1. NTNU 1 Solidification, Lecture 4 Three phase solidification Eutectic growth Types of eutectics Peritectic growth Segregation Macro / microsegregation Lever rule /Scheil segregation

2. NTNU 2 Eutectic Peritectic Monotectic l α + β l + α β l 1 α+l 2 Three phase solidification CeCe

3. NTNU 3 Eutectic solidification Fibrous Lamellar Regular Irregular Al-Mg Al-Si Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

4. NTNU 4 Eutectic growth Simultaneous, cooperative growth of 2 or more phases Diffusion parallel to growth front Isothermal growth front Characteristic lamellar spacing, determined by diffusion and curvature Growth direction

5. NTNU 5 Irregular eutectics One or both phases grows facetted Non isothermal growth Grows at high undercooling Al-Si

6. NTNU 6 Interface instabilities of eutectics Off-eutectic Composition 3:rd element Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

7. NTNU 7 Al 70 Cu 30 33% Coupled Zone Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

8. NTNU 8 Off eutectic growth 1 Al-30%Cu Low temperature gradient, high growth rate Dendrites + eutectic

9. NTNU 9 Off eutectic growth 2 Al-30%Cu High temperature gradient, low growth rate Coupled eutectic

10. NTNU 10 Off eutectic growth 3 Al-30%Cu High temperature gradient, high growth rate Cellular eutectic

11. NTNU 11 Decoupled, divorced eutectic Major phase grows on existing dendrites. Small amount of eutectic No cooperative growth Al-5Cu

12. NTNU 12 Ternary & higher eutectics Cooperative growth of 3 or more phases Chinese script Al-Mg-Si

13. NTNU 13 Peritectic solidification Primary: l→α Peritectic: l + α →β Eutectic: l → β+γ Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1991

14. NTNU 14 Peritectic solidification l + α →β Occurs at l/α interface Layer of β envelops α Further transformation requires solid state diffusion through β Seldom to completion α β

15. NTNU 15 Segregation Macrosegregation Scale: Casting Microsegregation Scale: Secondary dendrite arm spacing λ 2 Reproduced from:M. C. Flemings Solidification Processing Mc Graw Hill, 1974

16. NTNU 16 Solute redistribution l s T CC0C0 ClCl CsCs k=C s /C l Redistribution of solute since liquid- and solid solubility are different. Liquid enriched in solute (eutectic) Liquidus temperature decreases. Equilibrium at s/l front but not always in the solid or liquid due to slow diffusion D l ~10 -9 – 10 -8 m 2 /s D s ~ 10 -13 – 10 -12 m 2 /s

17. NTNU 17 Complete equilibrium Valid only in special cases, slow solidification, fast diffusion Lever rule: Solid with uniform composition C 0 l s T CC0C0 ClCl CsCs k=C s /C l flfl fsfs

18. NTNU 18 No solid diffusion, complete mixing in liquid Reasonable assumption: slow diff. in solid, faster diffusion, small diffusion distances, and convection in liquid. Gulliver-Scheil equation Reasonable predictions in most cases l s T CC0C0 ClCl CsCs k=C s /C l

19. NTNU 19 Limited solid diffusion, full liquid mixing Back diffusion of solute into solid Fourier number determines amount of diffusion Diffusion distance for dendritic structures l s T CC0C0 ClCl CsCs k=C s /C l

20. NTNU 20 Segregation with back diffusion Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

21. NTNU 21 Freezing point during segregation Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

22. NTNU 22 Microsegregation C T0T0 C0C0 l s T C 0 /k ΔT*ΔT* CeCe Freezing range, ΔT *, larger than equilibrium freezing range, ΔT 0 Liquidus concentration C l higher than C 0 /k, often reaches eutectic conc. C e Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

23. NTNU 23 Example Segregation in Al-1%Si How much eutectic? Assume full equilibrium. No eutectic 11.7 660 1.65 577 C0C0

24. NTNU 24 Example Segregation in Al-1%Si How much eutectic? Assume no diff in solid, full mixing in liquid Assume straight lines k=C s /C l =1.65/11.7=0.14 Fraction eutectic, f e = f l =(1-f s )when C l =C e f e = 0.06 11.7 660 1.65 577 C0C0

25. NTNU 25 How much eutectic? Assume some diffusion in solid Assume cooling rate 1K/s Assume λ 2 =60 μm Assume D=10 -12 m 2 /s m=dT/dC l =577-660/11.7=-7.1 Liquidus temperature, T l =T f +mC 0 =653C Freezing range, ΔT* : 653-577=76K t f = ΔT* /(dT/dt)=76s L= λ 2 /2=30μm α=0.08 f e =0.035 Example Segregation in Al-1%Si 11.7 660 1.65 577 C0C0

26. NTNU 26 Summary/ Conclusions Eutectic structures can be regular/irregular, depending on facetted or non-facetted growth. Eutectic structures can be lamellar or fibrous, depending on relative amounts of the phases. Eutectic grows with phases side by side in a coupled way with diffusion parallel to the front. The front is macroscopically flat and isothermal. Eutectics are characterized by a lamellar spacing, λ, which is controlled by diffusion and curvature and is a function of growth rate. Irregular eutectics grow at a higher undercooling and a non-isothermal front. Alloys with off-eutectic compositions can grow in a coupled way depending on temperature gradient and growth rate Small amounts of residual eutectics often solidify in a decoupled, “divorced” way

27. NTNU 27 Summary / Conclusions Peritectic reactions, l + α →β, occur at the interface between α and the melt. This means that α becomes isolated and further reaction can only occur by solid state diffusion through β which is a slow process.

28. NTNU 28 Summary/ Conclusions Redistribution of solute since liquid- and solid solubility are different leads to segregation. Microsegregation occurs as concentration variations on a scale of the secondary dendrite arm spacing Equilibrium solidification only occurs in special cases, fast solid diffusion, slow cooling. Assumption of no solid diffusion, complete mixing in liquid often realistic assumption Fourier number used to assess degree of back diffusion into solid during solidification Non-equilibrium segregation causes freezing range, ΔT* to be larger than equilibrium freezing range, ΔT 0 and liquidus concentrationC l to increase beyondC 0 /k, often up to C e.

29. NTNU Lars Arnberg Dept of Materials Science and Engineering Norwegian University of Science and Technology 7491 Trondheim, Norway arnberg@ntnu.no Tel: +47 930 03 212 (India: 948 2965 476) 29