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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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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