The present invention relates to a powderous material of hydroxide or oxyhydroxide of one or more metal elements for preparing positive electrode active material for batteries, wherein the one or more metal elements include at least one of Ni, Co and Mn, wherein the powderous material comprises particles having a core and a shell surrounding the core, wherein the core has a total area (Ac) and the shell has a total area (As) on a cross-section plane of the particle, wherein the shell has a void area percentage of at least 20% and at most 99% based on the total area of the shell (As), as determined based on cross-section SEM image analysis.