The Green function approach to several problems in crystal growth

Abstract In this paper several applications of Green function techniques in crystal growth are discussed. It is demonstrated that this technique enables one to transform the bulk transport problem in the mother phase into a surface problem. Indeed one obtains for arbitrary crystal shapes a (non-local) equation of motion for the crystal surface. The non-local character is shown to reflect the diffusional interaction, due to the competing diffusion fields in the volume around the growing crystal. Previous applications to the shape of stationary cellular interfaces, to the dendrite problem and to step movement are shortly reviewed. Finally, as a novel application we simulated numerically the time evolution of non-circular islands on (100) NaCl cleavage faces in contact with vacuum. New information about the coupled surface and edge diffusion process in this system is obtained.

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