Nickel-manganese composite hydroxide, method for producing the same, positive electrode active material for nonaqueous electrolyte secondary battery, method for producing the same, and nonaqueous electrolyte secondary battery

A nickel-manganese composite hydroxide represented by General Formula (1):

• NixMnyMz(OH)2+α
• wherein in Formula (1), M is at least one additional element selected from Co, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, Fe, and W;
• x satisfies 0.1≤x≤0.9, y satisfies 0.05≤y≤0.8, z satisfies 0≤z≤0.8, and x+y+z=1.0;
• and a satisfies 0≤α≤0.4,
• wherein the nickel-manganese composite hydroxide contains secondary particles, each of the secondary particles being formed of a plurality of flocculated primary particles,
• wherein the nickel-manganese composite hydroxide has a half width of a diffraction peak of a (001) plane obtained by X-ray diffraction measurement of at least 0.40° and
• wherein the nickel-manganese composite hydroxide has an average void density (%) within a range of from more than 22% to 40%, the average void density being determined by obtaining a cross-section from each of 20 of the secondary particles having a particle size of at least 80% of a volume-average particle diameter MV of the secondary particles, determining a void area within the cross-section from each of the 20 of the secondary particles, determining an area of the cross-section from each of the 20 of the secondary particles, determining a void density for each of the 20 of the secondary particles according to an equation
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• and averaging the void density of the 20 of the secondary particles to obtain the average void density.