FACETED NEEDLE CRYSTALS - AN ANALYTICAL APPROACH

Faceted dendrites have been observed in some crystal growth experiment s. It has previously been proposed that these diffusion-limited growin g shapes obey the classical equations of dendritic growth with modifie d boundary conditions on the interface. We analyse this new set of equ ations when capillary effects are neglected on the rough parts. In thi s limit, we find that it is not possible to require both a tangential matching of the rough and faceted parts and the same melting temperatu re on the front and trailing rough interface. An exact solution is obt ained when one of these physical constraints is relaxed. The consequen ces of this result for the full problem are considered and an approxim ate solution is proposed.