1. Solidification, Lecture 2
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 1

2. 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

3. Nucleation activation energy
Change in free energy
solidification s/l interface
Spontaneous growth
above radius
Activtion
energy

4. Nucleation
Rate
Undercoooling

5. Heterogeneous nucleation
Nucleation on solid substrate
Reduction of nucleation barrier
Wetting angle θ

6. Conditions for efficient nucleation
Small wetting angle, 
Low surface energy between substrate and crystal
Good crystallographic match
Lattice match between
Al and AlB2

7. Nucleation on AlB2 substrate particles, inoculation
AlB2 addition
No addition

8. Nucleation and growth in a pure metal
Undercooling ahead of solidification front is needed for nucleation of new grains.
Can be achieved by alloying.
Recallescence Tg
Growth
Nucleation Tn

9. 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!

10. Growth restriction in aluminium
Element m(k-1) max C0 (wt%) Ti Si Mg Fe Cu Mn

11. Aluminium grain refiner master alloys
Typical composition: Al-5%Ti-1%B
Formation of insoluble TiB2
Ti/B ratio in TiB2 : 2.2/1
Large TiAl3
10-50 m
Small TiB2
1-3 m
50 m

12. 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

13. Substrate particle size, d
Too small particles will need high underecooling
T for Grain Initiation

14. Industrial grain refinement practice
Alcoa

15. 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

16. 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

17. Electromagnetic stirring of steel
Stirring gives larger fraction of equiaxed grains

18. 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

19. 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

20. Facetted crystals Atomically smooth interface Large entropy of fusion
Growth by nucleation of new atomic layers
Large kinetic growth undercooling, ΔTk
Large growth anisotropy

21. Growth anisotropy Fastest growing planes disappear
Cubic crystal bounded by (111) planes
Growth of (100)
Bounded by (110) planes
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
Fastest growing planes disappear
Crystals bounded by slow growing planes

22. Growth anisotropy
Anisotropy increases with α

23. Growth mechanisms Twinning or dislocation:
Nucleation of new planes not necessary
Screw
dislocation
Twinning
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998

24. Growth rate Reproduced from:M. C. Flemings Solidification Processing
Mc Graw Hill, 1974

25. Modification of growth mechanism
Eutectic silicon crystals in Al-Si
Transition from coarse lamellar
to fine fibrous eutectic
Improves ductility
Addition of small amounts
(100 ppm) of Na, Sr, (Ca, Sb)
Increases porosity
100 ppm Sr

26. Mechanism of modification
Atoms of modifier
causes growth branching

27. Modification and growth undercooling
Eutectic growth
temperature
decreases about
10 K.
Fading due to
oxidation of
modifier.
Faster fading
with Na than Sr

28. 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

29. 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.

30. 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.

31. 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

32. 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.