Anomalous lattice expansions have been measured for the first time in monodisperse CeO2-x nanoparticles and in BaTiO3 single nanoparticles by electron diffraction. X-ray photoelectron spectroscopy studies on CeO2-x nanoparticles and ab initio computer simulation on BaTiO3 clusters show that the origin of expansion is the decrease of electrostatic force caused by valence reduction of Ce ions and the increase in ionicity of Ti ions, respectively. The lattice constant change of oxide (ionic) nanoparticles with the increase in ionicity would depend on the structure of the particles. Hence, first-principles calculations of large ionic clusters are indispensable.