  In this paper we study the localization transition induced by the disorder in
random antiferromagnetic spin-1/2 chains. The results of numerical large scale
computations are presented for the XX model using its free fermions
representation. The scaling behavior of the spin stiffness is investigated for
various disorder strengths. The disorder dependence of the localization length
is studied and a comparison between numerical results and bosonization
arguments is presented. A non trivial connection between localization effects
and the crossover from the pure XX fixed point to the infinite randomness fixed
point is pointed out.
