Commonly known processes for producing compound oxide powders include simultaneous powder firing methods wherein powders of metal oxides or their precursor carbonates or hydroxides are combined and fired, co-precipitation methods wherein an alkali is added to an aqueous solution of multiple metal inorganic salts for neutralization, producing a colloidal dispersion of oxides or hydroxides, and alkoxide methods wherein water is added to multiple metal alkoxides dissolved in an organic solvent, for hydrolysis. 
Simultaneous powder firing methods have a limitation in the degree of fineness of the powder, and require firing at high temperature to obtain compound oxides from the powder.  High-temperature firing results in particle growth and reduced surface area.  It is difficult in actuality to obtain fine powders of compound oxides, with large surface areas, which are completely homogeneous on the atomic level. 
Co-precipitation methods utilize neutralizing precipitation reaction of multiple inorganic ions in aqueous solution, and while the colloid particles produced have fine particle sizes, the precipitation reaction for each inorganic ion depends on the pH and therefore each of the individual colloid particles tend to comprise single metal oxides or metal hydroxides, such that a compound oxide homogeneously mixed at the atomic level is not obtained. 
Conventional alkoxide methods employ hydrolysis of multiple metal alkoxides in organic solvents but, as the stabilities and hydrolysis reaction rates differ depending on the metal alkoxide, the oxides of different metals are produced in different orders, and therefore it has not been possible to obtain compound oxides which are homogeneously mixed at the atomic level. 
On the other hand, there have been proposed methods of synthesizing catalytically active particles precious metal particles or compound oxide particles such as ceria-zirconia) in a microemulsion, and then simultaneously synthesizing an oxide carrier around the catalytically active particles in the reaction field (Japanese Unexamined Patent Publication HEI No.  10-216517, Japanese Unexamined Patent Publication HEI No.  7-246343).  These methods are for the purpose of inhibiting sintering by movement of the catalytically active particles and preventing heat deterioration of the catalyst, but they do not improve the diffusibility of the metal ions composing the compound oxides, as set forth by the present invention. 
One of the important uses of compound oxides is as catalysts or catalyst carriers and, particularly, as exhaust gas purification catalysts for internal combustion engines.  For example, addition of cerium oxide has been examined because of its performance for purification of hydrocarbons, carbon monoxide and nitrogen oxides in internal combustion engine exhaust gas, and for its oxygen storing function whereby it stores oxygen in oxidizing atmospheres while releasing oxygen in reducing atmospheres.  However, because cerium oxide undergoes a major reduction in performance at high temperatures, it has been proposed to use cerium-zirconium compound oxides, containing added zirconia and the like, to confer heat resistance (Japanese Unexamined.  Patent Publication HEI No.  8-215569).  Still, as cerium-zirconium compound oxides are produced by the alkoxide method mentioned above, the metal ions (elements) do not homogeneously mix on the atomic level with firing at about 600° C.
In light of the current situation of the prior art as described above, it is an object of the present invention to provide a novel process for production of compound oxides which allows production of compound oxides having the metal ions (elements) homogeneously mixed on the atomic level.