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 (v) and supersaturation or supercooling (d) 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

more »

... . 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.