TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The step (a) is performed by adding the transition metal precursor(s) to a solution of phosphoric acid in water or a mixture of water and the alcoholic cosolvent, adding cosolvent if necessary, and then adding lithium hydroxide. Preferred Components: The transition metal is iron or a mixture of iron and manganese at a mole ratio of 10:90-35:65. The precursor materials include at least one dopant metal precursor, and the dopant metal precursor is present in an amount of 1-3 mole-percent based on total moles of transition metal precursor(s) and dopant metal precursor. The microwave radiation has a frequency of 500-3000 MHz, and the mixture is exposed to the microwave radiation for 5-30 minutes. The super atmospheric pressure is 150-4000 kPa. The temperature in the step (b) is 160-225 degrees C. The olivine lithium transition metal particles are lithium manganese iron phosphate particles of formula (LiaMnbFecD1dPC).D1 = dopant metal;a = 0.5-1.5, preferably 0.96-1.1;b = 0.1-0.9, preferably 0.65-0.85;c = 0.1-0.9, preferably 0.15-0.35; andd = 0-0.03, preferably 0.65-0.85 0.01-0.03, where the sum of b, c and d is 0.75-1.25, preferably 0.95-1.02, and content of a+2(b+c+d) is 2.75-3.15, preferably 2.95-3.15.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The alcoholic cosolvent is one or more of methanol, ethanol, isopropanol, n-propanol, n-butanol, tert-butanol, secondary-butanol, n-pentanol, n-hexanol, ethylene glycol, diethylene glycol (preferred), triethylene glycol, tetraethylene glycol, propylene glycol, dipropylene glycol, tripropylene glycol, tetrapropylene glycol, 1,4-butane diol, a polyalkylene glycol having a molecular weight up to 1000, 2-methoxyethanol, 2-ethoxyethanol, glycerin or trimethylolpropane. The solvent mixture contains 40-60 wt.% of water and the alcoholic cosolvent. EXAMPLE - 0.009 M of manganese sulfate monohydrate and 0.003 M of iron sulfate heptahydrate were dissolved in a mixture of 0.012 M of phosphoric acid in 30 ml of deionized and deoxygenated water. After the salts were dissolved, 30 ml of diethylene glycol was added with stirring at 25 degrees C. 0.012 M moles of lithium hydroxide and 0.018 M of ammonium hydroxide were added with continued stirring and precipitate was formed upon addition of the lithium hydroxide. The container was closed, and the mixture was then exposed to 2450 MHz microwave radiation for five minutes, during which time the internal temperature was reached at 210 degrees C and the internal pressure was reached at 30 bar (3000 kPa). The mixture was then cooled to room temperature. The supernatant liquid was decanted from the precipitated particles, which were then washed repeatedly with deionized water and dried overnight at 80 degrees C. A portion of the resulting olivine lithium transition metal phosphate particles was taken for X-ray diffraction and inductive coupled plasma analysis. Another portion of the particles was milled with 18 wt.% of Ketjenblack (RTM: Superconductive carbon black) and dried at 200 degrees C for 12 hours under nitrogen to produce olivine lithium transition metal phosphate particles of electrode material.