Wavelength dependence of cells of finite depth in directional solidification

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Abstract
Finite-element calculations are presented for the two-dimensional cellular interface shapes in a spatially periodic microstructure that occurs during the directional solidification of a dilute binary alloy. The transition from small-amplitude sinusoidal shapes to cells separated by deep grooves as the growth rate is increased is computed as a function of spatial wavelength. The flatness of the neutral stability curve of growth rate versus spatial wavelength is responsible for secondary bifurcations that lead to tip splitting of the cells and to an apparent decrease in the wavelength of the pattern. Deep cells with round tips, long linear grooves, and pendant-shaped bottoms are computed for continuous ranges of wavelength and growth rate. A wavelength corresponding to the cell with maximum aspect ratio is computed as a function of the growth rate.