phase diagrams.pdf

1Chapter 7 Phase Equilibria and Phase Diagrams

The one-component phase diagram Gibbs Phase Rule

Phase equilibria in a two-component system The isomorphous diagram The lever rule Equilibrium solidification and microstructure of

isomorphous alloys Liquidius and solidus boundaries Deviations from ideal behavior

Chapter 7 Phase Equilibria and Phase Diagrams, Continued

Phase equilibria in a two-component system The eutectic phase diagram The peritectic phase diagram The monotectic phase diagram Complex diagrams Phase equilibria involving solid-to-solid reactions

2Why important ?Some properties that might be difficult to predict using a common sense without the knowledge of the phase diagrams

example 1: Melting temperature of a mixture AB (solution) of two components A and B could be either lower or higher than the melting point of each component (!). This could be a failure mechanism in electronic or mechanical components. But could also be used to your advantage.

example 2: Upon cooling to a lower temperature a phase transformation of a material could cause expansion, which could cause internal stresses and failure (e.g. tin food cans will crumble at low T)

example 3: No abrupt liquid-to-solid transformation when two components are present (solid + liquid in a temperature range)

Example: Chip-Solder-Joint-Failure

Why important ?Some properties that might be difficult to predict using a common sense without the knowledge of the phase diagrams

example 4: Tmelt (Sn) = 232 C, Tmelt (Pb) = 327 C

but Tmelt(Sn0.62Pb0.38) = 183 C, so this is a common soldering alloy

example 5: Tmelt (Au) = 1064 C, Tmelt (Si) = 2550 Cbut Tmelt(Au0.97Si0.03) = 363 C, so thin layer of gold is used to attach Si chip to a ceramic substrate (shock protection)

example 6: Mechanical properties (hardness and tensile strength) of an alloy could be substantially higher than that of the individual components (e.g. hardness (AgCu) about twice the harness of Ag or Cu)

3One-Component Phase Diagrams

F = C P + 2C- ComponentsP- Number of phasesF- Degrees of freedomF = 2

F = 1

F = 0

# of state variables (e.g. two: P and T)

Gibbs Phase rule:

Two-Component Phase Diagrams

F = C P + 1

F = 2

F = 1T

In a two-phase field need to specify either the temperature or the composition of one of the phases.

Xs Xl

Isomorphous system ( complete solubility over the composition range)

If pressure is fixed (1 atm)

Hume-Rothery Rules for substitutional solution: The size < ~15%. The electronegativities and valance

similar The crystal structures of the two species

must be the same to form a continuous series of solid solutions.

4Two-Component Phase Diagrams

Composition, XB

Tem

pera

ture ( )

( )( )( )

1

11

l s

o l l s s

l s

o l s s s

o l l s s s

o l s s l

o ls

s l

f fX X f X ff fX X f X fX X X f X fX X f X X

X Xf

X X

+ == +

= = += + =

= ( )( )s ol s lX X

fX X

=

The Lever Rule in a Two-Component System



Tem

pera

ture

, C

Composition, XBTime Time


Deviation from ideal behavior

Congruent melting maximum

EAB > 0.5 (EAA + EBB)


Deviation from ideal behavior Congruent melting

minimum

EAB > 0.5 (EAA + EBB)

7Eutectic Phase Diagrams

F = 1, must specify temperatureor the compositionof one of the phases

F = 1

F = 1

F = 1

F = 0

F = 0, temperatureand compositionsof the phase arefixed.

Composition, XB

TATB

X1 XE X2A B

Tem

pera

ture

F = 2

F = 2

F = 2, mustspecify temperatureand composition

F = 2 X X

TXs

XlT

Xs

Xl

T X X

Solvus

Cooling Curves and Phase Boundaries

Tem

pera

ture

Composition, XB

Time

Alloy 1

8Cooling Curves and Phase BoundariesTe

mpe

ratu

re

Composition, XB

Time

Alloy 2

Cooling Curves and Phase Boundaries

Tem

pera

ture

Composition, XB

Time

Alloy 3

9Various physical properties and their relationship to a eutectic phase diagram

Eutectic Phase Diagrams

Tem

pera

ture

Composition, in % B

1. For the alloy composition of 0.27 % B calculate the fraction of solid and the fraction of liquid that forms under equilibrium cooling at the eutectic T

2. Calculate the amount of and that will form from the liquid just below the eutectic isotherm

3. Calculate the amount of in the alloy at temperature just below the eutectic T

10

Eutectic Phase Diagrams

This liquid becomes theeutectic mixture of and when the temperature drops just below the eutectic temperature which is composedof: 0.73 0.37

0.73 0.200.68

f

f

0.37 0.200.73 0.200.32

f

f

Just above the eutectic temperature the fractionof liquid and solid are:

0.27 0.200.37 0.200.41

l

l

f

f

0.37 0.270.37 0.200.59

f

f

The first solid that formsis called primary Just below the eutectic temperaturethe microstructure is composed ofprimary that formed above the eutectic temperature and from the eutectic mixture

total primary eutecticf f f = +

0.59 (0.41)(0.68) 0.87total

f = + =0.73 0.270.73 0.20

f= 0.87f =or

Tem

pera

ture

Composition, in % B

Microstructure Above and Below the Eutectic Temperature for an Off-Eutectic Alloy

Just above TE Just below TE

11

Microstructure Above and Below the Eutectic Temperature for Off-Eutectic Alloys

Just below TE

Increasing primary Decreasing eutectic

Decreasing primary Increasing eutectic

Deviation from Hume-Rotherys Rules

Increasing deviation leads to decrease in the maximum solid solubility of B in .

Tem

pera

ture

Composition, XBA

12

Eutectic Phase Diagram, No Solid Solubility

Tem

pera

ture

Composition, XB

Eutectic Phase DiagramsAl-Si System

13

Methods for Determining a Phase Diagram

Primary -aluminum

aluminum / silicon eutectic

Microstructure of an Aluminum-Silicon Alloy

14

Phase Diagrams Containing Two Eutectics

Possible to have several solid solution regions: e.g. 2 eutectic reactions and 3 solid solutions (, , and )

Note that upon cooling from T max at the alloy composition X there is a phase change but no composition change (CONGRUENT melting)

Line compound

Peritectic Phase Diagrams

l + =

if both the L and S phases have a tendency to cluster, the liquidustemperature increase and the solidus temperature decreases

In addition, a miscibility gap(region of non-mixing) appears

A progressive increase in the clustering tendency leads to the PERITECTIC phase diagram

15

The Use of Cooling Curves for Determining a Peritectic Phase Diagram

Tem

pera

ture

Composition, XB TimeXP X2X2

TA

TL

TP

l + =

Analysis of a Peritectic Phase Diagram

Tem

pera

ture

Composition

Alloy 1 Alloy 2 Alloy 3

Alloy 3 at T20.88 0.600.88 0.30.48

l

l

f

f

= =

Alloy 3 at T5

0.90 0.600.90 0.340.54

f

f

= =

16

Monotectic Phase Diagrams

A region of immiscibility (non-mixing) develops in the L phase

example: oil and water

Liquid1 = Liquid2 + (solid)

L1 L2

XM

L2

L2

Review of Invariant Binary ReactionsEutectic Type

l

l2l1

Eutectic

Eutectoid

Monotectic

Monotectoid

l +

+

l1 + l2

1 2

2 1 +

Al-Si, Fe-C

Fe-C

Cu-Pb

Al-Zn, Ti-V

On cooling one phase going to two phases

17

Review of Invariant Binary ReactionsPeritectic Type

ll +

+

Peritectic

Peritectoid

Fe-C

Cu-Al

On cooling two phases going to one phase

HW Questions

1. When a solid melts congruently, the liquid and solid have different / the same composition(s).

2. At constant temperature the fraction of the phases in a two-phase field changes / remains the same when the overall composition of the alloy is

changed, but remains in the two-phase field.

3. Why would alloys close to the eutectic composition be suitable for castings rather than alloy compositions far from the eutectic composition?

4. On cooling when a two-phase liquid plus solid transforms to a solid phase the transformation is eutectic / peritectic in nature.

5. On cooling the peritectoid reaction written symbolically has one phase going to two / two phases going to one.

18

HW Questions

At what T an alloy containing 88% B will start melting?

At what T it will completely transform into liquid?

What is the composition of phase for this alloy @ T8?

What is the maximum solid solubility of B in a and A in b? Whose rules apply here?

For an alloy containing 88% B, calculate the fraction of the liquid and solid phases and their compositions at temperature T3, T4, and T5

At a temperature just below the eutectic temperature, how much is primary , what is the total fraction of , and what is the fraction in the eutectic. (Alloy composition is 88% B)

Tem

pera

ture

Composition, XB

TA

TB

A B

1. Label all phase fields.

2. Identify all invariant reactions.

Labeling Complex Phase Diagrams

19


Eutectic

Eutectic

PeritecticPeritectic

Eutectic

Eutectic l = +

l + =

l = +


20

Summary One-component phase diagrams with

temperature and pressure as the experimental variables that affect equilibrium.

Introduction to the Gibbs Phase Rule and its application to one-component systems.

Two-component systems and the rules that govern the composition of the phases, the number of phases and the amount of each phase at equilibrium.

The applications of these rules to complex, two-component systems illustrated that regardless of how complex the phase diagram appeared, the rules that were developed could be easily applied.

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