Disclosed is a method for manufacturing crystals of aluminates of one or more element(s) other than aluminium, referred to as “A. The method includes: placing starting reagents, including at least one aluminium element source and a source of the element(s) A that has a degree of oxidation of between 1 and 6, in suspension in a liquid medium, forming a suspension referred to as the “starting suspension”; milling the starting suspension at ≤50° C., in a three-dimensional liquid medium ball mill for ≤5 minutes; recovering, at the outlet of the three-dimensional ball mill, a suspension referred to as the “end suspension” including the starting reagents in activated form or crystals of aluminate of the element(s) A generally in hydrated form; if required, calcination of the end suspension when it includes the starting reagents in activated form, to obtain generally non-hydrated crystals of aluminate of the element(s) A.