Cellular interface morphologies in directional solidification. IV. The formation of deep cells

Abstract

Steadily growing, spatially periodic, two-dimensional cellular interfaces with groves up to 15 times longer than their wavelength are calculated by a novel finite-element method applied to the solutal model for solidification that includes diffusion in the solid. The deep cells are formed by either continuously decreasing the temperature gradient or increasing the growth velocity from the values for a marginally unstable planar interface. As predicted by previous finite-element calculations [L. Ungar and R. Brown, Phys. Rev. B. 29, 1367 (1984)], large-amplitude cells are found at half the spatial wavelength of the small-amplitude instability to the planar shape. Steady-state growth is predicted to end when droplets of the melt are detached from the bottom of the grooves between the cells. The influence of the ratio of solid to liquid diffusivities on the cell shape and the adjacent concentration field is examined.