Phase Diagram

Phase Diagrams

Group 10

Introduction-Topics to be covered

• Phase Diagrams• Gibbs Phase Rule• Binary phase diagrams• Equilibrium Solidification• Non-equilibrium solidification• Fe-C Alloy Phase diagrams• Intermediate Phases and reactions

Introduction-Topics to be covered

• Development of Microstructure• Cu-Zn Phase Diagram• Stability of Hume-Rothery Phases in Cu-Zn

alloys• Isothermal Transformation Diagram• Transformation Rate diagram

Phase Diagrams• A phase diagram is a type of chart used to show conditions at which

thermodynamic distinct phases can occur at equilibrium.• It conveniently and concisely displays the control of phase structure of a

particular system.• The three controllable parameters that will affect phase structure are

temperature, pressure, and composition.

Temperature-Composition phase diagram

Pressure-Temperaturephase diagram

Classification• Phase diagrams are classified based on the number of components in

the system Single component systems have unary diagrams. Two-component systems have binary diagrams and so on..

• To show phases are present at different compositions and temperatures under slow cooling (equilibrium) conditions.

• To indicate equilibrium solid solubility of one element/compound in another.

• To indicate temperature at which an alloy starts to solidify and the range of solidification.

• To indicate the temperature at which different phases start to melt. • Amount of each phase in a two-phase mixture can be obtained.

Significance

Cu-Ni phase diagramTemperature- CompositionBinary isomorphous diagram

CO2 phase diagramPressure-TemperatureUnary diagram

Examples

Gibbs Phase Rule

• A thermodynamic law which governs the conditions for phase equilibrium.

• Useful in interpreting Phase Diagrams.

P+F=C+N

Phase Diagram of CO2

• Used to find the composition of phases.

• Ws = Wo-Wl

Ws-Wl

• Wl = Ws-Wo

Ws-Wl

Lever rule

For eutectic systemsWl = Wo-W1

W2-W1

Wα = W2-W0

W2-W1

Binary Phase Diagrams

• A common phase diagram in which pressure is held constant whereas temperature and composition are kept variable parameters.

• They represent the relationships between temperatures and compositions of phases at the equilibrium.

• A common example for a binary isomorphous alloy is Cu-Ni system.

Equilibrium solidification

Reference: William Callister - Materials Science and Engineering - An Introduction 7 edition Wiley figure 9.4

Non-equilibrium solidificationIn practical situations diffusion is not as slow to allow the readjustments in diffusion while maintaining the equilibrium.

Its consequences?● Segregation occurs where the

concentration gradients are established across grains

● Formation of core-structure with center rich in high melting element whereas increase in concentration of low melting element on going towards grain boundary

● Melting below the equilibrium melting temperature of alloy may happen

● Loss in mechanical integrity due to thin liquid film that separates the grains.

Reference: William Callister - Materials Science and Engineering - An Introduction 7 edition Wiley figure 9.5

Intermediate Phases & Reactions

Intermediate Phases : ● Pure iron on heating undergoes two changes in the crystal structure before

melting.● At room temperature it exists in α-ferrite upto 1674 F, which has a

BCC crystal structure.● At 1185 F it get polymorphically transformed into FCC γ-austenite and

it persists till 2541 F when it reverts back to BCC δ-ferrite.● At 6.7% carbon concentration Cementite(Fe3C) is formed.● Iron melts at 2800 F.

Intermediate Reactions :● Eutectic :

• Eutectoid :

Development of MS in Fe-Fe3C systemCase 1 : At Eutectoid composition

>The above is the governing eqn.

> The phase changes from a to b.

> The pearlite structure forms due to the difference b/w parent & product phases.

> This is called Pearlite because of its look of a pearl.

727.C

Diffusion through minimal distance by C-atoms leads to layered structure.

)

Case 2 : At Hypoeutectoid Composition

• Composition left to the eutectoid, between 0.022 and 0.76 wt% C, is called hypoeutectoid alloy.

• At c, the microstructure consists entirely of γ-austenite grains.

• On cooling, at d, small α particles form along γ-grain boundaries.

• The composition becomes richer in carbon and α particles grow larger on cooling till 727.C.

• Once the temperature is lowered below 727.C all the γ-phase gets transformed into pearlite.

• α-phase is present as a continuous matrix phase surrounding the isolated pearlite colonies.

Case 3: At Hyper Eutectoid Composition

• Composition right to the eutectoid, between 0.76 and 2.14 wt% C, is called hyper eutectoid alloy.

• At g, the microstructure consists entirely of γ-austenite grains.

• On cooling, at h, small cementite particles starts forming along γ-grain boundaries.

• Cementite composition remains constant as the temperature changes until 727.C.

• On lowering the temperature below 727.C all the γ-phase gets transformed into pearlite.

• The resulting microstructure consists of pearlite and proeutectoid cementite as microconstituents.

Cu-Zn phase diagram

Stability of Hume-Rothery Phases in Cu-Zn alloys● Cu-Zn system displays a sequence of

phases along the alloy composition called Hume-Rothery phases.

● The criterion for the stability is a contact of the Brillouin zone (BZ) plane with the Fermi surface (FS) where FS is considered to be a sphere within the nearly free electron approximation.

● Interaction between the BZ boundary & FS opens a pseudo-gap and reduces the electronic energy.

● The close-packed α and β-structures begin to transform to new high-pressure phases, and the vacant γ-structure is shown to be stable up to at least 50 GPa.

● The γ-phase shows an anomalous behaviour of some physical properties which were accounted for by the band-structure effect associated with the BZ–FS interaction.

NUCLEATION During phase transformation normally at least one new phase is formed that has different physical or chemical characteristics or a different structure than parent phase. This is called as nucleation. Appearance of very small particles or nuclei of new phase involves in nucleation. Theory of nucleation involves thermodynamic parameter called free energy. There are two types of nucleation as follows.1. Homogeneous nucleation.2. Heterogeneous nucleation.HOMOGENEOUS NUCLEATION In case of homogeneous nucleation nuclei of new phase form

uniformly through parent phase. Let us consider homogeneous nucleation, and study the impact of free energy involved in it.

)((Surface). )(Volume).( ΔG G

).(4 ).(3

4 ΔG 23 rGr v

r2

r3

1

Neglected in L → Stransformations

)( TfGv

energystrain in increase energy surfacein increase energy freebulk in Reduction

nucleationon changeenergy Free

).(4 ).(3

4 ΔG 23 rGr v

By setting d(G)/dr = 0 the critical values (corresponding to the maximum) are obtained (denoted by superscript *)

Reduction in free energy is obtained only after r0 is obtained

0dr

Gd 0*1 r

vGr

2*2

Trivial

vGr

2*

2

3*

3

16

vGG

As Gv is ve, r*is +ve

r →G

→0G

vGr

30

Supercritical nucleiEmbryos

*r

0dr

Gd

0G

)( TfGv The bulk free energy reduction is a function of undercooling

Turnbull approximation

23

2 2

16

3 mT

GT H

r →

G →

Increasin

g T

Decreasing r*

Dec

reas

ing

G*

No. of critical sized particles

x Frequency with which they become supercritical

=

dt

dNI

kT

G

t eNN

*

*

kT

Hd

es ' *

Critical sized nucleus

s* atoms of the liquid facing the nucleus

Jump taking particle to supercriticality → nucleated (enthalpy of activation = Hd)

No. of particles/volume in L

Rate of nucleation

→ lattice vibration frequency (~1013 /s)

Critical sized nucleus

kT

HG

t

d

esNI

*

*

I →

T (

K)

→In

crea

sing

T

Tm

0

T = Tm → G* = → I = 0

G* ↑ I ↓

T ↑ I ↑

T = 0 → I = 0

Heterogeneous nucleation• Heterogeneous nucleation occurs much more often than homogeneous nucleation. It forms at structural homogeneities such as phase boundaries, Impurities, container surfaces, grain boundaries or dislocations and

require less energy than homogeneous nucleation.• Heterogeneous nucleation requires slight supercooling.

•To understand heterogeneous nucleation, Let us consider nucleation on planer surface of inclusion , of phase from phase.

)( )()(A )(V ΔG lenslens circlecirclev AAG

A lens

A circle

A circle

Created

Created

Lost

Cos

Surface tension force balance

Interfacial Energies

Vlens = h2(3r-h)/3 Alens = 2rh h = (1-Cos)r r circle = r Sin

Cos

Consider the nucleation of from on a planar surface of inclusion

0

0.25

0.5

0.75

1

0 30 60 90 120 150 180

vhetero G

r

2*0dr

Gd

3homo

* 324

1CosCosGG *

hetero

(degrees) →

G*hetero (0o) = 0

no barrier to nucleation

G*hetero (90o) = G*

homo/2

Complete wetting

No wetting

Partial wetting

32

3* 32

3

4CosCos

GG

vhetero

G*hetero (180o) = G*

homo no benefit

Cos

kT

G

eII

*hetero

0heterohetero

= f(number of nucleation sites)

~ 1042

= f(number of nucleation sites)

~ 1026

BUTthe exponential term dominates

I hetero > I homo

kT

G

eII

*homo

0homohomo

Choice of heterogeneous nucleating agent

Cos

Cos Small value of .

Choosing a nucleating agent with a low value of (low energy interface).

(Actually the value of ( ) will determine the effectiveness of the heterogeneous nucleating agent → high or low ).

low value of → Crystal structure of and are similar and lattice parameters are as close as

possible.

for example, Ni (FCC, a = 3.52 Å) is used a heterogeneous nucleating agent in the

production of artificial diamonds (FCC, a = 3.57 Å) from graphite

Isothermal transformation diagramIron-Iron carbide eutectoid reaction:

Temperature plays an important role in the rate of the austenite-to-pearlite transformation . The temperature dependence for an iron–carbon alloy of eutectoid composition is indicated in Figure.which plots S-shaped curves of the percentagetransformation versus the logarithm of time at three different temperatures.For each curve, data were collected after rapidly cooling a specimen composed of100% austenite to the temperature indicated; that temperature was maintained constantthroughout the course of the reaction.

ISOTHERMAL TRANSFORMATION DIAGRAMS

A more convenient way of representing both the time and temperature dependence of this transformation is in the bottom portion of Figure.

The dashed curve corresponds to 50% of transformation completion.

In interpreting this diagram, note first that the eutectoid temperature (1341F)is indicated by a horizontal line; at temperatures above the eutectoid.

The austenite-to-pearlite transformation will occur only if an alloy is super cooled to below the eutectoid; as indicated by the curves, the time necessary for the transformation to begin and then end depends on temperature.


The transformation rate increases with decreasing temperature such that at ( 1000 F) only about 3 s is required for the reaction to go to 50% completion.


In previous graph Very rapid cooling of austenite to a temperature is indicated by the near-vertical line AB, and the isothermal treatment at this temperature is represented by the horizontal segment BCD.

The transformation of austenite to pearlite begins at the intersection, point C (after approximately 3.5 s), and has reached completion by about 15 s, corresponding to point D. Figure 10.14 also shows schematic microstructures at various times during the progression of the reaction.

The thickness ratio of the ferrite and cementite layers in pearlite is approximately 8 to 1. However, the absolute layer thickness depends on the temperature at which the isothermal transformation is allowed to occur. At temperatures just below the eutectoid, relatively thick layers of both the -ferrite and Fe3C phases are produced; this microstructure is called coarse pearlite (shown in next slide) and the region at which it forms is indicated to the right of the completion curve on Figure 10.14


The thin-layered structure produced in the vicinity 540C of is termed fine pearlite; is the dependence of mechanical properties on lamellar thickness. Photomicrographs of coarse and fine pearlite for a eutectoid composition are shown in Figure .

For iron–carbon alloys of other compositions, a proeutectoid phase (either ferrite or cementite) will coexist with pearlite, Thus additional curves corresponding to a proeutectoid transformation also must be included on the isothermal transformation diagram. A portion of one such diagram for a 1.13 wt% C alloy

Summary

Acknowledgements

• Materials Science and Engineering by William Callister(Chapter 9: Phase Diagrams & Chapter 10: Phase Transformations: Development of Microstructure and Alteration of Mechanical Properties)

• Mechanical metallurgy by Dieter• Stability of Hume-Rothery phases in Cu–Zn

alloys at pressures up to 50 GPa by V F Degtyareva and O Degtyareva

Kumar Ishu

Paresh Raut

Pratik Koche

Anand Kumar

Pramod Kumar

Sunil Kumawat

Sunil Tandi

Hitesh Sahare

Vijay Thyagraj

Aniruddha Rajendra Kanere

Rajendra Thate

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Phase Diagram

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