Prediction of dendritic spacings in a directional-solidification experiment

Journal Article · Thu Apr 01 04:00:00 EST 1993 · Physical Review E; (United States)

DOI:https://doi.org/10.1103/PhysRevE.47.2702· OSTI ID:6710860

Warren, J A ^[1]; Langer, J S ^[2]

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1. Department of Physics, University of California, Santa Barbara, California 93106-4030 (United States)
2. Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States)

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)].

• DOE Contract Number: FG03-84ER45108
• OSTI ID: 6710860
• Journal Information: Physical Review E; (United States), Journal Name: Physical Review E; (United States) Vol. 47:4; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY LAYERS
CRYSTALS
DENDRITES
FLUCTUATIONS
GROWTH
INSTABILITY
LAYERS
MORPHOLOGICAL CHANGES
PHASE TRANSFORMATIONS
SOLIDIFICATION
VARIATIONS