NOVELTY - An active material has layer structure and composition containing lithium-nickel-cobalt-manganese-metal oxide (I). The ratio of primary particle diameter (D1) and average primary particle diameter (D2) of the active material is 3.57-5.39, measured using scanning electron microscope.    USE - Active material for positive electrode of lithium ion secondary battery (claimed) used as power supply for electric vehicles. Can also be used for electrochemical capacitors, e.g. lithium ion capacitors used for self-propelled micromachines and integrated circuit cards.    ADVANTAGE - The active material provides lithium ion secondary batteries with high capacity, and excellent charging/discharging cycle characteristics in high electric potential.    DETAILED DESCRIPTION - An active material has layer structure and composition containing lithium-nickel-cobalt-manganese-metal oxide of formula: LiyNiaCobMncMdOx (I), where M is silicon, barium or vanadium, a+b+c+d+y is 1.9-2.1, y is 1.05-1.3, a is 0-0.3 (excluding 0), b is 0-0.25, c is 0.3-0.7, d is 0-0.1 (excluding 0) and x is 1.90-2.1. The ratio (D1/D2) of primary particle diameter (D1) of the active material and average primary particle diameter (D2) of the active material measured using scanning electron microscope, is 3.57-5.39, and D1 is calculated using the formula: D1=6/(Sx ( rho )), where ( rho ) is the true density of the powder computed by BET method. An INDEPENDENT CLAIM is included for lithium ion secondary battery (100), which consists of positive electrode (10) having a positive electrode electrical power collector (12) and positive electrode active material layer (14) containing a positive electrode active material, negative electrode (20) having an anode collector (22) and a negative electrode active material layer (24) containing a negative electrode active material, a separator (18) located between the positive electrode active material layer and the negative electrode active material layer. The positive electrode active material contains the active material.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic cross-sectional view of a lithium ion secondary battery.    Positive electrode (10)    Positive electrode electrical power collector (12)    Positive electrode active material layer (14)    Separator (18)    Negative electrode (20)    Anode collector (22)    Negative electrode active material layer (24)    Lithium ion secondary battery (100)