chapter 3. crystal interfaces and microstructure
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Nano & Flexible
Device Materials Lab.1
Chapter 3.
Crystal Interfaces and Microstructure
Young-Chang Joo
Nano Flexible Device Materials Lab
Seoul National University
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.2
Contents
Interfacial Free Energy
Solid/Vapour Interfaces
Boundaries in Single-Phase Solids
Low-Angle and High-Angle Boundaries
Special High-Angle Grain Boundaries
Equilibrium in Polycrystalline Materials
Thermally Activated Migrations of Grain Boundaries
The Kinetics of Grain Growth
Interphase Interfaces in Solids
Interface Coherence
Second-Phase Shape: Interfacial Energy Effects
Second-Phase Shape: Misfit Strain Effects
Coherency Loss
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.3
Types of Interface
(c) Interphase interfaces (α/β interfaces)
(a) The Free Surfaces of a Crystal (solid/vapor interface)
(b) Grain Boundaries (α/α interfaces)
Marcelo O. et al., Mat. Rev. (2003)
G. Ghosh. et al., Cerm. Internat. (1999)
X-sialon
β-sialon
β-Si3N4
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.4
3.1 Interfacial Free Energy
G = G0+A γ
dG = γdA + Adγ = FdA
∴ F = γ + A𝑑γ𝑑𝐴
In the case of a liquid film dγ/dA= 0 → F = γ
In case of a solid,
in general dγ/dA≠ 0
at high temperature dγ/dA= 0
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.5
3.2 Solid/Vapor Interfaces
The Origin of surface free energy : Broken Bonds
For {111} planes
• Broken Bonds : 3 per atom
• Bond Strength : ε
• Lowering of Internal Energy per Bond : ε/2 per atom → 3 ε/2
• The Heat of Sublimation : LS = 12 Na ε/2
• The Energy of a {111} Surface : ESV = 0.25 LS /La
γ = E + PV - TS
γSV = 0.15 LS /La J / surface atom
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.6
3.2 Solid/Vapor Interfaces
Broken Bond Model for Surface Energy
22/)sincos( aESV
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.7
3.2 Solid/Vapor Interfaces
Wulff Construction
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.8
3.3 Boundaries in Single-Phase Solids (/)
Low angle Boundaries
Tilt boundary : Array of // edge dislocations
r
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.9
3.3 Boundaries in Single-Phase Solids (/)
Low angle Boundaries
Twist boundary : A cross-grid of two sets of screw dislocations
In general, boundaries are a mixture of the tilt and twist b.Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.10
3.3 Boundaries in Single-Phase Solids (/)
Cf) Asymmetric Tilt Boundary
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.11
3.3 Boundaries in Single-Phase Solids (/)
Grain Boundary Energy
1. Low angle boundary
The energy of 1-angle boundary = total energy of
dislocations within a unit area of boundaries
As → the strain field of the s ↓ increases at a
decreasing rate
//1 bDD
Phase Transformation in Materials
Nano & Flexible
Device Materials Lab.12
3.3 Boundaries in Single-Phase Solids (/)
2. High Angle Grain Boundary
If exceeds 10-15 degree, D is so small that cores overlap.
Impossible to identify the individual s.
is constant with grain boundary angle.
Disordered High Angle Grain BoundaryPhase Transformation in Materials
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