PHASE TRANSFORMATIONSPHASE TRANSFORMATIONS

Nucleation & Growth TTT

and CCT

Diagrams

APPLICATIONS Transformations in Steel

Precipitation Solidification & crystallization

Glass transition Recovery, Recrystallization & Grain growth

Phase Transformations in Metals and AlloysDavid Porter & Kenneth Esterling

Van Nostrand

Reinhold Co. Ltd., New York (1981)

When one phase transforms to another phase it is called phase transformation.

Often the word phase transition is used to describe transformations where there is no change in composition.

In a phase transformation we could be concerned about phases defined based on:

Structure

→ e.g. cubic to tetragonal phase

Property

→ e.g. ferromagnetic to paramagnetic phase

Phase transformations could be classified based on

(pictorial view in next page)

:

Kinetic:

Mass transport → Diffusional

or Diffusionless

Thermodynamic:

Order (of the transformation) → 1st

order, 2nd

order, higher order.

Often subtler aspects are considered under the preview of transformations. E.g. (i) roughening transition of surfaces, (ii) coherent to semi-coherent transition of interfaces.

Phase Transformations: an overview

Diffusional

PHASE TRANSFORMATIONS

Diffusionless

1nd

order nucleation & growth

PHASE TRANSFORMATIONS

2nd

(& higher) order Entire volume transforms

Based onMass

transport

Based onorder

E.g. MartensiticInvolves long range mass transport

Phases Defects Residual stress

Transformations in Materials

Defect structures can changePhases can transform Stress state can be altered

Phase Transformation

Defect Structure

Transformation

Stress-State

Transformation

Geometrical Physical

MicrostructureMicrostructurePhasesPhases

Microstructural TransformationsMicrostructural TransformationsPhases TransformationsPhases Transformations

Structural Property

Phase transformations are associated with change in one or more properties.

Hence for microstructure dependent properties we would like to additionally ‘worry about’

‘subtler’

transformations, which involve defect structure and stress state (apart from phases).

Therefore the broader subject of interest is Microstructural Transformations.

What is a Phase?

What kind of phases exist?

What constitutes a transformation?

How can we cause a phase transformation to occur?

The stimuli:

P, T, Magnetic field, Electric field etc.

What kind of phase transformations are there?

Why does a phase transformation occur?

Energy considerations of the system?

Thermodynamic potentials (G, A…)

Some of the questions we would like to have an answer for…

Answers for some these questions may be found in other chapters

Energies involved

Bulk Gibbs free energy ↓

Interfacial energy ↑

Strain energy ↑Important in solid to solid transformations

Revise concepts of surface and interface energy before starting on these topics

When a volume of material (V) transforms three energies have to be considered : (i) reduction in G (assume we are working at constant T & P), (ii) increase in

(interface free-energy), (iii) increase in strain energy.

In a liquid to solid phase transformation the strain energy term

can be neglected (as the liquid can flow and accommodate the volume/shape change involved

in the transformation-

assume we are working at constant T & P).

Volume of transformed material

New interface created

Energies involved

Bulk Gibbs free energy ↓

Interfacial energy ↑

Strain energy ↑

The origin of the strain energy can be understood using the schematics as below. Eshelby

construction is used for this purpose.

In general a solid state phase transformation can involve a change in both volume and shape. I.e. both dilatational and shear strains may be involved.

For simplicity we consider only change in volume of the material, leading to an increase in

the strain energy of the system (in future considerations).

Schematic of the Eshelby

construction to understand the origin of the stresses due to phase transformation of a volume (V): (a) region V before transformation, (b) the region V is cut out of the matrix and allowed to transform (the transformation could involve both shape and volume changes), (c) the transformed volume (V‘-

shown to be larger in the figure) is inserted into the hole (here only volume change is shown for simplicity), (c) the system is allowed to equilibrate. The continuity of the system is maintained during the transformation. The system is strained as a larger volume V’

is inserted into the hole of volume V.

Only volume change

(a)

(b)(c) (d)

Considering only volume change

Energies involved

Bulk Gibbs free energy ↓

Interfacial energy ↑

Strain energy ↑ Solid-solid transformation

Let us start understanding phase transformations using the example of the solidification of a pure metal. (This process is a first order transformation*. First order transformations involve nucleation and growth**).

There is no change in composition involved as we are considering

a pure metal. If we solidify an alloy this will involve long range diffusion.

Strain energy term can be neglected as the liquid melt can flow to accommodate the volume change (assume we are working at constant T & P).

The process can start only below the melting point of the liquid

(as only below the melting point the GLiquid

< GSolid

). I.e. we need to Undercool

the system. As we shall note, under suitable conditions (e.g. container-less solidification in zero gravity conditions), melts can be undercooled to a large extent without solidification taking place.

Click here to know more about order of a phase transformation

Nucleation

of

phase

Trasformation

→ +

Growth till

is exhausted

=1nd

order

nucleation & growth

*

**

↑

t

“For sufficient Undercooling”

Cru

de sc

hem

atic

!

Liqu

id→

Solid

phas

e tra

nsfo

rmat

ion:

Sol

idifi

catio

n

3

21

4

5 6

Liquid

SolidGrowth of Crystal

Two crystal going to join to form grain boundary

Growth of nucleated crystal

Solidification complete

Video snap shots of solidification of stearic

acid

Grain boundary

Caution: here we are seeing an increase time experiment and soon we will be ‘talking of’

increasing undercooling experiments

See video hereSee video here

Liquid

→ Solid

phase transformation

Liquid (GL

)

Tm T →

G →

T

Gv

Liquid stableSolid stable

T -

Undercooling

On cooling just below Tm

solid becomes stable, i.e. GLiquid

< GSolid

.

But

even when we are just below Tm

solidification does not ‘start’.

E.g. liquid Ni can be undercooled 250 K below Tm

.

We will try to understand Why?

The figure below shows G vs

T curves for melt and a crystal.

The undercooling is marked as T and the ‘G’

difference between the liquid and the solid (which will be released on solidification) is marked as Gv

(the subscript indicates that the quantity G is per unit volume). Hence, Gv

is a function of undercooling (T)

G → ve

G → +ve

Solid (GS)

In Homogenous 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

HeterogeneousNucleation

NucleationSolidification + Growth=

Heterogenous

nucleation sites

Liquid → solid

walls of container, inclusions

Solid → solid

inclusions, grain boundaries, dislocations, stacking faults

As pointed out before solidification is a first order phase transformation involving nucleation (of crystal from melt) and growth (of crystals such that the entire liquid is exhausted).

Nucleation

is a ‘technical term’

and we will try to understand that soon.

In solid solid phase transformation, which involve strain energy, heterogeneous nucleation

(defined below) is highly preferred. Even in liquid solid transformations heterogeneous nucleation plays an very important role.

of crystals from melt of nucleated crystals till liquid is exhausted

Homogenous nucleation

ΔG (Volume).( ) (Surface).( )VG

).(4 ).(34 ΔG 23 rGr v

r2

r3

1

)( TfGv

energystrain in increase energy surfacein increase energy freebulk in Reduction nucleationon changeenergy Free

r

( )f r

Neglected in L → S transformations

Let us consider LS

transformation taking place by homogenous nucleation. Let the system be undercooled to a fixed temperature T. Let us consider the formation of a spherical crystal of radius ‘r’

from the melt. We can neglect the strain energy contribution.

Let the change in ‘G’

during the process be G. This is equal to the decrease in bulk free energy + the increase in surface free energy. This can be computed for a spherical nucleus as below.

Note that below a value of ‘1’

the lower power of ‘r’

dominates; while above ‘1’

the higher power of ‘r’

dominates.

In the above equation these powers are weighed with other ‘factors/parameters’, but the essential logic remains.

Note that GV

is negative

Let us start with a ‘text-book’

description of nucleation before taking up an alternate perspective

A note on minimization versus criticality conditions.Funda

Check

In the above equation, the r3

term is +ve

and the r2

term is ve. Such kinds of equations are often encountered in materials science, where one term is opposing the process and the other is supporting it. Example of such processes are crack growth (where surface energy opposes the process and the strain energy stored in the material

supports crack growth).

In the current case it is the higher power is supporting the phase transformation. Since the higher power dominates above ‘1’, the function will go through a maximum as in fig. below. This implies the G function will go through a maximum. I.e. if the process just even starts it will lead to an increase in G! (more about this soon).

On the other hand the function with ve

contribution from the lower power (to G) will go through a minimum (fig. below) and such a process will take place down-hill in G and stop.

).(4 ).(34 ΔG 23 rGr v

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6x

x^n

x^2x^3

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

x

f(x)

(x - x^2)(x^2 - x) Goes through a maximum

Goes through a minimum

).(4 ).(34 ΔG 23 rGr v

As we have noted previously G vs

r plot will go through a maximum (implying that as a small crystal forms ‘G’

will increase and hence it will tend to dissolve).

The maximum of G vs

r plot is obtained by by

setting dG/dr

= 0. The maximum value of G corresponds to a value of ‘r’

called the critical radius (denoted by superscript *).

If by some ‘accident’

(technically a ‘statistical random fluctuation’) a crystal (of ‘preferred’

crystal structure) size > r*

(called

supercritical nuclei)

forms then it can grow down-hill in ‘G’. Crystals smaller than r* (called embryos) will tend to shrink to reduce ‘G’. The critical value of G at r* is called G*.

Reduction in G (below the liquid state) is obtained only after r0

is obtained (which can be obtained by setting G = 0).

0dr

Gd0*

1 r

vGr

2*2

Trivial solution

vGr

2*

2

3*

316

vGG

As Gv

is ve, r*is +ve

r →

G

→0G

0r

0G vGr

30

Supercritical nucleiEmbryos

Note that G is a function of T, r &

*rSh

rink Grow

0dr

Gd

Note that we are at a constant T

r →

G

→

Increasin

g T

Decreasing r*

Dec

reas

ing

G*

Tm

23

2 2

163

mTGT H

Using the Turnbull approximation (linearizing

the G-T

curve close to Tm

), we can get the value of G interms

of the enthalpy of solidification.

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

What is the effect of undercooling (T) on r* and G*?

We have noted that GV

is a fucntion

of undercooling (T). At larger undercoolings

GV

increases and hence r* and G* decrease. This is evident from the equations for r* and G* as below (derived before)

.

At Tm

GV

is zero and r* is infinity!

That the melting point is not the same as the freezing point!!

This energy (G) barrier to nucleation is called the

‘nucleation barrier’.

vGr

2*

2

3*

316

vGG

T →

G →

Turnbull’s approximation

Tm

Solid (GS)

Liquid (GL

)T

G

mf f

m m

T T TG H HT T

fΔH heat of fusion

2

* 3163

m

f

TGH T

How are atoms assembled to form a nucleus of r* “Statistical Random Fluctuation”QuantumQuantumQuantum

Jump Jump Jump

To cause nucleation (or even to form an embryo) atoms of the liquid (which are randomly moving about) have to come together in a order, which resembles the crystalline order, at a given instant of time. Typically, this crystalline order is very different from the order (local order), which exists in the liquid.This ‘coming together’

is a random process, which is statistical in nature i.e. the liquid is exploring ‘locally’

many different possible configurations and randomly (by chance), in some location in the liquid, this order may resemble the preferred crystalline order.Since this process is random (& statistical) in nature, the probability that a larger sized crystalline order is assembled is lower than that to assemble a smaller sized ‘crystal’.Hence, at smaller undercoolings

(where the value of r* is large) the chance of the formation of

a supercritical nucleus is smaller and so is the probability of solidification (as at least one nucleus is needed

which can grow to cause solidification). At larger undercoolings, where r* value is relatively smaller, the chance of solidification is higher.

↑

T

r*

Tm

Cha

nces

of n

ucle

atio

n in

crea

ses

Here we try to understand: “What exactly is meant by the nucleation barrier?”.

It is sometime difficult to fathom out as to the surface energy can make freezing of a small ‘embryo’

energetically ‘infeasible’

(as we have already noted that unless the crystallite size is > r0

the energy of the system is higher). Agreed that for the surface the energy lowering is not as much as that for the bulk*, but even the surface (with some ‘unsaturated bonds’) is expected to have a lower energy than the liquid state (where the crystal is energetically favoured). I.e. the specific concern being: “can state-1 in figure below be above the zero level (now considered for the liquid state)?”

“Is the surface so bad that it even negates the effect of the bulk lowering?”

We will approach this mystery from a different angle

by first asking the question: “what is meant by melting point?”

& “what is meant by undercooling?”.

What is meant by the ‘Nucleation Barrier’

an alternate perspective Funda

Check

* refer to surface energy and surface tension slides.

The plot below shows melting point of Au nanoparticles, plotted as a function of the particle radius. It is to be noted that the melting point of nanoparticles decreases below

the ‘bulk melting point’

(a 5nm particle melts more than 100C below Tm

bulk). This is due to surface effects (surface is expected to have a

lower melting point than bulk!?*) actually, the current understanding is that the whole nanoparticle melts simultaneously (not surface layer by layer).

Let us continue to use the example of Au. Suppose we are below Tmbulk

(1337K=1064C, i.e. system is undercooled

w.r.t

the bulk melting point)

at T1

(=1300K T = 37K)

and suppose a small crystal of r2

= 5nm

forms in the liquid. Now the melting point of this crystal is ~1200K this crystal will ‘melt-away’. Now we have to assemble a crystal of size of about 15nm (= r1

)

for it ‘not to melt’. This needless to say is much less probable (and it is better to undercool

even further so that the value of r* decreases). Thus the mystery of ‘nucleation barrier’

vanishes and we can ‘think of’

melting point

freezing point (for a given size of particle)!

Tm

is in heating for the bulk material and in cooling if we take into account the size dependence of melting point everything ‘sort-of’

falls into place .

Melting point, undercooling, freezing point (in the realm of homogenous nucleation)

Other materials like Pb, Cu, Bi, Si show similar trend lines

* Surface atoms are loosely bound as compared to the bulk atoms.

T1

r1

The process of nucleation (of a crystal from a liquid melt, below Tmbulk) we have described so

far is a dynamic one. Various atomic configurations are being explored in the liquid state

some of which resemble the stable crystalline order. Some of these ‘crystallites’

are of a critical size r*T

for a given undercooling (T). These crystallites can grow to transform the melt to a solid by becoming supercritical. Crystallites smaller than r* (embryos) tend to ‘dissolve’.

As the whole process is dynamic, we need to describe the process

in terms of ‘rate’

the nucleation rate [dN/dt

number of nucleation events/time].

Also, true nucleation is the rate at which crystallites become supercritical. To find the nucleation rate we have to find the number of critical sized crystallites (N*) and multiply it by the frequency/rate at which they become supercritical.

If the total number of particles (which can act like potential nucleation sites

in homogenous nucleation for now) is Nt

, then the number of critical sized particles given by an Arrhenius type function with a activation barrier of G*.

Atomic perspective of nucleation: Nucleation Rate

kTG

t eNN*

*

The number of potential atoms, which can jump to make the critical nucleus supercritical are the atoms which are ‘adjacent’

to the liquid let this number be s*.

If the lattice vibration frequency is

and the activation barrier for an atom facing the nucleus (i.e. atom belonging to s*) to jump into the nucleus (to make in

supercritical) is Hd

, the frequency with which nuclei become supercritical due atomic jumps into the nucleus is given by:

No. of critical sized particlesRate of nucleation

Frequency with which they become supercritical=

dtdNI

kTG

t eNN*

*

kTHd

es ' *

Critical sized nucleus (r*)

s*

atoms of the liquid facing the nucleus

Outline of critical sized nucleus

Jump taking particle to supercriticality

→ nucleated (enthalpy of activation = Hd

)

No. of particles/volume in L → lattice vibration frequency (~1013

/s)

kTHd

es ' *

T (K

) →

Incr

easi

ng

T

Tm

0 I →

T = Tm

→ G*

=

→ I = 0

T = 0 → I = 0

kTHG

t

d

esNI

*

*

G*

↑

I ↓

T ↑

I ↑

Note: G*

is a function of T

The nucleation rate (I = dN/dt) can be written as a product of the two terms as in the equation below.

How does the plot of this function look with temperature?

At Tm

, G* is I = 0

(as expected if there is no undercooling there is no nucleation).

At T = 0K again I = 0

This implies that the function should reach a maximum between T = Tm

and T = 0.

A schematic plot of I(T) (or I(T)) is given in the figure below.

An important point to note is that the nucleation rate is not a monotonic function of undercooling.

Heterogenous

nucleation

We have already talked about the ‘nucleation barrier’

and the difficulty in the nucleation process. This is all the more so for fully solid state phase transformations, where the strain energy term is also involved (which opposes the transformation).

The nucleation process is often made ‘easier’

by the presence of ‘defects’

in the system.

In the solidification of a liquid this could be the mold walls.

For solid state transformation suitable nucleation sites are: non-equilibrium defects such as excess vacancies, dislocations, grain boundaries, stacking faults, inclusions and surfaces.

One way to visualize the ease of heterogeneous nucleation

heterogeneous nucleation at a defect will lead to destruction/modification of the defect (make it less “‘defective’”). This will lead to some free energy Gd

being released → thus reducing the activation barrier (equation below)

.

hetro,defectΔG (V) A ( )v s dG G G

Increasing Gd

(i.e. decreasing G*)

Homogenous sites

Vacancies

Dislocations

Stacking Faults

Grain boundaries (triple junction…), Interphase

boundaries

Free Surface

Heterogenous

nucleation

Consider the nucleation of

from

on a planar surface of inclusion .

The nucleus will have the shape of a lens (as in the figure below).

Surface tension force balance equation can be written as in equation (1) below. The contact angle can be calculated from this equation (as in equation (3)).

Keeping in view the interface areas created and lost we can write the G equation as below (2).

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

Alens

Acircle

Acircle

Created

Created

Lost

CosSurface tension force balance

Interfacial Energies

Vlens

= h2(3r-h)/3 Alens

= 2rh h = (1-Cos)r rcircle

= r Sin

Cos

(1)

(2)

is the contact angle

(3)

vhetero G

r

2*

32

3* 32

34 CosCos

GG

vhetero

0

dr

Gd

3homo

* 3241 CosCosGG *

hetero

Using the procedure as before (for the case of the homogenous nucleation) we can find r*

for heterogeneous nucleation. Using the surface tension balance equation we can write the formulae for r*and G*

using a single interfacial energy

(and contact angle ).

Further we can write down in terms of and contact angle . *heteroG *

homoG

*

3hetero

homo

1 2 34*

G Cos CosG

Just a function of

the contact angle

*

3hetero

homo

1 2 3 ( )4*

G Cos Cos fG

= 0 f() = 0

= 90 f() = ½

= 180 f() = 1

The plot of / is shown in the next page.*heteroG *

homoG

Increasing contact angle

Complete wetting

No wetting

Partial wetting

Decreasing tendency to wet the substrate

0

0.25

0.5

0.75

1

0 30 60 90 120 150 180

(degrees)

→

G

* hete

ro/

G* ho

mo→

G*hetero

(0o) = 0

no barrier to nucleation G*

hetero

(90o) = G*homo

/2

G*hetero

(180o) = G*homo

no benefit

Complete wetting No wettingPartial wetting

Cos

Plot of G*hetero

/G*homo

is shown below. This brings out the benefit of heterogeneous nucleation vs

homogenous nucleation.

If the

phase nucleus (lens shaped) completely wets the substrate/inclusion (-phase) (i.e.

= 0)

then G*

hetero

= 0 there is no barrier to nucleation.

On the other extreme if -phase does not we the substrate (i.e.

= 180)

then G*

hetero

= G*homo

there is no benefit of the substrate.

In reality the wetting angle

is somewhere between 0-180

Hence, we have to chose a heterogeneous nucleating agent with a minimum ‘’

value.

Choice of heterogeneous nucleating agent

How to get a small value of ? (so that ‘easy’

heterogeneous nucleation).

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

)

Cos

Cos

How to get a low value of

?

We can get a low value of

if: (i) crystal structure of

and

are similar and (ii) lattice parameters are as close as possible

Examples of such choices:

In seeding rain-bearing clouds → AgI

or NaCl

are used for nucleation of ice crystals

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.

Heterogeneous nucleation has many practical applications.

During the solidification of a melt if only a few nuclei form and these nuclei grow, we will have a coarse grained material (which will have a lower strength as compared to a fine grained material-

due to Hall-Petch

effect).

Hence, nucleating agents are added to the melt (e.g. Ti for Al alloys, Zr

for Mg alloys) for grain refinement.

kTG

eII

*homo

0homohomo

kTG

eII

*hetero

0heterohetero

= f(number

of nucleation sites)~ 1042

= f(number

of nucleation sites)~ 1026

BUT

the exponential term dominates

Ihetero

> Ihomo

To understand the above questions, let us write the nucleation rate for both cases as a pre-

exponential term and an exponential term. The pre-exponential term is a function of the number of nucleation sites.

However, the term that dominates is the exponential term and due

to a lower G*

the heterogeneous nucleation rate is typically higher.

Why does heterogeneous nucleation dominate? (aren’t there more number of homogenous nucleation sites?)

Heterogeneous nucleation in AlMgZn

alloy

Nucleation of

phaseTransformation

→ + Growth of

phase till

is exhausted*=

Diffusional

transformations involve nucleation and growth. Nucleation involves the formation of a different phase from a parent phase (e.g. crystal

from melt). Growth involves attachment of atoms belonging to the matrix to the new phase (e.g. atoms ‘belonging’

to the liquid phase attach to the crystal phase).

Nucleation we have noted is ‘uphill’

in ‘G’

process, while growth is ‘downhill’

in G.

Growth can proceed till all the ‘prescribed’

product phase forms (by consuming the parent phase).

Growth

Hd

– vatom

Gv

Hd

phase

phase

At transformation temperature the probability of jump of atom from

→

(across the interface) is same as the reverse jump

Growth proceeds below the transformation temperature, wherein the activation barrier for the reverse jump is higher than that for the forward jump.

Growth

As expected transformation rate (Tr

)

is a function of

nucleation rate (I)

and growth rate (U).

In a transformation, if X

is the fraction of -phase formed, then dX

/dt

is the transformation rate.

The derivation of Tr

as a function of I & U

is carried using some assumptions (e.g. Johnson-Mehl

and Avarami

models).

Transformation rate

rate)Growth rate,on f(Nucleatiratetion Transforma

I,

U, Tr

→

T (K

) →

Incr

easi

ng

T

Tm

0

U

Tr

I

( , )r

dXT f I U

dt

Maximum of growth rate usually at higher temperature than maximum of nucleation rate

We have already seen the curve for the nucleation rate (I) as a function of the undercooling.

The growth rate (U) curve as a function of undercooling looks similar. The key difference being that the maximum of U-T* curve is typically above the I-T curve*.

This fact that T(Umax

) > T(Imax

) give us an important ‘handle’

on the scale of the transformed phases forming. We will see examples of the utility of this information later.

* The U-T

curve is an alternate way of stating the U-T

curve[rate sec1]

t →

X→

0

1.0

0.5

3 t UI π

β

43

e 1X

Fraction of the product () phase forming with time the sigmoidal

growth curve

Many processes in nature (etc.), e.g. growth of bacteria in a culture (number of bacteria with time), marks obtained versus study time(!), etc. tend to follow a universal curve the sigmoidal

growth curve.

In the context of phase transformation, the fraction of the product phase (X

) forming with time follows a sigmoidal

curve (function and curve as below

).

Linear growth regime ~constant high growth rate

Incubation period slow growth (but with increasing growth rate with time)

Saturation phase decreasing growth rate with time

From ‘Rate’

to ‘time’: the origin of Time –

Temperature –

Transformation (TTT) diagramsA type of phase diagram

Tr

(rate sec1)

→

T (K

) →

Tr

Tm

0

T (K

) →

Tm

0

Time for transformation

Small driving force for nucleation

Replot

( , )Rate f T t

Sluggish growth

The transformation rate curve (Tr

-T

plot) has hidden in it the I-T and U-T

curves.

An alternate way of plotting the Transformation rate (Tr

) curve is to plot Transformation time (Tt

) [i.e. go from frequency domain to time domain]. Such a plot is

called the Time-

Temperature-Transformation diagram (TTT

diagram).

High rates correspond to short times and vice-versa. Zero rate implies time (no transformation).

This Tt

-T

plot looks like the ‘C’

alphabet and is often called the ‘C-curve. The minimum time part is called the nose of the curve.

Tt

Tt

(time sec)

→

Nose of the ‘C-curve’

Understanding the TTT

diagram

Though we are labeling the transformation temperature Tm

, it represents other transformations, in addition to melting.

Clearly the Tt

function is not monotonic in undercooling. At Tm

it takes infinite time for transformation.

Till T3

the time for transformation decreases (with undercooling) [i.e.

T3

< T2

< T1

] due to small driving force for nucleation.

After T3

(the minimum) the time for transformation increases [i.e. T3

< T4

< T5

] due to sluggish growth.

This is a phase diagram where the blue region is the Liquid (parent) phase field and purplish region is the transformed product (crystalline solid).

The diagram is called the TTT

diagram because it plots the time required for transformation if we hold the sample at fixed temperature (say T1

) or fixed undercooling (T1

).

The time taken at T1

is t1

.

To plot these diagrams we have to isothermally

hold at various undercoolings

and note the transformation time.

I.e. instantaneous quench followed by isothermal hold.

Hence, these diagrams are also called Isothermal Transformation Diagrams.

Similar curves can be drawn for (solid state) transformation.

Clearly the picture of TTT

diagram presented before is incomplete transformations may start at a particular time, but will take time to be completed (i.e. between the L-phase field and solid phase field there must be a two phase region L+S!).

This implies that we need two ‘C’

curves one for start of transformation

and one for completion. A practical problem in this regard is related to the issue of how to define start and finish (is start the first nucleus which forms? Does finish correspond to 100%?) . Since practically it is difficult to find ‘%’

and ‘100%’, we use practical measures of start and finish, which can be measured experimentally. Typically this is done using optical

metallography and a reliable ‘resolution of the technique is about 1%

for start and 99% for finish.

Another obvious point: as x-axis is time any ‘transformation paths’

have to be drawn such that it is from left to right (i.e. in increasing time).

t (sec)

→T (K

) →

99% = finish

Increasing % transformation

TTT diagram

→

phase transformation

1% = start

Fraction transformed

f volume fraction of

volume fraction of at tffinal volumeof

How do we define the fractions transformed?

f(t,T) determined by

Growth rate

Density and distribution of nucleation sites

Nucleation rate

Overlap of diffusion fields from adjacent transformed volumes

Impingement of transformed volumes

How can we compute Tt

(T) (transformation time for each T)

The ‘C’

curve depends on various factors as listed in diagram below.

Some common assumptions used in the derivation are: (i) constant

number of nuclei, (ii) constant nucleation rate, (iii) constant growth rate.

( , )f F number of nucleation sites growth rate growth rate with time

Constant number of nuclei (these form at the beginning of the transformation)

One assumption to simplify the derivation is to assume that the number of nucleation sites remain constant and these form at the beginning of the transformation.

This situation may be approximately valid for example if a nucleating agent (inoculant) is added to a melt (the number of inoculant

particles remain constant).

In this case the transformation rate is a function of the number

of nucleation sites (fixed) and the growth rate (U).

Growth rate is expected to decrease with time.

In Avrami

model the growth rate is assumed to be constant (till impingement).

Parent phase has a fixed number of nucleation sites Nn

per unit volume (and these sites are exhausted in a very short period of time

Growth rate (U = dr/dt) constant and isotropic (as spherical particles) till particles

impinge on one another

Derivation of f(T,t): Avrami

Model

2 3 224 4 4n n nr Utf N N N U t dtdr Udt

At time t the particle that nucleated at t = 0 will have a radius r = Ut

Between time t = t and t = t + dt

the radius increases by dr

= Udt

The corresponding volume increase dV

= 4r2

dr

1dXf

X

This fraction (f) has to be corrected for impingement. The corrected transformed volume fraction (X) is lower than f by a factor (1X) as contribution to transformed volume fraction comes from untransformed regions only:

Without impingement, the transformed volume fraction (f) (the extended transformed volume fraction) of particles that nucleated between t = t and t = t + dt

is:

3 241 ndX N U t dt

X

3 2

0 0

41

X t t

nt

dX N U t dtX

3 3n4π N U t3

βX 1 e

Based on the assumptions note that the growth rate is not part of the equation it is only the number of nuclei.

Cellular Transformations → Constant growth rate

Cellular Precipitation

Pearlitic

transformation

Massive Transformation

Recrystallization

All of the parent phase is consumed by the product phase

Where do we see constant growth rate? In cellular transformations constant growth rate is observed.

Termination of transformation does not occur by a gradual reduction in the growth rate but by the impingement of the adjacent cells growing with a constant velocity.

E.g.: Pearlitic

transformation, Cellular precipitation, Massive transformation,

recrystallization.

( , )f F nucleation rate growth rate

Constant nucleation rate

growth rate with time

Another common assumption is that the nucleation rate (I) is constant.

In this case the transformation rate is a function of both the nucleation rate (fixed) and the growth rate (U).

Growth rate decreases with time.

If we further assume that the growth rate is constant (till impingement), then we get the Johnson-Mehl

model.

Parent phase completely transforms to product phase (

→ )

Homogenous Nucleation rate of

in untransformed volume is constant (I)

Growth rate (U = dr/dt) constant and isotropic (as spherical particles) till particles

impinge on one another

Derivation of f(T,t): Johnson-Mehl

Model

334 43 3

( )r U t If Id d

At time t the particle that nucleated at t = 0 will have a radius r = Ut

The particle which nucleated at t =

will have a radius r = U(t

)

Number of nuclei formed between time t =

and t =

+ d

→ Id

1dXf

X

This fraction (f) has to be corrected for impingement. The corrected transformed volume fraction (X) is lower than f by a factor (1X) as contribution to transformed volume fraction comes from untransformed regions only:

Without impingement, the transformed volume fraction (f) (called the extended transformed volume fraction) of particles that nucleated between t =

and t =

+ d

is:

334 41 3 3

( )Idr UdXX

t Id

0 0

3(41 3

)X t

U t IddXX

3 t UI π

β

43

e 1X

t →

X→

0

1.0

0.5

t →

X→

0

1.0

0.5

3π I U is a constant during isothermal transformation3

For a isothermal transformation

Note that X

is both a function of I and U. I & U are assumed constant

APPLICATIONS

of the concepts of nucleation & growth

TTT/CCT

diagrams

Phase Transformations in Steel

Precipitation

Solidification, Crystallization and Glass Transition

Recovery recrystallization & grain growthAs hyperlinks

Phase Transformations in Steel

Now we have the necessary wherewithal to understand phase transformations in steel

Phase diagram (Fe-Fe3

C) and

Concept of TTT

diagrams

We shall specifically consider TTT

and CCT

diagrams for eutectoid, hypo-

and hyper-

eutectoid steels.

Further we will consider the use of these diagrams to design heat treatments to get a specific microstructure (each microstructure will give us a different set of properties).

%C →

T →

Fe Fe3

C6.74.30.80.16

2.06

PeritecticL +

→ Eutectic

L →

+ Fe3

C

Eutectoid

→

+ Fe3

C

L

L +

+ Fe3

C

1493ºC

1147ºC

723ºC

Fe-Cementite

diagram

0.025 %C

0.1 %C

+ Fe3

C

We have already seen the Fe-Fe3

C phase diagram (please have a second look!)

Austenite

Pearlite

Pearlite

+ Bainite

Bainite

Martensite100

200

300

400

600

500

800723C

0.1 1 10 102 103 104 105

Eutectoid temperature

Ms

Mf

t (s) →

T →

Eutectoid steel (0.8%C)

+ Fe3

C

700

TTT

diagram for Eutectoid steel (0.8%C)

For every composition of steel we should draw a different TTT

diagram.

To the left of the start C curve

is the Austenite ()

phase field.

To the right of finish C curve

is the (

+ Fe3

C) phase field.

Above Eutectoid temperature there is no transformation

Important points to be noted:

The x-axis is log scale.

‘Nose’

of the ‘C’

curve is in ~sec and just below TE

transformation times may be ~day.

The starting phase has to .

The (

+ Fe3

C) phase field has more labels included.

There are horizontal lines labeled Ms

and Mf

.

‘Nose’

of ‘C’

curve

As pointed out before one of the important utilities of the TTT

diagrams comes from the overlay of microconstituents (microstructures) on the diagram.

Depending on the T, the (

+ Fe3

C) phase field is labeled with microconstituents like Pearlite, Bainite.

We had seen that TTT

diagrams are drawn by instantaneous quench to a temperature followed by isothermal hold.

Suppose we quench below (~225C, below the temperature marked Ms

), then Austenite transforms via a diffusionless

transformation (involving shear)

to a (hard) phase known as Martensite. Below a temperature marked Mf

this transformation to Martensite is complete. Once

is exhausted it cannot transform to (

+ Fe3

C).

Hence, we have a new phase field for Martensite. The fraction of Martensite formed is not a function of the time of hold, but the temperature to which we quench (between Ms

and Mf

).

Austenite

Pearlite

Pearlite + Bainite

Bainite

Martensite100

200

300

400

600

500

800723C

0.1 1 10 102 103 104 105

Eutectoid temperature

Ms

Mf

t (s) →

T →

Eutectoid steel (0.8%C)

+ Fe3C

700

Strictly speaking cooling curves (including finite quenching rates) should not be overlaid on TTT

diagrams (remember that TTT

diagrams are drawn for isothermal holds!).

Isothermal hold at: (i) T1

gives us Pearlite, (ii) T2

gives Pearlite+Bainite, (iii) T3

gives Bainite. Note that Pearlite

and Bainite

are both +Fe3

C (but their morphologies are different).

To produce Martensite we should quench at a rate such as to avoid the nose of the start ‘C’

curve. Called the critical cooling rate.

Austenite

Austenite

Pearlite

Pearlite + Bainite

Bainite

Martensite100

200

300

400

600

500

800723C

0.1 1 10 102 103 104 105

Eutectoid temperature

Not an isothermal

transformation

Ms

Mf

Coarse

Fine

t (s) →

T →

Eutectoid steel (0.8%C)

700

T1

T2

T3

If we quench between Ms

and Mf

we will get a mixture of Martensite and

(called retained Austenite).

In principle two curves exist for Pearlitic

and Bainitic

transformations → they are usually not resolved in plain C steel (In alloy steels they can be distinct).

Eutectoid steel (0.8%C)

For the transformations to both Pearlite

and Bainite, why do we have only one ‘C’

curve?Funda

Check

Atla

s of I

soth

erm

al T

rans

form

atio

n an

d C

oolin

g Tr

ansf

orm

atio

n D

iagr

ams,

ASM

Inte

rnat

iona

l, M

etal

s Par

k, O

H, 1

977.

TTT

Diagram: hypoeutectoid

steel

Hypo-Eutectoid steel

In hypo-

(and hyper-) eutectoid steels (say composition C1

) there is one more branch to the ‘C’

curve-NP (marked in red).

The part of the curve lying between T1

and TE

(marked in figs. below)

is clear, because in this range of temperatures we expect only pro-eutectoid

to form and the final microstructure will consist of

and .(E.g. if we cool to Tx

and hold-

left figure).

The part of the curve below TE

is a bit of a ‘mystery’

(since we are instantaneously cooling to below TE

, we should get a mix of + Fe3

C what is the meaning of a ‘pro’-eutectoid phase in a TTT

diagram? (remember ‘pro-’

implies ‘pre-’).(Considered next)

C1

Why do we get pro-eutectoid phase below TE

?

Suppose we quench instantaneously an hypo-eutectoid composition (C1

) to Tx

we should expect the formation of +Fe3

C (and not pro-eutectoid

first).

The reason we see the formation of pro-eutectoid

first is that the undercooling w.r.t

to Acm

is more than the undercooling w.r.t

to A1

. Hence, there is a higher propensity for the formation of pro-eutectoid .

Undercooling wrt

Acm(formation of pro-eutectoid )undercooling wrt

A1

line (formation of

+ Fe3

C)

C1

Funda

Check

Hyper-Eutectoid steel

T2

TE

Similar to the hypo-eutectoid case, hyper-eutectoid compositions (e.g. C2

in fig. below) have a +Fe3

C branch.

For a temperature between T2

and TE

(say Tm

(not melting point-

just a label)

) we land up with +Fe3

C.

For a temperature below TE

(but above the nose of the ‘C’

curve) (say Tn

), first we have the formation of pro-eutectoid Fe3

C followed by the formation of eutectoid +Fe3

C.

C2

Continuous Cooling Transformation (CCT) Curves

The TTT

diagrams are also called Isothermal Transformation Diagrams, because the transformation times are representative of isothermal hold treatment (following a instantaneous quench).

In practical situations we follow heat treatments (T-t

procedures/cycles) in which (typically) there are steps involving cooling of the sample. The

cooling rate may or may not be constant. The rate of cooling may be slow (as in a furnace which has been switch off) or rapid (like quenching

in water).

Hence, in terms of practical utility TTT

curves have a limitation and we need to draw separate diagrams called Continuous Cooling Transformation diagrams (CCT), wherein transformation times (also: products & microstructure) are noted

using constant rate cooling treatments. A diagram drawn for a given cooling rate (dT/dt) is typically used for a range of cooling rates (thus avoiding the need for a separate diagram for every cooling

rate).

However, often TTT

diagrams are also used for constant cooling rate experiments

keeping in view the assumptions & approximations involved.

The CCT

diagram for eutectoid steel is considered next. Blue curve is the CCT

curve and TTT

curve is overlaid for comparison.

Important difference between the CCT

& TTT

transformations is that in the CCT

case Bainite

cannot form.

Eutectoid steel (0.8%C)

Martensite100

200

300

400

600

500

800

723

100

200

300

400

600

500

800

723

0.1 1 10 102 103 104 105

Eutectoid temperature

Ms

Mf

t (s) →

T →

Original TTT lines

Cooling curvesConstant rate

Pearlite

1T 2T

Continuous Cooling Transformation (CCT) Curves

Important points to be noted:

As before the x-axis is log scale.

Bainite

cannot form by continuous cooling.

Constant rate cooling curves look like curves due to log scale in x-

axis. The higher cooling rate curve has a higher (negative) slope.

As time is one of the axes, no treatment curve can be drawn where time decreases or remains constant.

dT Tdt

Constant Cooling rate

1T 2T>

Start

Finish

The CCT

curves are to the right of the corresponding TTT

curves. Why?Funda

Check

As the cooled sample has spent more time at higher temperature, before it intersects the TTT

curve (virtually superimposed)

and the transformation time is longer at higher T (above the nose)

CCT

curves should be to the right of TTT

curves.

Eutectoid steel (0.8%C)

Martensite100

200

300

400

600

500

800

723

100

200

300

400

600

500

800

723

0.1 1 10 102 103 104 105

Eutectoid temperature

Ms

Mf

t (s) →T

→

Original TTT lines

Cooling curvesConstant rate

Pearlite

1T 2T

Common heat treatments involving cooling

Common cooling heat treatment labels (with increasing cooling rate) are:

Full anneal < Normalizing < Oil quench < Water quench

The microstructures produced for these treatments are:

Full Anneal (furnace cooling) Coarse Pearlite

Normalizing (Air cooling) Fine Pearlite

Oil Quench Matensite

(M) + Pearlite

(P)

Water Quench Matensite

To produce full martensite

we have to avoid the ‘nose’

of the TTT

diagram (i.e. the quenching rate should be fast enough).

Within water or oil quench further parameters determine the actual quench rate (e.g. was the sample shaken?).

Different cooling treatments

M = Martensite

P = PearliteM = Martensite

P = Pearlite

Eutectoid steel (0.8%C)

100

200

300

400

600

500

800

100

200

300

400

600

500

800

723

0.1 1 10 102 103 104 105t (s) →

T →

Water quench

Oil quench

Normalizing

Full anneal

Coarse P

P M M + Fine P

It is important to note that for a single composition, different

cooling treatments give different microstructures these give rise to a varied set of properties.

After even water quench to produce Martensite, further heat treatment (tempering) can be given to optimize properties like strength and ductility.

What are the typical cooling rates of various processes?

Process Cooling rate (K/s)Furnace cooling (Annealing) 105

– 103

Air Cooling 1 –

10

Oil Quenching* ~100

Water Quenching* ~500

Splat Quenching 105

Melt-Spinning 106

– 108

Evaporation, sputtering 109

(expected)

* Depends on conditions discussed later

Pearlite

Nucleation and growth Heterogeneous nucleation at grain boundaries Interlamellar

spacing is a function of the temperature of transformation Lower temperature → finer spacing → higher hardness

→

+ Fe3

C

Lamellae of Pearlite

in ~0.8% carbon steel

(100) || (111)C

Branching mechanismOrientation Relation: Kurdyumov-Sachs (010) || (110)C

(001) || (112)C

1

Let us consider the heterogeneous nucleation of one of the phases of the pearlitic

microconstituent (say Fe3

C), at a grain boundary of Austenite (). Further let this precipitate be bound by a coherent interface on one side and a incoherent interface on the other side. The incoherent interface will be glissile

(mobile) and will grow into the corresponding

grain (2

).

The orientation relation (OR) between

and Fe3

C is refered

to as the Kurdyumov-

Sachs OR (as in fig. below).

2,3 The region surrounding this Fe3

C precipitate will be depleted in Carbon and the conditions will be right for the nucleation of

adjacent to it.

4

The process is repeated to give rise to a pearlitic

colony.

Branching of an advancing plate may also be observed.

Mechanism of Pearlitic

transformation: arising of the lamellar microstructure

321 4

Bainite

Bainite

formed at high temperature (~ 350C) has a feathery appearance and is called ‘Feathery Bainite’.

Bainite

formed at lower temperature (~ 275C) has a needle-like appearance and is called ‘acicular Bainite’.

The process of formation of bainite

involves nucleation and growth

Acicular, accompanied by surface distortions

** Lower temperature → carbide could be ε

carbide (hexagonal structure, 8.4% C)

Bainite

plates have irrational habit planes

Ferrite in Bainite

plates possess different orientation relationship relative to the parent Austenite than does the Ferrite in Pearlite

→

+ Fe3

C**

Micrograph courtesy: Prof. Sandeep

Sangal

0.8% C steel, the sample was quenched in a salt bath having 400°C temperature

and then it was held for 2 hours.

More images of Bainite

Micrograph courtesy: Prof. Sandeep

Sangal, Swati

Sharma

AFM

image

Micrograph courtesy: Prof. Sandeep

Sangal, Swati

Sharma

Shape of the Martensite formed → Lenticular

(or thin parallel plates)

Associated with shape change (shear)

But: Invariant plane strain (observed experimentally)

→ Interface plane between Martensite and Parent remains undistorted and unrotated

This condition requires:

1)

Bain distortion

→ Expansion or contraction of the lattice along certain crystallographic directions leading to homogenous pure dilation

2)

Secondary Shear Distortion

→ Slip or twinning

3) Rigid Body rotation

Characteristic of Martensitic

transformations

Surface deformations caused by the Martensitic

plate

MartensiteC

BCTC

FCC Quench

% 8.0)( '

% 8.0)(

Martensitic

transformation can be understood by first considering an alternate unit cell for the Austenite phase as shown in the figure below.

If there is no carbon in the Austenite (as in the schematic below), then the Martensitic

transformation can be understood as a ~20%

contraction along the c-axis and a ~12%

expansion of the a-axis → accompanied by no volume change and the resultant structure has

a BCC lattice (the usual BCC-Fe) → c/a ratio of 1.0.

Change in Crystal Structure

~20% contraction of c-axis~12% expansion of a-axis

FCC → BCC

In Pure Fe after the Matensitic

transformationc = a

FCC Austenite alternate choice of Cell

Martensite

In the presence of Carbon in the octahedral voids of CCP

(FCC) -Fe (as in the schematic below) →

the contraction along the c-axis is impeded by the carbon atoms. (Note that only a fraction of the octahedral voids are filled with carbon as the percentage of C in Fe is small).

However the a1

and a2

axis can expand freely. This leads to a product with c/a ratio (c’/a’) >1 → 1-1.1.

In this case there is an overall increase in volume of ~4.3%

(depends on the carbon content)

→ the Bain distortion*.

C along the c-axis obstructs the contraction

Tetragonal MartensiteAustenite to Martensite → ~4.3 % volume increase

* Homogenous dilation of the lattice (expansion/contraction along crystallographic axis) leading to the formation of a new lattice is called Bain distortion. This involves minimum atomic movements.

Martensite in 0.6%C steel

But shear will distort the lattice!

Slip Twinning

Average shape remains undistorted

The martensitic

transformation occurs without composition change

The transformation occurs by shear without need for diffusion

The atomic movements required are only a fraction of the interatomic spacing

The shear changes the shape of the transforming region → results in considerable amount of shear energy → plate-like shape of Martensite

The amount of martensite

formed is a function of the temperature to which the sample is quenched and not of time

Hardness of martensite

is a function of the carbon content

→ but high hardness steel is very brittle as martensite

is brittle

Steel is reheated to increase its ductility → this process is called TEMPERING

Summary of characteristics of Martensitic

transformation

% Carbon →

Har

dnes

s (R

c) →

20

40

60

0.2 0.4 0.6

Harness of Martensite as a function of Carbon content

Properties of 0.8% C steel

Constituent Hardness (Rc

) Tensile strength (MN / m2)Coarse pearlite 16 710Fine pearlite 30 990Bainite 45 1470Martensite 65 -Martensite tempered at 250 oC 55 1990

ROLE OF ALLOYING ELEMENTSROLE OF ALLOYING ELEMENTS

• + Simplicity of heat treatment and lower cost•

Low hardenability•

Loss of hardness on tempering•

Low corrosion and oxidation resistance•

Low strength at high temperatures

Plain Carbon Steel

Element Added

Segregation / phase separationSolid solution

Compound (new crystal structure)

• ↑

hardenability• Provide a fine distribution of alloy carbides during tempering• ↑

resistance to softening on tempering• ↑

corrosion and oxidation resistance• ↑

strength at high temperatures• Strengthen steels that cannot be quenched• Make easier to obtain the properties throughout a larger section• ↑

Elastic limit (no increase in toughness)

Alloying elements

• Alter temperature at which the transformation occurs• Alter solubility of C in

or

Iron• Alter the rate of various reactions

Interstitial

Substitutional

P ►Dissolves in ferrite, larger quantities form iron phosphide

→ brittle (cold-shortness) S

►Forms iron sulphide, locates at grain boundaries of ferrite and pearlite

poor ductility

at forging temperatures (hot-shortness)

Si ► (0.2-0.4%) increases elastic modulus and UTS Cu

►0.8 % soluble in ferrite, can be used for precipitation hardening Pb

►Insoluble in steel Cr

►Corrosion resistance, Ferrite stabilizer, ↑

hardness/strength, > 11% forms passive films, carbide former

Ni

► Austenite stabilizer, ↑

strength ductility and toughness, Mo► Dissolves in

& , forms carbide, ↑

high temperature strength, ↓

temper embrittlement, ↑

strength, hardenability

Sample elements and their role

Alloying Element (%)

→

Brin

ellH

ardn

ess→

v

0 2 4 6 8 1060

100

140

180

Cr

Cr + 0.1%C

Mn

Mn

+0.1% C

Addition of Carbon

Additio

n of C

arbon

Alloying elements increase hardenability

but the major contribution to hardness comes from Carbon

Mn, Ni are Austenite stabilizers

Cr is Ferrite stabilizer Shrinking

phase field with ↑

Cr

C (%)

→

Tem

pera

ture

→

0 0.4 0.8 1.61.2

5% Cr

12% Cr15% Cr

0% Cr

C (%)

→

Tem

pera

ture

→

0 0.4 0.8 1.61.2

0.35% Mn

6.5% Mn

Outline of the

phase field

Austenite Pearlite

Bainite

Martensite100

200

300

400

600

500

800

Ms

Mf

t →

T →

TTT diagram for Ni-Cr-Mo low alloy steel

~1 min

TTT

diagram of low alloy steel (0.42% C, 0.78% Mn, 1.79% Ni, 0.80% Cr, 0.33% Mo)

U.S.S

Carilloy

Steels, United States Steel Corporation, Pittsburgh, 1948)

0

100

200

300

400

500

600

700

800

900

1000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35Engineering Strain (e)

Eng

inee

ring

Str

ess (

s) [M

Pa]

0.4% C - Slow cooled

0.8% C - Slow cooled

0.8% C - quenched

Effect of carbon content and heat treatment on properties of steel

150

200

250

300

350

400

450

0.5 0.6 0.7 0.8 0.9 1 1.1C %

Vik

ers H

ardn

ess

Slowly cooled- 0.6%CQuenched- 0.8% CSlowly cooled- 0.8% CSlowly cooled- 1.0% C

Hardness

Tensile Test

Precipitation

The presence of dislocation weakens the crystal → easy plastic deformation.

Putting hindrance to dislocation motion increases the strength of the crystal.

Fine precipitates dispersed in the matrix provide such an impediment.

Strength of Al → 100 MPa

Strength of Duralumin with proper heat treatment (Al + 4% Cu + other alloying elements) → 500 MPa

Precipitation Hardening

Al

% Cu →

T (ºC

)→

200

400

600

15 30 45 60

L

Sloping Solvus

line

high T → high solubility

low T → low solubility of Cu in Al

Al-Cu phase diagram: the sloping solvus

line and the design of heat treatments

4 % Cu

+

→

+

Slow equilibrium cooling gives rise to coarse

precipitates which is not good in impeding dislocation motion.*

RTCu

TetragonalCuAl

RTCu

FCC

CCu

FCCcoolslow

o

% 52)(

% 5.0)(

550 % 4

)( 2

*Also refer section on Double Ended

Frank-Read Source in the chapter on plasticity: max

= Gb/L

C

A

B

Heat (to 550oC) → solid solution

Quench (to RT) →

Age (reheat to 200oC)

→ fine precipitates

4 % Cu

+

CA

B

To obtain a fine distribution of precipitates the cycle A

→ B

→ C is used

Note:

Treatments

A,

B,

C are for the same

composition

supersaturated solution

Increased vacancy concentration

Log(t) →

Har

dnes

s → 180oC

100oC

20oC

Higher temperature

less time of aging to obtain peak hardness

Lower temperature

increased peak hardness

optimization between time and hardness required

Schematic curves →

Real experimental curves are in later slides

Note: Schematic curves shown-

real curves considered later

Log(t) →

Har

dnes

s →

180oC

OveragedUnderaged

Peak-aged

Region of solid solution strengthening

(no precipitation hardening)

Region of precipitation hardening

(but little/some solid solution strengthening)

Dispersion of fine precipitates

(closely spaced)

Coarsening of precipitates

with increased

interparticle

spacing

Log(t) →

Har

dnes

s →

180oC Peak-aged

Particle radius (r)

→

CR

SS In

crea

se→

21

r r1

Particle shearing

Particle By-pass

)(tfr

Cohe

rent

(GP

zone

s) In-coherent (precipitates)

Section of GP zone parallel to (200) plane

Log(t) →

Har

dnes

s →

Increasing size of precipitates with increasing interparticle

(inter-precipitate) spacing

A complex set of events are happening in parallel/sequentially during the aging process→ These are shown schematically in the figure below

Interface goes from coherent to semi-coherent to incoherent

Precipitate goes from GP zone → ’’

→ ’

→

Cu rich zones fully coherent with the matrix → low interfacial energy

(Equilibrium

phase has a complex tetragonal crystal structure which has incoherent interfaces)

Zones minimize their strain energy by choosing disc-shape

to the elastically soft <100> directions in the FCC matrix

The driving force (Gv

Gs

) is less but the barrier to nucleation is much less (G*)

2 atomic layers thick, 10nm in diameter with a spacing of ~10nm

The zones seem to be homogenously nucleated (excess vacancies seem to play an important role in their nucleation)

GP Zones

Atomic image of Cu layers in Al matrix

Bright field TEM micrograph of an Al-4% Cu alloy (solutionized and aged) GP zones.

5nm

5nm

Selected area diffraction (SAD) pattern, showing streaks arising from the zones.

Due to large surface to volume ratio the fine precipitates have a tendency to coarsen → small precipitates dissolve and large precipitates grow

Coarsening ↓

in number of precipitate ↑

in interparticle

(inter-precipitate) spacing

reduced hindrance to dislocation motion (max

= Gb/L)

Phase Transformations in Metals and Alloys, D.A. Porter and K.E. Easterling, Chapman & Hall, London, 1992.

''(001) || (001)

''[100] || [100]

'(001) || (001)

'[100] || [100]

10 ,100nmthick nm diameterDistorted FCC

TetragonalUC

composition Al4

Cu2

= Al2

Cu

Becomes incoherent as ppt. grows

BCT, I4/mcm (140), a = 6.06Å, c = 4.87Å, tI12

''

UC

composition Al6

Cu2

= Al3

Cu

UC

composition Al8

Cu4

= Al2

Cu

'

Phase Transformations in Metals and Alloys, D.A. Porter and K.E. Easterling,Chapman

& Hall, London, 1992.

Schematic diagram showing the lowering of the Gibbs free energy of the system on sequential transformation:

GP zones → ’’

→ ’

→

Successive lowering if free energy of the system

The activation barrier for precipitation of equilibrium () phase is large

If the transformation is broken down into a series of steps with smaller activation

barrier the processes can take place even with low thermal activation

But, the free energy benefit in each step is small compared to the overall single step process

Single step (‘equilibrium’) process

Schematic plot

Precipitation processes in solids, K.C. Russell, H.I. Aaronson (Eds.), The Metallurgical Society of AMIE, 1978, p.87

In this diagram additionally information has been superposed onto the phase diagram (which strictly do not belong there-

hence this diagram should be interpreted with care)

The diagram shows that on aging at various temperatures in the

+

region of the phase diagram various precipitates are obtained first

At higher temperatures the stable

phase is produced directly

At slightly lower temperatures ’

is produced first

At even lower temperatures ’’

is produced first

The normal artificial aging is usually done in this temperature range to give rise to GP zones first

Base Alloy Precipitation Sequence

Al Al-Ag GPZ (Spheres) ' (plates) (Ag2Al)

Al-Cu GPZ (Discs) '' (Discs) ' (Plates) (CuAl2)

Al-Cu-Mg GPZ (Rods) S' (Laths) S (Laths, CuMgAl2)

Al-Zn-Mg GPZ (Spheres) ' (Plates) (Plates/Rods, Zn2Mg)

Cu Cu-Be GPZ (Discs) ' (CuBe)

Cu-Co GPZ (Spheres) (Plates, Co)

Fe Fe-C -carbide (Discs) Fe3C (Plates)

Fe-N '' (Discs) Fe4N (Plates)

Ni Ni-Cr-Ti-Al ' (Cubes/Spheres)

Precipitation Sequence in some precipitation hardening systems(Morphology and compound stoichiometry are given in brackets)

[1] J.M. Silcock, T.J. Heal and H.K. Hardy, J. Inst. Metal. 82 (1953-54) 239.

Details in ‘practical’

aging curves

Points to be noted:

In low T aging (130C) The aging curves have more detail than the single peak as discussed schematically before.

In low T aging (130C) the full sequence of precipitation is observed (GPZ

'' ').

At high T aging (190C) '' directly forms (i.e. the full precipitation sequence is not observed).

Peak hardness increases with increasing Cu%.

For the same Cu%, the peak hardness is lower for the 190C aging treatment as compared to the 130C aging treatment.

Peak hardness is achieved when the microstructure consists of a ' or combination of (' + '').

’’

at start

There will be a range of particle sizes due to time of nucleation and rate of growth

As the curvature increases the solute concentration (XB

) in the matrix adjacent to the particle increases

Concentration gradients are setup in the matrix → solute diffuses from near the small particles towards the large particles

small particles shrink and large particles grow

with increasing time * Total number of particles decrease * Mean radius (ravg

) increases with time

Particle/precipitate Coarsening

Gibbs-Thomson effect

Gibbs-Thomson effect

Rate controlling factor

Interface diffusion rate

Volume diffusion rate

3 30avgr r kt

ek D X

r0

→ ravg

at t = 0 D → Diffusivity Xe

→ XB

(r = )

D is a exponential function of temperature

coarsening increases rapidly with T

2avg

avg

dr kdt r

small ppts

coarsen more rapidly

0r

avgr

Increasing T

t

3Linear versus relation may break down due to diffusion short-circuits

or if the process is interface controlledavgr t

Rateof coarsening depends on (diffusion controlled)eD X

Precipitation hardening systems employed for high-temperature applications must avoid coarsening by having low: , Xe

or D

Nimonic

alloys (Ni-Cr + Al + Ti)

Strength obtained by fine dispersion of ’

[ordered FCC Ni3

(TiAl)] precipitate in FCC Ni rich matrix

Matrix (Ni SS)/ ’

matrix is fully coherent [low interfacial energy

= 30 mJ/m2]

Misfit = f(composition) → varies between 0% and 0.2%

Creep rupture life increases when the misfit is 0% rather than 0.2%

Low

Nimonic 90: Ni 54%, Cr 18-21%, Co 15-21%, Ti 2-3%, Al 1-2%

ThO2

dispersion in W (or Ni) (Fine oxide dispersion in a metal matrix)

Oxides are insoluble in metals

Stability of these microstructures at high temperatures due to low value of Xe

The term DXe

has a low value

Low Xe

ThO2

dispersion in W (or Ni) (Fine oxide dispersion in a metal matrix)

Cementite

dispersions in tempered steel coarsen due to high D of interstitial C

If a substitutional alloying element is added which segregates to the carbide → rate of coarsening ↓

due to low D for the substitutional element

Low D