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Phase Transformati on Chapter 9

Phase Transformation

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Page 1: Phase Transformation

Phase Transformation Chapter 9

Page 2: Phase Transformation

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

Page 3: Phase Transformation

Czochralski crystal pulling technique for

single crystal Si

Page 4: Phase Transformation

Quenching of steel componentsa solid->solid phase transformation

Page 5: Phase Transformation

Liquid

solid

ifica

tion

evaporation

sublimation

Solid

gas

mel

ting

condensation

Solid state phase

transformationSolid 21

Page 6: Phase Transformation

Thermodynamic driving force for a phase transformation

Decrease in Gibbs free energy

Liquid-> solid

gs - gl = g = -ve

Page 7: Phase Transformation

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

Page 8: Phase Transformation

How does solidification begins?

Usually at the walls of the container

Why?

To be discussed later.

Heterogeneous nucleation.

Page 9: Phase Transformation

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

Page 10: Phase Transformation

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

Page 11: Phase Transformation

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

Page 12: Phase Transformation

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

Page 13: Phase Transformation

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

Page 14: Phase Transformation

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 <

Page 15: Phase Transformation

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

Page 16: Phase Transformation

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*

Page 17: Phase Transformation

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

Page 18: Phase Transformation

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

Page 19: Phase Transformation

Growth

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

dt

drU

T

U

Page 20: Phase Transformation

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

Page 21: Phase Transformation

Fraction transformed as a function of time

ts tf

X

t

Slow due to very few nuclei

Slow due to final impingement

Page 22: Phase Transformation

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

Page 23: Phase Transformation

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

Page 24: Phase Transformation

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

Page 25: Phase Transformation

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

Page 26: Phase Transformation

L+

T

log t

Tm

TTmTg

Log (viscosity)

12

18

crystal

Stable liquid

Undercooled liquid

glass

30

Fig. 9.17

Page 27: Phase Transformation

Tm

Specific volume Stable liquid

Undercooled liquid

Fast cool

Slow cool

Tgs

Tgf

crystal

Fig. 9.18

T

Page 28: Phase Transformation

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

Page 29: Phase Transformation

Corning’s new digital hot plates with PyroceramTM tops.

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.

Page 30: Phase Transformation

Czochralski crystal pulling technique for

single crystal Si

SSPL: Solid State Physics Laboratory, N. Delhi

J. Czochralski, (1885-1953)

Polish Metallurgist

Page 31: Phase Transformation

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

no more grades, no more pencils,no more sharing/using stencils,no more reading, no more books,no more teachers dirty looks,so when we hear that final bell,we drop our books and run like hell !!

Page 32: Phase Transformation

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

Page 33: Phase Transformation

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

Page 34: Phase Transformation

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

Page 35: Phase Transformation

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

Page 36: Phase Transformation

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

We need TTT diagram for

austenite-> pearlite

transformation

Page 37: Phase Transformation

Stable austenite

unstable austenite

TTT diagram for eutectoid steel

start

finish

Page 38: Phase Transformation

Stable austenite

unstable austenite

start

finishAnnealing:coarse pearliteNormalizin

g:fine pearlite

U

I

TTTT diagram for eutectoid steel

Page 39: Phase Transformation

Callister

Page 40: Phase Transformation

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

Page 41: Phase Transformation

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

Page 42: Phase 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

Page 43: Phase Transformation

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.)

Page 44: Phase Transformation

A

N

AT

TQ

heati

ng

T

Page 45: Phase Transformation

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

TEMPERING

CFetempering3

T<TE

?

Page 46: Phase Transformation

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

Page 47: Phase Transformation

Tempering Continued

Callister

Page 48: Phase Transformation

AustemperingBainite

Short needles of Fe3C embedded in plates of ferrite

Page 49: Phase Transformation

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

Page 50: Phase Transformation

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

Page 51: Phase Transformation

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

Page 52: Phase Transformation

Plain C steel

Alloy steel

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

Fig. 9.10

Page 53: Phase Transformation

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.

Page 54: Phase Transformation

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.

Page 55: Phase Transformation

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.

Page 56: Phase Transformation

Airbus A380 to be launched on October 2007

Page 57: Phase Transformation

A shop inside Airbus A380

Page 58: Phase Transformation

Alfred Wilm’s Laboratory 1906-1909

Steels harden by quenching

Why not harden Al alloys also by quenching?

Page 59: Phase Transformation

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

Page 60: Phase Transformation

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 !!

Page 61: Phase Transformation

As- quenched hardness

Hardness

time

Peak hardness

Overaging

Hardness initially increases: age hardening

Attains a peak value

Decreases subsequently: Overaging

Page 62: Phase Transformation

+

: 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

Page 63: Phase Transformation

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

Page 64: Phase Transformation

-grains

As quenched

-grains +

Aged

Peak aged

Dense distribution of fine

overaged

Sparse distribution of coarse

Driving force for coarsening

/ interfacial energy

Page 65: Phase Transformation

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

Page 66: Phase Transformation

U

I

T Stable

unstable

As-quenched

start finsh

+

Aging

Tsolvus

1

hardness

180ºC

100ºC 20ºC

100 ºC

180 ºC

Page 67: Phase Transformation

Recovery, Recrystallization and grain growth

Following slides are courtsey

Prof. S.K Gupta (SKG)

Or Prof. Anandh Subramaniam (AS)

Page 68: Phase Transformation

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

Page 69: Phase Transformation

Cold work↑ Hardness

↑ Strength

↑ Electrical resistance

↓ Ductility

AS

Page 70: Phase Transformation

Cold work Anneal

Recrystallization

Recovery

Grain growth

AS

Page 71: Phase Transformation

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

Page 72: Phase Transformation

POLYGONIZATION

Bent crystal

Low angle grain boundaries

Polygonization

AS

Page 73: Phase Transformation

Recrystallization

Strained grains Strain-free grains

Driving force for the Process =

Stored strain energy of dislocations

SKG

Page 74: Phase Transformation

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

Page 75: Phase Transformation

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

Page 76: Phase Transformation

Solute Drag Effect

SKG

Page 77: Phase Transformation

Grain Boundary Pinning

SKG

Page 78: Phase Transformation

Grain Growth

Increase in average grain size following recrystallization

Driving Force reduction in grain boundary

energy

Impurities retard the process

SKG

Page 79: Phase Transformation

Grain growth

Globally► Driven by reduction in grain boundary energy

Locally► Driven by bond maximization (coordination number maximization)

AS

Page 80: Phase Transformation

Bonded to4 atoms

Bonded to 3 atoms

Direction of grainboundary migration

Boundary moves towards itscentre of curvature

JUMP

AS

Page 81: Phase Transformation

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

Page 82: Phase Transformation

Cold work Recovery Recrystallization Grain growth

Tensile strength

Ductility

Electical conductivityInternal stress

Fig. 9.19

%CW Annealing Temperature

AS