Hypoeutectoid Steel

Fe 3

C (

cem

entit

e)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

(austenite)

+L

+ Fe3C

+ Fe3C

L+Fe3C

(Fe) Co , wt% C

1148°C

T(°C)

727°C

C0

0.76

proeutectoid ferritepearlite

100 m

R S

w =S/(R+S)wFe3C =(1-w)

wpearlite = wpearlite

r s

w =s/(r+s)w =(1- w)

Proeuctectoid Ferrite – Pearlite

0.38 wt% C: Plain Carbon – Medium Carbon Steel

Hypereutectoid Steel

Fe 3

C (

cem

entit

e)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

(austenite)

+L

+Fe3C

+Fe3C

L+Fe3C

(Fe) Co , wt%C

1148°C

T(°C)

0.7

6 Co

Adapted from Fig. 9.33,Callister 7e.

proeutectoid Fe3C

60 m

pearlite

R S

w =S/(R+S)wFe3C =(1-w )

wpearlite = wpearlite

sr

wFe3C =r/(r+s)w =(1-w Fe3C )

Fe3C

Proeutectoid Cementite - Pearlite

1.4 wt% C: Plain Carbon – High Carbon Steel

Phase Transformations• We just studied Phase Diagrams which are thermodynamic

maps which tell us the equilibrium phases present at any specific combination of temperature, pressure, and composition

• These phase diagrams are based on the concept of Gibbs Free Energy, G, which we have briefly introduced before: G is the thermodynamic driving force for a reaction If G is negative then there is a probability that a reaction will

occur. The more negative G becomes, the more driving force there is for

the reaction Thermodynamics tells us the probability of a reaction but not the

rate – the rate of a reaction is determined by Kinetics

Now we are going to shift perspectives and discuss the details of how we transform from one phase to another

Phase Transformations

Let’s categorize with 3 types:

1. Simple diffusion-dependent transformations in which there is no change in the number or composition of the phases present

Examples: Solidification of a pure metal Allotropic transformations Recrystallization and Grain Growth

2. Diffusion-dependent transformations in which there is a change in the phase compositions and or number of phases present

Examples: Eutectoid reaction Peritectic reaction

3. Diffusion-less transformations, in which a metastable phase is producedExamples: Martensitic and Bainitic transformations

Phase transformations involve some form of change in the microstructure

Nucleation

– nuclei (seeds) act as template to grow crystals– for nucleus to form, rate of addition of atoms to nucleus must

be faster than rate of loss– once nucleated, grow until reach equilibrium

Driving force to nucleate increases as we increase T– supercooling (eutectic, eutectoid reactions)

Small supercooling few nuclei - large crystals

Large supercooling rapid nucleation - many nuclei, small crystals

During Phase transformation – new phase formed with different physical/ chemical characteristics than the parent phase

Diffusion based Phase Transformations do not occur instantaneously – nucleated

Solidification: Nucleation Processes

• Homogeneous nucleation – nuclei form in the bulk of liquid metal– requires supercooling (typically 80-300°C max)

• Heterogeneous nucleation– much easier since stable “nucleus” is already present

• Could be wall of mold or impurities in the liquid phase– allows solidification with only 0.1-10ºC supercooling

Consider Solidification First

Let’s assume spherical nuclei

Why? Sphere has the smallest surface area/ surface energy for a given volume

Let’s Determine the equations that define behavior

r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)

Homogeneous Nucleation & Energy Effects

GT = Total Free Energy = GS + GV

Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface)

24 rGS

= surface tension

Volume (Bulk) Free Energy – stabilizes the nuclei (releases energy)

GrGV3

3

4

volume unit

energy free volume G

Surface area of sphere

G = free energy difference between the parent and daughter phase

embryo nucleus

Solidification

TH

Tr

S

m

2*

Note: HS = strong function of T

= weak function of T

r* decreases as T increases

For typical T r* ca. 100Å

HS = latent heat of solidification

Tm = melting temperature

= surface free energy

T = Tm - T = supercooling

r* = critical radius

T1 > T2

Other Effects of Temperature

Number of stable nuclei follows Arrhenius behavior (like vacancy densities)

Clustering of atoms by short range diffusion – Diffusivity has Arrhenius behavior

Maximum Nucleation Rate occurs at intercept of two curves

Heterogenous Nucleation

ml sm sl cos

cos (ml sm )

sl

Young’s Law:

3 2

2

44 ( )

3

(1 cos )( ) (2 cos )

4

het s v sl sl sm sm sm ml

het v sl

G V G A A A

G r G r S

S

r*2slGv

G*16sl3

3Gv2

S( )

Heterogeneous Nucleation

Note:G*het = Ghom S()

Heterogeneous vs Homogenous

G*het = Ghom S()

Lower activation energy barrier Less undercooling required Faster transformation rate

Nucleation vs Growth Rates• Growth is determined by long

range diffusion

• Arrhenius activation energy behavior

Overall transformation is equal to the product of Ġ and Ń

Rate = 1/time

Kinetics of Phase Transformation

• Discussed Thermodynamic driving forces in detail

• Kinetics – measures the approach to equilibrium vs. time– Hold temperature constant & measure conversion vs.

time

Rate of Phase Transformation

Avrami rate equation => y = 1- exp (-ktn)

– k & n fit for specific sample

All out of material - done

log tFra

ctio

n tr

an

sfo

rme

d, y

Fixed T

fraction transformed

time

0.5

By convention r = 1 / t0.5

maximum rate reached – now amount unconverted decreases so rate slows

t0.5

rate increases as surface area increases & nuclei grow

Rate of Phase Transformations

• In general, rate increases as T

r = 1/t0.5 = A e -Q/RT

– R = gas constant– T = temperature (K)– A = pre-exponential factor– Q = activation energy

Arrhenius expression

• r often small: equilibrium not possible!

135C 119C 113C 102C 88C 43C

1 10 102 104

Eutectoid Transformation Rate

Course pearlite formed at higher T - softer

Fine pearlite formed at low T - harder

Diffusive flow of C needed

• Growth of pearlite from austenite:

Adapted from Fig. 9.15, Callister 7e.

pearlite growth direction

Austenite ()grain boundary

cementite (Fe3C)

Ferrite ()

• Transformation rate increases with T.

675°C (T smaller)

0

50

y (%

pea

rlite

)

600°C (T larger)

650°C

100

Reaction rate is a result of nucleation and growth of crystals.

• Examples:

Nucleation and Growth

% Pearlite

0

50

100

Nucleation regime

Growth regime

log (time)t0.5

Nucleation rate increases with T

Growth rate increases with T

T just below TE

Nucleation rate low

Growth rate high

pearlite colony

T moderately below TE

Nucleation rate med Growth rate med.

Nucleation rate high

T way below TE

Growth rate low

Consider Eutectoid Transformation …

Eutectoid transformation (Fe-C): + Fe3C0.76 wt% C

0.022 wt% C6.7 wt% C

Fe 3

C (

cem

entit

e)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

(austenite)

+L

+Fe3C

+Fe3C

L+Fe3C

(Fe) Co , wt%C

1148°C

T(°C)

ferrite

727°C

Eutectoid:Equil. Cooling: Ttransf. = 727ºC

T

Undercooling by Ttransf. < 727C

0.7

6

0.0

22

Isothermal Transformation Diagrams

• Fe-C system, Co = 0.76 wt% C• Transformation at T = 675°C.

100

50

01 102 104

T = 675°C

y,

% tr

ansf

orm

ed

time (s)

400

500

600

700

1 10 102 103 104 105

0%pearlite

100%

50%

Austenite (stable) TE (727C)Austenite (unstable)

Pearlite

T(°C)

time (s)

isothermal transformation at 675°C

• Eutectoid composition, Co = 0.76 wt% C• Begin at T > 727°C• Rapidly cool to 625°C and hold isothermally.

Effect of Cooling History in Fe-C System

400

500

600

700

0%pearlite

100%

50%

Austenite (stable)TE (727C)

Austenite (unstable)

Pearlite

T(°C)

1 10 102 103 104 105

time (s)