1. MSE 440/540: Processing of Metallic Materials
Instructors: Yuntian Zhu
Office: 308 RBII
Ph:
Lecture 2: Solidification Theory
Homework: Problem from notes,
Text book,
Office hour, by appointment
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2. Solidification
Nearly every metal product started as a liquid at some point in time.
What is Solidification
What is the Melting Point?
What’s composition?
Quiz: how about the solidification of an alloy?
Why is there a thermal arrest?
What is the equilibrium temperature?
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3. Nucleation and Growth
During solidification, solid nuclei form in the liquid and subsequently grow until the entire volume is a solid.
What is the driving force for nucleation and growth?
Quiz
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4. Homogeneous Nucleation
Consider free energy change when small spherical nuclei of solid is formed in a liquid
G = H – TS L S
ΔG = ΔH – TΔS
At Tm, ΔG = 0, ΔH = L
ΔS = L/Tm
ΔGv(T) = L – T(L/Tm)
= L(1-T/Tm)
Quiz: is L positive or negative?
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5. Homogeneous Nucleation
There is a critical radius r*, at a given undercooling ΔT where embryos can grow and reduce the free energy.
r* occurs at
HOMEWORK: Show that:
r* =-2g/ΔGv
ΔG at r* ,
If ΔGv = LΔT/Tm, then
= thermodynamic barrier to nucleation or work of nucleation
Quiz: What is the physical origin of energy barrier for nucleation?
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6. Homogeneous Nucleation
Note that r* and ΔGv* decrease with increasing undercooling
Quiz: The effect of ΔT on solidification speed and microstructure.
Freeze beer/2:22
Quiz: What does this mean in terms of solidification speed and microstructure?
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7. Heterogeneous Nucleation
r* is the same as the homogeneous nucleation
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8. Heterogeneous Nucleation Rate
Innoculants (seeds):
C1 is # of atoms in contact with hetergeneous nucleation sites,
Quiz: Seeds requirement: 1. Low interfacial energy, 2. The seeds makes nucleation easier because ?
Nucleation of Melting:
Low undercooling is needed for heterogeneous nucleation
gSL + gLV < gSV
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9. Commercial Practice Dynamic Nucleation
- Vibrate melt to collapse internal cavities
- Fragmentation of existing solids; breaking of dendrite arms (crystal multiplication)
- Electromagnetic mixing and stirring
Nucleation during Melting
- Why does melting usually occur at Tm, even at high heating rates?
Most liquid metals wet their own solid, so the wetting angle Θ = 0  no energy barrier for nucleation
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10. Commercial Practice Characteristics of a good inoculant
- low interfacial energy, γSP, between nucleant and growing solid
- γSP decreases with decreasing lattice mismatch between solids and nucleant with increasing chemical affinity (coherent interface)
Should be as stable as possible in the liquid melt Tminoc > Tmmelt
possess a high surface area (rough or pitted)
Smaller particles
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11. Growth: Practical Results
Crystals grow in two ways after nucleating
Planar growth – heat extraction through the solid phase and a smooth solid/liquid interface
Dendritic growth – formation of branched skeleton structures.
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12. Reading Assignment Read Chapter 5 HW:
1. Calculate the volume change from fcc γ-iron to bcc α-iron. Hint: the atom radius is R, which does not change during phase transformation.
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