1. Phase Diagrams
Group 10

2. 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

3. 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

4. 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-Temperature
phase diagram

5. Significance
• 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.
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..

6. Examples
Cu-Ni phase diagram
Temperature- Composition
Binary isomorphous diagram
CO2 phase diagram
Pressure-Temperature
Unary diagram

7. Gibbs Phase Rule
• A thermodynamic law which governs the
conditions for phase equilibrium.
• Useful in interpreting Phase Diagrams.
P+F=C+N

8. Phase Diagram of CO2

9. Lever rule
• Used to find the composition of phases.
• Ws = Wo-Wl
Ws-Wl
• Wl = Ws-Wo
Ws-Wl

10. For eutectic systems
Wl = Wo-W1
W2-W1
Wα = W2-W0
W2-W1

11. 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.

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

13. Non-equilibrium solidification
In 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

15. 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 :

16. Development of MS in Fe-Fe3C system
Case 1 : At Eutectoid composition
>The above is the governing eqn.
> The phase changes from a to b.
727.C
> The pearlite structure forms due
to the difference b/w parent &
product phases.
> This is called Pearlite because
of its look of a pearl.

17. )
Diffusion through minimal distance by
C-atoms leads to layered structure.

18. Case 2 :
At Hypoeutectoid Composition

19. •
•
•
•
•
•
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.

20. Case 3:
At Hyper Eutectoid Composition

21. •
•
•
•
•
•
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 γgrain 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.

22. Cu-Zn phase diagram

23. 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 bandstructure effect associated with the BZ–
FS interaction.

25. 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.

26. Free energy change on nucleation 
Reduction in bulk free energy  increasein surfaceenergy  increasein strain energy
ΔG  (Volume).(G)  (Surface). )
(


4 3
ΔG   r .( Gv )  4r 2 .( )
3

Gv  f (T )
r3
r2
1
Neglected in L → S
transformations

27. 

4

ΔG   r 3 .( Gv )  4r 2 .( )
3

 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
dG
0
dr
r 0
*
1
r2*  
2
Gv
As Gv is ve, r*is +ve
Trivial
G  0
2
Gv
16  3
G  
3 Gv2
G  0
*
r0  
3
Gv
G →
r*  
dG
0
dr
r*
Embryos
Supercritical nuclei
r →

28. Gv  f ( T )
The bulk free energy reduction is a function of undercooling
Decreasing G*
Turnbull approximation
2
Tm
16 3
G  
3
T 2 H 2

G →
Decreasing r*
r →

29. Rate of nucleation =
dN
I
dt
No. of critical sized
particles
N *  Nt e
 G * 


 kT 


x
Frequency with which they
become supercritical
 '  s * e
No. of particles/volume in L
 H d 


kT 

 → lattice vibration frequency (~1013 /s)
s* atoms of the liquid facing the nucleus
Critical sized nucleus
Jump taking particle to supercriticality
→ nucleated (enthalpy of activation = Hd)
Critical sized nucleus

30. I  N t s*  e
 G *  H d


kT





 G* ↑  I ↓
T↑ I ↑
T = Tm → G* =  → I = 0
T (K) →
Increasing T
Tm
T=0→I=0
0
I →

31. 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.

32. Consider the nucleation of  from  on a planar surface of inclusion 




Interfacial Energies
Created


A lens 
Created
A circle 
Surface tension force balance
   
 Cos  
 
  Cos      
Lost
ΔG  (Vlens )Gv  (A lens )   ( Acircle )    ( Acircle )  
Vlens = h2(3r-h)/3
Alens = 2rh
h = (1-Cos)r
A circle 
r circle = r Sin

33. dG
0
dr
*
hetero
r

2 
G
*
hetero
Gv



1 *
*
Ghetero  Ghomo 2  3Cos  Cos 3
4
G*hetero (0o) = 0
no barrier to nucleation
1
3
4  
 
2  3Cos  Cos3
3 Gv2
0.75

G*hetero (180o) = G*homo
no benefit
0.5
G*hetero (90o) = G*homo/2
0.25
0
0
30
Complete wetting
60
90
120
150
180
 (degrees) →
Partial wetting
No wetting
    
Cos 
 

34. I hom o  I
0
hom o
e
*
 Ghom o 



 kT 


0
I hetero  I hetero e
*
 Ghetero 



 kT 


= f(number of nucleation sites)
= f(number of nucleation sites)
~ 1026
~ 1042
BUT
the exponential term dominates
I hetero > I homo

35. 


Choice of heterogeneous nucleating agent
 Small value of .




Cos 
 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
    
 

36. Isothermal transformation diagram
Iron-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 percentage
transformation versus the logarithm of time at three
different temperatures.
For each curve, data were collected after rapidly cooling
a specimen composed of
100% austenite to the temperature indicated; that
temperature was maintained constant
throughout the course of the reaction.

37. 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.

38. ISOTHERMAL
TRANSFORMATION DIAGRAMS
 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.

39. ISOTHERMAL
TRANSFORMATION DIAGRAMS
 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

40. ISOTHERMAL
TRANSFORMATION DIAGRAMS
 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

41. Summary

43. 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

44. Group Members
Kumar Ishu
120100056
Paresh Raut
120100022
Pratik Koche
120100019
Anand Kumar
120100048
Pramod Kumar
120100044
Sunil Kumawat
120100042
Sunil Tandi
120100046
Hitesh Sahare
120100020
Vijay Thyagraj
120100066
Aniruddha Rajendra Kanere
120100026
Rajendra Thate
120100023

45. THANK YOU!