PHASE TRANSFORMATIONSPHASE TRANSFORMATIONS

Nucleation

Growth

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)

Diffusional

PHASE TRANSFORMATIONS

Martensitic

1nd ordernucleation & growth

PHASE TRANSFORMATIONS

2nd orderEntire volume transforms

Based onMass

transport

Based onorder

Energies involved

Bulk Gibbs free energy ↓

Interfacial energy ↑

Strain energy ↑ Solid-solid transformation

Volume of transforming material

New interface created

The concepts are illustrated using solidification of a metal

Nucleationof

phase

Trasformation

→ +

Growthtill is

exhausted

=

1nd ordernucleation & growth

Liquid → Solid phase transformation

Solid (GS)

Liquid (GL)

Tm T →

G →

T

G

Liquid stableSolid stable

T - Undercooling

↑ t

“For sufficientUndercooling”

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

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

Homogenous nucleation

)((Surface). )(Volume).( ΔG G

).(4 ).(3

4 ΔG 23 rGr v

r2r3

1

Neglected in L → Stransformations

)( TfGv

energystrain in increase energy surfacein increase energy freebulk in Reduction

nucleationon changeenergy Free

).(4 ).(3

4 ΔG 23 rGr v

By setting dG/dr = 0 the critical values (corresponding to the maximum) are obtained (denoted by superscript *)

Reduction in free energy is obtained only after r0 is obtained

0dr

Gd 0*1 r

vGr

2*

2

Trivial

vGr

2*

2

3*

3

16

vGG

As Gv is ve, r*is +ve

r →

G →

0dr

Gd

0G

*r0r

0GvG

r3

0Supercritical nucleiEmbryos

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

r →

G →

Increasin

g T

Decreasing r*

Dec

reas

ing G

*

Tm 23

2 2

16

3 mT

GT H

Turnbull approximation

No. of critical sized particlesRate of nucleation x Frequency with which they

become supercritical=

dt

dNI

kT

G

t eNN

*

*

kT

Hd

es ' *

Critical sized nucleus

s* atoms of the liquid facing the nucleus

Critical sized nucleus

Jump taking particle to supercriticality → nucleated (enthalpy of activation = Hd)

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

kT

HG

t

d

esNI

*

*

I →

T (

K)

→In

crea

sing

T

Tm

0

T = Tm → G* = → I = 0

G* ↑ I ↓

T ↑ I ↑

T = 0 → I = 0

Heterogeneous nucleation

Consider the nucleation of from on a planar surface of inclusion

)( )()(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

0

0.25

0.5

0.75

1

0 30 60 90 120 150 180

vhetero G

r

2*

32

3* 32

3

4CosCos

GG

vhetero

0

dr

Gd

3homo

* 324

1CosCosGG *

hetero

(degrees) →

G* he

tero / G

* hom

o → 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

kT

G

eII

*homo

0homohomo

kT

G

eII

*hetero

0heterohetero

= f(number of nucleation sites)

~ 1042

= f(number of nucleation sites)

~ 1026

BUTthe exponential term dominates

Ihetero > Ihomo

Choice of heterogeneous nucleating agent

Small value of

Choosing a nucleating agent with a low value of (low energy interface)

(Actually the value of ( ) will determine the effectiveness of the heterogeneous nucleating agent → high or low )

low value of → Crystal structure of and are similar and lattice parameters are as close as

possible

Seeding rain-bearing clouds → AgI or NaCl → 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

Cos

Cos

Nucleationof

phase

Trasformation

→ +

Growthtill is

exhausted

=

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 activationbarrier for the reverse jump is higher

Growth

rate)Growth rate,on f(Nucleatiratetion Transforma

) ,( UIfdt

dXT

3

t UI π

β

43

e 1X

I, U, T →

T (

K)

→In

crea

sing

T

Tm

0

U

T

I

Maximum of growth rate usuallyat higher temperature than maximum of nucleation rate

t →

X

→

0

1.0

0.5

3

t UI π

β

43

e 1X

Time – Temperature – Transformation (TTT) diagrams A type of phase diagram

T (rate sec1) →

T (

K)

→ T

Tm

0t (sec) →

T (

K)

→

Tm

0

Time for transformation

Small driving force for nucleation

Growth sluggish

Replot

t (sec) →

T (

K)

→

99% = finish

Increasing % transformation

TTT diagram → phase transformation

1% = start

T →

G →

Turnbull’s approximation

Tm

Solid (GS)

Liquid (GL)T

G

mm

m

T

Th

T

TThG

sionheat of fuΔh 2

3*

3

16

Th

TG m

APPLICATIONS

Phase Transformations in Steel

Precipitation

Solidification and crystallization

Glass transition

Recovery recrystallization & grain growth

Phase Transformations in Steel

%C →

T →

Fe Fe3C6.74.30.80.16

2.06

PeritecticL + →

EutecticL → + Fe3C

Eutectoid → + Fe3C

L

L +

+ Fe3C

1493ºC

1147ºC

723ºC

Fe-Cementite diagram

0.025 %C

0.1 %C

+ Fe3C

Austenite

Austenite

Pearlite

Pearlite + Bainite

Bainite

Martensite100

200

300

400

600

500

800

723

0.1 1 10 102 103 104 105

Eutectoid temperature

Not an isothermal

transformation

Ms

Mf

Coarse

Fine

t (s) →

T →

Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation

Eutectoid steel (0.8%C)

AustenitePearlite

Pearlite + Bainite

Bainite

Martensite100

200

300

400

600

500

800

723

0.1 1 10 102 103 104 105

Eutectoid temperature

Ms

Mf

t (s) →

T →

Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation

Eutectoid steel (0.8%C)

+ Fe3C

Continuous Cooling Transformation (CCT) Curves Eutectoid steel (0.8%C)

Austenite

Martensite100

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

Eutectoid steel (0.8%C)

100

200

300

400

600

500

800

723

0.1 1 10 102 103 104 105

t (s) →

T →

Water quench O

il quench

Norm

alizing

Full anneal

Different cooling treatments

M = Martensite

P = Pearlite

Coarse P

P M M + Fine P

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

→ + Fe3C

[1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962

[1] [1]

Bainite

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

→ + Fe3C**

Bainite formed at 348oC Bainite formed at 278oC

[1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962

[1] [1]

Martensite

FCCAustenite

FCCAustenite

Alternate choice of Cell

Tetragonal Martensite

Austenite to Martensite → 4.3 % volume increase

Possible positions of Carbon atoms

Only a fraction ofthe sites occupied

20% contraction of c-axis12% expansion of a-axis

Refer Fig.9.11 in textbook

In Pure Fe after the Matensitic transformation

c = a

C along the c-axis obstructs the contraction

C

BCT

C

FCC Quench

% 8.0

)( '

% 8.0

)(

Martensite

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 towhich 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

% Carbon →

Har

dnes

s (

Rc)

→

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 16 710

Fine pearlite 30 990

Bainite 45 1470

Martensite 65 -

Martensite tempered at 250 oC 55 1990

Tempering

Heat below Eutectoid temperature → wait→ slow cooling

The microstructural changes which take place during temperingare very complex

Time temperature cycle chosen to optimize strength and toughness

Tool steel: As quenched (Rc 65) → Tempered (Rc 45-55)

Cementite

ORF

Ferrite

BCC

Martensite

BCT Temper )( Ce)( )( ' 3

AustenitePearlite

Pearlite + Bainite

Bainite

Martensite100

200

300

400

600

500

800

723

0.1 1 10 102 103 104 105

Eutectoid temperature

Ms

Mf

t (s) →

T →

+ Fe3C

MARTEMPERING

AUSTEMPERING

To avoid residual stresses generated during quenching Austenized steel is quenched above Ms for homogenization of temperature

across the sample The steel is then quenched and the entire sample transforms simultaneously Tempering follows

To avoid residual stresses generated during quenching Austenized steel is quenched above Ms Held long enough for transformation to Bainite

Martempering

Austempering

ALLOY STEELS

Various elements like Cr, Mn, Ni, W, Mo etc are added to plain carbonsteels to create alloy steels

The alloys elements move the nose of the TTT diagram to the right→ this implies that a slower cooling rate can be employed to obtain

martensite → increased HARDENABILITY

The ‘C’ curves for pearlite and bainite transformations overlap in the case of plain carbon steels → in alloy steels pearlite and bainite transformations can be represented by separate ‘C’ curves

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

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

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 (Al + 4% Cu + other alloying elements) → 500 MPa

Al% Cu →

T (

ºC)

→

200

400

600

15 30 45 60

L

Sloping Solvus line high T → high solubility low T → low solubilityof Cu in Al

Al rich end of the Al-Cu phase diagram

4 % Cu

+

→ + Slow equilibrium cooling gives rise tocoarse precipitates which is not goodin impeding dislocation motion.*

RT

Cu

TetragonalCuAl

RT

Cu

FCC

C

Cu

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 samecomposition

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

Log(t) →

Har

dnes

s →

180oC

OveragedUnderaged

Peak-aged

Region of solid solution strengthening

(no precipitation hardening)

Region of precipitation hardening

(but little solid solution strengthening)

Dispersion of fine precipitates(closely spaced)

Coarsening of precipitateswith increased

interparticle spacing

Log(t) →

Har

dnes

s →

180oC Peak-aged

Particle radius (r) →

CR

SS

Inc

reas

e →

2

1

r r

1

Particle shearing

Particle By-pass

)(tfr

Coh

eren

t (G

P zo

nes) In-coherent (precipitates)

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

Coarsening ↓ in number of particles ↑ in interparticle spacing

reduced hindrance to dislocation motion (max = Gb/L)

Solidification and Crystallization

↑ Hfusion

↓ Hd Log [Viscosity ()]

Crystallization favoured by

High → (10-15) kJ / mole

Low → (1-10) Poise

Metals

Enthalpy of activation for diffusion across the interface

Difficult to amorphize metals

Thermodynamic

Kinetic

Very fast cooling rates ~106 K/s are used for the amorphization of alloys → splat cooling, melt-spinning.

2* 1

fusionHG

Fine grain size bestows superior mechanical properties on the material

High nucleation rate and slow growth rate fine grain size

↑ Cooling rate lesser time at temperatures near Tm , where the peakof growth rate (U) lies ↑ nucleation rate

Cooling rates ~ (105 – 106) K/s are usually employed

Grain refinement can also be achieved by using external nucleating agents

Single crystals can be grown by pulling a seed crystal out of the melt

I, U →

T (

K)

→

Tm

0

U

I

↑ Hfusion

↓ Hd Log [Viscosity ()]

Crystallization favoured by

low

High → (1000) Poise

Silicates

Enthalpy of activation for diffusion across the interface

Easily amorphized

Thermodynamic

Kinetic

Certain oxides can be added to silica to promote crystallization

In contrast to metals silicates, borates and phosphates tend to form glasses

Due to high cation-cation repulsion these materials have open structures

In silicates the difference in total bond energy between periodic and aperiodic array is small (bond energy is primarily determined by the first neighbours of the central cation within the unit

A composite material of glass and ceramic (crystals) can have betterthermal and mechanical properties

But glass itself is easier to form (shape into desired geometry)

Glass-ceramic (pyroceram)

Shaping of material in glassy state

Heterogenous nucleating agents (e.g. TiO2) added (dissolved) to molten glass

TiO2 is precipitated as fine particles

Held at temperature of maximum nucleation rate (I)

Heated to temperature of maximum growth rate

t →T

→

Nucleation

Growth

Tmaximum I

Tmaximum U

Glass Partially crystallized Glass

Even at the end of the heat treatment the material is not fully crystalline Fine crystals are embedded in a glassy matrix Crystal size ~ 0.1 m (typical grain size in a metal ~ 10 m) Ultrafine grain size

good mechanical properties and thermal shock resistance Cookware made of pyroceram can be heated directly on flame

Glass Transition

“All materials would amorphize on cooling unless crystallization intervenes”

T →

Vol

ume

→

Or other extensivethermodynamic property → S, H, E

Liquid

Glass

Crystal

Tg Tm

Glass transition temperature

T →

Vol

ume

→Change in slope

Tf

Fictive temperature (temperature at which glass is metastableif quenched instantaneously to this temperature)

→ can be taken as Tg

T →

Vol

ume

→Effect of rate of cooling

1T

2T

21 TT

Slower cooling

Slower cooling Higher density

Lower Tg

Lower volume

As more time for atoms to arrange in closer packedconfiguration

T →

Log

(vi

scos

ity)

→

Glass

Crystal

Tg Tm

Supercooledliquid Liquid

On crystallization the viscosity abruptly changes from ~100 → ~1020 Pa s

A solid can be defined a material with a viscosity > 1012 Poise

Tg

Heat glass

Cool liquid

Tx

Often metallic glasses crystallize before Tg

Please read up paragraph on glassy polymers → p228 in text book

Recovery, Recrystallization & Grain Growth

Cold work

↑ dislocation density

↑ point defect density

Plastic deformation in the temperature range (0.3 – 0.5) Tm → COLD WORK

Point defects and dislocations have strain energy associated with them

(1 -10) % of the energy expended in plastic deformation is stored in the form of strain energy

)1010(~

)1010(~

1412

ndislocatio

96

ndislocatio

materialStrongermaterialAnnealed workCold

Cold work

↑ dislocation density

↑ point defect density

AnnealMaterial tends to lose the stored strain energy

Increase in strength of the material Softening of the material

Cold work Anneal

Recrystallization

RecoveryLow temperature

High temperature

Cold work Anneal

Recrystallization

Recovery

Grain growth

Cold work↑ Hardness

↑ Strength

Changes occur to almost all physical and mechanical properties

X-Ray diffration► Laue patterns of single crystals show pronounced asterism

→ due to lattice curvatures ► Debye-Scherrer photographs show line broadning

→ Residual stresses + deformations

↑ Electrical resistance

↓ Ductility

Recovery

Recovery takes place at low temperatures of annealing

“Apparently no change in microstructure”

Excess point defects created during Cold work are absorbed:► at surface or grain boundaries► by dislocation climb

Random dislocations of opposite sign come together and annihilate each other

Dislocations of same sign arrange into low energy configurations:► Edge → Tilt boundaries► Screw → Twist boundaries

POLYGONIZATION

Overall reduction in dislocation density is small

POLYGONIZATION

Bent crystal

Low angle grain boundaries

Polygonization

Recrystallization

Trecrystallization (0.3 – 0.5) Tm

“Nucleation” and growth of new, strain free crystals

Nucleation of new grains in the usual sense may not be present and grain boundary migrates into a region of higher dislocation density

G (recrystallization) = G (deformed material) – G (undeformed material)

TRecrystallization is the temperature at which 50 % of the material recrystallizes in 1 hour

Region of lower dislocation densityRegion of higher

dislocation density

Direction of grainboundary migration

Further points about recrystallization

Deformation ↑ recrystallization temperature (Trecrystallization) ↓

Initial grain size ↓ recrystallization temperature ↓

High cold work + low initial grain size finer recrystallized grains

↑ cold work temperature lower strain energy stored ↑ recrystallization temperature

Rate of recrystallization = exponential function of temperature

Trecrystallization = strong function of the purity of the material Trecrystallization (very pure materials) ~ 0.3 Tm

Trecrystallization (impure) ~ (0.5 – 0.6) Tm

► Trecrystallization (99.999% pure Al) ~ 75oC Trecrystallization (commercial purity) ~ 275oC

The impurity atoms segregate to the grain boundary and retard theirmotion → Solute drag (can be used to retain strength of materials athigh temperatures)

The impurity atoms seggregate to the grain boundary and retard theirmotion → Solute drag (can be used to retain strength of materials at high temperatures)

Second phase particles also pin down the grain boundary during its migration

Hot Work and Cold Work

Hot Work Plastic deformation above TRecrystallization

Cold Work Plastic deformation below TRecrystallization

Col

d W

ork

Hot

Wor

k

Recrystallization temperature (~ 0.4 Tm)

Grain growth

Globally► Driven by reduction in grain boundary energy

Locally► Driven by bond maximization (coordination number maximization)

Bonded to4 atoms

Bonded to 3 atoms

Direction of grainboundary migration

Boundary moves towards itscentre of curvature

JUMP

Cold work Recovery Recrystallization Grain growth

Tensile strength

Ductility

Electical conductivityInternal stress