Wavelength Selection in Directional Solidification
- 18 August 1986
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 57 (7), 858-861
- https://doi.org/10.1103/physrevlett.57.858
Abstract
Cell-spacing selection in directional solidification is investigated. An integral equation describing steady-state cells in the limit where the solute diffusion length is much larger than the cell spacing is derived and solved numerically by Newton's method. With surface tension and no crystalline anisotropy present the spatial periodicity of a one-dimensional array of cells with cusp singularities is found to be determined uniquely by a solvability condition. The inclusion of crystalline anisotropy has no other effect to shift the value of the selected spacing.Keywords
This publication has 18 references indexed in Scilit:
- A simple model for unidirectional crystal growthPhysics Letters A, 1984
- Interdendritic Spacing: Part II. A Comparison of Theory and ExperimentMetallurgical Transactions A, 1984
- Geometrical models of interface evolutionPhysical Review A, 1984
- Geometrical Approach to Moving-Interface DynamicsPhysical Review Letters, 1983
- Cellular patterns produced by the directional solidification of a binary-alloyPhysical Review B, 1983
- Instabilities and pattern formation in crystal growthReviews of Modern Physics, 1980
- Studies in the theory of interfacial stability—I. Stationary symmetric modelActa Metallurgica, 1977
- Convective instability: A physicist's approachReviews of Modern Physics, 1977
- Finite bandwidth, finite amplitude convectionJournal of Fluid Mechanics, 1969
- Stability of a Planar Interface During Solidification of a Dilute Binary AlloyJournal of Applied Physics, 1964