Jeff McFadden, NIST

1
Modeling of Flow during Coupled Monotectic Growth

• Jeff McFadden, NIST
• Sam Coriell, NIST
• Bill Mitchell, NIST
• Bruce Murray, SUNY Binghamton
• Barry Andrews, U. Alabama, Birmingham
• J. Arikawa, U. Alabama, Birmingham

NASA Physical Sciences Research Division
2
Rod Monotectic Growth

• Lamellar Eutectic Growth

Al-In Grugel Hellawell (1981)
Hunt Lu (1994)
Want better prediction of lamella and rod
spacings (monotectics)
3
Monotectic Flow Models
Flow
z
z
z
r
r
r
Circular Cap Model
Basic Domain
Density Change
Marangoni Flow
U V
Umgtgt V
Inter-rod Spacing
l
4

• Jackson-Hunt Theory (1966)

Analytical Model
5

• Seetharaman and Trevedi (1988)

(But the predicted spacing is 4 to 5 times too
small for some monotectics)
6

• Density-Change Flow

Modified Jackson-Hunt Theory
Still separable, but no lateral transport
Magnin Trivedi Acta Met. (1991), Coriell et
al. JCG (1997)
7

• Inclusion of Lateral Transport

8

• Stokes Flow (Sn-Pb)

9

• Tangential Velocity Component (Sn-Pb)

10

• Eutectic Lamellar Spacing (Sn-Pb)

Num
MJH
JH
(Predicted spacing consistent with experiment)
11

• Euctectic Lamellar Spacing (Fe-C)

JH
Num
MJH
(Predicted spacing is 5 X too small)
12

• Interface Concentration (Fe-C)

Numerical
Modified Jackson-Hunt
13

• Monotectic Rod Spacing (Al-In)

MJH
Num
JH
(Predicted spacing is 4 X too small)
14

• Rod Growth (Al-In)

Monotectic composition 2.0 mass
Monotectic composition
15

• Summary

• Relative to the Modified Jackson-Hunt theory
• Lateral flow increases spacing for Sn-Pb, Al-In
  (augments diffusion)
• Lateral flow decreases spacing for Fe-C (opposes
  diffusion)
• Predicted spacings are still too small for
  monotectics

Current Work
Linear stability of a planar fluid-fluid phase
boundary in directional solidification
(monotectic L1 L2 transition) Account for
bouyancy, density change, Marangoni flow

• Laplace-Young equation
• Gibbs-Thomson equation
• Classius-Clapyron equation