재 료 상 변 태

재 료 상 변 태

Phase Transformation of Materials

2008. 12. 08.

박 은 수

서울대학교 재료공학부

2

(b) Eutectoid Transformation (a) Precipitation

Composition of product phases differs from that of a parent phase.

5. Diffusion Transformations in solid

→

Which transformation proceeds by short-range diffusion?

(d) Massive Transformation (e) Polymorphic Transformation (c) Order-Disorder

Transformation

5. Diffusion Transformations in solid

Contents for previous class

• Precipitate growth

- Growth behind Planar Incoherent Interfaces

- Diffusion Controlled lengthening of Plates or Needles - Thickening of Plate-like Precipitates

• Overall Transformation Kinetics – TTT Diagram

- Johnson-Mehl-Avrami Equation

• Precipitation in Age-Hardening Alloys

- GP Zones

- Transition phases

Contents for today’s class

• Spinodal decompsotion

• Particle coarsening (ostwald Ripening)

• Precipitation of Ferrite from Austenite

• Eutectoid Transformation

• Bainite Transformation

• Massive Transformation

5.5.5 Spinodal Decomposition

Spinodal mode of transformation has no barrier to nucleation

2) If the alloy lies outside the spinodal, small variation in composition

leads to an increase in free energy and the alloy is therefore metastable.

2

2 0

d G dX <

The free energy can only be decreased if nuclei are formed with a composition very different from the matrix.

→ nucleation and growth How does it differ between

inside and outside the inflection point of Gibbs free energy curve?

1) Within the spinodal

2) Normal down-hill diffusion Outside the spinodal

1) Composition fluctuations within the spinodal

up-hill diffusion

interdiffusion coefficient

D<0

5.5.5 Spinodal Decomposition

down-hill diffusion

2) interfacial energy

3) coherency strain energy

2 2

/ 4 D

τ = − λ π ^τ

λ

* The Rate of Transformation

What would be an additional energy affecting spinodal decomposition?

Since spinodal decomposition is a diffusion process (D < 0), the composition fluctuation increases exponentially with time.

→

λ

5.5.5 Spinodal Decomposition

* Free Energy change for the decomposition

1) Decomposition of X₀ into X₀ + ΔX and X₀ - ΔX

2

( )

2 2

1

chem

2

G d G X

Δ = dX Δ

1) Decomposition of X₀ into X₀ + ΔX and X₀ - ΔX

+ L + ′′

+ ′

=

+ h

! 2

) a ( h f

) a ( f ) a ( f ) h a

( f

0 2

0 0 0

( )

( ) ( ) ( )

2!

G X + Δ X ≈ G X + G X ′ Δ + X G X ′′ Δ X

0 2

0 0 0

( )

( ) ( ) ( )

2!

G X − Δ X ≈ G X − G X ′ Δ + X G X ′′ Δ X

0 0

0 2

2 2

0

2

( ) ( )

( ) 2

( ) 1

2! 2

chem

G X X G X X

G G X

G X d G

X X

dX

+ Δ + − Δ

Δ = −

= ′′ Δ = Δ

Free Energy change for the decomposition

10

X

G

K

λ

⎛ Δ ⎞ Δ = ⎜ ⎝ ⎟ ⎠

2 2

2

2 2

2 ( )

2

2

d G K X

G E V

dX η

λ

⎧ ′ ⎫ Δ

Δ = ⎨ + + ⎬

⎩ ⎭

3) Coherency Strain Energy

(atomic size difference)

Interfacial Energy

(gradient energy)

2) During the early stages, the interface between A-rich and B-rich region is not sharp but very diffuse. → diffuse interface

2

G

E δ

Δ ∝ δ = ( da dX / ) Δ X a /

For a total composition difference ΔX,

5.5.5 Spinodal Decomposition

δ: misfit, E: Young’s modulus, a: lattice parameter K: atomic pair들의 bond energy에 비례하는 비례상수

η: fractional change in lattice parameter per unit composition change

2 2

1

( ) , , /(1 )

S m

G X E V where da E E

η ^′ η a dX ^{⎛ ⎞ ′} ν

Δ = Δ = ⎜ ⎝ ⎟ ⎠ = −

2

2

2 2

2 2

d G K

dX η E V

λ ^′

− > +

2

2

2

2

d G E V

dX = − η ^′

2

2 2

2 d G

2

K E V

λ > − ^⎛ ⎜ dX + η ^{′ ⎞} ⎟

⎝ ⎠

* Condition for Spinodal Decomposition

* The Limit for the decomposition

Wavelength for coherent spinodal

→ coherent spinodal

→ The minimum possible wavelength decreases with increasing undercooling below the coherent spinodal.

∞

λ →

5.5.5 Spinodal Decomposition

2 2

2

2 2

2 ( )

2

2

d G K X

G E V

dX η

λ

⎧ ′ ⎫ Δ

Δ = ⎨ + + ⎬

⎩ ⎭

Coherent Miscibility Gap

5.5.5 Spinodal Decomposition

13

( ) r

− r

= kt

where

k ∝ D X γ

Two Adjacent Spherical Precipitates with Different Diameters

r

k dt

d ∝ r

5.5.6. Particle Coarsening

- D and X_e ~ exp (-Q/RT)

전체 계면의 G 값이 최소가 아닐 때는 2상 합금의 미세조직은 열역학적으로 불안정

(Gibbs-Thomson effect)

<

<

체적확산이 속도 제어 인자라면,

(X_e: 매우 큰 입자와의 평형용해도)

-

14

The Rate of Coarsening

with Increasing Temperature

1) low

γ

heat-resistant Nimonic alloys based on Ni-Cr

→ ordered fcc Ni₃(Ti,Al) (=

γ′

γ′ 의 계면 완전 정합관계

(10 ~ 30 mJ m^-2)

→ creep 특성 향상 2) low X_e

fine oxide dispersion

ThO₂ (thoria) for W and Ni

금속에서 산화물의 낮은 용해도에 기인

r

k dt

d ∝ r

k ∝ D X γ

3) low D

Cementite → high D of carbon 매우 빠르게 조대화 a. substitutional alloying element

segregated in the carbide

b. strong carbide-forming elements (also low X_e)

How can you design an alloy with high strength at high T?

hint)

5.5.6. Particle Coarsening

~ 고온재료의 기계적 특성과 밀접한 관계

The Iron-Carbon Phase Diagram Microstructure (0.4%C) evolved by slow cooling (air, furnace) ?

5.6. The Precipitation of Ferrite from Austenite

(Grain boundary and the surface of inclusions)

Diffusional Transformation of Austenite into Ferrite

Fe-0.15%C

After being austenitized, held at (a) 800^oC for 150 s

(b) 750^oC for 40 s (c) 650^oC for 9 s (d) 550^oC for 2 s and

then quenched to room T.

What would be the microstructures?

5.6. The Precipitation of Ferrite from Austenite

Microstructures of an Fe-0.15%C alloy austenitized

(a) 800^oC for 150 s

(b) 750^oC for 40 s

(c) 650^oC for 9 s

(d) 550^oC for 2 s

5.6. The Precipitation of Ferrite from Austenite

입계타형

GB allotriomorphs

18

At small undercoolings, it is proposed that both semicoherent and incoherent interfaces can migrate at similar rates, while at large undercoolings only

incoherent interfaces can make full use of the increased driving force.

The reason for the transition from grain boundary allotriomorphs to Widman -stätten side-plates with increasing undercooling is not fully understood.

(Continuous growth)

Relative Velocity of Incoherent & Semicoherent Interfaces

5.6. The Precipitation of Ferrite from Austenite

Intragranular ferrite

Typical TTT curve for γ -> α transformation

A TTT diagram for the precipitation of ferrite

→ f (t,T)

5.6. The Precipitation of Ferrite from Austenite

) (

exp

1 kt ⁿ

f = − −

J-M-A Eq.

C Fe

+

→ α γ

Pearlite Reaction in Fe-C Alloys

Pearlite grows into the austenite grain with which it does not have an orientation relationship.

Eutectoid Transformation

Pearlite Reaction in Fe-C Alloys

Pearlite grows into the austenite grain with which it does not have an

orientation relationship.

Relative Positions of the Transformation curves

for Pearlite and Bainite in Plain Carbon Eutectoid Steels.

Growth of Pearlite

Upper Banite in medium-carbon steel Lower Bainite

in 0.69wt% C low-alloy steel

조직: 래스모양 →판상

탄화물 매우 미세하게 분산, M에서와 유사

Bainite Transformation

350 ~ 550oC, laths, K-S relationship, similar to Widmanstäten plates

Pearlite : no specific orientation relationship 24

Bainite : orientation relationship

5.8.4. Continuous Cooling Transformation diagrams

CCT diagrams TTT diagrams

Cu-Zn

Phase Diagram

Free energy-composition curves for α and β at 850^oC, 700^oC, 600^oC and 500^oC?

Massive Transformation

Free energy-composition curves for α and β : Τ

temp.

Massive Transformation

Massive 변태: 급냉시 500 ^oC 이하에서 β 상 유지, 이 온도에서 β→α 로 빠르게 변태

Massive α formed at the grain boundaries of β and grow rapidly into the surrounding β.

∼α/β 계면 가로지르는 속도로 성장 (∵α 조성 = β 조성)

Massive Transformation

Massive Transformation

열적활성화된 부정합계면의 이동에 의한 성장:

무확산 개별 변태 (diffusionless civilian trans.)

β상의 원자들이 협동적인 이동에 의해

평활이동 계면을 통과하여 α상으로 전단 변형 무확산 집단 변태 (diffusionless military trans.)

Effect of Cooling Rate on the Transformation Temperature of Pure Iron

Massive Transformation

Massive α in an Fe-0.002wt%C

Massive Transformation

Metastable phases can also form massively.

It is not even necessary for the

transformation product to be a single phase: two phases, at least one of which must be metastable, can form simultaneously provided they have the same composition as the parent phase.