Entropy-driven formation of a superlattice in a hard-sphere binary mixture

Abstract

A MIXTURE of two dissimilar species (A and B) may freeze to form a substitutionally ordered crystal, the structure of which can vary from a lattice with only a few atoms per unit cell to a complex 'superlattice'. For example, a mixture of sodium and zinc can form a solid with the AB₁₃ structure with 112 atoms per unit cell¹ (Fig. la). One might suspect that very specific energetic interactions are needed to stabilize a structure as complex as this. But recent experiments^2,3 show that the AB₁₃ structure is also formed in mixtures of spherical colloidal particles with different diameters, which interact only via simple repulsive potentials. This raises the possibility that the formation of an AB₁₃ superlattice might be sup-ported by entropic effects alone. To investigate this possibility, we present here computer simulations of a binary mixture of hard spheres. Our calculations show that entropy alone is indeed sufficient to stabilize the AB₁₃ phase, and that the full phase diagram of this system is surprisingly complex. Our results also suggest that vitrification or slow crystal nucleation in experimental studies of colloidal hard spheres can prevent the formation of equilibrium phases.