TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: At least part of the Li(I) is introduced as LiOH. At least part of the P(V) is introduced as H3PO4. The pH of the water-based mixture is obtained by adjusting the ratio of LiOH to H3PO4. The atmospheric boiling point of the water-based mixture is (above 100 - below 200, preferably 105 - 120)degreesC. The method further involves: post-treatment of the LiFePO4 powder by heating in non-oxidizing conditions, at above 200 - below 600degreesC.Preferred Composition: The powder (P1) has maximum particle size of below 500 nm; and a mono-modal particle size distribution, with the ratio (d90 - d10)/d50 of (less than 0.8, preferably less than 0.65, especially less than 0.5).    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The water-miscible boiling point elevation additive is dimethyl sulfoxide. EXAMPLE - A crystalline LiFePO4 powder was prepared as follows. In first step, dimethyl sulfoxide (DMSO) was added to an equimolar aqueous solution of 0.1 M Fe(II) in FeSO4.7H2O and 0.1 M P(V) in H3PO4, dissolved in H2O under stirring. The amount of DMSO was adjusted in order to reach a global composition of water (50 vol.%) and DMSO (50 vol.%). In a second step, an aqueous solution of 0.3 M LiOH-H2O was added to the solution at 25degreesC, to increase the pH up to 7 - 7.5. The final Li:Fe:P molar ratio in the solution obtained was close to 3:1:1. In a third step, the temperature of the solution was increased up to the boiling point of the solvent, which was 108 - 110degreesC, to begin precipitation of LiFePO4. After 1 hour, the precipitate was filtered and washed thoroughly with H2O. A thermal treatment was finally performed by putting the dry precipitate at 500degreesC for 3 hours in a slightly reducing N2/H2 (95/5) gas flow. The volumetric particle size distribution of the product was measured using image analysis, which showed the d50 value of about 140 nm, while the relative span, defined as (d90 -d10)/d50, was about 0.5. A slurry was prepared by mixing 95% of the invented LiFePO4 powder with ketjen carbon black (5 wt.%) and N-methyl-2-pyrrolidone (NMP) and deposited on an aluminium current collector. The obtained electrode was used to manufacture coin cells, using a loading of 3 mg/cm2 active material, and a plot of specific capacity (mAh/g) relative to the active material as a function of discharge rate (C). The battery showed that excellent discharge capacity was maintained up to at least a discharge rate of 5C. The capacity at 1C was 151 mA/g, corresponding to 88% of the theoretical capacity of LiFePO4. As a comparative example, results as reported by Nuspl et al., showed a lower overall reversible capacity and higher losses, especially at rates above 1C, even though only 79% of active material was used in the electrode mixture, together with a loading of only 2.3 mg/cm2. The lower active material content and the lower loading indeed tended to give an upward bias to the measured reversible capacity. The capacity retention using the invented product proved also excellent, as no significant degradation was apparent after 200 charge-discharge cycles at C/2 and at 5C. The capacity of the cells appeared to fade by less than 0.04% per cycle in the above discharge conditions, a performance on par with the current industrial demand.