A layered double hydroxide is represented by the following formula (I): Ni.sup.2+.sub.1?(x+y+z)Fe.sup.3+.sub.xV.sup.3+.sub.yCo.sup.3+.sub.z(OH).sub.2A.sup.n?.sub.(x+y+z)/n.Math.mH.sub.2O . . . (I). In one embodiment, in the formula (I), (x+y+z) is from 0.2 to 0.5, x represents more than 0 and 0.3 or less, y represents from 0.04 to 0.49, and z represents more than 0 and 0.2 or less.

A method of recovering cobalt and nickel includes the steps of: adding alkaline to an acidic solution containing aluminum together with cobalt and nickel, adjusting pH of the acidic solution to 5 to 7, and converting the cobalt, the nickel and the aluminum into hydroxides thereof; recovering the hydroxides by solid-liquid separation, mixing the recovered hydroxides with an alkaline solution, and leaching aluminum contained in the hydroxides under a liquid condition of pH 8 or more; and recovering a cobalt hydroxide and a nickel hydroxide that aluminum is separated therefrom by solid-separation on a leachate.

A method of recovering cobalt and nickel includes the steps of: adding alkaline to an acidic solution containing aluminum together with cobalt and nickel, adjusting pH of the acidic solution to 5 to 7, and converting the cobalt, the nickel and the aluminum into hydroxides thereof; recovering the hydroxides by solid-liquid separation, mixing the recovered hydroxides with an alkaline solution, and leaching aluminum contained in the hydroxides under a liquid condition of pH 8 or more; and recovering a cobalt hydroxide and a nickel hydroxide that aluminum is separated therefrom by solid-separation on a leachate.

A method for producing a nickel cobalt complex hydroxide includes first crystallization of supplying a solution containing Ni, Co and Mn, a complex ion forming agent and a basic solution separately and simultaneously to one reaction vessel to obtain nickel cobalt complex hydroxide particles, and a second crystallization of, after the first crystallization, further supplying a solution containing nickel, cobalt, and manganese, a solution of a complex ion forming agent, a basic solution, and a solution containing said element M separately and simultaneously to the reaction vessel to crystallize a complex hydroxide particles containing nickel, cobalt, manganese and said element M on the nickel cobalt complex hydroxide particles crystallizing a complex hydroxide particles comprising Ni, Co, Mn and the element M on the nickel cobalt complex hydroxide particles.

A method for producing a nickel cobalt complex hydroxide includes first crystallization of supplying a solution containing Ni, Co and Mn, a complex ion forming agent and a basic solution separately and simultaneously to one reaction vessel to obtain nickel cobalt complex hydroxide particles, and a second crystallization of, after the first crystallization, further supplying a solution containing nickel, cobalt, and manganese, a solution of a complex ion forming agent, a basic solution, and a solution containing said element M separately and simultaneously to the reaction vessel to crystallize a complex hydroxide particles containing nickel, cobalt, manganese and said element M on the nickel cobalt complex hydroxide particles crystallizing a complex hydroxide particles comprising Ni, Co, Mn and the element M on the nickel cobalt complex hydroxide particles.

A method of making Co.sub.3O.sub.4 nanorods by thermal decomposition of a cobalt salt is described. A method of using Co.sub.3O.sub.4 nanorods as an electrocatalyst component to a porous carbon electrode is also described. The carbon electrode may be made of carbonized filter paper. Together, this carbon-supported Co.sub.3O.sub.4 electrode may be used for water electrolysis.

A method of making Co.sub.3O.sub.4 nanorods by thermal decomposition of a cobalt salt is described. A method of using Co.sub.3O.sub.4 nanorods as an electrocatalyst component to a porous carbon electrode is also described. The carbon electrode may be made of carbonized filter paper. Together, this carbon-supported Co.sub.3O.sub.4 electrode may be used for water electrolysis.

A positive electrode active material includes positive electrode active material particles including a composite oxide with a hexagonal crystal structure. The composite oxide includes Li, Co, and at least one element M1 selected from the group consisting of Ni, Fe, Pb, Mg, Al, K, Na, Ca, Si, Ti, Sn, V, Ge, Ga, B, As, Zr, Mn and Cr, and the at least one element M1 is provided on a surface of the positive electrode active material particles. An atomic ratio of a total amount of the at least one element M1 to an amount of Co on the surface of the positive electrode active material particles is from 0.6 to 1.3.

A positive electrode active material includes positive electrode active material particles including a composite oxide with a hexagonal crystal structure. The composite oxide includes Li, Co, and at least one element M1 selected from the group consisting of Ni, Fe, Pb, Mg, Al, K, Na, Ca, Si, Ti, Sn, V, Ge, Ga, B, As, Zr, Mn and Cr, and the at least one element M1 is provided on a surface of the positive electrode active material particles. An atomic ratio of a total amount of the at least one element M1 to an amount of Co on the surface of the positive electrode active material particles is from 0.6 to 1.3.

The present disclosure discloses a method for recycling all types of lithium batteries. First, the lithium battery waste is acid-leached to obtain a solution containing most of metal ions. After filtering, the solution is separated from the remaining solids, and then the obtained solution is subjected to separate precipitation many times. After separately adjusting the pH value of the solution many times, adding precipitants with a high selectivity ratio, and matching with filtration and separation reaction, all ions in the lithium battery waste are sequentially precipitated in forms of iron phosphate (FePO.sub.4), aluminum hydroxide (Al(OH).sub.3), manganese oxide (MnO.sub.2), dicobalt trioxide (cobalt oxide, Co.sub.2O.sub.3), nickel hydroxide (Ni(OH).sub.2), and lithium carbonate (Li.sub.2CO.sub.3).