Fundamentals of Solidification

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Fundamentals of Solidification

• Lecture 4 Nucleation and growth

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Outline

• Introduction
• Homogeneous nucleation
• Heterogeneous nucleation
• Growth and microstructure
• Summary

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Introduction

• There are two types of solidification
• Glass formation
• Physical properties such as viscosity change
  smoothly across the solidifying region
• Phase transition
• Some physical properties change abruptly, such as
  viscosity, heat capacity

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Temperature vs. time in glass solidification and
phase transition solidification
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Viscosity vs. temperature in glass solidification
and phase transition solidification
(a) Glass solidification (b)
Phase-transition solidification
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Density vs. temperature in glass solidification
and phase transition solidification
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Heat capacity of Fe
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Introduction

• Solidification by phase transition is modelled as
  two stage
• Nucleation
• Homogeneous nucleation
• Heterogeneous nucleation
• Growth

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Homogeneous nucleation
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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
solid
Free energy density
liquid
temperature
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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(No Transcript)
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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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Casting refinement

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

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Growth and microstructure
T. F. Brower and M.C. Flemings, Trans. AIME, 239,
1620 (1967)
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Growth and microstructure
H.B. Dong and P.D. Lee, Acta Mater. 53 (2005) 659
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Outer chilled zones
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Outer chilled zones
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Outer chilled zones
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Outer chilled zones
Pure metals Formation of shell because
temperature gradient is the key factor in grain
growth.
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Outer chilled zones
Pouring temperature
re-melted?
survived?
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Microstructure of ingot

• Chilled zone
• Fine equiaxed grains.
• Pure substance Continuous shell.
• Solution Particles
• Particles flushed away from wall into the central
• Re-melted
• Survived nucleus

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Intermediate columnar zone
The grain is overtaken by neighbors.
Columnar grains grows
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Intermediate columnar zone
Growth and overtaken
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Intermediate columnar zone
Columnar growth blocked
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Central equiaxed zone

• Equiaxed grain
• Nucleation
• Supercooling
• Falling particles
• Dendrite fragments

• Elevated pouring temperature
• Larger equiaxed grains

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Structure and properties

• More columnar zone
• Anisotropic properties
• Magnetic materials
• Turbo blade.
• More equiaxed zone
• Isotropic properties
• Less segregation

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Summary

• Casting
• Heat management
• Thermodynamics
• Nucleation and growth