Solidification, Lecture 4

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

2. Three phase solidification Eutectic Peritectic Monotectic l α + β l + αβ l1α+l2 Ce

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

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

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. Al70Cu30 33% Coupled Zone Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

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

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

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

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

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

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. 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. Segregation Macrosegregation Scale: Casting Microsegregation Scale: Secondary dendrite arm spacing λ2 Reproduced from:M. C. Flemings Solidification Processing Mc Graw Hill, 1974

16. T l Cl Cs s C0 C k=Cs/Cl Solute redistribution • 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 • Dl~10-9 – 10-8 m2/s • Ds~ 10-13 – 10-12 m2/s

17. T l Cl Cs s C0 C k=Cs/Cl Complete equilibrium • Valid only in special cases, slow solidification, fast diffusion • Lever rule: • Solid with uniform composition C0 fl fs

18. T l Cl Cs s C0 C k=Cs/Cl 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

19. T l Cl Cs s C0 C k=Cs/Cl Limited solid diffusion, full liquid mixing • Back diffusion of solute into solid • Fourier number determines amount of diffusion • Diffusion distance for dendritic structures

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

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

22. T l C0 T0 ΔT* C0/k s Ce Microsegregation Freezing range, ΔT*, larger than equilibrium freezing range, ΔT0 Liquidus concentration Cl higher than C0/k, often reaches eutectic conc. Ce Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998 C

23. C0 660 577 1.65 11.7 Example Segregation in Al-1%Si How much eutectic? Assume full equilibrium. No eutectic

24. C0 660 577 1.65 11.7 Example Segregation in Al-1%Si How much eutectic? Assume no diff in solid, full mixing in liquid Assume straight lines k=Cs/Cl=1.65/11.7=0.14 Fraction eutectic, fe= fl=(1-fs)when Cl=Ce fe= 0.06

25. C0 660 577 1.65 11.7 Example Segregation in Al-1%Si How much eutectic? Assume some diffusion in solid Assume cooling rate 1K/s Assume λ2=60 μm Assume D=10-12m2/s m=dT/dCl=577-660/11.7=-7.1 Liquidus temperature, Tl=Tf+mC0=653C Freezing range, ΔT* : 653-577=76K tf= ΔT*/(dT/dt)=76s L= λ2/2=30μm α=0.08 fe=0.035

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. 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. 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, ΔT0 and liquidus concentrationCl to increase beyondC0/k, often up to Ce.

29. 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)