02 Phase Diagrams

7/29/2019 02 Phase Diagrams

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Phase Diagrams

a ReviewTopic 2


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Review of

Phase TransformationDiagrams


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Example: Solubility of salt in waterThere exists a maximum amount of salt that can be

completely dissolved in water; excess of salt stays as solid.

This maximum amount is the solubilityof salt in water.

The solution containing the maximum concentration of saltis a saturated solution.

Cooling of saturated solution results in the formation ofsolid salt from the solution, indicating that solubility

decreases with decreasing T. This process is called

precipitation and the solid formed is a precipitate.

Heating the solution will lead to the dissolving of theprecipitate back into solution.

Salty water the solution

Solid salt theprecipitate

The same concepts apply to solids: solid solution, saturation, solubility, precipitation

In this example there exist two phases in the system and the two phases stay in

equilibrium:

Solution Soliddissolving

precipitation

Solution and Solubility


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Phase diagrams are used to map outthe existence and conditions ofvarious phases of a give system.The phase diagram of water is acommon example. Water may stay

in liquid, solid or gaseous states indifferent pressure-temperatureregions. Boundaries of the regionsexpress the equilibrium conditions interms of P and T. Water is amonolithic system. For binarysystems, which contains two

constituents, such as binary alloys,phase diagrams are often expressedin the temperature-compositionplane.

Liquid

Solid

Gas

Super-critical

fluid

Triplepoint

Criticalpoint

Temperature

0C 100C 374C

0 bar

1 bar

221 bar

Pressure

phase diagram of water

Phase Diagrams


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The simplest type of binary phasediagrams is the isomorphous system, in

which the two constituents form a

continuous solid solution over theentire composition range. An example

is the Ni-Cu system.

Solidification of alloy Co starts on

cooing at T1. The first solid formed has

a composition of Cs1 and the liquid

Co. On further cooling the solid

particles grow larger in size and change

their composition to Cs2 and then Co,

following the solidus whereas the liquiddecrease in volume and changes its

composition from Co to CL3 following

the liquidus. The solidification

completes at T3.

1455C

1085C

Cu Ni

phase (fcc) -Solid solutionof Cu and Ni

liquid phase -

Solution ofCu and Ni

Composition

Temp

erature CS

1

T1

CL

2

Co

T2

T3

CS

2CoCL

3

L

Binary Phase Diagrams


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The simplest type of binary phasediagrams is the isomorphous system, in

which the two constituents form a

continuous solid solution over the

entire composition range. An exampleis the Ni-Cu system.

Compositions of phases is determinedby the tie line

The relative fractions of the phases are

determined by the lever rule

W1 W2

L2L1

1455C

1085C

Cu Ni

phase (fcc) -Solid solutionof Cu and Ni

liquid phase -Solution ofCu and Ni

Composition

Temperature

CST*C

L

Co

Binary Phase Diagrams


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W1 W2

L2L1

Weight fractions:

Lever Rule


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Read from the tie line:Liquid phase:Cu-30%Ni-phase: Cu-55%Ni

CL CSCo

At temperature T1, alloy Co is in the dual phase region,

comprising the liquid phase and the -phase.

(i) Determine the compositions of the two phases;(ii) Determine the weight fractions of the two phases

50%NiCu Ni

1455C

1085C

CS

C0

CLT1

55%Ni30%Ni

Example

55 500.2 20%

55 30

s o

L

s L

C CW

C C

= = = =

50 30 0.8 80%55 30

1 1 0.2 0.8 80%

o L

s L

L

C CWC C

or

W W

= = = =

= = = =


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determination of Phase diagrams

T1085C

II

(thermal arrest)

T

t

T2

T1

I

Cu Ni

T

%

II I III

1455C

1085C

T1

T2

Solidus

Liquidus

Cooling Curves


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Pb-Sn phase diagram

phase: solid

solution of Pb in

tetragonal Sn

phase: solid

solution of Sn

in fcc Pb

Liquid

Pb

(Fcc)

Sn

(Tetra)

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100

Temperature

Wt%

The Pb-Sn system is

characteristic of a valley in themiddle. Such system is known as

the Eutectic system. The

central point is the Eutecticpoint and the transformationthough this point is called

Eutectic reaction: L+

Pb has a fcc structure and Sn has

a tetragonal structure. The

system has three phases: L, and.

solvus

solvus

solidus

Liquidus

Eutecticpoint

+

+ LL +

Eutectic Systems


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Alloy I:At point 1: LiquidSolidification starts at liquidusAt point 2: L+The amount with TSolidification finishes at solidus

At point 3:Precipitation starts at solvusAt point 4:+Further cooling leads to formation

and growth of more precipitateswhereas Sn% in decreasesfollowing the solvus.

The cooling curve of this alloy is

similar to cooling curve I shown in

slide 9.

I

1

2

3

4

III II

Solidification of Eutectic Systems

Pb-Sn phase diagram

Liquid

Pb

(Fcc)

Sn

(Tetra)

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100

Temperatu

re

Wt%


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L

L

(1)

L

(2)

(4)

(3)

Precipitates in a Al-Si alloy;(a) optical microscopy,(b) scanning electron

microscopy of fracture surface

(a)

(b)


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Pb-Sn phase diagram

Liquid

Pb

(Fcc)

Sn

(Tetra)

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100

Temperatu

re

Wt%

III

2

3

III

1

Alloy II:At point 1: LiquidSolidification starts at eutectic

point (where liquidus and solidus

join)At point 2: L(+) (eutecticreaction)

The amounts of and increasein proportion with time.Solidification finishes at the same

temperature.At point 3:+Further cooling leads to the

depletion of Sn in and the

depletion of Pb in .

The cooling curve of this alloy is

similar to cooling curve II shown

in slide 9.



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L

L

(1)

L(2)

Pb-Sn eutectic

(3) Nucleation of coloniesof and laminates

Eutectic structure ofintimate mix of and to

minimise diffusion path


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Pb-Sn phase diagram

Liquid

Pb

(Fcc)

Sn

(Tetra)

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100

Temperatu

re

Wt%

III

Alloy III:At point 1: LiquidSolidification starts at liquidusAt point 2: LL+ (pre-eutectic )The amount with TAt point 3: L (+) (eutectic

reaction)Solidification finishes at the eutectic

temperatureAt point 4:+ (pre-eutectic +(+) eutectic mixture)Further cooling leads to the depletion

of Sn in and the depletion of Pb in

.

The cooling curve of this alloy is a

combination of the two cooling curves

shown in slide 9.

I

2

II

1

3

4



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L

L

(1)

L

(2)

L

(3)

Eut

(3)

Eutectic laminateof and

Cu-Ag alloyPre-eutectic

Cooling curve


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Can you describe the

solidification process of alloy IV,

including microstructure

evolution, morphology of phasesand cooling curve?

Sn

I III II IV

Liquid

Pb

+

0

50

100

150

200

250

300

350

Hypoeutectic Hypereutectic



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Gibbs phase rule F =C+N-PF: degree of freedomC: number of chemical variablesN: number of non-chemical variablesP: number of phases

Application of Gibbs phase rule:For a binary system at ambient pressure:C=2 (2 elements)

N=1 (temperature, no pressure)For single phase: F=2: % and T(a region)For a 2-phase equilibrium: F=1:% or T (a line)For a 3-phase equilibrium: F=0, (invariant

point)

May we have a 4-phase equilibrium, in a

binary system, or in any system?

Pb Sn

+

L one-phase region

two-phaseequilibrium (line)

three-phaseequilibrium (point)

Gibbs Phase Rule


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Some transformations do not cause changes in composition, such as the

solidification of a pure metal, whereas some other do, such as thesolidification of an alloy into a solid solution. The former is known as

congruent transformation and the latter incongruent

transformations. Congruent transformations are cooling rate insensitive

and incongruent transformations are cooling rate sensitive they rely oninterdiffusion to proceed. Solidification under a fast cooling rate, where

diffusion is insufficient to homogenise the composition simultaneously

during the process is known as the non-equilibrium solidification.

A common consequence of non-equilibrium solidification is coring.

Non-Equilibrium Solidification


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Alloy Co starts solidification at T1. The first

solid formed has composition Cs1. On

further cooling to T2, an outer shell of

composition Cs2 is formed surrounding

Cs1. Due to inadequate diffusion on fast

cooling, a composition difference is created.

The average composition of the solid

composite at T2 is, thus, somewherebetween Cs1 and Cs2: Cs2*. The same

situation continues throughout the process.Under equilibrium condition solidification

completes at T3. However, under non-

equilibrium condition, the average

composition of solid at T3 is Cs3*


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L

Cs1

T1

Cs1

Cs2

T2

T3

Average solid

composition: Cs2*

Average solid

composition: Cs3*

T4

Average solidcomposition:Co

The cored structure: composition segregation,

enrichment of high-Tm constituent in the core

A %B

Equilibriumsolidus

T2

T3 (end of solidification

under equilibrium)

T4 (actual end of

solidification)

T1 (start of solidification)

Effective

solidus

Co

Cs1

Cs

2

Cs

2*

Cs

3*

Coring


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A B

+

L

Coring leads to increase of weight fractionof eutectic products

a b c d

coAccording to the lever rule, the

weight fraction of the eutecticproducts can be computed as:

Under equilibrium condition:

Under non-equilibrium condition:

eut

c bW

d b

=

*

eut

c aW

d a

=

*

eut eut W W>

Coring in Eutectic Systems


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A %B

LS

S L

Co

CS

CL

CS

CL

Co

C

x

x

T Tm

T

Supercooling window caused by

rising Tm, resulting in unstable

interface

Constitutional Supercooling


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A consequence of constitutional supercooling and destabilisation of solid-liquid interface is

the formation of dendritic structure, as commonly found in alloy castings. In such structure,

gaps between dendrites and between dentitic fingers are regions rich of low-meltingtemperature phases and impurities. Dendritic branches themselves are often cored, too.

This often require post-casting heat treatment to homogenise the structure.

Dendrite Structure of Metals

02 Phase Diagrams

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