TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Process: The concentration of cerium nitrate in the aqueous solution is 0.005-0.04 M. The concentration of hexamethylenetetramine in the aqueous solution is 0.05-1.5 M, preferably 0.5-1.5 M. The mixture is maintained at less than 300 degrees K for 2-24 hours, preferably 12-24 hours. The mixture containing nanoparticles is further maintained at less than 320 degrees K. The separated nanoparticles are sintered in air at 400-800 degrees C. The cerium oxide nanoparticles include single crystalline nanoparticles, soaked in a solution comprising chloroplatinic acid solution. Alternatively, the preparation of cerium oxide nanoparticles involves providing one of the aqueous solutions in a mixing vessel having inlet(s), and pumping the other aqueous solution into the mixing vessel through inlet(s) to cause rapid mixing.    TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred Apparatus: The mixing vessel includes a mechanical stirrer having a vertical stirring rod with several stirring elements. The vertical stirring rod has an aperture for fitting primary inlet feed for introducing cerium nitrate aqueous solution, and an aperture for fitting secondary inlet feed for introducing hexamethylenetetramine aqueous solution. The vertical stirring rod further includes an outlet for removal of liquid from mixing vessel. The apparatus has a centrifuge for separating nanoparticles from the mixture. EXAMPLE - An aqueous solution of 0.00375 M cerium nitrate (750 ml) was placed in primary compartment of a mixing vessel. An aqueous solution of 0.5 M hexamethylenetetramine (750 ml) was placed in a secondary compartment, separated form the first by a retractable partition. The partition was retracted and the mixture was stirred at 300 degrees K for 12 hours to yield cerium oxide (CeO(2-y), where y = 0-0.35) nanoparticles with diameter of 12 nm. The yield of nanoparticles was 30%. The average nanoparticle growth rate was one monolayer/15 minutes.