A manufacturing method of a particulate solid

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Provided is a process for readily producing fine particles of a solid solution having a small particle size, comprising a solid solution of zirconia, ceria and a rare earth oxide in a desired composition, and being highly crystalline. The process for producing the fine particles of the solid solution comprises the following steps in the order named : obtaining a melt comprising, in terms of mol% on an oxide basis, from 5 to 50% ZrO 2 , CeO 2 and RE 2 O 3 (where RE is at least one member selected from rare earth elements other than Ce) in total, from 10 to 50% RO (where R is at least one member selected from the group consisting of Mg, Ca, Sr, Ba and Zn), and from 30 to 75% B 2 O 3 ; quenching the melt to obtain an amorphous material; heating the amorphous material to obtain precipitates containing crystals of a solid solution with ZrO 2 , CeO 2 and RE 2 O 3; and separating the crystals of the solid solution from the precipitates to obtain fine particles of the solid solution.