Simulation of eutectic solidification structures of binary alloys: a multiparticle diffusion limited aggregation model
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I. INTRODUCTION
THE microstructure that develops during a solidification process can exhibit a variety of morphological forms. Eutectic structures belong to the most frequently observed solidification microstructures upon solidification of binary alloys. This reaction can be described by liquid → a 1 d, on cooling below the eutectic temperature.[1] The two solid phases a and d grow simultaneously, frequently in regular forms, e.g., lamellar or fibrous. Eutectic microstructures are of special interest from a theoretical point of view in terms of pattern formation and selection of growth mode during (directional) solidification, but also from a practical point of view recognizing the properties associated with an aligned microstructure.[2,3] The basic theory for steady-state diffusion-controlled growth of eutectic structures concerns systems where both product phases possess low entropy of fusion and the rate of growth is rather isotropic resulting in so-called regular eutectic structures (sometimes called nonfaceted/nonfaceted eutectic structures).[4] This treatment has later been extended to growth of irregular (faceted/nonfaceted) eutectic structures, where one of the phases possesses a low entropy of fusion and the energy of the interface between the two phases is dependent on the crystallographic orientation of the interface.[5,6] Still later modifications in this continuum theory involve instability analysis of the growing eutectic interface, which led to the prediction of oscillatory[7,8] and tilting modes of growth,[9,10] as observed in some experimental systems.[11,12] In contrast to the continuum approach, a microscopic approach to eutectic solidification has obtained limited attention until now. A microscopic approach appears in particular promising for studying the development of various solidification structures as a direct result of both diffusion and A. DAS, Postdoctoral Researcher, is with the Max Planck Institute for Metals Research. E.J. MITTEMEIJER, Professor and Director, is with the Max Planck Institute for Metals Research and the Institute for Physical Metallurgy, University of Stuttgart, Seestrasse 92, D-70174 Stuttgart, Germany. Manuscript submitted February 10, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
surface kinetics on an atomic scale. Since the introduction of the diffusion-limited aggregation (DLA) model for the aggregation of colloidal particles,[13,14] progress has been made applying this concept in the investigation of crystal growth from the vapor or melt.[15–22] However, the DLA approach considers the motion of one single particle at a time until it reaches the solid agglomerate or escapes through an outer boundary of the system; the other particles are considered to be absent effectively. The multiparticle variant of the DLA (MPDLA) model was introduced to simulate more realistically actual growth by allowing all particles to be mobile at the same time, and therefore, enabling study of the dependance of growth on concentration.[23,24] In contrast with the DLA approach, an
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