Solidification, Lecture 2

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 AlB2 addition No addition

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

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 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

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 Cubic crystal bounded by (111) planes Growth of (100) Bounded by (110) planes Growth of (100) 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. Screw dislocation Twinning Growth mechanisms Twinning or dislocation: Nucleation of new planes not necessary 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.