  Using computed x-ray tomography we determine the three dimensional (3d)
structure of binary hard sphere mixtures as a function of composition and size
ratio of the particles, q. Using a recently introduced four-point correlation
function we reveal that this 3d structure has on intermediate and large length
scales a surprisingly regular order, the symmetry of which depends on q. The
related structural correlation length has a minimum at the composition at which
the packing fraction is highest. At this composition also the number of
different local particle arrangements has a maximum, indicating that efficient
packing of particles is associated with a structure that is locally maximally
disordered.
