends on the temperature
microstructure
Microstructure
  • the structure of a prepared surface of material as revealed by a microscope above 25× magnification
  • The microstructure of a material can strongly influence properties such as strength, toughness, ductility, hardness, corrosion resistance, high/low temperature behavior, wear resistance, etc
components and phases
Components and Phases

• Components:

The elements or compounds which are present in the mixture

(e.g., Al and Cu)

• Phases:

The physically and chemically distinct material regions

that result (e.g., a and b).

Aluminum-

Copper

Alloy

b

(lighter

phase)

a

(darker

phase)

effect of t composition c o

B (100°C,70)

1 phase

D (100°C,90)

2 phases

100

L

80

(liquid)

+

60

L

S

Temperature (°C)

(

liquid solution

(solid

40

i.e., syrup)

sugar)

A (20°C,70)

2 phases

20

0

0

20

40

60

70

80

100

Co

=Composition (wt% sugar)

Effect of T & Composition (Co)

path A to B.

• Changing T can change # of phases:

  • Changing Co can change # of phases:

path B to D.

water-

sugar

system

phase equilibria
PHASE EQUILIBRIA
  • Free Energy -> a function of the internal energy of a system, and also the disorder of the atoms or molecules (or entropy)
  • A system is at equilibrium if its free energy is at a minimum under some specified combination of temperature, pressure, and composition
  • A change in temperature, pressure, and/or composition for a system in equilibrium will result in an increase in the free energy
  • And in a possible spontaneous change to another state whereby the free energy is lowered
unary phase diagram
Unary Phase Diagram
  • Three externally controllable parameters that will affect phase structure: temperature, pressure, and composition
  • The simplest type of phase diagram to understand is that for a one-component system, in which composition is held constant
  • Pure water exists in three phases: solid, liquid and vapor
pressure temperature diagram water
Pressure-Temperature Diagram (Water)
  • Each of the phases will exist under equilibrium conditions over the temperature–pressure ranges of its corresponding area
  • The three curves (aO, bO, and cO) are phase boundaries; at any point on one of these curves, the two phases on either side of the curve are in equilibrium with one another
  • Point on a P–T phase diagram where three phases are in equilibrium, is called a triple point
binary phase diagrams
Binary Phase Diagrams
  • A phase diagram in which temperature and composition are variable parameters, and pressure is held constant—normally 1atm
  • Binary phase diagrams are maps that represent the relationships between temperature and the compositions and quantities of phases at equilibrium, which influence the microstructure of an alloy.
  • Many microstructures develop from phase transformations, the changes that occur when the temperature is altered
phase equilibria1
Phase Equilibria

Simple solution system (e.g., Ni-Cu solution)

  • Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility.
  • Ni and Cu are totally miscible in all proportions.
phase diagrams

T(°C)

• 2 phases:

1600

L

(liquid)

1500

L (liquid)

a

(FCC solid solution)

• 3 phase fields:

1400

L

a

liquidus

+

1300

a

L +

L

solidus

a

a

1200

(FCC solid

1100

solution)

1000

wt% Ni

0

20

40

60

80

100

Phase Diagrams

• Indicate phases as function of T, Compos, and Press.

• For this course:

-binary systems: just 2 components.

-independent variables: T and Co (P = 1 atm is almost always used).

•Phase

Diagram

for Cu-Ni

system

phase diagrams and types of phases

T(°C)

1600

L (liquid)

1500

a

1 phase:

Cu-Ni

phase

diagram

liquidus

B

(1250°C, 35):

(1250°C,35)

1400

solidus

a

2 phases: L +

a

a

+

1300

L

B

(FCC solid

1200

solution)

1100

A(1100°C,60)

1000

wt% Ni

0

20

40

60

80

100

Phase Diagrams:# and types of phases

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

--the number and types of phases present.

• Examples:

A(1100°C, 60):

phase diagrams composition of phases

Cu-Ni system

T(°C)

A

T

C

= 35 wt% Ni

A

o

tie line

liquidus

L (liquid)

At T

= 1320°C:

1300

A

a

+

L

Only Liquid (L)

B

T

solidus

B

C

= C

( = 35 wt% Ni)

L

o

a

a

At T

= 1190°C:

+

D

L

(solid)

1200

D

a

Only Solid (

)

T

D

C

= C

( = 35 wt% Ni

)

a

o

32

35

4

3

20

30

40

50

At T

= 1250°C:

C

C

C

a

B

L

o

wt% Ni

a

Both

and L

C

= C

( = 32 wt% Ni here)

L

liquidus

C

= C

( = 43 wt% Ni here)

a

solidus

Phase Diagrams:composition of phases

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

--the composition of each phase.

• Examples:

phase diagrams weight fractions of phases
Phase Diagrams:weight fractions of phases

Cu-Ni system

T(°C)

A

T

C

= 35 wt% Ni

A

o

tie line

liquidus

L (liquid)

At T

: Only Liquid (L)

1300

a

A

+

L

B

W

= 100 wt%, W

= 0

a

L

T

solidus

B

S

R

a

At T

:

Only Solid (

)

D

a

a

+

W

= 0, W

= 100 wt%

L

a

L

(solid)

1200

D

T

a

D

At T

:

Both

and L

B

32

35

4

3

20

3

0

4

0

5

0

S

=

WL

C

C

C

a

L

o

wt% Ni

R

+

S

R

=

= 27 wt%

Wa

R

+

S

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

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

• Examples:

the lever rule

T(°C)

tie line

liquidus

L (liquid)

1300

a

+

M

ML

L

B

solidus

T

B

a

a

+

L

(solid)

1200

R

S

S

R

20

3

0

4

0

5

0

C

C

C

a

L

o

wt% Ni

The Lever Rule
  • Tie line – connects the phases in equilibrium with each other - essentially an isotherm
  • How much of each phase? Think of it as a lever (teeter-totter)
ex cooling in a cu ni binary
Ex: Cooling in a Cu-Ni Binary

T(°C)

L: 35wt%Ni

L (liquid)

Cu-Ni

system

a

130

0

A

+

L

L: 35 wt% Ni

B

a: 46 wt% Ni

35

46

C

32

43

D

L: 32 wt% Ni

24

36

a

a

:

43 wt% Ni

+

120

0

E

L

L: 24 wt% Ni

a

:

36 wt% Ni

a

(solid)

110

0

35

20

3

0

4

0

5

0

wt% Ni

C

o

• 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; a phase

field extends from

0 to 100 wt% Ni.

• Consider

Co = 35 wt%Ni.

cored vs equilibrium phases
Cored vs Equilibrium Phases

Uniform C

:

a

a

First

to solidify:

35 wt% Ni

46 wt% Ni

a

Last

to solidify:

< 35 wt% Ni

• Ca changes as we solidify.

• Cu-Ni case:

First a to solidify has Ca = 46 wt% Ni.

Last a to solidify has Ca = 35 wt% Ni.

• Fast rate of cooling:

Cored structure

• Slow rate of cooling:

Equilibrium structure

mechanical properties cu ni system

60

%EL

for pure Cu

400

%EL

for

50

pure Ni

TS for

Elongation (%EL)

40

pure Ni

Tensile Strength (MPa)

300

30

TS for pure Cu

200

20

0

20

40

60

80

100

0

20

40

60

80

100

Cu

Ni

Cu

Ni

Composition, wt% Ni

Composition, wt% Ni

Mechanical Properties:Cu-Ni System

• Effect of solid solution strengthening on:

--Tensile strength (TS)

--Ductility (%EL,%AR)

--Peak as a function of Co

--Min. as a function of Co

eutectic system
Eutectic System

A eutectic system is a mixture of chemical compounds or elements that has a single chemical composition that solidifies at a lower temperature than any other composition

binary eutectic systems
Binary-Eutectic Systems

• Eutectic transition

L(CE) (CE) + (CE)

has a special composition

with a min. melting T.

2 components

Cu-Ag

system

T(°C)

Ex.: Cu-Ag system

1200

• 3 single phase regions

L (liquid)

a, b

(L,

)

1000

a

L

+

a

• Limited solubility:

b

L

+

779°C

b

800

TE

a

: mostly Cu

8.0

71.9

91.2

b

: mostly Ag

600

• TE

: No liquid below TE

a

+

b

400

• CE

: Min. melting TE

composition

200

80

100

0

20

40

60

CE

Co

,

wt% Ag

ex pb sn eutectic system 1
EX: Pb-Sn Eutectic System (1)

T(°C)

300

L (liquid)

a

L

+

a

b

b

L

+

200

183°C

18.3

61.9

97.8

C- CO

150

S

R

S

=

W

=

a

R+S

C- C

100

a

+

b

99 - 40

59

=

=

= 67 wt%

99 - 11

88

100

0

11

20

60

80

99

40

CO - C

R

W

C

C

Co

=

=

C, wt% Sn

C - C

R+S

40 - 11

29

=

= 33 wt%

=

99 - 11

88

• For a 40 wt% Sn - 60 wt% Pb alloy at 150°C, find...

--the phases present:

a + b

Pb-Sn

system

--compositions of phases:

CO = 40 wt% Sn

Ca = 11 wt% Sn

Cb = 99 wt% Sn

--the relative amount of each phase:

ex pb sn eutectic system 2
EX: Pb-Sn Eutectic System (2)

T(°C)

CL - CO

46 - 40

=

W

=

a

CL - C

46 - 17

300

L (liquid)

6

a

L

+

=

= 21 wt%

29

220

a

b

b

R

L

+

S

200

183°C

100

a

+

b

100

17

46

0

20

40

60

80

C

CL

Co

C, wt% Sn

CO - C

23

=

W

=

= 79 wt%

L

CL - C

29

• For a 40 wt% Sn - 60 wt% Pb alloy at 220°C, find...

--the phases present:

a + L

Pb-Sn

system

--compositions of phases:

CO = 40 wt% Sn

Ca = 17 wt% Sn

CL = 46 wt% Sn

--the relative amount of each phase:

microstructures in eutectic systems i
Microstructures in Eutectic Systems: I

T(°C)

L: Cowt% Sn

400

L

a

L

300

L

a

+

a

200

(Pb-Sn

a: Cowt% Sn

TE

System)

100

b

+

a

0

10

20

30

Co

,

wt% Sn

Co

2

(room T solubility limit)

• Co< 2 wt% Sn

• Result:

--at extreme ends

--polycrystal of a grains

i.e., only one solid phase.

microstructures in eutectic systems ii
Microstructures in Eutectic Systems: II

L: Co wt% Sn

T(°C)

400

L

L

300

a

L

+

a

a: Cowt% Sn

a

200

TE

a

b

100

b

+

a

Pb-Sn

system

0

10

20

30

Co

,

wt% Sn

Co

2

(sol. limit at T

)

18.3

room

(sol. limit at TE)

  • • 2 wt% Sn < Co< 18.3 wt% Sn
  • • Result:
    • Initially liquid + 
    • then  alone
    • finally two phases
      • a polycrystal
      • fine -phase inclusions
microstructures in eutectic systems iii
Microstructures in Eutectic Systems: III

Micrograph of Pb-Sn

T(°C)

eutectic

L: Co wt% Sn

microstructure

300

L

Pb-Sn

system

a

L

+

a

b

L

200

183°C

TE

100

160m

a

: 97.8 wt% Sn

: 18.3 wt%Sn

0

20

40

60

80

100

97.8

18.3

CE

C, wt% Sn

61.9

• Co = CE

• Result: Eutectic microstructure (lamellar structure)

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

microstructures in eutectic systems pb sn iv
Microstructures in Eutectic Systems (Pb-Sn): IV

• Just above TE :

L

T(°C)

L: Co

wt% Sn

a

C

= 18.3 wt% Sn

a

L

a

CL

= 61.9 wt% Sn

300

L

Pb-Sn

system

S

W

a

L

+

a

= 50 wt%

=

R

+

S

a

b

WL

= (1-

W

)

= 50 wt%

b

L

+

a

R

S

200

TE

S

R

• Just below TE :

C

= 18.3 wt% Sn

a

a

b

100

+

a

primary

C

= 97.8 wt% Sn

b

a

eutectic

S

b

eutectic

W

a

= 73 wt%

=

R

+

S

0

20

40

60

80

100

W

= 27 wt%

b

18.3

61.9

97.8

Co, wt% Sn

• 18.3 wt% Sn < Co < 61.9 wt% Sn

• Result:a crystals and a eutectic microstructure

hypo eutectic hyper eutectic
Hypoeutectic & Hypereutectic

hypoeutectic: Co = 50 wt% Sn

hypereutectic: (illustration only)

a

b

a

b

a

a

b

b

a

b

a

b

175 mm

300

L

T(°C)

a

L

+

a

b

b

L

+

(Pb-Sn

200

TE

System)

a

+

b

100

Co, wt% Sn

0

20

40

60

80

100

eutectic

61.9

eutectic: Co=61.9wt% Sn

160 mm

eutectic micro-constituent