Phase Transformation

Phase Transformation Chapter 9

Shiva-Parvati, Chola Bronze

Ball State University

Q: How was the statue made?

A: Invest casting

Liquid-to-solid transformation

An example of phase transformation

Czochralski crystal pulling technique for

single crystal Si

Quenching of steel componentsa solid->solid phase transformation

Liquid

solid

ifica

tion

evaporation

sublimation

Solid

gas

mel

ting

condensation

Solid state phase

transformationSolid 21

Thermodynamic driving force for a phase transformation

Decrease in Gibbs free energy

Liquid-> solid

gs - gl = g = -ve

ggL

gS

gS < gL

gL < gSLiquid is

stable

TmT

Gibbs free energy as a function of temperature, Problem 2.3

gL

gS

g

Solid is stable

Tfreesing

sT

g

p

T

c

T

g p

p

2

2

Fig. 9.1

How does solidification begins?

Usually at the walls of the container

Why?

To be discussed later.

Heterogeneous nucleation.

Spherical ball of solid of radius R in the middle of the liquid at a temperature below Tm

Homogeneous nucleation

gL = free energy of liquid per unit volumegS = free energy of solid

per unit volume

r

g = gS - gL

Change in free energy of the system due to formation of the solid ball of radius r :

r

)(3

4 3Ls ggrf

+ve: barrier to nucleation 24 r

)(3

4 3Ls ggr

rr*

f

24 r

grf 3

3

4

24 r

gr 3

3

4

rr*

f

24 rSolid balls of radius r < r* cannot grow as it will lead to increase in the free energy of the system !!!

Solid balls of radii r > r* will grow

r* is known as the CRITICAL RADIUS OF HOMOGENEOUS NUCLEATION

grf 3

3

4 24 r

gr 3

3

4

rr*

f

24 r

0*

rrr

f

gr

2*

*f

2

3

)(3

16*

gf

Eqn. 9.5

Eqn. 9.4

T

g

Tm

gL

gS

T

g (T)

LS ggg )()()( TsTThTg

)()( mThTh )()( mTsTs

0)()()( mmmm TsTThTg

m

mm T

ThTs

)()(

)()()( mm TsTThTg

m

mm T

ThTTh

)()(

)( mm

m ThT

TT

mm

hT

TTg

)( Eqn.

9.7

grf 3

3

4 24 r

gr

2*

2

3

)(3

16*

gf

)(3

4)( 3 TgrTf 24 r

f

rm

m

hT

TTg

)(

m

m

hT

Tr

2*

22

23

)()(3

16*

m

m

hT

Tf

Eqn. 9.8

Eqn. 9.7

Fig. 9.3

r1*

f1*

f2*

r2*

T1T2 <

Critical particle

Fig. 9.4

Formation of critical nucleus by statistical flucctuation

Atoms surrounding the critical particle

Diffuse jump of a surrounding atom to the critical particle makes it a nucleation

The Nucleation Rate

Nt=total number of clusters of atoms per unit volumeN* = number of clusters of critical size per unit volume

By Maxwell-Boltzmann statistics

RT

fNN t

*exp*

RT

fNN t

*exp*

s*= no. of liquid phase atoms facing the critical sized particle

Hd = activation energy for diffusive jump from liquid to the solid phase = atomic vibration frequency

The rate of successful addition of an atom to a critical sized paticle

RT

Hsv dexp*' Eqn. 9.10

Eqn. 9.9

Rate of nucleation, I , (m3 s-

1)

'*NI

RT

HfsN d

t

*exp*

With decreasing T

1. Driving force increases

2. Atomic mobility decreases

= No. of nucleation events per m3 per sec

= number of critical clusters per unit volume (N*)x

rate of successful addition of an atom to the critical cluster (’)

RT

Hs

RT

fN d

t exp**

exp

Eqn. 9.11

T

I

Tm

Growth

Increase in the size of a product particle after it has nucleated

dt

drU

T

U

Overall Transformation Kinetics

),( IUfdT

dX

U

I

dX/dt

TI : Nucleation rate

U : Growth rate

dt

dr

Overall transformation rate (fraction transformed per second)

X=fraction of product phase

Fraction transformed as a function of time

ts tf

X

t

Slow due to very few nuclei

Slow due to final impingement

TTT Diagram for liquid-to-solid transformation

TStable liquid

UnderCooled liquid

crystal

Crystallization begins

L+

Crystallization ends

dX/dt

T

log t

X

log tts tf

0

1

Tm C-curves

L+

TStable liquid

UnderCooled liquid

log t

Tm

TTT Diagram for liquid-to-solid transformation

U

I

T

Coarse grained crystals

Fine grained crystals

glass

T

log t

ts metals

ts SiO2

RT

HfsNI d

t

*exp*

22

23

)()(3

16*

m

m

hT

Tf

Hd ∝ log (viscosity)

Metals: high hm, low viscosity

SiO2: low hm, high viscosity

Silica glassMetallic glass

Eqn. 9.11

Eqn. 9.8

Cooling rate 106 ºC s-1

Inert gas pressure

Molten alloy

Heater coil

Quartz tube

Rotating cooledmetal drum

Jet of molten metal

Ribbon ofglassy metal

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Melt Spinning for metallic glass ribbons

L+

T

log t

Tm

TTmTg

Log (viscosity)

12

18

crystal

Stable liquid

Undercooled liquid

glass

30

Fig. 9.17

Tm

Specific volume Stable liquid

Undercooled liquid

Fast cool

Slow cool

Tgs

Tgf

crystal

Fig. 9.18

T

log t

U

I

T

L+

TStable liquidUndercooled liquid

Tm

devitrification

time

T

Glass ceramics

nucleation

growth

glass

Glass ceramic

Liquid

glass crystal

Very fine crystals

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Corningware PyroceramTM heat resistant cookware

ROBAX® was heated until red-hot. Then cold water was

poured on the glass ceramic from above - with NO

breakage.

Czochralski crystal pulling technique for

single crystal Si

SSPL: Solid State Physics Laboratory, N. Delhi

J. Czochralski, (1885-1953)

Polish Metallurgist

You may collect slide handouts for chapters 6, 7 and 8 from Scoops Xerox Shop

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A

Steel

Hardness

Rockwell C

15 0.8

Wt% C Micro-structureCoarsepearlite

finepearlite

bainiteTempered martensite

martensite

0.8

0.8

0.8

0.8

30

45

55

65

Heattreatment

Annealing

normalizing

austempering

tempering

quenching

B

C

D

E

TABLE 9.2

HEAT TREATMENT

Heating a material to a high temperature,

holding it at that temperature for certain

length of time followed by cooling at a

specified rate is called heat treatment

A

N

AT

TQ

heati

ng

holding

time

T

Annealing Furnace cooling RC 15

Normalizing Air cooling RC 30

Quenching Water cooling RC 65

Tempering Heating after quench RC 55

Austempering Quench to an inter- RC 45mediate temp and hold

Eutectoid Reaction

CFeCo

3725

0.8 0.02

6.67

cool

Pearlite

Ammount of Fe3C in PearliteRed Tie Line below eutectoid temp

117.065.6

78.0

02.067.6

02.08.03

pearliteCFf

Phase diagrams do not have any information about time or rates of transformations.

We need TTT diagram for

austenite-> pearlite

transformation

Stable austenite

unstable austenite

TTT diagram for eutectoid steel

start

finish

Stable austenite

unstable austenite

start

finishAnnealing:coarse pearliteNormalizin

g:fine pearlite

U

I

TTTT diagram for eutectoid steel

Callister

Stable austenite

unstable austenite

start

finish

TTT diagram for eutectoid steel

A+M

M

Ms

Mf

Ms : Martensite start temperature

Mf : Martensite finish temperature

’: martensite (M)

' coolingrapid

QUENCHING

Hardness RC 65

Extremely rapid, no C-curves

BCT

Amount of martensite formed does not depend upon time, only on temperature.Atoms move only a fraction of atomic distance during the transformation:

1. Diffusionless (no long-range diffusion)2. Shear (one-to-one correspondence between and ’ atoms) 3. No composition change

Martensitic transformation

Problem 3.1

BCT unit cell of (austenite)

414.12 a

c

BCT unit cell of ’ (martensite)

08.100.1 a

c

0% C (BCC)

1.2 % C

Contract ~ 20%

Expand ~ 12%

Martensitic transformation (contd.)

Fig. 9.12

Hardness of martensite as a function of C content

Wt % Carbon →

20

40

60

0.2 0.4 0.6

Hard

ness

, R

C

Hardness of martensite depends mainly on C content and not on other alloying additions

Fig. 9.13

Martensitic transformation (contd.)

A

N

AT

TQ

heati

ng

T

Heating of quenched steel below the eutectoid temperature, holding for a specified time followed by ar cooling.

TEMPERING

CFetempering3

T<TE

?

Tempering (contd.)

+Fe3

CPEARLITE

A distribution of fine particles of Fe3C in matrix known as TEMPERED MARTENSITE.

Hardness more than fine pearlite, ductility more than martensite.

Hardness and ductility controlled by tempering temperature and time.

Higher T or t -> higher ductility, lower strength

Tempering Continued

Callister

AustemperingBainite

Short needles of Fe3C embedded in plates of ferrite

Problems in Quenching

Quench Cracks

High rate of cooling:

surface cooler than interior

Surface forms martensite before the interior

Austenite

martensite

Volume expansion

When interior transforms, the hard outer martensitic shell constrains this expansion leading to residual stresses

But how to shift the C-curve to higher times?

Solution to Quench cracks

Shift the C-curve to the right (higher times)

More time at the nose

Slower quenching (oil quench) can give martensite

By alloying

All alloying elements in steel (Cr, Mn, Mo, Ni, Ti, W, V) etc shift the C-curves to the right.

Exception: Co

Substitutional diffusion of alloying elements is slower than the interstitial diffusion of C

Plain C steel

Alloy steel

Alloying shifts the C-curves to the right.Separate C-curves for pearlite and bainite

Fig. 9.10

Hardenability

Ability or ease of hardening a steel by formation of martensite using as slow quenching as possible

Alloying elements in steels shift the C-curve to the right

Alloy steels have higher hardenability than plain C steels.

Hardnenability Hardness

Ability or ease of hardening a steel

Resistance to plastic deformation as measured by indentation

Only applicable to steels

Applicable to all materials

Alloying additions increase the hardenability of steels but not the hardness.

C increases both hardenability and hardness of steels.

High Speed steel

Alloy steels used for cutting tools operated at high speeds

Cutting at high speeds lead to excessive heating of cutting tools

This is equivalent to unintended tempering of the tools leading to loss of hardness and cutting edge

Alloying by W gives fine distribution of hard WC particles which counters this reduction in hardness: such steels are known as high speed steels.

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A shop inside Airbus A380

Alfred Wilm’s Laboratory 1906-1909

Steels harden by quenching

Why not harden Al alloys also by quenching?

time

Wilm’s Plan for hardening Al-4%Cu alloy

Sorry! No increase in hardness.

550ºC

T

Heat

Quench

Hold

Check hardness

Eureka ! Hardness

has Increased

!!

One of the greatest technological achievements of 20th century

Hardness increases as a function of time: AGE HARDENING

Property = f (microstructure)

Wilm checked the microstructure of his age-hardened alloys.

Result: NO CHANGE in the microstructure !!

As- quenched hardness

Hardness

time

Peak hardness

Overaging

Hardness initially increases: age hardening

Attains a peak value

Decreases subsequently: Overaging

+

: solid solution of Cu in FCC Al: intermetallic compound CuAl2

4

Tsolvus

supersaturated saturated +

FCC FCC Tetragonal

4 wt%Cu 0.5 wt%Cu 54 wt%Cu

Precipitation of in

Stable

unstable

Tsolvus

As-quenched

start finsh

+

Aging

TTT diagram of precipitation of in

A fine distribution of precipitates in matrix causes hardening

Completion of precipitation corresponds to peak hardness

-grains

As quenched

-grains +

Aged

Peak aged

Dense distribution of fine

overaged

Sparse distribution of coarse

Driving force for coarsening

/ interfacial energy

0.1 1 10 100

hardness

Aging time

(days)

180ºC

100ºC 20ºC

Aging temperature

Peak hardness is less at higher aging temperaturePeak hardness is obtained in shorter time at higher aging temperature

Fig. 9.15

U

I

T Stable

unstable

As-quenched

start finsh

+

Aging

Tsolvus

1

hardness

180ºC

100ºC 20ºC

100 ºC

180 ºC

Recovery, Recrystallization and grain growth

Following slides are courtsey

Prof. S.K Gupta (SKG)

Or Prof. Anandh Subramaniam (AS)

Cold work

↑ dislocation density

↑ point defect density

Plastic deformation in the temperature range above(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

AS

Cold work↑ Hardness

↑ Strength

↑ Electrical resistance

↓ Ductility

AS

Cold work Anneal

Recrystallization

Recovery

Grain growth

AS

Recovery, Recrystallization and Grain Growth

During recovery

1. Point Defects come to Equilibrium

2. Dislocations of opposite sign lying on a slip plane annihilate each other

(This does not lead to substantial decrease in the dislocation density)

SKG

POLYGONIZATION

Bent crystal

Low angle grain boundaries

Polygonization

AS

Recrystallization

Strained grains Strain-free grains

Driving force for the Process =

Stored strain energy of dislocations

SKG

Recrystallization Temperature:

Temperature at which the 50% of the cold-worked material recrystallizes in one hour

Usually around 0.4 Tm (m.p in K)

SKG

Factors that affect the recrystallization temperature:

1. Degree of cold work

2. Initial Grain Size

3. Temperature of cold working

4. Purity or composition of metal

Solute Drag Effect

Pinning Action of Second Phase Particle

SKG

Solute Drag Effect

SKG

Grain Boundary Pinning

SKG

Grain Growth

Increase in average grain size following recrystallization

Driving Force reduction in grain boundary

energy

Impurities retard the process

SKG

Grain growth

Globally► Driven by reduction in grain boundary energy

Locally► Driven by bond maximization (coordination number maximization)

AS

Bonded to4 atoms

Bonded to 3 atoms

Direction of grainboundary migration

Boundary moves towards itscentre of curvature

JUMP

AS

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)

AS

Cold work Recovery Recrystallization Grain growth

Tensile strength

Ductility

Electical conductivityInternal stress

Fig. 9.19

%CW Annealing Temperature

AS