Further discussion on the free growth behavior in the solidification of undercooled eutectic melts
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Communications Further Discussion on the Free Growth Behavior in the Solidification of Undercooled Eutectic Melts MINGJUN LI and KAZUHIKO KURIBAYASHI In constrained eutectic solidification, i.e., directional eutectic solidification, the growth of the coupling eutectic phases usually proceeds in a stable manner. Jackson and Hunt[1] developed a classical model to describe this diffusionlimited process (JH model) under two assumptions of a low interface undercooling and a small Peclet number. Trivedi et al.[2] (TMK model) relaxed those two assumptions and extended the JH model to a high interface undercooling and a large Peclet number for two types of eutectic phase diagrams (the first is that solidus and liquidus lines are parallel below the eutectic temperature, i.e., so-called “cigar shape” diagram; and second is that the distribution coefficients are equal in terms of α and β phases, i.e., kα = kβ) under the rapid solidification conditions (e.g., in laser surface remelting experiments). In both models, the interface undercooling, growth velocity, and lamellar spacing are correlated either via constants or as a function of Peclet number and growth velocity. It should be pointed out that nucleation is generally not involved after eutectic growth starts from the preset crystal seed, container wall, or substrate. Therefore, both the aforementioned models deal with only eutectic growth under a steady-state growth condition. Furthermore, it should be noted that the crystallization heat is released to surroundings via the careful control of the exterior heating system in order to achieve a stable temperature gradient. Hence, a steady-state thermal flux can be frequently superimposed on a steady-state growing planar interface. In unconstrained eutectic solidification, i.e., free solidification of a eutectic melt from an undercooled state, it has been well documented that a morphology transition from the regular lamellae to a mixture of regular and anomalous eutectics and then purely anomalous eutectics with the increase of melt undercoolings has been observed in many metallic eutectic alloys.[3–12] In the meanwhile, several mechanisms[3,4,6] have been proposed to account for the formation of anomalous eutectics from the viewpoint of crystal growth based on the conventional nucleation concept; i.e., once an effective nucleus is generated, it is sufficient to activate an undercooled melt to crystallize and then the solid/liquid interface will sweep immediately across the entire sample. Following this conventional idea, some photosensing techniques, for instance, a two-photodiodes method or a cine camera, have been employed to measure the growth velocity in many eutectic alloys.[5,9,13–16] However, the MINGJUN LI, Postdoctoral Research Fellow, and KAZUHIKO KURIBAYASHI, Professor, are with the Institute of Space and Astronautical Science, Kanagawa 229-8510, Japan, Contact e-mail: mingjun@materials. isas.ac.jp KAZUHIKO KURIBAYASHI is also with CREST. Japan Science and Technology Corporation, Ibaraki 305-0047, Japan. Manuscript
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