Modeling of Flow during Coupled Monotectic Growth Jeff

Modeling of Flow during Coupled Monotectic Growth Jeff Mc. Fadden, 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

Lamellar Eutectic Growth Rod Monotectic Growth Al-In [Grugel & Hellawell (1981)] [Hunt & Lu (1994)] Want better prediction of lamella and rod spacings (monotectics)

Monotectic Flow Models z Flow z z r r r Basic Domain Circular Cap Model Density Change Marangoni Flow U~V L 2 Um>> V S L 2 l Inter-rod Spacing S

Jackson-Hunt Theory (1966) Analytical Model:

Seetharaman and Trevedi (1988) (But the predicted spacing is 4 to 5 times too small for some monotectics)

Density-Change Flow Modified Jackson-Hunt Theory [Still separable, but no lateral transport…] Magnin & Trivedi [Acta Met. (1991)], Coriell et al. [JCG (1997)]

Inclusion of Lateral Transport

Stokes Flow (Sn-Pb)

Tangential Velocity Component (Sn-Pb)

Eutectic Lamellar Spacing (Sn-Pb) Num MJH JH (Predicted spacing consistent with experiment)

Euctectic Lamellar Spacing (Fe-C) JH Num MJH (Predicted spacing is 5 X too small)

Interface Concentration (Fe-C) Numerical Modified Jackson-Hunt

Monotectic Rod Spacing (Al-In) MJH Num JH (Predicted spacing is 4 X too small)

Rod Growth (Al-In) Monotectic composition + 2. 0 mass% Monotectic composition

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 L 1 – L 2 transition) Account for bouyancy, density change, Marangoni flow • Laplace-Young equation • Gibbs-Thomson equation • Classius-Clapyron equation