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NTNU
1
Solidification, Lecture 2
1
Nucleation
Homogeneous/heterogeneous
Grain refinement
Inoculation
Fragmentation
Columnar to equiaxed transition
Crystal morphology
Facetted – non-facetted growth
Growth anisotropy / growth mechanisms
Modification of Al-Si and cast iron
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Nucleation
Spontaneous formation of new crystals
Cluster formationHomogeneous nucleationNumber of clusters with radius r:
Gr cluster free energyn0 total number of atomsk Boltzmans constantT temperature
kTG
rrnn exp0
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Nucleation activation energy
Change in free energy solidification s/l interface
Spontaneous growthabove radius
Activtionenergy
€
G =4
3πr3Δg+ 4πr2σ
€
r* =2σ
Δs fΔT
€
G* =16πσ 3
3Δs f2 (ΔT)2
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Heterogeneous nucleation
Nucleation on solid substrateReduction of nucleation barrierWetting angle θ
)(hom fGGhet
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Conditions for efficient nucleation
• Small wetting angle, • Low surface energy between substrate and crystal• Good crystallographic match
Lattice match betweenAl and AlB2
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Tg
Tn
T
Nucleation and growth in a pure metal
Undercooling ahead of solidification front is needed for nucleation of new grains.
Can be achieved by alloying.
Nucleation
Growth
Recallescence
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Conditions for grain refinement
•Substrate particles
•Potent
•Large number
•Well dispersed
•Undercooling
•Constitutional
•Growth restriction
•Strongly segregatingalloying elements
A pure metal can not be efficiently grain refined!
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Growth restriction in aluminium
10 kmCQ
Element m(k-1) max C0 (wt%)
Ti 246 0.15Si 6.1 12Mg 3.0 35Fe 2.9 1.8Cu 2.8 33Mn 0.1 1.9
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Aluminium grain refiner master alloys
Typical composition: Al-5%Ti-1%BFormation of insoluble TiB2
Ti/B ratio in TiB2 : 2.2/1
Small TiB2
1-3 m
Large TiAl3
10-50 m
50 m
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Grain refinement of aluminium
X-ray video of Al-20%Cu
Al-5%Ti-1%B type grain refinerAddition 1g / kg melt
Growth from top
Dendrite coherency – network formation
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0
0.2
0.4
0.6
0.8
1
0 2 4 6 8
T fo
r G
rain
Initi
atio
n (K
)
Particle Diameter (m)
Substrate particle size, d
Too small particles will need high underecooling T
for
Gra
in In
itia
tion
€
d =4σ
Δs fΔT
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Dendrite fragmentation
X-ray video of Al-20wt%Cu
Growth of collumnar front
Dendrite fragment by melting
Formation of new grain
New front established
New fragments melt
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Columnar-to-equiaxed transition;dendrite fragmentation
• Fragmentation mechanism– Mechanical fracture– Melting
• Transport of fragments out of mushy zone– Gravity/buoyancy– Convection - stirring
• Survival and growth of dendrite fragments– Low temperature gradients– Constitutional undercooling
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Growth
Controlling phenomenon Importance Driving force
Diffusion of heat Pure metals ΔTt
Diffusion of solute Alloys ΔTc
Curvature Nucleation ΔTr
DendritesEutectics
Interface kintetics Facetted crystals ΔTk
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Interface morphology
• Facetted• Atomically smooth• =sf /R>2 • Non-metals•Intermetallic phases
• Non-facetted• Atomically rough• =sf/R<2• metals
Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998
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Facetted crystals
• Atomically smooth interface• Large entropy of fusion• Growth by nucleation of new atomic layers
• Large kinetic growth undercooling, ΔTk
• Large growth anisotropy
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Growth anisotropy
Cubic crystal bounded by (111) planesGrowth of (100)
Bounded by (110) planesGrowth of (100)
•Fastest growing planes disappear
•Crystals bounded by slow growing planes
Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998
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Growth mechanisms
Screwdislocation
Twinning
Twinning or dislocation: Nucleation of new planes not necessary
Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998
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Growth rate
Reproduced from:M. C. FlemingsSolidification ProcessingMc Graw Hill, 1974
€
V =K1ΔTk
€
V =K2(ΔTk )2
€
V =K3 exp(−K4
ΔTk)
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Modification of growth mechanismEutectic silicon crystals in Al-Si
100 ppm Sr
Transition from coarse lamellarto fine fibrous eutectic
Improves ductility
Addition of small amounts(100 ppm) of Na, Sr, (Ca, Sb)
Increases porosity
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Modification and growth undercooling
Eutectic growthtemperaturedecreases about10 K.
Fading due tooxidation ofmodifier. Faster fadingwith Na than Sr
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Modification of graphite in cast iron
Small additions of Mg and FeSi to cast iron changes morphologyof facetted graphite from flakey to nodular
Effect of both nucleation and growth mechanism
Grey cast iron Ductile iron
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Summary / conclusions
• Spontaneous formation of solid clusters. Homogeneous nucleation• Energy barrier due to s/l interface large at small crystal sizes. Needs
undercooling• Heterogeneous nucleation on solid substrate. Lower activation energy
– lower undercooling• Low wetting angle – potent substrate for nucleation – good
crystallographic match between substrate / growing crystal• Undercooling ahead of growing front necessary for nucleation of new
equiaxed grains. Provided by strongly segregating alloying elements• Efficient grain refinement can be achieved in aluminium alloys by
inoculation of substrate particles, TiB2 and Ti for growth restriction
• Substrate particles must not be too small. That will give large undercooling.
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Summary / conclusions
• Columnar to equiaxed transition – grain refinement can be achieved by fragmentation of columnar dendrites. Provided by convection. Transport out of M.Z and survival in undercooled melt at low temperature gradient.
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Summary / conclusions
• Metals have low entropies of fusion and grow in a non-facetted way with an atomically rough interface
• Non-metals and intermetallic compounds have normally high fusion entropies and grow in a facetted way with a smoth interface.
• Growth of facetted crystals occurs by successive nucleation of new atom planes at high kinetic undercooling
• Facetted crystals show large growth anisotropy. Fast growing planes disappear while slowest growing planes bounds the crystals
• Facetted crystals often provide nucleation sites for new atom planes at twin boundaries or screw dislocations
• Growth rate of non-facetted crystals is proportional to kinetic undercooling. Dislocation growth shows a parabolic law and growth by two-dimensional nucleation an exponential growth law