Time dependence of tip morphology during cellular/dendritic arrayed growth
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I.
INTRODUCTION
DIRECTIONAL solidification of alloys in a positive thermal gradient (G,) at a constant growth speed (R) produces an arrayed morphology of dendrites or cells. The microstructure and chemical homogeneity of directionally solidified materials are significantly affected by the tip morphology of these arrays. Therefore, considerable effort has gone into developing an understanding of the tip shape. Thermal gradient, growth speed, and alloy composition dependence of the tip morphology have been extensively examined in transparent organic alloys, such as succinonitrile-acetone, t',2,3] pivalic acid-ethanol, [4] and succinonitrile-salol.lS] The experimental observations generally showed that a steady-state tip morphology develops for an alloy growing at constant Gt and R, for both the cellular and dendritic arrays. Several analytical [~-'~ and numericalt,,.,z.,3] analyses have been carried out to explain the steady-state morphology of cells and dendrites. However, there has been little attempt to experimentally examine the time dependence of the tip morphology during constrained growth of binary alloys in order to ascertain if they do keep a steady-state shape. Indeed, recent theoretical analysesu3,'4] suggest that there may not be a sharp selection of primary arm spacings (tip morphology) during dendritic arrayed growth. It is also important to note that the tip morphology data on transparent materials have mostly been generated in thin (about 100 to 200/xm) slab-shaped crucibles. Since the solid succinonitrile is known to preferentially wet the glass walls, the experimentally observed tip morphologies may not represent the true three-dimensional behaviors of the arrays, especially for the cells with tip radii and primary arm spacings about the size of the melt thickness. The question of whether the cells and dendrites grow with a steady-state shape is crucial for the development of a sound theoretical understanding of the arrayed growth during directional solidification. This research was aimed at answering this question. Succinonitrile-acetone alloy was selected for this study because of the ease of visualization, its well-characterized physical properties, and its metal-like
H. SONG, Research Associate, and S.N. TEWARI, Professor, are with the Chemical Engineering Department, Cleveland State University, Cleveland, OH 44115. Manuscript submitted July 25, 1995. METALLURGICALAND MATERIALSTRANSACTIONS A
solidification behavior. A range of growth speeds has been used to examine the behavior from near the breakdown of the planar liquid-solid interface to the fully developed dendritic arrayed growth. Time dependence of the tip morphology has been examined for the dendritic and cellular arrays. The observed variation (scatter) in the tip shape has been compared with that reported in the literature t2.'5,'~J for growth in thin slab-shaped crucibles, without any convection in the melt. II.
EXPERIMENTAL
Details of the alloy preparation and directional solidification techniques have been presented earlier, t'7]
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