byeong-joo lee cmse.postech.ac.kr byeong-joo lee postech - mse [email protected] interfaces...

Byeong-Joo Lee cmse.postech.ac.kr

Byeong-Joo LeeByeong-Joo Lee

POSTECH - MSEPOSTECH - [email protected]@postech.ac.kr

Interfaces & Interfaces & MicrostructurMicrostructur

ee


ScopeScope

Fundamentals

1. Free Surfaces vs. Grain Boundaries vs. Interphase Interfaces

2. Concept of Surface Energy/Surface Tension 3. Origin of Surface Energy and its Anisotropy4. Grain Boundary/Interfacial Energy

Interface Phenomena

1. Curvature Effect2. Multi-component system • Segregation3. General

• Grain Growth • Morphological Evolution


SurfacesSurfaces


Fdxdxl 2l

F

2

PTA

G

,

dAVdPSdTdG

Concept of Surface Energy and Surface Concept of Surface Energy and Surface TensionTension for liquid film

Generally,

AγGG 0 dAFAdγdAdG Tension Surface

dA

dAγF Tension Surface


A

s

N

Hw

42

3

As ZNH 5.0

15.13

2

)111(

)100(

For Cu: a = 3.615 Å △Hs =337.7J/mol γ(111) = 2460 erg/cm2 (1700 by expt.)

For fcc ※ Origin of Anisotropy

Pair approximation

Necessary Work for Creationof (111) surface in fcc (/atom)

For fcc (111): N/A = 4/(31/2a2) fcc (100): N/A = 2/a2

Estimation of Solid Surface Energy Estimation of Solid Surface Energy -- Origin of Origin of Surface EnergySurface Energy

A

N

N

H

A

s

4


Comparisons Comparisons

High Index Surface EnergyHigh Index Surface Energy

1. W.R. Tyson and W.A. Miller, Surf. Sci. 62, 267 (1977).2. L.Z. Mezey and J. Giber, Jpn. J. Appl. Phys., Part 1 21, 1569 (1982).

Estimation of Solid Surface Energy Estimation of Solid Surface Energy -- Orientation dependenceOrientation dependence


Equilibrium shape of a Crystal Equilibrium shape of a Crystal -- WulffWulff constructionconstruction


Equilibrium shape of a Crystal Equilibrium shape of a Crystal - Numerical - Numerical ExampleExample

102

22 c

caES

2

122

a

c

.4

22 const

caA

cc

afor

2

2210


Pure W W + 0.4wt% Ni

Vaccum Annealing

An issue for thinking An issue for thinking - Surface Transition and - Surface Transition and Alloying EffectAlloying Effect


Note Note - Estimation of Surface Energy- Estimation of Surface Energy

J. Park, J. Lee, Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 135–141


Grain

Boundaries

Grain

Boundaries


Grain boundaries in Solids Grain boundaries in Solids - Misorientation- Misorientation

(RD) 1x

TD)(2x

ND)(3x

cx2

cx1

cx1

cx1

cx1

cx1

cx1

cx2cx2

cx2

cx2

cx2

cx3

cx3

cx3

cx3

cx3

cx3

MisorientationMisorientation

vs.vs.

InclinationInclination


Grain boundaries in Solids Grain boundaries in Solids - tilt vs. twist - tilt vs. twist boundariesboundaries

D

1γ


[100] Twist Boundary Structure in pure Cu[100] Twist Boundary Structure in pure Cu

33oo 4 4oo 7 7o o 10o

1515oo 20 20oo 30 30o o 45 45o


[100] Twist Grain Boundary Energy of [100] Twist Grain Boundary Energy of CopperCopper


Special High-Angle Grain BoundariesSpecial High-Angle Grain Boundaries


· Incoherent boundary energy is insensitive to orientation. ※ Special boundaries with low energy

[100] and [110] tilt Boundary energy of [100] and [110] tilt Boundary energy of Al Al

Special High-Angle Grain BoundariesSpecial High-Angle Grain Boundaries


2

31

3

12

1

23

sinsinsin

Equilibrium Microstructure Equilibrium Microstructure - balance of GB - balance of GB tensionstensions

θ

LV cosLVLSSV

LS SV


Normal Grain Growth Normal Grain Growth - the mechanism- the mechanism


Effect of particles on Grain Growth Effect of particles on Grain Growth - Zener - Zener pinning effectpinning effect

0max 45, rF sincosr2F

Consider the balance between the dragging force (per unit area)

and the pressure from the curvature effect

• dragging force due to one particle of size r

• number of ptl. per unit area of thickness 2r

⇒ drive it !

• total dragging force per unit area

2r2

3f

D

2γ

2r

3fγπrγ

2ππ

3fP

2

3f

4rDmax • Maximum grain size


Abnormal Grain Growth Abnormal Grain Growth – – Mechanism ?Mechanism ?


Effect of Anisotropic GBE and Precipitates Effect of Anisotropic GBE and Precipitates on Abnormal GGon Abnormal GG

C.-S. Park et al., Scripta Mater. (2012)


Grain Boundary Identification SchemeGrain Boundary Identification Scheme

(RD) 1x

TD)(2x

ND)(3x

cx2

cx1

cx1

cx1

cx1

cx1

cx1

cx2cx2

cx2

cx2

cx2

cx3

cx3

cx3

cx3

cx3

cx3

How to uniquely define misorientation and inclination between two neighboring grains

H.-K. Kim et al., Scripta Mater.

(2011)


Sigma (Σ) Theta (θ) (hkl) plane Sigma (Σ) Theta (θ) (hkl) plane5 36.87 100 11 144.9 3103 70.53 110 5 180 310

11 50.48 110 7 115.38 3109 38.94 110 3 146.44 3113 60 111 9 67.11 3117 38.21 111 11 180 3113 131.81 210 5 95.74 3119 96.38 210 11 100.48 3207 73.4 210 7 149 3205 180 210 7 180 3213 180 211 9 123.75 3215 101.54 211 9 152.73 322

11 62.96 211 11 82.16 3317 135.58 211 7 110.92 3319 90 221 5 154.16 3315 143.13 221 11 180 332

Grain Boundary Energy of BCC FeGrain Boundary Energy of BCC FeH.-K. Kim et al., Scripta Mater.

(2011)


Phase field simulation of grain growthPhase field simulation of grain growth

- Isotropic GB mobility- Random crystallographic orientation vs. weakly-textured orientation (LAGB = 1.4 % vs. 4.9 %)

- Isotropic GBE - Anisotropic GBE (realistic GBE

DB)

H.-K. Kim et al.

(2013)


Wetting angle : 36o Wetting angle : 120o

Fe - 0.5% Mn – 0.1% C, dT/dt = 1 oC/s

from SG Kim, Kunsan University

Phase Field Simulation of Phase Field Simulation of γ→αγ→α transformation in steelstransformation in steels


Interphase

Interfaces

Interphase

Interfaces


Interfaces in Solids Interfaces in Solids – Coherent, Semi-Coherent & – Coherent, Semi-Coherent & Incoherent InterfacesIncoherent Interfaces

chγ

defchγ

δ

dD β

α

αβ

d

ddδ

δdef


from Y.S. from Y.S. YooYoo

KIMSKIMS

Interfaces in Solids Interfaces in Solids – Shape of Coherent Second-– Shape of Coherent Second-Phase Phase

min.γAΔG iistrain )(

※ Equilibrium Shape


γ’ precipitates of Ni-Al alloy system, D.Y. Yoon et al. Metals and Materials

Strain Energy vs. Interfacial Energy Strain Energy vs. Interfacial Energy - Mechanism - Mechanism of particle splittingof particle splitting

Phase Field Method Simulation

by P.R. Cha, KMU


Morphological Evolution Morphological Evolution - from Y.S. Yoo, - from Y.S. Yoo,

KIMSKIMS

byeong-joo lee cmse.postech.ac.kr byeong-joo lee postech - mse [email protected] interfaces...

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