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Phase Diagrams

Chapter 10 (part 1)

Introduction

• (^) Solubility Limits

Phases

Phase Equilibrium

• (^) Interpretation of Phase Diagrams

Binary Isomorphous Systems (Cu-Ni)

Development of Microstructure

• (^) Mechanical Properties

Binary Eutectic Systems

Development of Eutectic Alloy Microstructure

Phase Equilibria: Solubility Limit

• Solution – solid, liquid, or gas solutions, single phase
• Mixture – more than one phase

Question: What is the

solubility limit for sugar in

water at 20 °C?

Answer: 65 wt% sugar.

At 20°C, if C < 65 wt% sugar: syrup

At 20°C, if C > 65 wt% sugar: syrup + sugar

• Solubility Limit:

Maximum concentration for

which only a single phase

solution exists.

Sugar/Water Phase Diagram

Sugar

Temperature (°C)

C = Composition (wt% sugar)

L

(liquid solution

i.e., syrup)

Solubility

Limit

L

(liquid)

S

(solid

(^20) sugar)

Water

Equilibrium

A system is at equilibrium if its free energy is at a

minimum, given a specified combination of

temperature, pressure and composition.

The (macroscopic) characteristics of the system

do not change with time — the system is stable.

• (^) A change in T, P or C for the system will result in

an increase in the free energy and possible

changes to another state whereby the free

energy is lowered.

7

Phase Diagrams

• Indicate phases as a function of Temp, Comp and Pressure.
• Focus on:
  • binary systems: 2 components.
  • independent variables: T and C (P = 1 atm is almost always used).

Cu-Ni

system

• 2 phases:

L

(liquid)

(FCC solid solution)

• 3 different phase fields:

L

L + 

wt% Ni

T(°C)

L (liquid)

(FCC solid

solution)

L

liquidus

solidus

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

Effect of Temperature & Composition (C

o

wt% Ni 0 20 40 60 80 100

T(°C)

L (liquid)

(FCC solid solution)

L

liquidus

solidus

A

B

D

Cu

Cu-Ni

system

• Rule 2: If we know T and C o

, then we know:

--the composition of each phase.

• Examples:

wt% Ni

20

1200

1300

T(°C)

L (liquid)

(solid)

30 40 50

T

A

A

D

TD

TB

B

tie line

CLCo

C

Cu-Ni

system

Phase Diagrams: composition of phases

At T

A

= 1320°C:

Only Liquid (L) present

C

L

= C

0

( = 35 wt% Ni)

At T

B

= 1250°C:

Both



and L present

At T

D

= 1190°C:

Only Solid () present

C



= C

0

( = 35 wt% Ni)

C

L

= C

liquidus

( = 32 wt% Ni)

C



= C

solidus

( = 43 wt% Ni)

• Rule 3: If we know T and C o

, then we know:

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

Cu-Ni system

• Examples:

At T

B

: Both  and L

At T

A

: Only Liquid (L)

W

L

= 100wt%, W

At T

D

: Only Solid ()

W

L

= 0, W

= 100wt%

C

o

= 35wt%Ni

wt% Ni

20

1200

1300

T(°C)

L (liquid)

(solid)

30 40 50

T

A

A

D

TD

TB

B

tie line

CLCo

C

R S

Phase Diagrams: weight fractions of phases

W

L



S

R



S

W 

R

R



S

 73 wt%



R

R



S



S

R

 S

W

L



C

 C

o

C

 C

L

= 27wt %



R

R



S

W



C

o

 C

L

C

 C

L

W

L



S

R



S

W 

R

R



S

• Development of

microstructure during

the non-equilibrium

solidification of a 35 wt

% Ni-65 wt% Cu alloy

outcome:

• (^) Segregation-

nonuniform distribution

of elements within

grains.

• Weaker grain

boundaries if alloy is

reheated.

• C 

changes as it solidifies.

• Cu-Ni case:
• Fast rate of cooling:

Cored structure

• Slow rate of cooling:

Equilibrium structure

First  to solidify has C



= 46wt%Ni.

Last  to solidify has C



= 35wt%Ni.

First  to solidfy:

46wt%Ni

Uniform C  :

35wt%Ni

Last  to solidfy:

< 35wt%Ni

Cored vs Equilibrium Phases

• (^) Coring can be eliminated by means of a homogenization heat treatment carried out at

temperatures below the alloy’s solidus. During the process, atomic diffusion produces grains

that are compositionally homogeneous.

Binary Isomorphous Systems

Cu-Ni system:

The liquid L is a homogeneous liquid solution composed of

Cu and Ni.

• (^) The α phase is a substitutional solid solution consisting of

Cu and Ni atoms with an FCC crystal structure.

• (^) At temperatures below 1080 C, Cu and Ni are mutually

soluble in each other in the solid state for all compositions.

• (^) The complete solubility is explained by their FCC structure,

nearly identical atomic radii and electro-negativities, and

similar valences.

• (^) The Cu-Ni system is termed isomorphous because of this

complete liquid and solid solubility of the 2 components.

Cu-Ni

phase

diagram

Isomorphous Binary Phase Diagram

• Phase diagram:

Cu-Ni system.

• System is:

-- binary

2 components:

Cu and Ni.

-- isomorphous

i.e., complete

solubility of one

component in

another;  phase

field extends from

0 to 100 wt% Ni.

wt% Ni 0 20 40 60 80 100

T(°C)

L (liquid)

(FCC solid

solution)

L

liquidus

solidus

Importance of Phase Diagrams

• There is a strong correlation between

microstructure and mechanical properties,

and the development of alloy

microstructure is related to the

characteristics of its phase diagram.

• Phase diagrams provide valuable

information about melting, casting,

crystallization and other phenomena.