Introduction to Solidification 3. Kinetics

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Introduction to Solidification3. Kinetics

• Rongshan QIN
• http//cml.postech.ac.kr/rqin

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In this lecture

• Homogeneous nucleation
• Heterogeneous nucleation

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Solidification

• Two types of solidification

Viscosity vs. temperature in (a) Glass
formation. (b) Metal casting.
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Solidification
Temperature
liquid
Glass formation
Metal casting
solid
time
Temperature vs. time during solidification
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Solidification
Molecular/atom arrangements in (a) Glass. (b)
Crystal.
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Metal solidification

• Nucleation

• Growth

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Homogeneous nucleation

• No preferred nucleation sites
• Spontaneous
• Random
• Those of preferred sites
• Boundary
• Surface
• Inclusion,

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Local free energy change
1. Liquid to solid
2. Interface
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Local free energy change
Spherical nucleus
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Single nucleus
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Critical radius
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(GL-GS) vs. supercooling
Free energy density vs. temperature
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Parameters
For FCC Copper, r?1 nm, which contains 310 Cu
atoms in each nucleus.
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System free energy

• Ideal solution Particle of different sizes
• ni particles with each contains i atoms
• n particles with each contains 1 atom

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Number of nuclei

• At equilibrium

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Number of nuclei
when
Boltzmann formula
Critical nuclei
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Heterogeneous nucleation

• Nucleation site
• Mold walls
• Inclusion
• Interface
• Surface
• Impurity

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Heterogeneous nucleation
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Heterogeneous nucleation
Force equilibrium
where ?IL, ?IN and ?NL are the interface energies
of inclusion-liquid, inclusion-nucleus and
nucleus-liquid, respectively. ? is the
nucleus-inclusion wetting angle. The nucleus is a
spherical cap of radius r.
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Free energy change
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Free energy change
Using
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Thermodynamic barriers
Heterogeneous nucleation barrier
Homogeneous nucleation barrier
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Thermodynamic barrier vs. wetting angle
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Number of nuclei with critical radius
where ns is the total number of atom around the
incubating agents surface in liquid.
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Inoculating agents

• Small interface energy
• Similar crystal structure
• Similar lattice distance
• Same physical properties
• Same chemical properties

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Effect of surface geometry
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Casting refinement

• Adding inoculating agents
• Overheat might melt the agents
• Surface refinement
• Coat agents on mold walls
• Pattern induced solidification

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In summary

• Two types of solidification
• Glass formation
• crystallization
• Solidification
• Nucleation
• Growth
• Homogeneous and heterogeneous nucleation

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References

• M.C. Flemings, Solidification processing, 1974.
• A. L. Greer, Kinetics, Cambridge.