 Solution

At high density, disorder can frustrate efficient local packing and leave particles with very little room to move. An ordered arrangement can give every particle a larger cage of allowed displacements. The extensive gain in vibrational/configurational freedom within these cages can outweigh the loss of distinct spatial arrangements of cages. Visual order is therefore not a reliable measure of entropy. At low density the fluid's freedom to rearrange dominates, whereas sufficiently dense packing can favour a crystal through accessible free volume.