Morphological control of crystal growth

Crystal growth is a classical example of a phase transformation from the liquid phase to the solid phase via heat transfer. A remarkable feature observed during crystal growth is the occurrence of complex solid/liquid interface morphologies due to the Mullins-Sekerka instability. This problem is re-examined using linear stability theory, nonlinear analysis and numerical simulations of evolving crystals. The study reveals that the Mullins-Sekerka instability may be suppressed by using a prescribed heat flux at the far-field boundary instead of a supercooling (far-field temperature). In particular, there exist critical flux conditions such that a non-circular (spherical) crystal can grow self-similarly.; A stability analysis of self-similar solutions reveals that self-similar shapes are stable to perturbations of the critical flux for self-similar growth, in the sense that the symmetry of the crystal remains unchanged. Shape perturbations may grow or decay. At long times, there exists nonlinear stabilization even though unstable growth may be significant at early times. This nonlinear stabilization leads to the growth of compact crystals. In particular, we observe three types of growth behavior: universal, limiting and oscillatory. Universal behavior occurs when the shape of the long time evolving crystal becomes independent of both time and the initial shape. Limiting behavior occurs when the shape of the long time evolving crystal becomes independent of time, but depends on the initial shape. Finally, oscillatory behavior occurs when the long time evolving shape depends on both time and the initial shape, though its growth is bounded. If the surface tension is anisotropic, the crystal morphologies are determined by a complex competition between the heat transport (far-field flux) and the strength of surface tension anisotropy. Unlike the isotropic case where universal shapes have an arbitrary symmetry that depends only on the far-field flux, the surface tension anisotropy selects the symmetry of the universal shape.