TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Production: Step (a) is carried out in air or under an atmosphere of an inert gas. The cerium(III) salt is cerium(III) nitrate, ammonium cerium(III) nitrate, cerium(III) sulfate, ammonium cerium(III) sulfate, cerium(III) chloride, cerium(III) carbonate, cerium(III) acetate or cerium(III) oxalate. The lanthanum(III) or neodymium (III) salt is the nitrate, chloride, acetate or oxalate.Preferred Abrasive: The abrasive is adjusted to pH 1-6 with an acidic substance, or to pH 8-13 with a basic substance. EXAMPLE - A reactor was charged with 253 g of aqueous 25% ammonia solution (corresponding to molar ratio NH3/(Ce + La) of 8) under nitrogen gas flow. Separately, 693 g of an aqueous cerium(III) nitrate solution (11.5 wt.% CeO2) were mixed with 28.5 g of an aqueous lanthanum(III) nitrate solution (14.0 wt.% La2O3) to give a La/(Ce + La) molar ratio of 0.05. The mixed solution was gradually added to the ammonia solution over 30 minutes to obtain a suspension of hydroxides. The suspension was heated to 80 deg. C and the gas flow was switched from nitrogen to air (0.5 l/minute) to oxidize cerium(III) to cerium(IV). The oxidation reaction was completed in 7 hours. The cooled reaction solution contained white fine particles and had a pH of 7.9 and an electrical conductivity of 148 mS/cm.    The solution was washed with the aid of a suction funnel to obtain 310 g of white slurry having a solid content of 24.5 wt. %, a pH of 5.2 and an electrical conductivity of 43 microS/cm. The resulting particles had a primary particle size of 50-100 nm. The yield of the particles was approximately 100%. Powder X-ray diffraction observation of the dried particles revealed that they had characteristic peaks coinciding with those of crystalline cerium oxide of cubic crystal system. The particles contained lanthanum in La/(Ce + La) molar ratio of 0.05 and had specific surface area (BET) of 23.3 m2/g.    Nitric acid was added in amount HNO3/CeO2 = 0.12 wt.%. The resulting mixture was adjusted (with pure water) to a solids content of 10 wt.% to prepare an abrasive sol having a pH of 4.6, an electrical conductivity of 145 microS/cm and a viscosity of 1.3 mPa.S.