Studying growth: The diffusion-controlled kinetic (DCK) model and the surface chemical thermodynamics (SCT) model have been successfully applied to interpret the nucleation and growth mechanism of CeF(3) (see TEM images) and NaCeF(4) nanocrystals, and may generally give light to the size-control and morphology prediction of rare-earth fluorides at the nanoscale level.Monodisperse CeF(3) and NaCeF(4) nanocrystals have been synthesized by using the liquid-solid-solution (LSS) approach. The nucleation and growth of nanocrystalline CeF(3) and NaCeF(4) were controlled by both kinetics and thermodynamics, which can be investigated by the diffusion-controlled kinetic (DCK) model and surface chemical thermodynamics (SCT) theory. The DCK and SCT models were introduced to explain how the ripening time, reaction temperature, and initial concentrations affected the size transition of CeF(3) and NaCeF(4) nanocrystals in detail. Also, these models are believed to be universal and can be applied to explore the morphology evolution of almost all rare-earth fluoride nanocrystals.