INFLUENCE OF FREEZING RATE OSCILLATIONS AND CONVECTION

ON EUTECTIC MICROSTRUCTURELiya 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

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

T above melting point

T below melting point

Insulated or linear T

melt

solid

V

Bridgman-Stockbarger Technique

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.

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.

Undercooling in eutectic solidification

compositional undercooling

total undercooling

curvature undercooling

Convection lowers the compositional undercooling.

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).

Interfacial melt composition of fibrous eutectic

= (dU/dz)o2/D

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.

DC CurrentSource

Mo wire

Mo wire

Melt

Interface

Solid

Graphite electrode

Fused part

Fused part

Growth ampoule used in the current pulsing experiments

10m[d]10m[a]

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

15m[d]

With current pulses, some grains exhibit irregular microstructures or lack MnBi completely.V=2.1cm/hr, t=4.5s, T=18s, I=40A/cm2

X 1.1cm/hr; 4.4cm/hr; 2.1cm/hr; 5.5cm/hr;

2.1cm/hr. Different current pulsing conditions.

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80

Current density (A/cm2)

Pe

rce

nt

of

qu

as

i-re

gu

lar

mic

ros

tru

ctu

re

1

2

3

4

5

6

7

8

0 20 40 60 80

Current density (A/cm2)

(

m)

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

1.5

2

2.5

3

3.5

0 20 40 60 80

current density(A/cm2)

(

m)

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

: V=5.5cm/hr, t=3s, T=6s (-)

%MnBi = 3.5 + 0.02 I

r2 = 0.47

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

0 10 20 30 40 50 60 70 80

Current density (A/cm2)

Mn

Bi

per

cen

t

Area percent MnBi versus current density

Rod roundness versus average .: no current : 40 A/cm2 contin : 8A/cm2 X: 40 A/cm2 : 72 A/cm2

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1 2 3 4 5 6 7 8

Average (m)

Ro

d r

ou

nd

nes

s

round = 0.90 - 0.035 r2 = 0.75

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.

0.1 1 10 100 1000 100000

2

4

6

8

numerical solution

= 10-3 cm

Frequency of oscillations, , rad/s

Am

plit

ud

e o

f o

scill

atio

ns,

C(1) , 1

0-4 a

t.fr

ac

C

C

0.0

0.2

0.4

0.6

0.8

Ph

ase lag, , rad

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

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

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

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.

2 4 6

0.8

0.9

1.0

1.1

No lead distance With the effect of lead distance

En

tro

py

pro

du

cti

on

rate

, 10-8 J

/K/c

m3 /s

Eutectic spacing , 10-3 cm

Result from entropy production model

0.0 0.2 0.4 0.6 0.8 1.0

0.85

0.90

0.95

1.00

Phase lag =0 (low frequency)

Phase lag =/4 (high frequency)

No

rmal

ized

sp

acin

g / S

S

Dimensionless freezing rate amplitude

Entropy production predicts small change in

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.