Lithium complex oxide

A lithium complex oxide comprising a mixture of first particles and second particles, the lithium complex oxide represented by the following Chemical Formula 1 and having a full width at half maximum (FWHM) (deg., 2θ) of a 104 peak in an XRD peak, defined by a hexagonal lattice having an R-3m space group, in a range of the following Relational Formula 1:

• wherein in Chemical Formula 1, M is at least one selected from the group consisting of:
• B, Ba, Ce, Cr, F, Mg, Al, Cr, V, Ti, Fe, Zr, Zn, Si, Y, Nb, Ga, Sn, Mo, W, P, Sr, and any combination thereof, 0.9≤a≤1.3, 0.6≤x≤1.0, 0.0≤y≤=0.4, 0.0≤z≤0.4, and 0.0≤1−x−y−z≤0.4,
• wherein FWHM(104) in Relational Formula 1 is represented by the following Relational Formula 2,
• wherein in Relational Formula 2, FWHMChemical Formula 1 powder (104) is a FWHM of a 104 peak observed near 44.5° (2θ) in an XRD measurement value of the lithium complex oxide,
• FWHMSi powder (220) is a FWHM of a 220 peak observed near 47.3° (2θ) in an XRD measurement value of a Si powder that is Sigma-Aldrich No. 215619 Si powder,
• xfirst particle=(x−xsecond particle*mass ratio of second particles)/mass ratio of first particles, xsecond particle meaning a Ni molar rate of the second particles, and x is as defined above in Chemical Formula 1, and
• the mass ratios mean a mass rate with respect to the total mass of the first particles and the second particles, and
• wherein xfirst particle and xsecond particle are different from each other.