Fractal structures of dendrites in GaSe crystals

Abstract

Solidification of melts at substantial supercooling is associated with instability on the growth front. This causes growth of dendrites, which form as a branched tree in a crystal. In the layered melt-grown GaSe crystals dendrites are observed, if growth rates are rather high [N.N. Kolesnikov, E.B. Borisenko, D.N. Borisenko, V.K. Gartman, Influence of growth conditions on microstructure and properties of GaSe crystals, J. Crystal Growth 300 (2) (2007) 294–298]. Models based on solution of the thermal diffusion problem are traditionally used to describe dendrite growth. Solution of this problem requires information about several physical parameters, such as diffusion coefficient, heat conductivity coefficient and supercooling at the solid/liquid interface. The study of scale invariance of dendrites formed in a crystal provides a new approach to solution of the dynamic growth problem. The calculated fractal dimensionality of the experimentally observed dendrites in GaSe crystals is D=1.7. It coincides with dimensionality of the clusters obtained through computer simulation in terms of the model of diffusion-limited aggregation (DLA). This result provides a new approach to description of the dynamics of dendrite growth. We have shown that the dendrite growth mechanism in the layered semiconductor crystals can be described by a two-dimensional DLA model. It is shown that probabilistic simulation can be used to show the development of a dendrite in any material. In contrast to the classical theories of dendrite growth, this approach does not require information on physical parameters.