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Chapter 3.

Crystal Interfaces and Microstructure

Young-Chang Joo

Nano Flexible Device Materials Lab

Seoul National University

Phase Transformation in Materials

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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

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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

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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

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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

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3.2 Solid/Vapor Interfaces

Broken Bond Model for Surface Energy

22/)sincos( aESV

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3.2 Solid/Vapor Interfaces

Wulff Construction

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3.3 Boundaries in Single-Phase Solids (/)

Low angle Boundaries

Tilt boundary : Array of // edge dislocations

r

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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

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3.3 Boundaries in Single-Phase Solids (/)

Cf) Asymmetric Tilt Boundary

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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

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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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3.3 Boundaries in Single-Phase Solids (/)

SVb 3

1

Soap Bubble Model Experimentally

Phase Transformation in Materials