Method for producing a lithium ion secondary battery active material particles, electrodes and lithium-ion secondary battery

With good surface smoothness of the active material particles, while suppressing an increase in the internal resistance of the active material layer can improve cycle characteristics, and produce a lithium ion secondary battery active material particles decomposition is suppressed in the electrolyte even at a high potential to. A lithium secondary battery active material particles (X), [Li, Mg, Ca, Sr, Ba, Pb, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Fe, Co, Ni, Cu, Zn, Al, In, Sn, Sb, Bi, La, Ce, Pr, Nd, Gd, Dy, Er, and a compound having a metal element (M) selected from the group] consisting of Yb ( composition comprising a), and