Lamella / Rod Transformation as described by the Criterion of Minimum Entropy Production

Yıl 2010, Cilt: 13 Sayı: 2, 35 - 42, 01.06.2010

Waldemar Wołczyński

Öz

A general theory for the lamella -> rod transformation is presented. The analysis has been developed in two steps: first, taking into account the condition of minimum Gibbs' free energy, next, using the criterion of minimum entropy production together with the concept of marginal stability. The present theory provides a justification for theoretical determination of a threshold growth rate at which solidification begins to form a rod-like structure instead of a lamellar one. Additionally, the so-called operating range for transformation is justified by the oscillation between the trajectory of minimum entropy production and the trajectory of marginal stability. A model of the evolution of the mechanical equilibrium is introduced to satisfy some changes of the curvature of the solid / liquid interface with increasing growth rate. A consideration associated with the Gibbs' free energy allows to formulate a new criterion which predicts whether the lamellar structure is the stable form or a rod-like structure is the stable form (for a given phase diagram). An application of the criterion of minimum entropy production, together with a model of the instability of the solid/liquid interface (referred to as marginal stability), allows for determining a/ a trajectory at which a regular structure is forming and b/ a trajectory of marginal stability at which the maximum destabilization of the s/l interface of the non-faceted phase is observed together with the faceted phase branching.

Anahtar Kelimeler

spacing oscillation; marginal stability; attractor; threshold rate for the lamella / rod transformation

Kaynakça

• Atasoy, O., 1984, “Effects of Unidirectional Solidification Rate and Composition on Inter-particle Spacing in Al-Si Eutectic Alloy”, Aluminium, Vol. 60, pp.109-116.
• Cupryś, R., Major, B., Wołczyński, W., 2000, “Transition of Flake into Fibre Structure in Eutectic Al-Si” , Materials Science Forum, Vol. 329/330, pp.161-166.
• Elliott, R., 1977, “Eutectic Solidification”, International Metals Reviews, Vol. 219, pp. 161-186.
• Fisher, D.J., Kurz, W., 1980, “A Theory of Branching Limited Growth of Irregular Eutectics”, Acta Metallurgica, Vol. 28, pp. 777-794.
• Glansdorff, P., Prigogine, I., 1971, Thermodynamic Theory of Structure, Stability and Fluctuations, John Wiley & Sons, Ltd. London-New York – Sydney- Toronto.
• Jackson, K.A., Hunt, J.D., 1966, “Lamellar and Rod Eutectic Growth”, Transactions of the AIME, Vol. 236, pp. 1129-1142.
• Lesoult, G., Turpin, M., 1969, “Etude theorique sur la croissance des eutectiques lamellaires”, Revue Scientifique de Metallurgie, Vol. 9, pp. 619-631.
• Major, J.F., Rutter, J.W., 1989, “Effect of Strontium and Phosphorus on Solid/Liquid Interface of Al-Si Eutectic”, Materials Science and Technology, Vol. 5, pp. 645-656.
• Steen, H.A.H., Hellawell, A., 1975, “ The Growth of Eutectic Silicon – Contributions to Undercooling”, Acta Metallurgica, Vol. 23, pp. 529-536.
• Toloui, B., Hellawell, A., 1976, “Phase Separation and Undercooling in Al-Si Eutectic Alloy – The Influence of Freezing Rate and Temperature Gradient”, Acta Metallurgica, Vol. 24, pp. 565-572.
• Wołczyński, W., Billia, B., 1996, “Influence of Control and Material Parameters on Regular Eutectic Growth and Interlamellar Spacing Selection”, Materials Science Forum, Vol. 215/216, pp.313-322.