byeong-joo lee cmse.postech.ac.kr byeong-joo lee postech - mse [email protected] interfaces...
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Byeong-Joo Lee cmse.postech.ac.kr
Byeong-Joo LeeByeong-Joo Lee
POSTECH - MSEPOSTECH - [email protected]@postech.ac.kr
Interfaces & Interfaces & MicrostructurMicrostructur
ee
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
SurfacesSurfaces
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
Equilibrium shape of a Crystal Equilibrium shape of a Crystal -- WulffWulff constructionconstruction
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
Grain
Boundaries
Grain
Boundaries
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
Grain boundaries in Solids Grain boundaries in Solids - tilt vs. twist - tilt vs. twist boundariesboundaries
D
1γ
Byeong-Joo Lee cmse.postech.ac.kr
[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
Byeong-Joo Lee cmse.postech.ac.kr
[100] Twist Grain Boundary Energy of [100] Twist Grain Boundary Energy of CopperCopper
Byeong-Joo Lee cmse.postech.ac.kr
Special High-Angle Grain BoundariesSpecial High-Angle Grain Boundaries
Byeong-Joo Lee cmse.postech.ac.kr
· 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
Byeong-Joo Lee cmse.postech.ac.kr
2
31
3
12
1
23
sinsinsin
Equilibrium Microstructure Equilibrium Microstructure - balance of GB - balance of GB tensionstensions
θ
LV cosLVLSSV
LS SV
Byeong-Joo Lee cmse.postech.ac.kr
Normal Grain Growth Normal Grain Growth - the mechanism- the mechanism
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
Abnormal Grain Growth Abnormal Grain Growth – – Mechanism ?Mechanism ?
Byeong-Joo Lee cmse.postech.ac.kr
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)
Byeong-Joo Lee cmse.postech.ac.kr
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)
Byeong-Joo Lee cmse.postech.ac.kr
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)
Byeong-Joo Lee cmse.postech.ac.kr
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)
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
Interphase
Interfaces
Interphase
Interfaces
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
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
Byeong-Joo Lee cmse.postech.ac.kr
Morphological Evolution Morphological Evolution - from Y.S. Yoo, - from Y.S. Yoo,
KIMSKIMS
Byeong-Joo Lee cmse.postech.ac.kr
Morphological Evolution Morphological Evolution - from Y.S. Yoo, - from Y.S. Yoo,
KIMSKIMS