Short Course on solidification at IISc
October – November 2012
Lars Arnberg, NTNU
1. Introduction – basic concepts
29/10
1. Nucleation - grain refinement
Crystal morphology
31/10
3. Interface stability
Cells and dendrites
5/11
4. Three phase solidification
Segregation
7/11
NTNU
1
Solidification, Lecture 1
NTNU
Introduction / Basic concepts
Simple heat flow during solidification
Mushy Zone
Columnar / equiaxed solidification
Curvature effects
Phase diagrams – solute redistribution
2
Microstructure
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Solidification of metals is a crystallisation process
Microstructure development
Depends on
Microstructure
Composition (constitution)
Concentration, C
Phase diagram, k, m
Casting conditions
Growth rate, V
Temperature gradient, G
Cooling rate, G*V
Crystal types, phases
Crystal morphology
Crystal size
Chemical composition
3
Microstructure
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Increasing concentration
Increasing constitutional
undercooling (Tc)
Increasing morphological
instability
Increasing cooling rate (G*V)
Structure refinement
4
Heat flow
NTNU
A
dT
dfs
q  c
 H
v
dt
dt
dT
A dfs H
 q 
dt
vc dt c

Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
5
Mushy zone
NTNU
Alloys will solidify over a
temperature Interval, ΔTf
M. Z. is where solidification
occurs
Depending on freezing
range and temp gradient
a
a
Tf
G
6
Controlled solidification
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a: Bridgman furnace
Independent control of G & V.
G & V constant
b: Directional chill casting
G & V time dependant
dT/dt = GV
s=Kt1/2
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
7
Growth modes
morphology & temperature distribution
Directional
Growth of
columnar
crystals
NTNU
Free growth
of equiaxed
crystals
Pure metal
Alloy
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
Positive G
Negative G
8
Structure of castings
NTNU
9
Capillary effects; solid/liquid interface
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• Undercooling
T  K
• Curvature
2/r for
sphere
dA
K=
dV
• Gibbs Thomson
~ 10-7 Km


s f

Solidification microstructures
given by competition between:
•Curvature : tends to maximise scale
•Diffusion: tends to minimise scale
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
10
Phase digram, solute redistribution
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• Eutectic phase diagram
T
l
C0
Tl
T0
Ts
s
Cs C0
• Lower solubility
of alloying elements
in s than in l
• k=Cs/Cl<1 (distribution
coefficient)
Cl
• m= dTl/dC<0
C
• k and m constants if solidus
& liquidus lines are straight
C0 (1 k)
T0  mC0  m
k
11
Al-Fe
Al-Mg
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Al-Si
Al-Mn
Eutectic Al
phase diagrams
for important
alloying
elements
12
Al-Fe
k=0.03
Al-Mn
k=0.90
AlMg
k=0.44
Al-Si
k=0.14
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Al phase
diagrams with
different
partition
coefficients
k=Cs/Cl
13
Summary/ Conclusions
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• 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)
14
Summary/ Conclusions
NTNU
• 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.
15
Symbols
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C: concentration
k: distribution coefficient k=Cs/Cl
m: liquidus slope, dT/dC
V: growth rate m/s
T: temperature: K
ΔT: undercooling, K
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, K
G: temperature gradient, dT/dx K/m
Δsf: entropy of fusion, J/(m3K)
σ: solid/liquid interface energy, J/m2
Cl: liquid concentration
Cs: solid concentration
C0: Initial alloy concentration
16