Abstract
The stability of the shape of a moving planar liquid-solid interface during the unidirectional freezing of a dilute binary alloy is theoretically investigated by calculating the time dependence of the amplitude of a sinusoidal perturbation of infinitesimal amplitude introduced into the planar shape. The calculation is accomplished by using gradients of the steady-state thermal and diffusion fields satisfying the perturbed boundary conditions (capillarity included) to determine the velocity of each element of interface, a procedure justified in some detail. Instability occurs if any Fourier component of an arbitrary perturbation grows; stability occurs if all components decay. A stability criterion expressed in terms of growth parameters and system characteristics is thereby deduced and is compared with the currently used stability criterion of constitutional supercooling; some very marked differences are discussed.
Keywords
PlanarSupercoolingPerturbation (astronomy)InstabilityAmplitudeBinary numberMechanicsThermodynamicsMaterials scienceChemistryClassical mechanicsPhysicsOpticsMathematics
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Publication Info
- Year
- 1964
- Type
- article
- Volume
- 35
- Issue
- 2
- Pages
- 444-451
- Citations
- 3079
- Access
- Closed
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Cite This
W. W. Mullins,
Robert F. Sekerka
(1964).
Stability of a Planar Interface During Solidification of a Dilute Binary Alloy.
Journal of Applied Physics
, 35
(2)
, 444-451.
https://doi.org/10.1063/1.1713333
Identifiers
- DOI
- 10.1063/1.1713333