Phase Transformations
Kinetics
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EBB512 –Phase Equilibria and Phase Diagrams
Why study Phase Transformation ( in Metal)
Development of a set of desirable mechanical
properties results from a phase transformation →
heat treatment
Time- Temperature dependencies of some phase
transformation are conveniently represented on a
modified phase diagrams
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EBB512 –Phase Equilibria and Phase Diagrams
It is important to know how to use the
diagram in order to design heat treatment
that will yield room temperature mechanical
properties
Eg. Tensile strength of an iron-carbide alloy
of eutectoid composition (0.76%C) can be
varied bet.~700MPa to 2000MPa depending
on heat treatment employed
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EBB512 –Phase Equilibria and Phase Diagrams
Phase transformations (change of the microstructure)
can be divided into three categories:
 Diffusion-dependent with no change in phase
composition or number of phases present
 Diffusion-dependent with changes in phase
composition and/or number of phases (eg.
Eutectoid transformations)
 Diffusionless phase transformation – produces a
metastable phase by cooperative small
displacement of atoms in structure.
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EBB512 –Phase Equilibria and Phase Diagrams
 Phase transformations do not occur instantaneously
 Diffusion-dependent phase transformations can be
rather slow and the final structure often depend on
the rate of cooling/heating.
 Hence need to consider the kinetics of the phase
transformation
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EBB512 –Phase Equilibria and Phase Diagrams
Kinetics of Phase Transformations
Most phase transformations involve
change in composition >> redistribution
of atoms via diffusion is required.
The process involves :
Nucleation of new phase –formation of
stable small particles (nuclei) of new phase.
Nuclei are often formed at grain boundaries and
other defects.
Growth of new phase
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EBB512 –Phase Equilibria and Phase Diagrams
Plot of fraction
reacted versus
the logarithmic of
time typical of
many solid-state
transformation in
which
temperature is
held constant.
f = fraction transformation
t= time
f=1–
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exp(-ktn)
……….Avrami equation
EBB512 –Phase Equilibria and Phase Diagrams
k and n is a time-dependent
constants for particular
reaction.
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EBB512 –Phase Equilibria and Phase Diagrams
Precipitation of a single-phase solid- nucleation
Precipitation within a homogeneous liquid matrix –
homogeneous nucleation
The more common case is precipitation occuring at
some structural imperfection such as foreign surfaceheterogeneous nucleation
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EBB512 –Phase Equilibria and Phase Diagrams
G  43 GV (  )  4r 2   43 r 3
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EBB512 –Phase Equilibria and Phase Diagrams
For solid –state trnasformations
displaying kinetic behavior shown
in Fig. fraction transformation y is
afunction time t as follows:
Y = 1 – exp(-ktn) ….
Eqn 8.1
Avrami Equation
k and n (0.5 -5)are time-dependent constants for
a particular rxn.
By convention rate of transformation r is taken
as the reciprocal of time required for the
transformation to proceed halfway to
completion, t0.5
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EBB512 –Phase Equilibria and Phase Diagrams
r = 1/t0.5 …………..eqn 8.2
rate increases with temp. according to
Arrhenius eqn, characteristic for thermally
activated process
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EBB512 –Phase Equilibria and Phase Diagrams
rate increases with temp. according to
Arrhenius eqn, characteristic for thermally
activated process
r= Aexp(-Q/kT) = A exp(-Q/RT) ………… 8.3
per atom
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per mole
EBB512 –Phase Equilibria and Phase Diagrams
Superheating and supercooling
Upon crossing a phase boundary on the compositiontemperature phase diagram phase transformation towards
equilibrium state is induced
But the transition to the equilibrium structure takes time
and transformation is delayed.
During cooling, transformation occur at temperatures less
than predicted by phase diagram: supercooling
During heating, transformation occur at temperatures
greater than predicted by phase diagram: superheating
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EBB512 –Phase Equilibria and Phase Diagrams
Degree of supercooling/super heating increases with rate
of cooling/heating
Meta stable states can be formed as a result of fast
temperature change. Microstructure is strongly affected by
cooling rate
We will consider the effect of time on phase
transformation using iron-carbon alloy as an example
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EBB512 –Phase Equilibria and Phase Diagrams
The S-shaped curves are shifted to a longer times at
higher T indicating transformation is dominated by
nucleation and not by diffusion
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EBB512 –Phase Equilibria and Phase Diagrams
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EBB512 –Phase Equilibria and Phase Diagrams
(Referring to earlier diagram)
Euctectoid temp. indicated by the horizontal line
→austenite is stable for all times
The austenite to pearlite transformation will only occur if alloy
supercooled to below the eutectoid temp.
The required will depend on the temp.
 From eqn 8.2 transformation rate at some particular temp
inversely propnl. To the time required for rxn proceed 50%
completion.
Eg. Temp just below eutectoid 105 s , while at 540oC ~ 3 s
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EBB512 –Phase Equilibria and Phase Diagrams
This rate –temp behavior contradict eqn 8.3 → rate increases
with increasing temperature
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EBB512 –Phase Equilibria and Phase Diagrams
The above Fig. is isothermal transformation diagram or commonly
known as TTT diagram – temperature,time, and transformation.
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EBB512 –Phase Equilibria and Phase Diagrams
 This Fig shows the progress of transformation that can be
traceby a group of curves showing different percentages of
completion
Using the industrially important eutectoid transformation in
steels as an eg.
 2 types of transformation:
1. Diffusional transformation in solid – eutectoid
transformation
2. Diffusionless (martensitic) transformations
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EBB512 –Phase Equilibria and Phase Diagrams
1. Diffusional transformation in solid –
eutectoid transformation
 Involve a change of structure due to
the long range migration of atoms
 Fig 8-7 shows TTT diagram of
eutectoid stell (Fe with 0.77 wt%C
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EBB512 –Phase Equilibria and Phase Diagrams
Fig 8-7
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EBB512 –Phase Equilibria and Phase Diagrams
 The most important new info provided in Fig 8-7 –
pearlite is not the only microstructure that can
develop from cooling of austenite
 For certain temp. bainite rather than pearlite is
formed
 Base p.d eutecticand eutectoid structures are
generally fine - grained
• But for slow cooling near the eutectoid tempcoarse pearlite
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EBB512 –Phase Equilibria and Phase Diagrams
Reason: low nucleation rates and high diffusion
rates near eutectoid temp lead to relatively coarse
structure
Fine pearlite formed at low temperature
bcos transformation is diffusion control.
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EBB512 –Phase Equilibria and Phase Diagrams
Bainite Formation
 Pearlite formation – from eutectoid temp (727oC)
down to about 400oC
 Below 400oC, ferrite and cementite form as
extremely fine needles in microstructure known as
bainite
 Eventhough various morphologies develop over
the range of temperatures- all have the same
phase composition and relative amount of each
phase.
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EBB512 –Phase Equilibria and Phase Diagrams
A slow cooling path that leads to coarse pearlite formation is
superimposed on the TTT diagram for eutectoid steel. This type of
thermal history was assumed,in general, throughout previous
lectures
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EBB512 –Phase Equilibria and Phase Diagrams
The microstructure of bainite involves extremely fine needles of -Fe and
Fe3C, in contrast to the lamellar structure of pearlite. (From Metals
Handbook,8th Ed., Vol. 7: Atlas of Microstructures, American Society for
Metals, Metals Park, Ohio, 1972.)
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EBB512 –Phase Equilibria and Phase Diagrams
The interpretation of TTT diagrams requires consideration of the thermal
history ìpath.î For example, coarse pearlite, once formed, remains stable
upon cooling. The finer-grain structures are less stable because of the
energy associated with the grain boundary area. (By contrast, phase
diagrams represent equilibrium and identify stable phases independent of
the path used to reach a given state point.)
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EBB512 –Phase Equilibria and Phase Diagrams
2. Diffusionless (martensitic) transformations
Fig 8-11
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EBB512 –Phase Equilibria and Phase Diagrams
Diffusionless (martensitic) transformations
 Fig 8-11 shows ver different process occur at lower
temp. – below 250oC
 Two horizontal lines are added mto represent the
occurrence of a diffusionless process known as
martensitic transformation
 This is a generic term referring to a broad family of
diffusionless transformation in metals an nonmetals alike.
 Common eg. trsnfmtn in eutectoid steel – product
from the quenched austenite – martensite
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EBB512 –Phase Equilibria and Phase Diagrams
 Quenching austenite rapidly enough bypassing the pearlite
knee (~550oC) – suppress diffusional transformation
 The austenite increasingly become unstable with
decreasing
 At about 215oC the austenite transform
spontaneously to martensite (~1% of the austenite)
 Instead of diffusional migration of C to form α and
Fe3C , there is sudden reorientation of C and Fe
from fcc SS of γ-Fe to bct SS – which is martensite
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EBB512 –Phase Equilibria and Phase Diagrams
In (a),the bct unit cell is shown relative to the fcc lattice by the h100i axes.
In (b), the bct unit cell is shown before (left) and after (right) the
transformation.
The open circles represent iron atoms. The solid circle represents an
interstitially dissolved carbon atom.
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EBB512 –Phase Equilibria and Phase Diagrams
 Complex crystal structure,and supersaturated conc. Of
carbon atoms in martensite lead to a characteristically brittle
nature
 The start of martensitic transformation - line Ms
 If quenching below this line austenite increasingly become
unstable and more will transfrom to martensite.
 Various stages of martensitic transformation in Fig 8-11
 - 46oC transformation complete.
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EBB512 –Phase Equilibria and Phase Diagrams
The End
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EBB512 –Phase Equilibria and Phase Diagrams