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T (°C). 1600. d. L. 1400. g. + L. g. g. g. 1200. L +Fe 3 C. 1148°C. (austenite). g. g. g. 1000. g. g. + Fe 3 C. g. g. Fe 3 C (cementite). r. s. 800. a. g. g. 727°C. a. a. a. g. g. R. S. 600. a. + Fe 3 C. w. =. s. /(. r. +. s. ). a. w. =. (1-. w.

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hypo eutectoid steel

T(°C)

1600

d

L

1400

g

+L

g

g

g

1200

L+Fe3C

1148°C

(austenite)

g

g

g

1000

g

g

+Fe3C

g

g

Fe3C (cementite)

r

s

800

a

g

g

727°C

a

a

a

g

g

R

S

600

a

+Fe3C

w

=

s

/(

r

+

s

)

a

w

=

(1-

w

)

g

a

400

0

1

2

3

4

5

6

6.7

a

Co, wt% C

(Fe)

C0

0.76

pearlite

w

=

w

g

pearlite

100 mm

w

=

S

/(

R

+

S

)

a

w

=

(1-

w

)

a

Fe3C

pearlite

proeutectoid ferrite

Hypoeutectoid Steel
proeuctectoid ferrite pearlite
Proeuctectoid Ferrite – Pearlite

0.38 wt% C: Plain Carbon – Medium Carbon Steel

hyper eutectoid steel

T(°C)

1600

d

L

1400

g

+L

g

g

g

1200

L+Fe3C

1148°C

g

g

(austenite)

g

1000

g

g

+Fe3C

g

g

Fe3C (cementite)

Fe3C

s

r

800

g

g

a

g

g

R

S

600

a

+Fe3C

w

=

r

/(

r

+

s

)

Fe3C

w

=(1-

w

)

g

Fe3C

400

0

1

2

3

4

5

6

6.7

Co, wt%C

(Fe)

pearlite

w

=

w

g

pearlite

w

=

S

/(

R

+

S

)

a

60mm

w

=

(1-

w

)

a

Fe3C

pearlite

proeutectoid Fe3C

Adapted from Fig. 9.33,Callister 7e.

Hypereutectoid Steel

Co

0.76

proeutectoid cementite pearlite
Proeutectoid Cementite - Pearlite

1.4 wt% C: Plain Carbon – High Carbon Steel

phase transformations
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, DG, which we have briefly introduced before:
    • DG is the thermodynamic driving force for a reaction
    • If DG is negative then there is a probability that a reaction will occur.
    • The more negative DG 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 transformations1
Phase Transformations

Phase transformations involve some form of change in the microstructure

Let’s categorize with 3 types:

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

Examples:

    • Eutectoid reaction
    • Peritectic reaction
  • Diffusion-less transformations, in which a metastable phase is produced

Examples:

    • Martensitic and Bainitic transformations
nucleation
Nucleation

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

Diffusion based Phase Transformations do not occur instantaneously – nucleated

  • 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

solidification nucleation processes
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
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

homogeneous nucleation energy effects

Surface Free Energy-destabilizes

the nuclei (it takes energy to make

an interface)

g = surface tension

Homogeneous Nucleation & Energy Effects

Surface area of sphere

DGT = Total Free Energy

= DGS + DGV

Volume (Bulk) Free Energy –

stabilizes the nuclei (releases energy)

embryo

nucleus

DGn = free energy difference between the parent and daughter phase

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

solidification

r* = critical radius

g = surface free energy

Tm = melting temperature

HS = latent heat of solidification

DT = Tm - T = supercooling

 r* decreases asT increases

For typicalTr* ca. 100Å

Solidification
  • Note:HS = strong function of T

T1 > T2

 =weak function ofT

other effects of temperature
Other Effects of Temperature

Maximum Nucleation Rate occurs at intercept of two curves

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

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

heterogeneous nucleation
Heterogeneous Nucleation

Note: DG*het = DGhom S(q)

heterogeneous vs homogenous
Heterogeneous vs Homogenous

DG*het = DGhom S(q)

  • Lower activation energy barrier
  • Less undercooling required
  • Faster transformation rate
nucleation vs growth rates
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
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

All out of material - done

maximum rate reached – now amount

unconverted decreases so rate slows

rate increases as surface area increases & nuclei grow

By convention r = 1 / t0.5

Rate of Phase Transformation

Fixed T

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

  • k & n fit for specific sample

Fraction transformed, y

0.5

t0.5

log t

time

fraction transformed

rate of phase transformations

135C

119C

113C

102C

88C

43C

1

10

102

104

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!
eutectoid transformation rate

• Growth of pearlite from austenite:

Diffusive flow

of C needed

Austenite (g)

cementite (Fe3C)

grain

a

Ferrite (a)

a

a

boundary

g

g

a

g

g

a

pearlite

a

Adapted from Fig. 9.15, Callister 7e.

a

growth

a

direction

a

• Transformation

rate increases

with DT.

100

600°C

(DT larger)

650°C

50

y (% pearlite)

675°C

(DT smaller)

0

Eutectoid Transformation Rate

Course pearlite  formed at higher T - softer

Fine pearlite  formed at low T - harder

nucleation and growth
Nucleation and Growth

100

Nucleation rate increases with T

% Pearlite

Growth

Growth rate increases with T

regime

50

Nucleation

regime

t

log(time)

0.5

0

pearlite

colony

g

g

g

T just below

TE

T moderately below

TE

T way below

TE

Nucleation rate low

.

Nucleation rate med

Nucleation rate high

Growth rate high

Growth rate med.

Growth rate low

Reaction rate is a result of nucleation andgrowth of crystals.

• Examples:

consider eutectoid transformation

1600

T(°C)

d

L

1400

g

+L

g

1200

L+Fe3C

1148°C

(austenite)

1000

g

+Fe3C

a

Eutectoid:

Fe3C (cementite)

ferrite

Equil. Cooling: Ttransf. = 727ºC

800

727°C

DT

a

+Fe3C

600

Undercooling by DTtransf. < 727C

0.022

0.76

400

0

1

2

3

4

5

6

6.7

Co, wt%C

(Fe)

Consider Eutectoid Transformation …

Eutectoid

transformation (Fe-C):

g

Þ

a

+

Fe3C

0.76 wt% C

6.7 wt% C

0.022 wt% C

isothermal transformation diagrams
Isothermal Transformation Diagrams

T(°C)

Austenite (stable)

TE(727C)

700

Austenite

(unstable)

Pearlite

600

isothermal transformation at 675°C

500

100%

50%

0%pearlite

400

time (s)

2

3

4

5

1

10

10

10

10

10

• Fe-C system, Co = 0.76 wt% C

• Transformation at T = 675°C.

100

T = 675°C

y,

% transformed

50

0

2

4

time (s)

1

10

10

effect of cooling history in fe c system
Effect of Cooling History in Fe-C System

2

3

4

5

1

10

10

10

10

10

T(°C)

Austenite (stable)

TE (727C)

700

Austenite

(unstable)

Pearlite

600

g

g

g

g

g

g

100%

500

50%

0%pearlite

400

time (s)

• Eutectoid composition, Co = 0.76 wt% C

• Begin at T > 727°C

• Rapidly cool to 625°C and hold isothermally.

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