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Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
MSE 260
Phase Transformations
Ing. Anthony Andrews (PhD)Department of Materials Engineering
Faculty of Mechanical and Chemical Engineering
College of Engineering
Website: www.anthonydrews.wordpress.com www.knust.edu.gh
Processing/Structure/Properties/
Performance
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Kinetics and
Phase Transformations
• Phase diagrams show which phases are in equilibrium
under certain conditions, such as temperature
• A system cannot change instantaneously, i.e. phase
transformations occur over a period of time.
• Kinetics deals with the rates of transformations
– A diffusion controlled process involves the movement of
atoms over “long” distances (more than a few lattice constant
lengths) to form the new more stable phase(s)
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Issues to Address
• Transforming one phase to another takes time.
• How does the rate of transformation depend on time and
temperature?
• How can we slow down the transformation so that we can
engineer non-equilibrium structures?
• Are the mechanical properties of non-equilibrium structures
better?
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Thermodynamics of Phase
Transformations
• Gibbs free energy of a system:
G = H – TS
• Criterion for stability:
dG = 0
• Criterion for phase transformation:
∆𝐺 = 𝐺𝐴 − 𝐺𝐵 < 0
For phase transformations (constant T & P) relative stability of the
system is defined by its Gibb’s free energy (G).
But ……… How fast does the phase transformation occur?
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Kinetics of Phase Transformations
Phase transformations in metals/alloys occur by
nucleation and growth
• Nucleation: New phase (β) appears at certain sites within
the metastable parent (α) phase.
• Homogeneous Nucleation: Occurs spontaneously &
randomly without preferential nucleation site.
• Heterogeneous Nucleation: Occurs at preferential
sites such as grain boundaries, dislocations or
impurities.
• Growth: Nuclei grows into the surrounding matrix.
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Driving Force for Solidification
Example: Solidification, L → S
At a temperature T:
GL = HL - TSL ; GS = HS - TSS
ΔG = GL – GS = ΔH – TΔS
At equilibrium melting point (Tm):
ΔG = ΔH – TmΔS = 0
∆𝑆 =∆𝐻
𝑇𝑚
Liquid → Solid phase transformation
Solid (GS)
Liquid (GL)
Tm T →
G
→
T
G
Liquid stableSolid stable
T - Undercooling
↑ t
“For sufficient
Undercooling”
On cooling just below Tm solid becomes stable
But solidification does not start
E.g. liquid Ni can be undercooled 250 K below Tm
G → ve
G → +ve
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Driving Force for Solidification
For small undercooling (ΔT) we can
assume that ΔH and ΔS are
independent of temperature (neglect
the difference in Cp between liquid
and solid)
∆𝑮 ≈𝑳∆𝑻
𝑻𝒎
ΔH = L (Latent heat of fusion)
Nucleation
The probability of nucleation occurring at point in the parent phase is
same throughout the parent phase
In heterogeneous nucleation there are some preferred sites in the
parent phase where nucleation can occur
Homogenous
Heterogenous
Nucleation
NucleationSolidification + Growth=
Liquid → solid
walls of container, inclusions
Solid → solid
inclusions, grain boundaries,
dislocations, stacking faults
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Homogenous Nucleation
Nucleation of a spherical solid particle in a liquid
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Energies involved
Bulk Gibbs free energy ↓
Interfacial energy ↑
Strain energy ↑ Solid-solid transformation
Volume of transforming material
New interface created
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r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy)
Homogeneous Nucleation & Energy Effects
GT = Total Free Energy
= GS + GV
Surface Free Energy - destabilizes
the nuclei (it takes energy to make
an interface)
24 rGS
= surface tension
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
GrGV3
3
4
volume unit
energy free volume G
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Homogeneous Nucleation
23
3
16*
2*
0
V
V
T
GG
and
Gr
or
r
G
• At the critical cluster size
23 43
4rGrG vT
Total free energy change is given by
r
+
-ΔGv
ΔGs
ΔGT
r*
ΔGT
0GvG
r
3
0
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Homogeneous Nucleation
∆𝐺𝑣 =∆𝐻𝑓(𝑇𝑚 − 𝑇)
𝑇𝑚
𝑟∗ = −2𝛾𝑇𝑚∆𝐻𝑓
1
𝑇𝑚 − 𝑇
∆𝐺∗ =16𝜋𝛾3𝑇𝑚
2
3∆𝐻𝑓2
1
𝑇𝑚 − 𝑇 2
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Homogeneous Nucleation
Schematic free energy-versus-embryo/nucleus radius curves for
two different temperatures.
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Homogeneous Nucleation
n* = number of stable nuclei
K1 = total number of nuclei of the
solid phase
𝑛∗ = 𝐾1𝑒𝑥𝑝 −∆𝐺∗
𝑘𝑇
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Homogeneous Nucleation
vd = frequency of attachment
Qd = activation energy for diffusion
K2 = temperature dependent constant
𝑣𝑑 = 𝐾2𝑒𝑥𝑝 −𝑄𝑑𝑘𝑇
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Homogeneous Nucleation
𝑁= nucleation rate
K3 = number of atoms on a nucleus
surface
𝑁 = 𝐾3𝑛∗𝑣𝑑 = 𝐾1𝐾2𝐾3 exp −
∆𝐺∗
𝑘𝑇𝑒𝑥𝑝 −
𝑄𝑑𝑘𝑇
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Heterogeneous Nucleation
• Occurs at a preexisting imperfection, such as a grain boundary
(during solid state transformation) or the mold wall (during
solidification of an ingot)
• During nucleation, two types of interfaces that require energy are
formed
Solid-liquid (SL) and Solid-Imperfection (SI)
• One type of interface, the Liquid-Imperfection (IL) interface is
removed. This provides additional energy to drive the
transformation
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Heterogeneous Nucleation
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Heterogeneous Nucleation
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Heterogeneous Nucleation
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Growth Process
• Begins once the embryo has exceeded the critical radius,
r*, and becomes stable nucleus
• Particle growth occurs by long-range atomic diffusion
which involves several steps:-
– Diffusion through the parent phase, across a phase
boundary, and then into the nucleus
• Hence, growth rate is determined by rate of diffusion
which depends on temperature
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Diffusion controlled growth
• It can be shown that the radius (r) of a spherical particle
will increase according to the equation below, where D
is the diffusion coefficient
𝑟 = 𝛽 𝐷𝑡, where
𝐷 = 𝐷𝑜𝑒𝑥𝑝−𝑄𝑑
𝑅𝑇
• As the temperature T decreases, the diffusion coefficient
decreases exponentially. This results in a rapid decrease
in growth rate
Growth Process
• The overall rate of transformation depends on both nucleation and growth
• At low under-cooling, nucleation rate is low resulting in a low transformation rate
• At high under-cooling, the growth rate is low, also resulting in a low transformation rate
• The fastest transformation occurs at an intermediate temperature
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Transformation rate and time
• The time that a transformation takes is proportional to the inverse
of the transformation rate
• The figure above shows schematically, the rate and time for 50%
of the transformation to complete
– i.e., half of the liquid has solidified
• The time-temperature-transformation curve shows a characteristic
“C” shape www.knust.edu.gh
Isothermal Transformation Diagram• The isothermal transformation diagram has the typical “C” shape
because
– At high temperatures, close to the transformation temperature
(melting point, solvus temperature, eutectoid temperature, etc)
the nucleation rate is low because ∆T is small, while growth
rate is high. Transformation is slow because there simply aren’t
enough nuclei to grow
– At low temperatures well below the transformation
temperature, nucleation rate is very high, and a large number of
small nuclei will form, but growth rate is low. The nuclei are
generally too small to be observed, and the transformation is
therefore sluggish
– At an intermediate temperature, nucleation rate is high, and the
growth rate is also sufficiently high that the overall
transformation occurs rapidly
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Kinetics of Solid State
Transformations
• Kinetics – the time dependence of rate of transformation
– The fraction of reaction that has occurred is measured
as a function of time
– Hold temperature constant and measure conversion vs.
time
s conversion measured?
– X-ray diffraction – have to do many samples
– Electrical conductivity – follow one sample
– Sound waves – one sample
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Diffusion controlled transformation
• The extent of
transformation varies with
time in a sigmoidal
fashion
• Avrami equation is often
used to describe such
transformations
𝑦 = 1 − 𝑒𝑥𝑝 −𝑘𝑡𝑛
• where k and n are time
independent constants that
depend on the temperature
and geometry of the
transformation process. 5.0
1
trtiontransformaofrate
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Temperature Dependence of Transformation
Rate
RTQAetr /
5.0/1
For the recrystallization of Cu,
𝑟 =1
𝑡0.5= 𝐴𝑒− 𝑄 𝑅𝑇
o R = gas constant, T = temperature (K), A = pre-exponential factor
Q = activation energy
135C 119C 113C 102C 88C 43C
1 10 102 104
Arrhenius expression
Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Microstructural and Property
Changes in Iron – Carbon Alloys
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Isothermal Transformation Diagram of
Eutectoid Reaction - Pearlite
Eutectoid reaction:
γ (0.76 wt% C) → α (0.022 wt% C) + Fe3C
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Generation of Isothermal Transformation
Diagrams
Determination of a TTT
diagrams
• Find the time
corresponding to y=0.01
and y=0.99 for each
temperature curve
• Replot as lines of
y=0.01 and y=0.99 on a
T vs. t plot
TTT Diagrams
Example
log t
Fraction
transformed
y
log t
T
700°C
675°C
650°C
Effect of Cooling in Fe-C System
The absolute layer
thickness depends
on the temperature
of the
transformation.
The higher the
temperature, the
thicker the layers.
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- Smaller T:
colonies are larger
- Larger T:
colonies are smaller
• Ttransf just below TE
--Larger T: diffusion is faster
--Pearlite is coarser.
Two cases:
• Ttransf well below TE
--Smaller T: diffusion is slower
--Pearlite is finer.
Pearlite Morphology
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Coarse pearlite Fine pearlite
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Pearlite Morphology
TTT diagram for 1.13wt% C
A = austenite
C = proeutectoid cementite
P = pearlite
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TTT Diagrams
1. Holding the material at 400°C for 1
sec is not sufficient for the
transformation
3. Holding at 400°C for 1000 sec, the
transformation is complete, only B
remain.
2. Holding at 400°C for 10 sec, you
get a mixture of A+B => yields
some transformation
4. Cooling rapidly (quench) to freeze in
a microstructure. At room
temperature the kinetics are too slow
to allow further transformations.
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Non-equilibrium Transformation
Products - Bainite
• Bainite is a microconstituents that are products of
austenitic transformation
• Microstructure consist of ferrite and cementite phases =>
diffusional processes are involved in the transformation
• Forms needles or plates depending on temperature of
transformation
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Non-equilibrium Transformation Products
- Bainite
• Bainite microstructure
– Elongated particles of Fe3C
– Ferrite matrix
– Diffusion controlled
– Surrounding the needle is
martensite
– No proeutectoid phase is formed
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Formation of Bainite Microstructure
If transformation
temperature is low
enough (≤540oC)
bainite rather than fine
pearlite forms
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Formation of Bainite Microstructure –
TTT Diagram
Upper bainite - 300-
540oC, consists of
needles of ferrite
separated by long
cementite particles
Lower bainite - 200-
300oC, consists of thin
plates of ferrite
containing very fine rods
or blades of cementite
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Formation of Bainite Microstructure
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Spheroidite Formation• Spherodite – anneal pearlitic or bainitic microstructures at elevated
temperatures just below eutectoid (e.g. 24h at 700oC)
– spheres of cementite in a ferrite matrix (instead of lamellae pearlite)
• Composition or relative amounts of ferrite and cementiteunchanged in this transformation
– only shape of the cementite inclusions is changing
• Transformation proceeds by carbon diffusion => needs high temperature
• Driving force for the transformation – reduction in total ferrite-cementite boundary area
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Spheroidite Formation
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Non-equilibrium Martensite Formation
• Martensite forms when austenite is rapidly cooled (quenched) to room temperature
• The austenite-martensite does not involve diffusion
• Any diffusion process can lead to the formation of ferrite and cementite phases
• Martensite is metastable –will transform to equilibrium phases on annealing at an elevated temperature
• Since martensite is metastable non-equilibrium phase, it does not appear in Fe-C phase diagram
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Martensite Structure
Fe
C
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TTT Diagram including Martensite
γ to M transformation
Is rapid
% transformation
depends on T only
Athermal
transformations
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53
Martensite Formation
(FCC) (BCC) + Fe3Cslow cooling
tempering
quench
M (BCT)
Martensite (M) – single phase
– has body centered tetragonal (BCT)
crystal structure
Diffusionless transformation BCT if C0 > 0.15 wt% C
BCT few slip planes hard, brittlewww.knust.edu.gh
martensite
coarse pearlite
fine pearlite
upper bainite
lower bainite
Where are the accessible
microstructures?
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coarse pearlite
fine pearlite
upper bainite
lower bainite
martensite
How do I obtain the accessible
microstructures?
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Phase Transformation of Alloys
• Effect of adding alloying elements other than carbon changes
transition temperatures
• Cr, Ni, Mo, W, and Mn retard austenite-to-pearlite transformation.
These include:
– Shift to longer times the nose of the austenite-to-pearlite
transformation
– The formation of separate bainite nose
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Phase Transformation of Alloys
An iron-carbon alloy of eutectoid
composition
An alloy steel type 4340 (1.6-2.0 Ni,
0.4-0.9 Cr, 0.2-0.3 Mo)
An Fe-C Alloy of Eutectoid Composition
Example problem:
Specify the nature of the final microstructure (in terms of
microconstituents present and approx. percentage) of a small
specimen that has been subjected to the following time-temperature
treatments. The specimen begins at 760oC and has been held at this
temperature long enough to have a complete austenitic structure.
(a) Rapid cool to 350oC hold for 104s and quenched to Tr
(b) Rapid cool to 250oC hold for 100s and quenched to Tr
(c) Rapid cool to 650oC hold for 20s rapidly cooled to 400oC, hold
for 103s, and quenched to Tr
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(a) Rapidly cool to 350°C, hold
for 104 s, and quench to room
temperature.
The sample starts as austenite
and the transforms from ~10 s
through 500 s to bainite.
=> At 104 s, 100% bainite is
obtained. No further
transformation possible though
line passes through martensite
region
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(b) Rapidly cool to 250°C, hold
for 100 s, and quench to
room temperature.
100% austenite remain at
250°C but when cooled the
austenite converts to martensite
(starting at about 215°C)
=> Microstructure at room
temperature is 100% martensite
(c) Rapidly cool to 650°C, hold for
20 s, rapidly cool to 400°C,
hold for 103 s, and quench to
room temperature.
The sample begins to transform to
pearlite after 7s; to about 50%
after 20s.
Very little transformation takes
place during rapid cooling to
400oC
At 400oC, the remaining austenite
converts to bainite.
In the end, you have 50% pearlite
and 50% bainite.
Practical considerations
inside is slow cooled (~0.1°C/sec)
inside, slow
cooled - pearlite
outside is fast cooled (~800°C/sec)
outside, fast cooled -
martensite
Hard case on a ductile interior
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Continuous Cooling
Transformation Diagrams• Isothermal heat treatment are not the most practical
– Alloy must be rapidly cooled to and maintained at high
temperature from a higher temperature above the eutectoid
• Most heat treatment of steels involve continuous cooling of a
specimen to room temperature
– Diagram must be modified for transformations that occur as
the temperature is constantly changing
• For continuous cooling, the time required for a reaction to begin
and end is delayedwww.knust.edu.gh
Continuous Cooling Transformation
Diagrams
• Isothermal curves are
shifted to longer times
and lower temperatures
• A modified curves are
called continuous
cooling transformation
(CCT) diagrams
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Continuous Cooling Transformation Diagrams
• Two cooling curves: moderately fast and slow rates
• Microstructures obtained => fine and coarse pearlite
• Plain carbon steels will not form bainite when continuously cooled to room temperature
• 100% austenite-to-pearlite transformation is reached by the time bainite transformation is possible
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Slower cooling curves
allow for equilibrium
microstructures to appear.
There appears a critical
cooling rate at which
the material bypasses
all the equilibrium
phases
Martensites will exist
for quenching rates
greater than the critical
Steel alloys
Dynamic Phase Transformation
On the isothermal transformation diagram for 0.45 wt% C
in Fe-C alloy, sketch and label the temperature-time paths to
produce the following microstructures:
a) 42% proeutectoid ferrite and 58% coarse pearlite
b) 50% fine pearlite and 50% bainite
c) 100% martensite
d) 50% martensite and 50% austenite
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Example problem for Co = 0.45 wt%
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Example problem for Co = 0.45 wt%
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Example problem for Co = 0.45 wt%
Kwame Nkrumah University of
Science & Technology, Kumasi, Ghana
Mechanical Behaviour of
Iron – Carbon Alloys
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Introduction
• For all the microstructures (except martensite), two
phases are present
– Ferrite
– Cementite
• Cementite is harder and more brittle than ferrite =>
increasing cementite fraction makes harder, less ductile
material
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Mechanical Properties – Influence of C
content
0.76
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Mechanical Properties –
Influence of C content
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Mechanical Properties – Fine Pearlite vs.
Coarse Pearlite vs. Spherodite
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Mechanical Effects of the Microstructure -Bainite
Because bainite steels have finer structure (i.e. smaller α-ferrite and
Fe3C particles), they are stronger and harder than pearlitic ones
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Mechanical Properties of Martensite
Tempered martensite phase
transforms to Fe3C and α-Fe
As it phase transforms the
soft matrix of α-Fe leads to
the drop in hardness.
Tempered Martensite
Micrograph of tempered martensite
• Produces extremely small Fe3C particles surrounded by α ferrite
• Decreases TS, YS but increases % RA
Summary: Austenite Transformation
Solid lines are diffusional transformations,
dashed are diffusionless martensitic
transformation
Summary: Processing Options
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Bainite
coarse fine
Austenite
Martensite
Moderate cooling (AS)
Isothermal treatment (PCS)
Tempered
Martensite
Pearlite
AS: Alloy Steel
PCS: Plain-carbon Steel
Slow
Cooling
Rapid
Quench
Spheroidite
Re-heat
Re-heat
Summary of microstructures and mechanical properties of Fe-C alloys