Abstract
In this work, we analyse the growth of nuclei precipitating from a supersaturated liquid. Two simultaneous habits of crystal growth are considered: interface-controlled three-dimensional growth with a growth rate u up to a threshold radio R c and then diffusion-controlled growth when steady growth is achieved at the initial stages owing to the large supersaturation in between the nucleus and the liquid neighbourhood. The threshold radio R c determines the growth habit of each grain. For isothermal processes, we discover that the temporal dependence of the crystalline fraction follows scaling laws. Two parameters summarize the master curves: firstly, a dimensionless magnitude named P, where P = (π/3)ID4 eff/u 5, where D eff is the effective diffusion coefficient and I the nucleation frequency; secondly, the time t c needed by the first created embryo to reach the threshold radio R c. At t c the growth switches from one mechanism to the other. These two quantities are also scaling factors for the temporal evolution of the density of grains and the mean grain size. We discuss the applicability of the model to real systems.
