Metal composite hydroxide and method for producing same, positive electrode active material for non-aqueous electrolyte secondary battery and method for producing same, and non-aqueous electrolyte secondary battery

A positive electrode active material for non-aqueous electrolyte secondary battery comprising a lithium-metal composite oxide represented by a general formula (4):

• Li1+αNi1-x-yCoxMnyMzO2+β (where −0.05≤a≤0.50, 0.02≤x≤0.3, 0.02≤y≤0.3, 0≤z≤0.05, −0.5≤β≤0.5, and M is at least one element selected from the group consisting of Mg, Ca, Al, Si, Fe, Cr, V, Mo, W, Nb, Ti, and Zr), wherein
• [(D90−D10)/MV] of the positive electrode active material that indicates a dispersion of a particle size in particle size distribution calculated by D90, D10 and the volume average particle diameter (MV) by a laser diffraction scattering method is 0.80 or more,
• the lithium-metal composite oxide contains a secondary particle formed of primary particles and having a core portion formed of the primary particles which are aggregated inside the secondary particle and a shell portion formed around the core portion,
• a composition of the core portion in the secondary particle is represented by a general formula (5):
• Li1+a1Ni1-x1-y1Cox1Mny1Mz1O2+β1 (where −0.05≤a1≤0.50, 0.7≤(1−x1−y1)≤0.96, 0≤z1≤0.05, and −0.5≤β1≤0.5 are satisfied),
• a composition of the shell portion in the secondary particle is represented by a general formula (6):
• Li1+a2Ni1-x2-y2Cox2Mny2Mz2O2+β2 (where −0.05≤a2≤0.50, (1−x1−y1)/(1−x2−y2)>1.0, 0<(1−x2−y2)<0.6, 0≤z2≤0.05, −0.5≤β2≤0.5 are satisfied), and
• the shell portion has a thickness to be 10% or more and 40% or less of a radius of the secondary particle in a direction from a surface to a center of the secondary particle in the secondary particle having a particle size that is in a range of ±10% of the volume average particle diameter (MV) of the positive electrode active material, and
• the core portion has a radius to be 60% or more and 90% or less of the radius of the secondary particle in a direction from the center thereof in the secondary particle having the particle size that is in the range of ±10% of the volume average particle diameter (MV) of the positive electrode active material.