Phase dynamics in directional solidification

A phase diffusion equation valid at arbitrary distances above the Mullins- Sekerka threshold is derived from the front integral equation. The steady- state solutions and the associated adjoint functions are computed numerically. As a first exploitation of the phase equation, the range of the phase-s...

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Bibliographic Details
Published in:Physical review letters 1990-04, Vol.64 (16), p.1935-1938
Main Authors: BRATTKUS, K, MISBAH, C
Format: Article
Language:English
Subjects:
Condensed matter: structure, mechanical and thermal properties
Equations of state, phase equilibria, and phase transitions
Exact sciences and technology
General theory of equations of state and phase equilibria
Physics
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Summary:A phase diffusion equation valid at arbitrary distances above the Mullins- Sekerka threshold is derived from the front integral equation. The steady- state solutions and the associated adjoint functions are computed numerically. As a first exploitation of the phase equation, the range of the phase-stable band of steady solutions is determined. Even very close to threshold a strong deviation from the Landau-Ginzburg theory is found. Far from threshold, it is found that the wavelength on the long-wavelength edge of the Eckhaus band scales with the inverse square root of the growth velocity, as does the experimentally observed wavelength. (Author)
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.64.1935