ntnu 1 solidification, lecture 2 1 nucleation homogeneous/heterogeneous grain refinement inoculation...

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Solidification, Lecture 2

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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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Nucleation

Undercoooling

Rate

€

N = Aexp(−B

(ΔT)2 )

€

r* =2σ

Δs fΔT kT

Gr

rnn exp0

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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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Nucleation on AlB2 substrate particles, inoculation

AlB2

AlB2 addition

No addition

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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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Industrial grain refinement practice

Alcoa

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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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Electromagnetic stirring of steel

Stirring gives larger fraction of equiaxed grains

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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


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Growth anisotropy

Anisotropy increases with α

€

V =K(hkl )ΔTk

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Growth mechanisms

Screwdislocation

Twinning

Twinning or dislocation: Nucleation of new planes not necessary


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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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Mechanism of modification

Atoms of modifiercauses growth branching

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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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• 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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• 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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• 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.

ntnu 1 solidification, lecture 2 1 nucleation homogeneous/heterogeneous grain refinement inoculation...

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