NOVELTY - A family of cathode materials comprises: substantially a defective crystalline lithium transition metal oxide phosphate.    USE - For a lithium-ion battery (claimed), useful in power tools, vehicles, and large-scale family use power batteries.    ADVANTAGE - The family of defective lithium transition metal phosphate cathode materials and the lithium-ion battery produced from them exhibit excellent electrochemical properties, and can be easily synthesized at low temperature in air atmosphere, to yield excellent charge/discharge rate capability (greater than 20C of rate capability) and cycling capability; as compared to the prior art defective crystalline cathode materials that require a costly gas-tight furnace having an inert gas atmosphere to control the decomposition of carbon and the amount of residual carbon. The formation of defects is achieved by incorporating various lithiated transition metal oxides with distinct stoichiometry into LiFePO4 structure. The method can be easily scaled-up for commercial applications, provides easy control of the quality of the resultant materials; and further saves the cost of inert gas, and reduces the overall cost of the synthesis protocol. The heating at low temperature in an air atmosphere, not only enhances the consistency of the cathode material, but also maintains the batch-to-batch consistency of the synthesized materials. The low temperature heat treatment minimizes the possibility of decomposition of the defective material, and further lower temperature heat treatment i.e. lower than the decomposition temperature of carbon black at approximately 600degreesC also reduces the variations of residual carbon content and distribution during the heat treatment. The use of Fe2O3, Li2CO3 and H3PO4 starting materials that form CO2 and H2O are low cost starting materials. The enhancement in the electrical conductivity of the defective crystalline cathode material, the ise of excess carbon and the existence of carbon content in the resultant material is not necessary.    DETAILED DESCRIPTION - A family of cathode materials comprises: substantially a defective crystalline lithium transition metal oxide of formula LiFe(1-x)MxP(1-x)O2(2-x) (Ia), or Li(1-x/2)MxFe(1-x)P(1-x)O2(2-x) (Ib).    x=0.01-0.3;    M=transition metal selected from nickel, titanium, vanadium, chromium, manganese, iron, cobalt and/or aluminum.    INDEPENDENT CLAIMS are included for the following:    (1) method (M1) for forming a cathode material for a lithium-ion battery involving: (a) providing a crystalline lithium transition metal oxide; (b) providing starting chemicals of Li:Fe:P:C in a molar ratio of 1:1:1:2; (c) combining and milling the materials of steps (a) and (b) to form a mixture of the materials of steps (a) and (b) in particulate form; (d) heating the material of step (c) in a vessel in air, to form a cathode material having a defective crystalline structure of a crystalline compound of formula (Ia) or (Ib), with the surfaces of the material facing the air covered by a layer of inert blanket, which is porous and allows air permeation and escaping gases caused by the heating;    (2) method (M2) for forming a cathode for a lithium-ion battery involving: steps (a)-(d); (e') preparing a slurry containing (wt.%) the material of step (d) (85-95), carbon (2-7), a soluble binding material (2-7), and a solvent for the soluble binding material; (f') coating at least one side of a foil with the slurry; and (g') drying the slurry coating; and    (3) method (M3) for forming a Li-ion battery involving: (a2) forming several cathodes by the method of (M2); (b2) forming several anodes; (c2) arranging the several cathodes and anodes in alternating sequence; and (d2) providing an electrolyte between the alternative cathodes and anodes.