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NTNU
Short Course on solidification at IISc October – November 2012Lars Arnberg, NTNU
1. Introduction – basic concepts 29/10
1. Nucleation - grain refinement 31/10
Crystal morphology
3. Interface stability 5/11
Cells and dendrites
4. Three phase solidification 7/11
Segregation
1
NTNUSolidification, Lecture 1
Introduction / Basic concepts
Simple heat flow during solidification
Mushy Zone
Columnar / equiaxed solidification
Curvature effects
Phase diagrams – solute redistribution
2
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Microstructure
Solidification of metals is a crystallisation process
Microstructure development Microstructure
Crystal types, phasesCrystal morphologyCrystal sizeChemical composition
Depends on
Composition (constitution)Concentration, CPhase diagram, k, m
Casting conditionsGrowth rate, VTemperature gradient, GCooling rate, G*V
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Microstructure
Increasing concentration
Increasing constitutionalundercooling (Tc)
Increasing morphologicalinstability
Increasing cooling rate (G*V)
Structure refinement
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Heat flow
Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998
€
qA
v= −c
dT
dt+ ΔH
dfs
dt
€
dT
dt= −q
A
vc+
dfs
dt
ΔH
c
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Mushy zone
a
Alloys will solidify over a temperature Interval, ΔTf
M. Z. is where solidificationoccurs
Depending on freezing range and temp gradient
€
a =ΔTf
G
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Controlled solidification
a: Bridgman furnaceIndependent control of G & V. G & V constant
b: Directional chill castingG & V time dependant
dT/dt = GV
s=Kt1/2
Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998
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Growth modesmorphology & temperature distribution
Directional Growth of columnarcrystals
Free growthof equiaxedcrystals
Positive G Negative G
Pure metal
Alloy
Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998
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Structure of castings
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Capillary effects; solid/liquid interface
• Undercooling
• Curvature
2/r for sphere
• Gibbs Thomson
~ 10-7 Km
dAK
dV=
Solidification microstructuresgiven by competition between:
•Curvature : tends to maximise scale
•Diffusion: tends to minimise scale
Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998
€
T = KΓ
€
Γ=σs f
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Phase digram, solute redistribution
Cs C0
T0
C0l
s
T
Cl
Tl
Ts
• Eutectic phase diagram
• Lower solubility of alloying elements in s than in l
• k=Cs/Cl<1 (distribution coefficient)
• m= dTl/dC<0
• k and m constants if solidus & liquidus lines are straight
C
€
T0 = −mΔC0 = −mC0(1 − k)
k
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Al-Fe Al-Mg
Al-MnAl-Si
Eutectic Alphase diagramsfor importantalloyingelements
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Al-Fek=0.03
AlMgk=0.44
Al-Mnk=0.90
Al-Sik=0.14
Al phasediagrams withdifferentpartitioncoefficients
k=Cs/Cl
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Summary/ Conclusions
• Solidification is accomplished by external cooling of a melt. Needed for decreasing the temperature and removing latent heat of fusion
• Metals solidify at a distinct freezing point, alloys have a solidification interval (freezing range)
• Solidification microstructure will depend on both composition, (C0) constitution (k, m) and process (G, V)
• Control of V and G will differ between casting processes• Solidification will occur in mushy zone. Extent of MZ will depend on
temperature gradient and freezing range• Crystal may grow directionally as columnar grains (G>0) or freely from
an undercooled melt as equiaxed grains (G<0)
• Creation of s/l interface will require undercooling. ΔTr will increase with increased curvature (small crystal radii)
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Summary/ Conclusions
• Scale of solidification microstructure will be determined by diffusion (decreasing) and curvature (increasing)
• Solidification of alloys means redistribution of solute between s and l. Determined by distribution coefficient, k.
NTNUSymbols
C: concentration G: temperature gradient, dT/dx K/m
k: distribution coefficient k=Cs/Cl Δsf: entropy of fusion, J/(m3K)
m: liquidus slope, dT/dC σ: solid/liquid interface energy, J/m2
V: growth rate m/s Cl: liquid concentration
T: temperature: K Cs: solid concentration
ΔT: undercooling, K C0: Initial alloy concentration
q: heat flux W/m2
A: area m2
V: volume m3
t: time, s
ΔH: heat of fusion J/m3
c: heat capacity: J/(m3K)
fs: fraction solid
ΔTf: freezing range, K16