Cellular-to-dendritic transition during the directional solidification of binary alloys
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I. INTRODUCTION
ONE of the critical problems in directional-solidification microstructures that is still pending is the criterion for the cell-dendrite transition (CDT). Approximate criteria have been proposed in the literature[1–4] that show that the CDT occurs at some critical condition relating the thermal gradient (G), the growth rate (V ), and the alloy composition (C0). It has been shown that none of these models predict experimentally observed transition conditions.[5] Also, experimental studies[6–9] have shown that cells and dendrites coexist over a range of velocities under fixed values of G and C0. It has been postulated that this coexistence occurs due to the spectrum of primary spacings and that the transition from cell to dendrite occurs in an array where the local spacing is large.[3,6] Consequently, the CDT condition must incorporate local spacing in addition to the control parameters G, V, and C0. The aim of this article is to examine how the presence of a spectrum of primary spacings influences the CDT and to obtain a quantitative relationship for this transition that incorporates local spacing. The transition condition can be related to the onset of sidebranch formation, which was first described by Zel’dovich et al.[10] for flame fronts by considering the amplification of perturbation at the tip region. Theoretical models based on this noise-induced instability have been developed for dendrites,[11,12], and phase-field models have shown that no sidebranches will form if the numerical noise is kept small.[13–16] These models, however, have been developed for thermal dendrites in an undercooled melt. In directional solidification, the local spacing between the cells influences the solute field near the cell-tip region, and this interaction will determine the amplification of the noise at the cell tip. R. TRIVEDI, Professor, Ames Laboratory, United States Department of Energy, and Department of Materials Science and Engineering, and YUNZUE SHEN, Graduate Student, and SHAN LIU, Research Scientist, Department of Materials Science and Engineering, are with Iowa State University, Ames, IA 50011. Contact e-mail: [email protected] Manuscript submitted June 11, 2002. METALLURGICAL AND MATERIALS TRANSACTIONS A
The effect of local spacing on the CDT was proposed by Billia and Trivedi[3] and was experimentally examined by Georgelin and Pocheau[6] in impure succinonitrile (SCN). To quantitatively establish the CDT criterion that properly incorporates the effect of local spacing, we have carried out experiments in a well-characterized model-transparent system of SCN-salol. The transparent nature of this system allowed us to examine the critical nearest-neighbor spacing of a given cell that just formed sidebranches. We found that lower and upper critical ratios of V/G exist such that only cells are stable below the lower critical ratio, and only dendrites are stable above the upper critical ratio. Between these two critical ratios, where cells and dendrites coexist, a critical spacing (cd) is found above whic
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