NOVELTY - Manufacture of lithium iron phosphate and lithium iron silicate involves performing hydrothermal reaction of mixture slurry containing iron compound, phosphoric acid compound or silicic acid compound, lithium compound and water within pressure-resistant container (2). The hydrothermal reaction is carried out by installing synthetic container (1) containing mixture slurry in container (2), extracting slurry out of container (2) from piping (3) linked to the synthetic container, stirring slurry in synthetic container, and returning slurry discharged from pump through piping (5).    USE - Manufacture of lithium iron phosphate and lithium iron silicate used as positive electrode material for lithium-ion secondary battery (claimed) used for portable electronic device, hybrid vehicle and electric vehicle.    ADVANTAGE - The lithium iron phosphate and lithium iron silicate having fine and uniform particle size, are manufactured by simple method, with high purity and yield. The battery containing the lithium iron phosphate and lithium iron silicate has high capacity and charging/discharging characteristics.    DETAILED DESCRIPTION - Manufacture of lithium iron phosphate and lithium iron silicate involves performing hydrothermal reaction of mixture slurry containing iron compound, phosphoric acid compound or silicic acid compound, lithium compound and water within pressure-resistant container. The hydrothermal reaction is carried out by installing synthetic container (1) containing the mixture slurry in pressure-resistant container (2), extracting the mixture slurry out of pressure-resistant container from piping (3) linked to the synthetic container using a pump (4), stirring the slurry in synthetic container, and returning the mixture slurry discharged from pump through piping (5) different from the piping (3) in the synthetic container.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of the reaction apparatus used during manufacture of lithium iron phosphate and lithium iron silicate. (Drawing includes non-English language text)    Synthetic container (1)    Pressure-resistant container (2)    Pipings (3,5)    Pump (4)    Heating steam (6)