What is claimed is:
1. A positive electrode active material for a lithium ion battery which has a layer structure represented by a compositional formula:
Li α (Ni β Me 1-β )O γ ,
wherein Me represents at least one type selected from the group consisting of Mn, Co, Al, Mg, Cr, Ti, Fe, Nb, Cu and Zr,
α denotes a number from 0.9 to 1.2,
β denotes a number from 0.70 to 0.79, and
γ denotes a number of 1.9 or more,
wherein measured coordinates of lattice constant a and a compositional ratio (Li/M) of Li to M, wherein M is the sum of all metals excluding Li in the above compositional formula, are within a region enclosed by three lines given by a set of equations: y=1.108, y=−37.298x+108.27, and y=75.833x−217.1 on a graph in which the x-axis represents a lattice constant a and the y-axis represents the compositional ratio (Li/M) of Li to M, and measured coordinates of lattice constant c is from 14.2 to 4.25.
2. The positive electrode active material for a lithium ion battery according to claim 1 , wherein the coordinates of the lattice constant a and compositional ratio (Li/M) are within the region enclosed by three lines given by the equations: y=5x−13.311, y=49.737x−142.02, and y=−60x+173.56.
3. The positive electrode active material for a lithium ion battery according to claim 1 , wherein Me is one metal selected from the group consisting of Mn, Co, and Al.
4. A positive electrode for a lithium ion battery comprising the positive electrode active material described in claim 1 .
5. A lithium ion battery comprising the positive electrode for lithium ion battery described in claim 4 .
6. A positive electrode for lithium ion battery comprising the positive electrode active material described in claim 2 .
7. A positive electrode for lithium ion battery comprising the positive electrode active material described in claim 3 .
8. A lithium ion battery comprising the positive electrode for lithium ion battery described in claim 6 .
9. A lithium ion battery comprising the positive electrode for lithium ion battery described in claim 7 .