Metal composite hydroxide and method for producing the same, positive electrode active material for lithium ion secondary battery and method for producing the same, and lithium ion secondary battery using the same

A metal composite hydroxide that contains nickel, manganese, and tungsten and optionally cobalt and element M and has a mass ratio of the respective metal elements represented by Ni:Mn:Co:W:M=x:y:z:a:b (x+y+z=1, 0.3≤x≤0.95, 0.05≤y≤0.55, 0≤z≤0.4, 0<a≤0.1, 0≤b≤0.1, and M is one or more elements selected from the group consisting of Mg, Ca, Al, Ti, V, Cr, Zr, Nb, Mo, Hf, and Ta), the metal composite hydroxide comprising:

• secondary particles with a plurality of aggregated primary particles, wherein
• the secondary particles have a multilayer structure including a center at which the primary particles are densely disposed, a void at which the primary particles are more sparsely disposed than the center, and a solid portion which corresponds to a surface portion of the secondary particles at which the primary particles are densely disposed from a center of the secondary particles toward a surface,
• a tap density is 0.75 g/cm3 or more and 1.35 g/cm3 or less,
• a tungsten-concentrated layer is formed at a surface part of the solid portion such that tungsten is contained in the surface part of the solid portion at a higher concentration than in the void and the center in the secondary particles,
• an average particle size of the composite hydroxide is 4.0 μm or more and 9.0 μm or less, and
• a thickness of the tungsten-concentrated layer is 100 nm or less.