The role of grain corners in nucleation
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The authors are grateful to Brent Blaha, Ruben Bons, and Adel Omrani for their assistance in verifying the calculations. This work was supported, in part, by the Microgravity Science and Applications Division, NASA, under Grant No. NAS8-37292.
D E h H
NOMENCLATURE solute concentration (wt pct H 2 0 ) solute concentration of inlet liquid (wt pct H20) solutal diffusion coefficient (cm2/s) dimensionless pressure gradient half-spacing between dendrites (cm) dendrite surface curvature (1/cm)
P
(dyne 1 pressure \-~-m2]
C
Co
Pe F Fbot ?'top
R
T u
U
u., V~ x
X Y Y
solntal Peclet number dendrite radius (cm) dendrite radius at Y = - 1 (cm) dendrite radius at Y = + 1 (cm) ideal gas constant (J/mol K) temperature (K) liquid velocity (cm/s) dimensionless liquid velocity mean liquid velocity (cm/s) molar volume of solid phase (cm3/mol) distance along dendrite arm (cm) dimensionless distance along dendrite arm (cm) distance perpendicular to dendrite arm (cm) dimensionless distance perpendicular to dendrite arm (cm) denotes liquid phase
7. R.T. DeHoff: Thermodynamics in Materials Science, McGraw-Hill, New York, NY, 1993. 8. M.H. McCay, J.A. Hopkins, and T.D. McCay: Metall. Mater. Trans. B, 1993, vol. 24B, pp. 669-75. 9. T.D. McCay, M.H. McCay, and J.A. Hopkins: J. Mater. Processing Manufacturing Sci., 1992, vol. 1 (3), pp. 315-30.
The Role of Grain Corners in Nucleation WEIMING HUANG and MATS HILLERT The driving force for the nucleation of a new phase in a binary alloy at a fixed undercooling depends on the compositions of the two phases. It increases rapidly with the composition difference between the two phases, m Thus, the driving force for an allotropic transformation is generally weak because the difference in composition is small. The austenite ~ ferrite transformation in Fe-C alloys is a typical example. Ferrite is almost 100 pct Fe and austenite is typically more than 95 pct Fe. Thus, homogeneous nucleation is not possible and only strong heterogeneities are active at reasonable degrees of undercooling. Since ferrite is almost pure Fe, the driving force for its nucleation in austenite can be estimated as AGe = RT In (avJa~
= R T In (xvJx~
~-- RT(xFo-X~
where xFo is the Fe content of the austenite matrix and X~ is the equilibrium Fe content of austenite in contact with ferrite. As shown by Clemm and Fisher,t2a grain comers may be very active nucleation sites and they may even give rise to nucleation without any nucleation barrier. Next comes grain edges and then grain faces. It is surprising that there have been very few attempts to test this prediction experimentally. An exception is a series of articles by Aaronson and
transport coefficient ( ~ -~) /x g;
dynamic viscosity (g/cm s) dimensionless concentration
REFERENCES 1. M.C. Flemings: Solidification Processing, McGraw-Hill, New York, NY, 1974. 2. M.H. McCay, J.A. Hopkins, and T.D. McCay: J. Cryst. Growth, 1994, vol. 144, pp. 346-52. 3. M.H. McCay, J.A. Hopkins, and T.D. McCay: Metall. Mater. Trans. A, 1995, vol. 26A, pp. 227-29. 4. F. White: Viscous
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