Lithium complex oxide

1. A lithium complex oxide comprising a mixture of first particles in which n1 (n1>40) number of primary particles are aggregated and second particles in which n2 (n2≤20) number of primary particles are aggregated, 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:

Li a Ni x Co y Mn z M 1-x-y-z O 2 ,  [Chemical Formula 1]

wherein 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 a 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,

−0.025≤FWHM (104) −{0.04+( x first particle −0.6)×0.25}≤0.025,  [Relational Formula 1]

where FWHM (104) in Relational Formula 1 is represented by the following Relational Formula 2,

FWHM (104) ={(FWHM Chemical Formula 1 powder(104) −0.1×mass ratio of second particles)/mass ratio of first particles}−FWHM Si powder(220) ,  [Relational Formula 2]

wherein Relational Formula 2, FWHM Chemical 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,

FWHM Si 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,

x first particle =(x−x second particle *mass ratio of second particles)/mass ratio of first particles, x second 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.

2. The lithium complex oxide of claim 1 , wherein an average particle diameter of the first particles is in a range of 8 to 20 μm.

3. The lithium complex oxide of claim 1 , wherein an average particle diameter of the second particles is in a range of 0.1 to 7 μm.

4. The lithium complex oxide of claim 1 , wherein a crystal structure of the lithium complex oxide is a hexagonal α-NaFeO 2 .

5. The lithium complex oxide of claim 1 , wherein when a nickel content x is in a range of 0.97 to 0.99, the range of the FWHM (104) represented by the above Relational Formula 2 satisfies 0.108° (2θ) to 0.162° (2θ).

6. The lithium complex oxide of claim 1 , wherein when a nickel content x is in a range of 0.93 to 0.95, the range of FWHM (104) represented by the above Relational Formula 2 satisfies 0.098° (2θ) to 0.152° (2θ).

7. The lithium complex oxide of claim 1 , wherein when a nickel content x is in a range of 0.87 to 0.89, the range of the FWHM (104) represented by the above Relational Formula 2 satisfies 0.083° (2θ) to 0.137° (2θ).

8. The lithium complex oxide of claim 1 , wherein when a nickel content x is in a range of 0.79 to 0.81, the range of the FWHM (104) represented by the above Relational Formula 2 satisfies 0.063° (2θ) to 0.117° (2θ).

9. A method for preparing the lithium complex oxide of claim 1 , the method comprising:

preparing a first positive electrode active material by synthesizing a first positive electrode active material precursor including first particles in which n1 (n1>40) number of primary particles are aggregated and then firing the first positive electrode active material precursor after adding a lithium compound to the first positive electrode active material precursor;

synthesizing a second positive electrode active material precursor including second particles in which n2 (n2≤20) number of primary particles are aggregated and then firing the second positive electrode active material precursor after adding a lithium compound to the second positive electrode active material precursor;

preparing a second positive electrode active material by pulverizing a material formed in the synthesizing and the firing of the second positive electrode active material precursor;

mixing the first positive electrode active material and the second positive electrode active material; and

coating or doping the mixed material with a material M and then heat-treating the coated or doped material.

10. The method of claim 9 , wherein in the adding of the lithium compound to the first positive electrode active material precursor and in the adding of the lithium compound to the second positive electrode active material precursor, the added lithium compound is LiOH.

11. The method of claim 9 , wherein an average particle diameter of the first positive electrode active material prepared in the preparing of the first positive electrode active material is in a range of 8 to 20 μm.

12. The method of claim 9 , wherein an average particle diameter of the second positive electrode active material prepared in the preparing of the second positive electrode active material is in a range of 0.1 to 7 μm.

13. The method of claim 9 , further comprising washing, after firing of the first positive electrode active material precursor, after firing of the second positive electrode active material precursor, or after pulverizing of the material.

14. The method of claim 9 , further comprising washing, after heat-treating of the coated or doped material.

15. The method of claim 9 , wherein in the coating or doping of the mixed material with the material M, the material 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.