On the unsteadiness time of primary dendritic growth

The evolution of the growth rate of a dendritic tip for nonisothermal crystal growth from the moment of crystal formation to the moment when the growth rate attains its steady-state value is considered. Gibbs–Thomson condition for highly nonequilibrium rapidly moving crystallization of a pure one-component liquid is used to determine the time dependence of the growth rate of a dendritic tip. It is shown that the dependence of the growth rate on overcooling has the form of an exponential law. Under the condition of constant overcooling an estimation of the time of reaching the steady-state regime of growth is obtained. The analytically derived velocity of growth as a function of time coincides with numerical calculations.