1. INFLUENCE OF FREEZING RATE OSCILLATIONS AND CONVECTION ON EUTECTIC MICROSTRUCTURE Liya L. Regel, William R. Wilcox, Dimitri Popov, Fengcui Li International Center for Gravity Materials Science and Applications, Clarkson University, Potsdam, New York Paper IAA-99-IAA.12.1.07, International Astronautical Congress Amsterdam, October 1999

2. Outline Background –Experiments on MnBi-Bi showing influence of convection during solidification on MnBi fiber spacing. –Theory for influence of convection on via change in composition of the melt at the freezing interface Application of electric current pulses during solidification of MnBi-Bi eutectic. Theory for influence of an oscillatory freezing rate on  Conclusions

4. T above melting point T below melting point Insulated or linear  T melt solid V Bridgman-Stockbarger Technique

5. Prior experimental results on MnBi shown on following slides. Larson & Pirich: Microgravity and magnetic field lower MnBi fiber spacing by same amount. Mustafa and Smith: Microgravity has no effect on fiber spacing. Eisa and Wilcox: ACRT stirring increases fiber spacing.

9. Prior Theory at Clarkson Convection causes the interfacial melt composition to deviate less from the eutectic for given. This increases for minimum undercooling. Negligible, however, for buoyancy-driven convection Negligible difference if include Soret effect, fibers versus lamellae, one phase leading the other.

10. Convection lowers the compositional undercooling.

11. The following slide shows the results of Caram and Wilcox for the influence of convection on the composition at the freezing interface with rod growth of a eutectic. On the left is the composition field without convection for a rectangular area that intersects 4 rods. On the right is the same area with melt flow in the x direction. The next slide shows the increase in rod spacing (vertical scale) with increasing melt velocity (horizontal scale).

12. Interfacial melt composition of fibrous eutectic

13. = (dU/dz) o 2 /D

14. Possible Explanations for experiments The bulk melt is not at the eutectic composition, greatly increasing sensitivity to convection. The average interfacial composition is not at the eutectic because the material does not freeze with minimum undercooling (“extremum”). The freezing rate fluctuates, with different kinetics for fiber termination and nucleation. A habit-modifying impurity is present. Convection changes its concentration at the growth interface.

15. DC Current Source Mo wire Melt Interface Solid Graphite electrode Fused part Growth ampoule used in the current pulsing experiments

16. 10  m [d] 10  m [a] Cross sections of MnBi/Bi eutectic solidified at 4.3 cm/hr: [a] no current [d] 3s pulses of 40 A/cm 2 with 6s period

17. 15  m [d] With current pulses, some grains exhibit irregular microstructures or lack MnBi completely. V=2.1cm/hr, t=4.5s, T=18s, I=40A/cm 2

18. X 1.1cm/hr;   4.4cm/hr;  2.1cm/hr;  5.5cm/hr; 2.1cm/hr. Different current pulsing conditions.

19. Rod spacing versus positive current density. : V=1.1cm/hr, t=0.25s, T=2s (+);  continuous  : V=2.1cm/hr, t=0.75s, T=6s (+); : V=2.1cm/hr, t=4.5s, T=18s (+);  continuous  : V=4.3cm/hr, t=3s, T=6s (+);  continuous

20. Average rod spacing for negative current  : V=4.4cm/hr, t=3s, T=6s (-)  : V=5.5cm/hr, t=3s, T=6s (-)

21. Area percent MnBi versus current density

22. Rod roundness versus average.  : no current  : 40 A/cm 2 contin  : 8A/cm 2 X: 40 A/cm 2  : 72 A/cm 2

23. Theories for Oscillatory Freezing Rate All with no convection in the melt. Sharp interface model (no interface curvature) - Specified freezing rate oscillations - One phase leading the other - Nucleation when supersaturation sufficient Minimum entropy production model Phase field model - Curvature, nucleation, termination all occur naturally.

29. Steady-state example of phase-field modeling of eutectic solidification

30. Phase-field simulation of the evolution of a lamellar microstructure caused by decreasing the freezing rate (top to bottom).

31. Phase-field simulation of the evolution of a lamellar microstructure caused by increasing the freezing rate (top to bottom).

32. Evolution of the interface shape when the freezing rate oscillates with insufficient amplitude to nucleate or terminate lamellae. Note that the angles at which the phases meet at the tri-junctions remain constant while the volume fractions of the two phases change slightly. Here (d) corresponds to the maximum freezing rate and (g) the minimum freezing rate.

33. Result from entropy production model

34. Entropy production predicts small change in

35. SUMMARY Literature shows convection increases. Prior theory for steady state with eutectic composition in bulk and at freezing interface shows buoyancy-driven convection has negligible influence on. Electric current pulsing decreases. Models all predict that oscillatory freezing rate decreases  Sharp interface and phase-field models predict that an oscillatory freezing rate causes the average interfacial composition to deviate from the eutectic and for the region of perturbed concentration to extend much farther into the melt.