NOVELTY - Microwave-assisted, solvothermal method for making olivine lithium transition metal phosphate particles, comprises (a) combining precursor materials including source of lithium ions, transition metal ions, and hydrogen phosphate ions in a solvent mixture of water and liquid alcoholic cosolvent, (b) exposing formed mixture to microwave radiation in a closed container to heat the mixture in the closed container and convert the precursor materials to an olivine lithium transition metal phosphate, and (c) separating the olivine lithium transition metal particles from the solvent mixture.    USE - The microwave-assisted, solvothermal method is useful for making olivine lithium transition metal phosphate particles (claimed) used in lithium batteries for vehicles such as electric vehicles, hybrid electric vehicles, plug-in hybrid electric vehicles, aerospace vehicles and equipment, electronic-bikes, and electrical and electronic devices such as computers, cameras, video cameras, cell phones, personal digital assistant, MPEG audio layer 3 (MP3) and other music players, tools, TV, toys, video game players, household appliances, and medical devices such as pacemakers and defibrillators.    ADVANTAGE - The method rapidly and simply produces the olivine lithium transition metal phosphate particles with good thermal stability and low toxicity and high rate capability (high power density) that exhibit unexpectedly high specific and theoretical capacities in producing high energy and power density batteries, and reduces raw material cost associated with the use of an excess of that expensive reagent as approximate stoichiometric amount of lithium precursor is provided to the reaction mixture.    DETAILED DESCRIPTION - Microwave-assisted, solvothermal method for making olivine lithium transition metal phosphate particles, comprises (a) combining precursor materials including at least one source of lithium ions, at least one source of transition metal ions, and at least one source of hydrogen phosphate ions (HxPO4), in which x is 0-2, in a solvent mixture of 20-80 wt.% of water and at least one liquid alcoholic cosolvent, which is miscible with water at the relative proportions of water and cosolvent that are present, to form a mixture, (b) exposing the mixture formed in the step (a) to microwave radiation in a closed container to heat the mixture to a temperature of at least 150 degrees C, form super atmospheric pressure in the closed container and convert the precursor materials to an olivine lithium transition metal phosphate and (c) separating the olivine lithium transition metal particles from the solvent mixture.