Some problems are pointed out in the derivation process of the Thomson-Freundlich equation and in extended applications of the equation for the estimation of solubility and vapour pressure at the curved surface or interface. A serious misunderstanding in the derivation process is in the evaluation of the contribution of free energy of the surface or interface on the solubility or the vapour pressure. New ideas are proposed to solve these problems and using these results, the rate process for treating the deformation of a surface pattern is discussed theoretically.