Cellular interface morphologies in directional solidification. III. The effects of heat transfer and solid diffusivity

Lyle H. Ungar, Mark J. Bennett, and Robert A. Brown
Phys. Rev. B 31, 5923 – Published 1 May 1985
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Abstract

The shape and stability of two-dimensional finite-amplitude cellular interfaces arising during directional solidification are compared for several solidification models that account differently for latent heat released at the interface, unequal thermal conductivities of melt and solid, and solute diffusivity in the solid. Finite-element analysis and computer-implemented perturbation methods are used to analyze the families of steadily growing cellular forms that evolve from the planar state. In all models a secondary bifurcation between different families of finite-amplitude cells exists that halves the spatial wavelength of the stable interface. The quantitative location of this transition is very dependent on the details of the model. Large amounts of solute diffusion in the solid retard the growth of large-amplitude cells.

  • Received 1 November 1984

DOI:https://doi.org/10.1103/PhysRevB.31.5923

©1985 American Physical Society

Authors & Affiliations

Lyle H. Ungar, Mark J. Bennett, and Robert A. Brown

  • Department of Chemical Engineering and Materials Processing Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

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Issue

Vol. 31, Iss. 9 — 1 May 1985

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