Stability of a Planar Interface During Solidification of a Dilute Binary Alloy

Mullins, W. W.; Sekerka, R. F.

doi:doi:10.1063/1.1713333

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Journal of Applied Physics / Volume 35 / Issue 2

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J. Appl. Phys. 35, 444 (1964); http://dx.doi.org/10.1063/1.1713333 (8 pages)

Stability of a Planar Interface During Solidification of a Dilute Binary Alloy

W. W. Mullins¹ and R. F. Sekerka²

¹Department of Metallurgical Engineering, Carnegie Institute of Technology, Pittsburgh, Pennsylvania
²Physics Department, Harvard University, Cambridge, Massachusetts

(Received 15 July 1963)

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Abstract

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Citing Articles (965)

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.