Positive active material precursor for secondary lithium battery, the positive active material, and secondary lithium battery including the positive active material

A positive active material precursor for a secondary lithium battery, which is represented by the following Chemical Formula 1 and has an intensity ratio of I/Iof more than or equal to about 2 of the peak Iof a (001) plane peak to the peak Iof a (100) plane peak according to X-ray diffraction analysis, a W/Wratio of less than about 2 of the full width at half maximum Wof a (100) plane peak to the full width at half maximum Wof a (001) plane peak according to X-ray diffraction analysis, and an S/Sratio of less than or equal to about 0.265 of the area Sof a (001) plane peak and the area Sof a (100) plane peak according to X-ray diffraction analysis. [Chemical Formula 1] NiCoMnM(OH)wherein, M is a metal selected from Al, Mg, Ti, Zr or a combination thereof, 0.45≤x≤0.65, 0.15≤y≤0.25, 0.15≤z≤0.35, 0≤k≤0.1, and x+v+z+k=1.