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

1 . A lithium metal composite oxide comprising:

a secondary particle which is an aggregate of primary particles; and

a single particle which exists independently of the secondary particle,

wherein the lithium metal composite oxide has a layered rock-salt structure, is represented by Composition Formula (I) below, satisfies (1) and (2) below,

L

⁢

i

x

⁢

Ni

1

⁢

‐

⁢

y

⁢

‐

⁢

z

⁢

‐

⁢

w

⁢

Co

y

⁢

Mn

z

⁢

X

⁢

1

w

⁢

O

2

(

I

)

(here, Composition Formula (I) satisfies 0.9≤x≤1.2, 0≤y≤0.4, 0≤z≤0.4, 0≤w≤0.1, and y+z+w≤1, and X1 represents one or more elements selected from the group consisting of Mg, Ca, Sr, Ba, Zn, B, Al, Ga, Ti, Zr, Ge, Fe, Cu, Cr, V, W, Mo, Sc, Y, Nb, La, Ta, Tc, Ru, Rh, Pd, Ag, Cd, In, and Sn),

1.2

≤

L

A

/

L

B

<

1.6

(

1

)

(L A is a crystallite diameter obtained from a diffraction peak 1 within a range of 2θ=18.8±1° and L B is a crystallite diameter obtained from a diffraction peak 2 within a range of 2θ=38.3±1° in a diffraction peak obtained from powder X-ray diffraction using CuKα rays), and

(2): a Me occupancy at a lithium site in the layered rock-salt structure is 2.5% or less, as determined by analyzing the diffraction peaks by the Rietveld analysis method, and the Me is Ni, Co, Mn, or X1.

2 . The lithium metal composite oxide according to claim 1 ,

wherein z satisfies 0≤z≤0.2.

3 . The lithium metal composite oxide according to claim 1 ,

wherein a BET specific surface area is 1.0 m 2 /g or less.

4 . The lithium metal composite oxide according to claim 1 , wherein the single particle has an average particle diameter of 2.0 μm or more and 10 μm or less.

5 . The lithium metal composite oxide according to claim 1 ,

wherein (3) below is satisfied,

0.3

≤

P

⁢

1

/

D

5

⁢

0

(

3

)

(P1 is an average particle diameter (μm) of the single particle, and D 50 is a 50% cumulative volume particle diameter (μm) of the lithium metal composite oxide, as obtained from a volume-based cumulative particle size distribution curve measured by a laser diffraction scattering method.)

6 . The lithium metal composite oxide according to claim 1 ,

wherein L B is 1000 Å or less.

7 . A positive electrode active material for a lithium secondary battery, comprising:

the lithium metal composite oxide according to claim 1 .

8 . A positive electrode for a lithium secondary battery, comprising:

the positive electrode active material for the lithium secondary battery according to claim 7 .

9 . A lithium secondary battery comprising:

the positive electrode for the lithium secondary battery according to claim 8 .

10 . The lithium metal composite oxide according to claim 2 ,

wherein a BET specific surface area is 1.0 m 2 /g or less.

11 . The lithium metal composite oxide according to claim 2 , wherein the single particle has an average particle diameter of 2.0 μm or more and 10 μm or less.

12 . The lithium metal composite oxide according to claim 2 ,

wherein (3) below is satisfied,

0.3

≤

P

⁢

1

/

D

5

⁢

0

(

3

)

(P1 is an average particle diameter (μm) of the single particle, and D 50 is a 50% cumulative volume particle diameter (μm) of the lithium metal composite oxide, as obtained from a volume-based cumulative particle size distribution curve measured by a laser diffraction scattering method.)

13 . The lithium metal composite oxide according to claim 2 ,

wherein L B is 1000 Å or less.

14 . A positive electrode active material for a lithium secondary battery, comprising:

the lithium metal composite oxide according to claim 2 .

15 . A positive electrode for a lithium secondary battery, comprising:

the positive electrode active material for the lithium secondary battery according to claim 14 .

16 . A lithium secondary battery comprising:

the positive electrode for the lithium secondary battery according to claim 15 .