INFLUENCE OF FREEZING RATE OSCILLATIONS AND CONVECTION

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• 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

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Outline

• Background
• Experiments on MnBi-Bi showing influence of
  convection during solidification on MnBi fiber
  spacing l.
• Theory for influence of convection on l 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 l.
• Conclusions

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

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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.

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Convection lowers the compositional undercooling.
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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).
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Interfacial melt composition of fibrous eutectic
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(dU/dz)lo2/D
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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.

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Cross sections of MnBi/Bi eutectic solidified at
4.3 cm/hr a no current d 3s pulses of 40
A/cm2 with 6s period
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With current pulses, some grains exhibit
irregular microstructures or lack MnBi
completely. V2.1cm/hr, t4.5s, T18s, I40A/cm2
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X 1.1cm/hr ? ? 4.4cm/hr ? 2.1cm/hr ?
5.5cm/hr ? 2.1cm/hr. Different current pulsing
conditions.
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Rod spacing ? versus positive current density. ?
V1.1cm/hr, t0.25s, T2s () ? continuous ?
V2.1cm/hr, t0.75s, T6s () ? V2.1cm/hr,
t4.5s, T18s () ? continuous ? V4.3cm/hr,
t3s, T6s () ? continuous
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Average rod spacing ? for negative current
? V4.4cm/hr, t3s, T6s (-) ?
V5.5cm/hr, t3s, T6s (-)
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Area percent MnBi versus current density
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Rod roundness versus average ?. ? no current
? 40 A/cm2 contin ? 8A/cm2 X 40 A/cm2
? 72 A/cm2
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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.

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Steady-state example of phase-field modeling of
eutectic solidification
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Phase-field simulation of the evolution of a
lamellar microstructure caused by decreasing the
freezing rate (top to bottom).
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Phase-field simulation of the evolution of a
lamellar microstructure caused by increasing the
freezing rate (top to bottom).
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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.
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Result from entropy production model
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Entropy production predicts small change in l
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SUMMARY

• Literature shows convection increases l.
• Prior theory for steady state with eutectic
  composition in bulk and at freezing interface
  shows buoyancy-driven convection has negligible
  influence on l.
• Electric current pulsing decreases l .
• Models all predict that oscillatory freezing rate
  decreases l.
• 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.