Crystal growth of dendrite.

Abstract

Historical review of the experiments and theories of dendritic crystal growth and also the review of recent studies of pattern formations in diffusion field are presented. In early experiments the relation between tip-veiocity (υ) and supersaturation or supercooling (Delta;) were concerned. The theoretical analysis on the above relationship was made for a needle crystal and by using the Gibbs-Thomson's boundary condition. The maximum velocity condition was assumed, but was found to be incorrect later. In Muller-Krumbhaar theory, dendritic growth are considered as non-linear and non-equilibrium phenomena. The theory could explain the results of 3-dimensional dendritic growth experiments. However, the marginal stability condition assumed in the theory has not been proved mathematically yet. The next theoretical development was achieved by finding the importance of anisotropy and the solvability condition of the steady state. The origin of the side-branches was then discussed. The possibility of the noise-indused mechanism was reported theoretically and experimentally. The recent experimental understandings of pattern formations in diffusion field are also reviewed. The dendritic problem is not limited only to crystal growth. Finally, various modes of dendritic growth are discussed and the necessity of measurement of diffusion field in dendritic crystal growth is emphasized.