PowerPoint 프레젠테이션

재 료 상 변 태

Phase Transformation of Materials

2008. 10. 30.

박 은 수

서울대학교 재료공학

Contents for previous class

• Thermally Activated Migration of Grain Boundaries

- Grain coarsening at high T, annealing

• The Kinetics of Grain Growth

- Grain boundary migration by thermally activated atomic jump - mobility of grain boundary

• Grain Growth

- Normal grain growth Abnormal grain growth

• Effect of second-phase particle

- Zener Pinning

Contents for today’s class

• Interphase Interfaces in Solid ( α / β )

• Second-Phase Shape: Interface Energy Effects

• Second-Phase Shape: Misfit Strain Effects

• Coherency Loss

• Glissil Interfaces

• Solid/Liquid Interfaces

3.4 Interphase Interfaces in Solids

Interphase boundary

- different two phases : different crystal structure different composition

Coherent, semicoherent incoherent

(1) Coherent interfaces Perfect atomic matching at interface

3.4.1 Interface Coherence

Which plane and direction will be coherent between FCC and HCP?

: Interphase interface will make lowest energy and thereby the lowest nucleation barrier

(111) //(0001) [110] //[1120]

α κ

α κ

γ_α-κ

of Cu-Si ~ 1 mJM

^-2

In general,

γ (coherent) ~ 200 mJM^-2

ex) hcp silicon-rich κ phase in fcc copper-rich α matrix of Cu-Si alloy

γ

(coherent) =

γ_ch

γ_coherent = γ_structure + γ_chemical

= γ_chemical

→

the same atomic configuration

→

Orientation relation

How can this coherent strain can be reduced?

When the atomic spacing in the interface is not identical Between the adjacent phase, what would happen?

→

lattice distortion

→

Coherency strain

→

strain energy

Lattice가 같지 않아도 Coherent interface를 만들 수 있다.

If coherency strain energy is sufficiently large, →

misfit dislocations

→

semi-coherent interface

b: Burgers vector of disl.

(2) Semicoherent interfaces

d_α < d_β

δ

= (d

_β

- d

_α

)/ d

_α

: misfit

→

D vs.

δ

vs. n (n+1) d

_α

= n d

_β

= D

δ

= (d

_β

/ d

_α

) – 1, (d

_β

/ d

_α

) = 1 + 1/n = 1 +

δ

→ δ

= 1/n

D = d

_β

/

δ ≈

b /

δ

[b=(d

_α

+ d

_β

)/2]

γ

0.25 δ

1 dislocation per 4 lattices semi

γsemicoherent

: 200~500 mJ/m

²

γ

_st

∝ δ for small δ

γ ( semicoherent ) = γ

_ch

+ γ

_st

γ_st → due to structural distortions caused by the misfit dislocations

3) Incoherent Interfaces

γ_incoherent

→

large

≈

500 ~ 1000 mJ/m

² 1) δ > 0.25

2) different crystal structure (in general)

incoherent

110 111 001 101 ( )

_bcc

//( ) , [

_fcc

]

_bcc

//[ ]

_fcc

110 111 1 11 0 11

( )

_bcc

//( ) , [

_fcc

]

_bcc

//[ ]

_fcc

Nishiyama-Wasserman (N-W) Relationship

Kurdjumov-Sachs (K-S) Relationships If bcc α is precipitated from fcc

γ,

which interface is expected?

Which orientation would make the lowest interface energy?

4) Complex Semicoherent Interfaces

Complex Semicoherent Interfaces

Semicoherent interface observed at boundaries formed by low-index planes.

(atom pattern and spacing are almost equal.)

3.4.2 Second-Phase Shape: Interfacial Energy Effects γ =

∑ A

^{i i}

minimum

GP(Guinier- Preston) Zone in Al – Ag Alloys

ε

_a

=

^A

−

^B

= 0 7 . %

A

r r r

→ negligible contribution to the total free energy

A. Fully Coherent Precipitates

- If α, β have the same structure

- Happens during early stage of many ppt hardening - Good match can have any shape spherical

How is the second-phase shape determined?

B. Partially Coherent Precipitates

Coherent or Semi-coherent in one Plane;

Disc Shape (also plate, lath, needle-like shapes are possible)

It should be noted that the observed ppt shape is a growth shape, not an equilibrium shape.

- α, β have different structure and one plane which provide close match

4%

hcp γ ′ Precipitates in Al − Ag Alloys → plate

broad face parallel to the {111}_α matrix planes

Alloys Cu

Al Phase − θ ′

α θ

α

θ

// ( 001 ) [ 100 ] // [ 100 ] )

001

(

_{′ ′}

β ′

S phase in Al-Cu-Mg alloys ; Lath shape

phase in Al-Mg-Si alloys ; Needle shape

C. Incoherent precipitates

- when α, β have completely different structure Incoherent interfaces - Interface energy is high for all plane spherical shape

- Polyhedral shapes from coherent or semi-coherent interfaces

alloys Cu

Al in

phase −

θ

Precipitates on Grain Boundaries

1) incoherent interfaces with both grains

2) a coherent or semi-coherent interface with one grain and an incoherent interface with the other,

3) coherent or semi-coherent interface with both grains

Precipitates on Grain Boundaries

A, B; Incoherent, C; Semi-coherent

3.4.3. Second-Phase Shape: Misfit Strain Effects

β α

α

δ = −

Unconstrained Misfit

a a

a

β α

α

ε = ′ −

Constrained Misfit

a a

a

2 1 3

3 0 5

, , /

. ,

E E

E E

β α

β α

ε δ ν

δ ε δ

= = =

≤ ≤ ≠

A. Fully Coherent Precipitates

Coherency Strain

i i S

A γ + Δ G = minimum

∑

4

2

G

S

μδ V

Δ = ⋅

disc sphere

sphere Shape

Zone

Misfit Zone

Cu Zn

Ag Al

A radius Atom

o

−

−

− +

− 0 . 7 % 3 . 5 % 10 . 5 % )

(

28 . 1 : 38

. 1 : 44

. 1 : 43

. 1 : )

( δ

Elastically Anisotropic Materials Elastically Isotropic Materials

2 2 2

2 2 2

1

x y z

a + a + c =

2

2

( / )

S

3

G μ V f c a

Δ = Δ ⋅ ⋅

For Elliptical Inclusions

B. Incoherent Inclusions

Volume Misfit V

V Δ = Δ

for a homogeneous

incompressible inclusion in an isotropic matrix

μ: the shear modulus of the matrix

C. Plate-like precipitates

(a) Bright-field TEM image showing G.P. zones, and (b) HRTEM image of a G.P. zone formed on a single (0 0 0 1)_α plane. Electron beam is parallel to in both (a) and (b).

Coherency Loss

2 3 2

2

( ) 4 4 4

3

( ) 4 ( )

ch

ch st

G coherent r r

G non coherent r

μδ π π γ

π γ γ

Δ = ⋅ + ⋅

Δ − = ⋅ +

,

_st

for small δ γ ∝ δ

Coherency loss for a spherical precipitate

Coherent Coherency strain replace by dislocation loop.

In perspective

Glissile Interfaces

FCC: ABCABCAB…

HCP: ABABABAB…

close packed plane: (0001) close packed directions:

>

< 11 2 0

close packed planes: {111}

close packed directions:

< 110 >

a

b = <

6

112 >

→ Shockley partial dislocation B → C sites

Glissile Interfaces

Solid / Liquid Interfaces

Solid / Liquid Interfaces