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Nucleation
Spontaneous formation of new
crystals
Cluster formation
Homogeneous nucleation
Number of clusters with radius r:
Gr cluster free energy
n0 total number of atoms
k Boltzmans constant
T temperature
kT
G
r
r
n
n
exp
0
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Conditions for efficient nucleation
• Small wetting angle,
• Low surface energy between substrate and crystal
• Good crystallographic match
Lattice match between
Al 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 segregating
alloying elements
A pure metal can not be efficiently grain refined!
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Growth restriction in aluminium
1
0
k
mC
Q
Element m(k-1) max C0 (wt%)
Ti 246 0.15
Si 6.1 12
Mg 3.0 35
Fe 2.9 1.8
Cu 2.8 33
Mn 0.1 1.9
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Aluminium grain refiner master alloys
Typical composition: Al-5%Ti-1%B
Formation 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 refiner
Addition 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
for
Grain
Initiation
(K)
Particle Diameter (m)
Substrate particle size, d
Too small particles will
need high
underecooling
T
for
Grain
Initiation
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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
Dendrites
Eutectics
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 Solidification
Trans 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) planes
Growth of (100)
Bounded by (110) planes
Growth of (100)
•Fastest growing planes disappear
•Crystals bounded by slow growing planes
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
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Modification of growth mechanism
Eutectic silicon crystals in Al-Si
100 ppm Sr
Transition from coarse lamellar
to 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 growth
temperature
decreases about
10 K.
Fading due to
oxidation of
modifier.
Faster fading
with Na than Sr
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Modification of graphite in cast iron
Small additions of Mg and FeSi to cast iron changes morphology
of 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
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Summary / conclusions
• Growth mechanisms in facetted crystals can be very sensitive to
impurities. Can be utilised for modification of morphology, Examples
are modification of Si in Al-Si by Na or Sr and modification of graphite
in cast iron eutectics by Mg.
