TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The chemical compound containing lithium ion is selected from lithium carbonate, lithium dihydrogen phosphate, lithium hydroxide, lithium oxalate, lithium formate, lithium silicate, lithium laurate, and/or lithium citrate. The chemical compound containing transition metal ion is selected from carbonate, sulfate, phosphate, oxalate, halide, and/or oxide. The chemical compound containing X element is selected from phosphoric acid, ammonium dihydrogen phosphate, amine phosphate, lithium phosphate, ferric phosphate, ferrous phosphate, ferrous amine phosphate, ammonium phosphate, and/or lithium dihydrogen phosphate; silicic acid, silicon dioxide, ethyl orthosilicate, tetramethylsilane, hexamethyldisilazane, silica solution, trimethylsilylacetylene, and/or ganister sand; or sulfuric acid, sulfurous acid, lithium sulfate, manganous sulfate, ferric sulfate, ferrous sulfate, ammonium sulfate, ferric ammonium sulfate, and/or ammonium persulfate.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The liquid dispersion medium is selected from water, ethyl alcohol, acetone, propanol ethyl carbinol, isopropyl alcohol, ethylene glycol, n-butanol, hexamethylene, and/or ethylenediamine.    TECHNOLOGY FOCUS - POLYMERS - Preferred Method: The dispersant is selected from cationic surface active agent, zwitterionic surface active agent, non-ionic surface active agent, aliphatic acid, ester of fatty acid, fatty alcohol, and/or aliphatic amine. The dispersant is selected from cocoamidopropyl dimethylamine propionate, dodecyl dimethyl amine oxide, oil-based dimethyl amine oxide, cocodimethyl amine oxide, lauryl betaine, coco-betaine, oleyl betaine, 1-ethoxy-2-coco-tetrahydroglyoxaline acetate, glycol ethers laurate, linear 9-11C alkyl polyoxyethylene ether, octylphenol glycol ethers, nonyl phenol glycol ethers, glycerol caprylate, glycerol monolaurate, glyceryl dilaurate, glycerol trilaurate, glyceryl cocoate, glyceryl myristate, glyceryl stearate, glyceryl hydroxystearate, glycerol tristearate, glycerol triisostearate, glyceryl oleate, glycerol trioleate, sorbitan monolaurate, sorbitan palmitate, sorbitan stearate, sorbitan sesquiisostearate, sorbitan tristearate, sorbitan monooleate, sorbitan trioleate, pentaerythritol tetraoleate, pentaerythritol tetrastearate, sucrose glyceryl cocoate, sucrose ascorbyl stearate, sucrose distearate, caprylate hexadecyl ester, caprylate octadecyl ester, myristic acid hexadecyl ester, octyl palmitate, hexadecyl ester palmitate, hexadecyl stearate, tridecyl stearate, octadecyl stearate, oleyl alcohol ester, acetyl monoisopropanolamine, lauryl monoethanolamine, lauryl diethanolamine, cocoyl monoethanolamine, cocoyl diethanolamine, oleic acid diethanolamine, oleic acid monoisopropanolamine, linoleoyl diethanolamine, bean oil diethanolamine, linoleic acid, oleic acid, linolenic acid, palm oil acid, octanoic acid, lauric acid, cetylic acid, myristic acid, methyl ester laurate, hexyl laurate, isopropyl myristic acid, butyl ester myristic acid, methyl ester cetylic acid, isopropyl cetylic acid, methyl ester stearic acid, isopropyl stearic acid, butyl ester stearic acid, isopropyl isostearic acid, methyl ester oleic acid, isopropyl oleic acid, butyl ester oleic acid, methyl ester oxystearic acid, trilaurin lactic acid, hexadecyl ester lactic acid, propylene glycol lauric acid, glycol ester distearic acid, propylene glycol stearate, propylene glycol oxystearate, propylene glycol oleate, hexadecyl alcohol, stearyl alcohol, stearyl alcohol, isostearyl alcohol, oleyl alcohol, behenic alcohol, soya sterol, cholesterol, laurylamine, cocamine, tallow amine, tallow amine hydride, soyamine, octadecyl amine, lauryl dimethyl tert-amine, cocoyl dimethyl tert-amine, and/or stearyl dimethyl tert-amine. The dispersant is at 5-50 wt.%, based on the weight of chemical compound(s) containing lithium ion, transition metal ion, and X element. The carbon source is selected from acetylene black, graphite, citric acid, ascorbic acid, cane sugar, dextrose, cellulose, and/or phenolic resin. The grinding time is 1-30 hours. The calcination temperature is 300-900 degrees C; and the calcination time is 5-30 hours. Calcination is protected by the atmosphere of nitrogen, inert gases, hydrogen, ammonia, mixed gas of nitrogen and hydrogen, or mixed gas of argon and hydrogen.