Transition metal composite hydroxide and method for producing the same, positive electrode active material for a non-aqueous electrolyte secondary battery and method for producing the same, and non-aqueous electrolyte secondary battery

A method for manufacturing a transition metal composite hydroxide, wherein the method is for manufacturing a transition metal composite hydroxide which is a precursor of the positive electrode active material for a non-aqueous electrolyte secondary battery by mixing a raw material aqueous solution including at least a transition metal element and an aqueous solution including an ammonium ion donor to form a reaction aqueous solution, and performing a crystallization reaction, the method is characterized in comprising:

• a nucleation step in which nucleation is performed in a non-oxidizing atmosphere having an oxygen concentration of 5% by volume or less in which the pH value of the reaction aqueous solution at a standard liquid temperature of 25° C. is adjusted to be within a range of 12.0 to 14.0;
• and
• a particle growth step in which at a standard liquid temperature 25° C. the pH value of the reaction aqueous solution including the nuclei obtained in the nucleation step is adjusted to be lower than the pH value of the nucleation step and to be within a range of 10.5 to 12.0 so as to grow the nuclei;
• wherein
• an atmosphere control is performed such that the non-oxidizing atmosphere is maintained in the early period and the middle period of the particle growth step which is in a range of 70% to 90% of time from the initiation of the particle growth step with respect to the entire period of the particle growth step, and in the latter period of the particle growth step, the non-oxidizing atmosphere is switched to the oxidizing atmosphere where the oxygen concentration exceeds 5% by volume, and then the oxidizing atmosphere is switched to the non-oxidizing atmosphere again.