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Chapter 9: Phase Diagrams, Lecture notes of Chemistry

Phase diagram: information about phases as function of T, composition, and pressure ... Sucrose/Water Phase Diagram. Pure. Sugar. Temperature (°C).

Typology: Lecture notes

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Chapter 9 - 1
• 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?
Chapter 9: Phase Diagrams
Phase B
Phase A
Nickel atom
Copper atom
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  • 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?

Chapter 9: Phase Diagrams

Phase B Phase A

Nickel atom

Copper atom

Definitions and basic concepts

  • Component: pure metals and/or compounds of which an

alloy is composed

  • System: a specific body of material under consideration
  • A phase: a homogeneous portion of a system that has

uniform physical and chemical characteristics

  • Equilibrium: a system is at equilibrium if its free energy is

at a minimum under some specified combination of

temperature, pressure, and composition.

  • Phase equilibrium: minimum energy for a system with

multiple phases

  • Phase diagram: information about phases as function of T,

composition, and pressure

Phase Equilibria: Solubility Limit

65

Sucrose/Water Phase Diagram

Pure Sugar

Temperature (°C)

(^0 ) (^40 60 80 )

C o

=Composition (wt% sugar)

L

(liquid solution

i.e., syrup)

Solubility

Limit L

(liquid)

+

S

(solid

(^20) sugar)

4 0

6 0

8 0

10 0

Pure Water

Question: What is the

solubility limit at 20C?

Answer: 65wt% sugar.

If C

o

< 65wt% sugar: syrup

If C

o

> 65wt% sugar: syrup

+ sugar.

• Solubility limit increases

with T:

e.g., if T = 100C, solubility

limit = 80wt% sugar.

Effect of T & Composition ( C

o

  • Changing T can change # of phases:

Adapted from

Fig. 9.1,

Callister 7e.

D (100°C,90)

2 phases

B (100°C,70)

1 phase

path A to B.

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

A (20°C,70)

2 phases

Temperature (°C)

C

o

=Composition (wt% sugar)

L

( liquid solution

i.e., syrup)

20

100

40

60

80

0

L

(liquid)

S

(solid

sugar)

water-

sugar

system

Phase Diagrams

  • Indicate phases as function of T , C o

, and P.

  • For this course:

-binary systems: just 2 components.

-independent variables: T and C

o

( P = 1 atm is almost always used).

  • Phase

Diagram

for Cu-Ni

system

Adapted from Fig. 9.3(a), Callister 7e.

(Fig. 9.3(a) is adapted from Phase

Diagrams of Binary Nickel Alloys , P. Nash

(Ed.), ASM International, Materials Park,

OH (1991).

  • 2 phases:

L (liquid)

α (^) (FCC solid solution)

  • 3 phase fields:

L

L + α

wt% Ni 0 20 40 60 80 100

1000

1100

1200

1300

1400

1500

1600

T (°C)

L (liquid)

α

(FCC solid

solution)

wt% Ni

20

1200

1300

T (°C)

L (liquid)

α

(solid)

30 40 50

Cu-Ni

system

Phase Diagrams:

composition of phases

  • Rule 2: If we know T and C o

, then we know:

--the composition of each phase.

  • Examples:

T

A

A

C

o

C

L

At T A

= 1320°C:

Only Liquid ( L )

C

L

= C

o

( = 35 wt% Ni)

At T B

= 1250°C:

Both α^ and L

C

L

= C

liquidus

( = 32 wt% Ni here)

C

α

= C

solidus

( = 43 wt% Ni here)

At T D

= 1190°C:

Only Solid ( α)

C

α

= C

o

( = 35 wt% Ni)

C

o

= 35 wt% Ni

Adapted from Fig. 9.3(b), Callister 7e.

(Fig. 9.3(b) is adapted from Phase Diagrams

of Binary Nickel Alloys , P. Nash (Ed.), ASM

International, Materials Park, OH, 1991.)

B

T

B

D

T

D

tie line

C

α

  • Tie line – connects the phases in equilibrium with

each other - essentially an isotherm

The Lever Rule

How much of each phase?

Think of it as a lever (teeter-totter)

M L

M α

R S

wt% Ni

20

1200

1300

T (°C)

L (liquid)

α

(solid)

3 0 4 0 5 0

B

T

B

tie line

C

o

C L

C α

R S

Adapted from Fig. 9.3(b),

Callister 7e.

wt% Ni

20

120 0

130 0

3 0 4 0 5 0

110 0

L (liquid)

(solid)

T (°C)

A

C

o

L : 35wt%Ni

Cu-Ni

system

  • 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; α phase

field extends from

0 to 100 wt% Ni.

Adapted from Fig. 9.4,

Callister 7e.

  • Consider

C

o

= 35 wt%Ni.

Ex: Cooling in a Cu-Ni Binary

46

35

43

32

α: 43 wt% Ni

L : 32 wt% Ni

L : 24 wt% Ni

α: 36 wt% Ni

B

α: 46 wt% Ni

L : 35 wt% Ni

C

D

E

24 36

: Min. melting T

E

2 components

has a special composition

with a min. melting T.

Adapted from Fig. 9.7,

Callister 7e.

Binary-Eutectic Systems

- Eutectic transition

L ( C E

) α( C α E

) + β( C β E

)

  • 3 single phase regions

( L , α,^ β)

  • Limited solubility:

α: mostly Cu

β: mostly Ag

  • T E

: No liquid below T

E

  • C E

composition

Ex.: Cu-Ag system

Cu-Ag

system

L (liquid)

α L^ +^ α

L +β^

α + β

C o

, wt% Ag

0 20 40 60 80 100

200

1200

T (°C)

400

600

800

1000

C E

T E 8.0 71.9 91.

779°C

Binary eutectic systems (Example)

  • Explain how spreading

salt on ice that is at a

temperature below 0

0 C

can cause the ice to

melt.

L +β

α + β

200

T (°C)

C , wt% Sn

20 60 80 100 0

300

100

L (liquid)

α

β

L

183 °C

  • For a 40 wt% Sn-60 wt% Pb alloy at 200°C, find...

--the phases present:

Pb-Sn

system

Adapted from Fig. 9.8,

Callister 7e.

EX: Pb-Sn Eutectic System (2)

α + L

--compositions of phases:

C

O

= 40 wt% Sn

--the relative amount

of each phase:

W

α

C

L

- C

O

C

L

- C

α

= 21 wt%

W

L

C

O

- C

α

C

L

- C

α

= 79 wt%

40

C o

46

C L

17

C α

220

R S

C

α

= 17 wt% Sn

C

L

= 46 wt% Sn