the present invention will now be described in detail based on examples . note that the present invention is not limited by examples below , and can be suitably modified without departing from the scope of the present invention . lithium hydroxide ( lioh ) was added to an aqueous solution containing ni , co , and mn to prepare nickel - cobalt - manganese ( nicomn ) hydroxide . the nickel - cobalt - manganese hydroxide and lithium carbonate were mixed with each other so as to satisfy a stoichiometric ratio of lini 0 . 15 co 0 . 70 mn 0 . 15 o 2 . the mixture was then fired in the air at 900 ° c . for 24 hours to produce a first active material . the particle size of the first active material was measured using a laser diffraction particle size analyzer , and the average particle size ( d 50 ) was 12 μm . the average particle size ( d 50 ) was defined as the particle size at which , when the numbers of particles are accumulated in ascending order of particle size , the cumulative number reaches 50 % of the total number of particles . as a result of the analysis of the first active material by powder x - ray diffraction , it was confirmed that the first active material had a layered structure that belongs to the space group r3 - m . lithium hydroxide ( lioh ) was added to an aqueous solution containing ni , co , and mn to prepare nickel - cobalt - manganese hydroxide . the nickel - cobalt - manganese hydroxide and lithium carbonate were mixed with each other so as to satisfy a stoichiometric ratio of li 1 . 2 mn 0 . 54 ni 0 . 13 co 0 . 13 o 2 . the mixture was then fired in the air at 900 ° c . for 24 hours to produce a second active material . the particle size of the second active material was measured in the same manner as described above , and the average particle size ( d 50 ) was 6 μm . as a result of the analysis of the second active material by powder x - ray diffraction , it was confirmed that the second active material had a layered structure that belongs to the space group c2 / m and a layered structure that belongs to the space group r3 - m . the first active material and the second active material were mixed with each other at a mass ratio of 5 : 5 . the mixed positive electrode active material , acetylene black , and polyvinylidene fluoride were mixed with each other at a mass ratio of 90 : 5 : 5 . n - methyl - 2 - pyrrolidone ( nmp ) was then added to the mixture to prepare a slurry . the slurry was applied onto a current collector made of aluminum foil and dried in the air at 120 ° c . to produce an electrode . the obtained electrode was rolled and cut into pieces each having a size of 20 mm × 50 mm to produce a positive electrode a1 . a positive electrode a2 was produced in the same manner as in example 1 , except that , in the production process of the first active material , the nickel - cobalt - manganese hydroxide and lithium carbonate were mixed with each other so as to satisfy a stoichiometric ratio of lico 0 . 50 ni 0 . 25 mn 0 . 25 o 2 . the particle size of the first active material was measured in the same manner as described above , and the average particle size ( d 50 ) was 12 μm . as a result of the analysis of the first active material by powder x - ray diffraction , it was confirmed that the first active material had a layered structure that belongs to the space group r3 - m . a positive electrode a3 was produced in the same manner as in example 1 , except that , in the production process of the first active material , the nickel - cobalt - manganese hydroxide and lithium carbonate were mixed with each other so as to satisfy a stoichiometric ratio of lico 1 / 3 ni 1 / 3 mn 1 / 3 o 2 . the particle size of the first active material was measured in the same manner as described above , and the average particle size ( d 50 ) was 12 μm . as a result of the analysis of the first active material by powder x - ray diffraction , it was confirmed that the first active material had a layered structure that belongs to the space group r3 - m . a positive electrode b1 was produced in the same manner as in example 1 , except that , in the production process of the first active material , lico 2 and co 2 o 4 were mixed with each other so as to satisfy a stoichiometric ratio of licoo 2 . the particle size of the first active material was measured in the same manner as described above , and the average particle size ( d 50 ) was 12 μm . as a result of the analysis of the first active material by powder x - ray diffraction , it was confirmed that the first active material had a layered structure that belongs to the space group r3 - m . a positive electrode b2 was produced in the same manner as in example 1 , except that only the second active material in example 1 was used as a positive electrode active material . a positive electrode b3 was produced in the same manner as in example 1 , except that only the first active material in example 1 was used as a positive electrode active material . a positive electrode b4 was produced in the same manner as in example 2 , except that only the first active material in example 2 was used as a positive electrode active material . a positive electrode b5 was produced in the same manner as in example 3 , except that only the first active material in example 3 was used as a positive electrode active material . a positive electrode b6 was produced in the same manner as in comparative example 1 , except that only the first active material in comparative example 1 was used as a positive electrode active material . three - electrode cells a1 to a3 and b1 to b6 shown in fig1 were produced using the positive electrodes a1 to a3 and b1 to b6 , respectively . the positive electrodes a1 to a3 and b1 to b6 were each used as a working electrode 1 . a nonaqueous electrolyte 2 was prepared by dissolving lipf 6 , in a concentration of 1 mol / l , in a nonaqueous electrolytic solution which was prepared by mixing ethylene carbonate with diethyl carbonate at a volume ratio of 3 : 7 . lithium metal was used as a counter electrode 3 and a reference electrode 4 . a polyethylene separator was used as a separator 5 . the three - electrode cells a1 to a3 and b1 to b6 were each charged at room temperature at a constant current of 100 ma / g until the working electrode potential on a reference electrode basis reached 4 . 6 v ( li / li + ), charged at a constant voltage of 4 . 6 v ( li / li + ) until the current value reached 5 ma / g , and then discharged at a constant current of 100 ma / g until the working electrode potential on a reference electrode basis reached 2 v ( li / li + ). the discharge capacity at this time was defined as a discharge capacity of the 1st cycle . the charge - discharge operation was further repeatedly performed 28 times under the same conditions . the capacity retention ratio after the charge - discharge cycle test was determined by dividing the discharge capacity of the 29th cycle by the discharge capacity of the 1st cycle . table 1 shows the results . as is clear from table 1 , the capacity retention ratio of a1 that contains both the first active material and second active material is higher than the capacity retention ratio of b2 that contains only the second active material and the capacity retention ratio of b3 that contains only the first active material . thus , it is found that , when the positive electrode active material contains both the first active material and second active material , a larger - than - expected effect is produced due to the combined effect of the first and second active materials . it is also found that such a larger - than - expected effect is also produced in a2 and a3 . it is clear that the capacity retention ratios of a1 to a3 are higher than the capacity retention ratio of b1 . this means that a high capacity retention ratio is achieved when x in the general formula of the first active material is 0 . 7 or less . the reason for this is unclear , but is believed to be as follows . the first active material of b1 contains a large amount of co and thus the reactivity between a positive electrode and an electrolytic solution is increased . as a result , the electrolytic solution is excessively decomposed and the capacity retention ratio of b1 is decreased . herein , in the case where the positive electrode is charged to 4 . 5 v ( li / li ±) or more on a lithium metal basis , the above - described reactivity between a positive electrode and an electrolytic solution is believed to be further increased . the nickel - cobalt - manganese hydroxide and lithium carbonate were mixed with each other so as to satisfy a stoichiometric ratio of lico 1 / 3 ni 1 / 3 mn 1 / 3 o 2 . the mixture was then fired in the air at 900 ° c . for 24 hours to produce a first active material . the particle size of the first active material was measured in the same manner as described above , and the average particle size ( d 50 ) was 14 . 1 μm . as a result of the analysis of the first active material by powder x - ray diffraction , it was confirmed that the first active material had a layered structure that belongs to the space group r3 - m . the nickel - cobalt - manganese hydroxide and lithium carbonate were mixed with each other so as to satisfy a stoichiometric ratio of li 1 . 2 mn 0 . 54 ni 0 . 13 co 0 . 13 o 2 . the mixture was then fired in the air at 900 ° c . for 24 hours to produce a second active material . the particle size of the second active material was measured in the same manner as described above , and the average particle size ( d 50 ) was 12 . 7 μm . as a result of the analysis of the second active material by powder x - ray diffraction , it was confirmed that the second active material had a layered structure that belongs to the space group c2 / m and a layered structure that belongs to the space group r3 - m . the first active material and the second active material were mixed with each other at a mass ratio of 8 : 2 . subsequently , a three - electrode cell a4 was produced in the same manner as in example 1 . a three - electrode cell a5 was produced in the same manner as in example 4 , except that the first active material and the second active material were mixed with each other at a mass ratio of 6 : 4 . a three - electrode cell a6 was produced in the same manner as in example 4 , except that the first active material and the second active material were mixed with each other at a mass ratio of 4 : 6 . a three - electrode cell a7 was produced in the same manner as in example 4 , except that the first active material and the second active material were mixed with each other at a mass ratio of 2 : 8 . a three - electrode cell b7 was produced in the same manner as in example 4 , except that only the first active material in example 4 was used as a positive electrode active material . a three - electrode cell b8 was produced in the same manner as in example 4 , except that only the second active material in example 4 was used as a positive electrode active material . the three - electrode cells a4 to a7 , b7 , and b8 were subjected to the charge - discharge test in the same manner as described above . table 2 shows the results . as is clear from table 2 , a high capacity retention ratio is achieved when the ratio of the mass of the first active material to the total mass of the first active material and second active material is 20 % to 80 % by mass . the nickel - cobalt - manganese hydroxide and lithium carbonate were mixed with each other so as to satisfy a stoichiometric ratio of lini 1 / 3 co 1 / 3 mn 1 / 3 o 2 . the mixture was then fired in the air at 900 ° c . for 24 hours to produce a first active material . the particle size of the first active material was measured in the same manner as described above , and the average particle size ( d 50 ) was 14 . 1 μm . the nickel - cobalt - manganese hydroxide and lithium carbonate were mixed with each other so as to satisfy a stoichiometric ratio of li 1 . 2 mn 0 . 54 ni 0 . 13 co 0 . 13 o 2 . the mixture was then fired in the air at 900 ° c . for 24 hours to produce a second active material . the particle size of the second active material was measured in the same manner as described above , and the average particle size ( d 50 ) was 6 . 3 μm . a positive electrode a8 was produced in the same manner as in example 4 , except that the obtained first active material and the obtained second active material were mixed with each other at a mass ratio of 8 : 2 . a positive electrode a9 was produced in the same manner as in example 8 , except that the first active material and the second active material were mixed with each other at a mass ratio of 6 : 4 . the mass ( g ), thickness ( cm ), and area ( cm 2 ) of each of the positive electrodes a4 , a5 , a8 , and a9 were measured to calculate the packing density . the packing density was calculated from the following formula : packing density =( mass of positive electrode − mass of current collector )/{( thickness of positive electrode − thickness of current collector )× area of positive electrode )}. furthermore , between the average particle sizes ( d 50 ) of the first active material and second active material , a large average particle size was denoted as r and a small average particle size was denoted as r , and a value of r / r was determined . table 3 shows the results . as is clear from table 3 , in the comparison between electrodes containing the first active material at the same mass ratio , a high packing density is achieved when 0 . 20 & lt ; r / r & lt ; 0 . 60 is satisfied .