Prediction of dendritic spacings in a directional-solidification experiment
- 1 April 1993
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 47 (4), 2702-2712
- https://doi.org/10.1103/physreve.47.2702
Abstract
We present a theoretical analysis of the formation of a dendritic array in a directional-solidification experiment. Our calculation contains three sequential ingredients: acceleration of an initially flat interface and the concomitant buildup of a solutal boundary layer in front of it; onset of a morphological instability, triggered by thermal fluctuations, producing a relatively finely spaced array of dendritic tips; coarsening of this array and final selection of a steady-state primary spacing. For sufficiently large growth speeds, where the resulting dendrites interact with each other weakly, we find–with no adjustable parameters–good agreement with the experiments of Trivedi and Somboonsuk [Acta Metall. 33, 1061 (1985)] and Somboonsuk, Mason, and Trivedi [Metall. Trans A 15A, 967 (1984)].Keywords
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