Eutectic colony formation: A phase field study

Eutectic two-phase cells, also known as eutectic colonies, are commonly observed during the solidification of ternary alloys when the composition is close to a binary eutectic valley. In analogy with the solidification cells formed in dilute binary alloys, colony formation is triggered by a morphological instability of a macroscopically planar eutectic solidification front due to the rejection by both solid phases of a ternary impurity that diffuses in the liquid. Here we develop a phase-field model of a binary eutectic with a dilute ternary impurity and we investigate by dynamical simulations both the initial linear regime of this instability, and the subsequent highly nonlinear evolution of the interface that leads to fully developed two-phase cells with a spacing much larger than the lamellar spacing. We find a good overall agreement with our recent linear stability analysis [M. Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a destabilization of the front by long-wavelength modes that may be stationary or oscillatory. A fine comparison, however, reveals that the assumption commonly attributed to Cahn that lamella grow perpendicular to the envelope of the solidification front is weakly violated in the phase-field simulations. We show that, even though weak, this violation has an important quantitative effect on the stability properties of the eutectic front. We also investigate the dynamics of fully developed colonies and find that the large-scale envelope of the composite eutectic front does not converge to a steady state, but exhibits cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.

Numerical And Experimental Analysis Of Macrosegregation During Upward And Downward Solidification Of A Ternary Al-cu-si Alloy

In this article macrosegregation phenomena in ternary Al-Cu-Si alloys are investigated by a numerical modeling technique and by upward and downward unidirectional solidification experiments. In particular, vertically aligned casting experiments of a ternary Al-8wt%Cu-3wt%Si alloy samples are considered. An X-ray fluorescence spectrometer was used to determine the segregation profiles along the castings. The experimental segregation profiles are compared with theoretical predictions furnished by the numerical model, with transient metal/mold heat transfer coefficient profiles being determined in each experiment. The numerical method consists of an explicit/implicit time integration scheme for coupling solutal and thermal fields. It has been observed that the numerical predictions generally conform to the experimental segregation measurements. The model is able to compute the inverse (Cu) solute concentration profile, which occur for upward solidification. For downward solidification only a small region of inverse (Cu) segregation close to the casting surface has been detected. For both solidification arrangements, no macrosegregation has been observed for the silicon content along the length of the directionally solidified casting, except for a short initial transient of normal (upward) and inverse (downward) segregation.1251258Flemings, M.C., (1974) Solidification Processing, pp. 214-258. , New York, NY: McGraw-HillFlemings, M.C., Our understand of macrosegregation: Past and present (2000) ISIJ International, 40, pp. 833-841Minakawa, S., Samarasekera, I.V., Weinberg, F., Inverse segregation (1985) Metallurgical and Materials Transactions B, 16 B, pp. 595-604Scheil, E., Beitrag zum problem der blockseigerung (1947) Metallforschung, 2, pp. 69-75Flemings, M.C., Nereo, G.E., Macrosegregation: Part I (1967) Transactions of TMS-AIME, 239, pp. 1449-1461Flemings, M.C., Mehrabian, R., Nereo, G.E., Macrosegregation, Part II (1968) Transactions of TMS-AIME, 242, pp. 41-49Flemings, M.C., Nereo, G.E., Macrosegregation, Part III (1968) Transactions of TMS-AIME, 242, pp. 50-55Voller, V.R., A numerical scheme for solidification of an alloy (1998) Canadian Metallurgical Quarterly, 37, pp. 169-177Ferreira, I.L., Siqueira, C.A., Santos, C.A., Garcia, A., Theoretical and experimental analysis of inverse segregation during unidirectional solidification of Al-6.2 wt.%Cu alloy (2003) Scripta Materialia, 49, pp. 339-344Ferreira, I.L., Santos, C.A., Voller, V.R., Garcia, A., Analytical, numerical and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys (2004) Metallurgicall and Materials Transactions B, 35 B, pp. 285-297Ferreira, I.L., Garcia, A., Nestler, B., On the macrosegregation in ternary Al-Cu-Si alloys: Numerical and experimental analysis (2004) Scripta Materialia, 50, pp. 407-411Swaminathan, C.R., Voller, V.R., Towards a general numerical scheme for solidification systems (1997) Canadian Metallurgical Quarterly, 40, pp. 2859-2868Patankar, S.V., (1980) Numerical Heat Transfer and Fluid Flow, p. 258. , New York, NY: HemisphereVoller, V.R., Sundarraj, S., A model of inverse segregation: The role of microporosity (1995) International Journal of Heat and Mass Transfer, 38, pp. 1009-1018Ni, J., Beckermann, C., A volume-averaged two-phase model for transport phenomena during solidification (1991) Metallurgical and Materials Transactions. A, 22 A, pp. 349-361Siqueira, C.A., Cheung, N., Garcia, A., The columnar to equiaxed transition during solidification of Sn-Pb alloys (2003) Journal of Alloys and Compounds, 351, pp. 126-134Sundman, B., Thermodynamics for materials design (1993) Journal of Chemical Physics, 90, pp. 275-280Diao, Q.Z., Tsai, H.L., Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys (1993) Metallurgical and Materials Transactions A, 24 A, pp. 963-973Rocha, O.L., Siqueira, C.A., Garcia, A., Heat flow parameters affecting dendrite spacings during unsteady state solidification of Sb-Pb and Al-Cu alloys (2003) Metallurgical and Materials Transactions A, 34 A, pp. 995-1006Clyne, T.W., Kurz, W., Solute redistribution during solidification with rapid state diffusion (1981) Metallurgical Transactions A, 12 A, pp. 965-971Brody, H.B., Flemings, M.C., Solute redistribution in dendritic solidification (1966) Transactions AIME, 236, pp. 615-624Santos, C.A., Quaresma, J.M.V., Garcia, A., Determination of transient interfacial heat transfer coefficient in chill mold castings (2001) Journal of Alloys and Compounds, 319, pp. 174-18