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:

at least Li and Ni,

wherein the following (1) and the following (2) are satisfied,

(1) in a pore size distribution of an adsorption isotherm which is obtained by measuring an adsorption isotherm and a desorption isotherm with a nitrogen gas according to a Barrett-Joyner-Halenda method, a pore volume in a range where a pore size is 2 nm or more and 10 nm or less is more than 0.4× 10 −3 cm 3 /g and 1.0×10 −3 cm 3 /g or less,

(2) A/D 50 is 0.9×10 −3 or more and 3.4×10 −3 or less,

(A is an average pore size (nm) based on a pore size distribution of a desorption isotherm obtained by measuring an adsorption isotherm and a desorption isotherm with a nitrogen gas according to a Barrett-Joyner-Halenda method, and D 50 is a value (μm) of a particle diameter at 50% cumulative from a fine particle side in a cumulative particle size distribution curve obtained by a particle size distribution measurement of the lithium metal composite oxide).

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

wherein the following (3) is satisfied,

(3) A/D 10 is 6.5× 10 −3 or less,

(D 10 is a value (μm) of a particle diameter at 10% cumulative from the fine particle side in the cumulative particle size distribution curve).

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

wherein the following (4) is satisfied,

(4) A/D 90 is 1.9×10 −3 or less,

(D 90 is a value (μm) of a particle diameter at 90% cumulative from the fine particle side in the cumulative particle size distribution curve).

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

wherein the following (5) is satisfied,

(5) in the pore size distribution of the adsorption isotherm, a pore volume in a range where a pore size is more than 10 nm and 200 nm or less is 8.0×10 −3 cm 3 /g or less.

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

wherein a BET specific surface area is 0.5 m 2 /g or more and 1.5 m 2 /g or less.

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

wherein the A is 10 nm or more and 40 nm or less.

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

wherein a tap density is 2.5 g/cm 3 or more and 3.1 g/cm 3 or less.

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

wherein the D 50 is 5 μm or more and 20 μm or less.

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

wherein the lithium metal composite oxide is represented by the following compositional formula (I),

Li

[

Li

x

(

Ni

(

1

-

y

-

z

)

⁢

M

⁢

1

y

⁢

M

⁢

2

z

)

1

-

x

]

⁢

O

2

(

I

)

(in the compositional formula (I), M1 is one or more elements selected from the group consisting of Co, Mn, and Al, M2 is one or more elements selected from the group consisting of Fe, Cu, Ti, Mg, W, Mo, Nb, Zn, Sn, Zr, Ga, B, Si, S, and P, and the compositional formula (I) satisfies −0.1 ≤x≤0.2,0<y≤0.7, and 0≤z≤0.2).

10 . The lithium metal composite oxide according to claim 9 ,

wherein the compositional formula (I) satisfies 0<y+z≤0.3.

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

the lithium metal composite oxide according to claim 1 .

12 . A positive electrode for lithium secondary battery, comprising: the positive electrode active material for lithium secondary battery according to claim 11 .

13 . A lithium secondary battery comprising: the positive electrode for lithium secondary battery according to claim 12 .