TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The content of residue when heating the organic compound for 8 hours at 700 degrees C under inert atmosphere or reducing gas, is 15 %mass or less, with respect to total content of organic compound. The carbon-type electroconductivity substance is carbon black, graphite, acetylene black, and/or amorphous carbon. The usage-amount of carbon source in secondary crushing process is 1-50 %mass. The compound containing element (A) is carbonate, hydrogencarbonate, hydroxide, silicate, phosphate, borate, fluoride, chloride, nitrate, sulfate and/or organic acid salt of element (A). The compound containing element (M) is oxide, hydroxide, oxyhydroxide, silicate, phosphate, borate, fluoride, chloride, nitrate, sulfate, organic acid salt and/or alkoxide of element (M). The compound containing element (X) is oxide and/or alkoxide of element (X), and silicate of element (A) or (M), phosphate of element (A) or (M), borate of element (A) or (M), aluminate of element (A) or (M), vanadate of element (A) or (M), molybdate of element (A) or (M), tungstate of element (A) or (M), germanium acid salt of element (A) or (M) and/or antimonate of element (A) or (M). The compound containing element (X) is organic acid salt. The compound containing element (Z) is fluoride of element (A) or (M), and/or chloride of element (A) or (M). The positive electrode active materials are particles of olivine-type crystal structure whose at least one portion is covered with electroconductive carbon. Preferred Conditions: The grinding process in the secondary crushing process is carried out in presence of a solvent. The primary heating process is carried out at 500-1000 degrees C. The secondary heating process is carried out at 300-800 degrees C. The cooling rate of molten material in the cooling process is -103 degrees C/second to -10-10 degrees C/second. Preferred Property: The positive electrode active material has specific surface area of 10-70 m2/g.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Composition: The solvent is water, ethanol, isopropyl alcohol, acetone, hexane, and/or toluene.    TECHNOLOGY FOCUS - POLYMERS - Preferred Composition: The organic compound is preferably polyethyleneglycol, polyvinyl alcohol, stearic acid, ethyl cellulose, melamine, camphor and/or polyacrylic acid. Preferred Definitions:    A=Li;and    M=Fe or Mn.