fosl4
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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
rr
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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
SLLSbeforeafter AGGVGGG
SLSL rGGrG 23 43
4
Spherical nucleus:
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Single nucleus
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Critical radius
0/ drGd
SL
SL
GGr
2*
2
3
3
16*
SL
SL
GGG
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(GL-GS) vs. supercooling
Free energy density vs. temperature
liquid
solid
temperature
Free energy density
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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
STGnG ic
ii
ii nn
nn
nn
nnkS lnln
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Number of nuclei
• At equilibrium
0/ ic nG
i
i
nn
n
kT
Gln
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inn
kT
Gnni exp
kT
Gnni
*exp*
when
Number of nuclei
Boltzmann formula:
Critical nuclei:
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Heterogeneous nucleation
• Nucleation site
– Mold walls
– Inclusion
– Interface
– Surface
– Impurity
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Liquid
Inclusion
Nucleus IL
NL
IN
R
r
h
a
Heterogeneous nucleation
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cosNLINIL
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.
Heterogeneous nucleation
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Free energy change
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Free energy change
Using cosNLINIL
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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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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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H.B. Dong and P.D. Lee, Acta Mater. 53 (2005) 659
Growth and microstructure
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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
re-melted?
Pouring temperature
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
Columnar grains grows
The grain is overtaken by neighbors.
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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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• More columnar zone
– Anisotropic properties
• Magnetic materials
• Turbo blade.
• More equiaxed zone
– Isotropic properties
– Less segregation
Structure and properties
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Summary
• Casting
• Heat management
• Thermodynamics
• Nucleation and growth