Nonlinear dynamics theory on the steady state interface pattern during solidification of a dilute binary alloy

The nonlinear dynamics equations of the time dependence of the perturbation amplitude of the solidi liquid interface during unidirectional solidification of a dilute binary alloy are established. The solutions to these equations are obtained, and the condition of the initial steady state growth of the cellular and dendritic structure Idler the planar solid/liquid interface bifurcates (mG(c) > G) with the increase of the growth rate is given. The condition of the steady state growth of fine cellular and dendritic structure in the beginning after the coarse dendrites bifurcate (mG(c) < Gamma omega(2) + G) under the rapid solidification is obtained. The relationship of the steady state cell and dendrite tip radius, the perturbation amplitude and wavelength at the solid/liquid interface is presented.