Effect of thermosolutal convection on microstructure formation in the Pb-Bi peritectic system
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PERITECTIC systems are exhibited by many alloys that include the commercially important Fe-C and Cu-Sn, superconducting YBCO, and magnetic Sm-Co alloys. The design of microstructure in these systems is crucial in controlling the properties. Of particular interest is the twophase region in which a rich variety of microstructures have been observed to form. These include (1) cellular/dendritic growth of the primary a phase,[1–4] (2) a composite microstructure of the two phases,[2,5–9] (3) a banded microstructure in which the two phases form alternately in the growth direction,[10–15] (4) the nucleation of the peritectic b phase ahead of the a/liquid interface, and (5) the cellular/dendritic growth of b phase. Conditions for the selection of these microstructures have been examined mostly for diffusive growth conditions. In reality, the presence of convection in the melt alters microstructure lengthscales and even results in formation of microstructures not predicted under diffusive growth conditions.[11,14] The effect of convection on the formation of banded microstructures has been examined by Park and Trivedi[11] in the Sn-Cd system in which a heavier solute (Cd) is rejected during growth. In this article, we shall examine the stability of banded microstructures in the presence of convection in the Pb-Bi system in which the rejected solute, Bi, is much lighter than Pb so that a positive density gradient will be present in the liquid at the interface. In this case, significant fluid flow can occur due to double diffusive instability, which is related with the density change caused by both thermal and solutal fields. The double diffusive instability was first discussed by Coriell et al.[16] and subsequently analyzed by Le Marek et al.[17] and Solomon SHAN LIU, Associate Scientist, is with the Materials and Engineering Physics Program, Ames Laboratory–United States Department of Energy. Contact e-mail: [email protected] ROHIT TRIVEDI, Senior Scientist, is with the Materials and Engineering Physics Program, Ames Laboratory– United States Department of Energy, and Professor, Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011. Manuscript submitted February 22, 2006. METALLURGICAL AND MATERIALS TRANSACTIONS A
et al.[18] Flow patterns in the melt can be complex and give rise to axial and radial segregation in cylindrical samples. When the convection effect is reduced by using capillary ampoules, laminar flow is found to be present, which gives rise to a homogeneous solute layer in the radial direction, except near the wall of a sample, and diffusion occurs within a small hydrodynamic boundary layer near the interface with complete mixing outside this layer.[19] Complete mixing increases the bulk composition as solidification proceeds so that microstructure evolution depends on the solidification fraction. The boundary layer model of convection was first proposed by Nernst[20] and later used successfully by Burton et al.,[21] in predicting macrosegregation in crystal growth. The effect of this bo
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