On the incorrect use and interpretation of the model for colloidal, spherical crystal growth

Abstract Hypothesis The standard model for diffusion and surface kinetics driven growth of a single spherical particle in solution is applied incorrectly throughout the literature. This leads to inaccurate values for parameter values, such as the diffusion and surface kinetics coefficients. The model cannot even distinguish between diffusion or surface kinetics driven growth. Findings It is shown that crystal growth occurs in two distinct stages. The standard model only holds during the late time. Fitting to experimental data, including the early time, leads to incorrect values for the coefficients. It is shown that diffusion and surface kinetics are interchangeable in the model and so indistinguishable. The growth is controlled by a single non-dimensional group. Previous studies, where more independent parameters are calculated have redundancy. The Gibbs-Thomson relation plays an important role but, in the cases studied here, this is only noticeable during the first growth stage where the model does not hold. For the first time an explicit relation for the variation of the radius with time is given. Excellent agreement with experimental data on CdSe growth is shown.