LITHIUM METAL COMPOSITE OXIDE POWDER, POSITIVE ELECTRODE ACTIVE SUBSTANCE FOR LITHIUM SECONDARY BATTERY, POSITIVE ELECTRODE, AND LITHIUM SECONDARY BATTERY

A lithium metal composite oxide powder including: secondary particles that are aggregates of primary particles, and single particles that are present independently of the secondary particles, wherein the lithium metal composite oxide is represented by composition formula (I), and the single particles have an average crushing strength exceeding 80 MPa: Li[Li(NiCoMnM)]O (I) wherein M is one or more metal elements selected from the group consisting of Fe, Cu, Ti, Mg, Al, W, B, Mo, Nb, Zn, Sn, Zr, Ga, La and V, −0.1≤x≤0.2, 0≤y≤0.4, 0≤z≤0.4, and 0≤w≤0.1.