Dense Sphere Packing in the NaZn13 Structure Type

The packing density of binary (A 13 B) and ternary (A 12 BC) hard-sphere systems with the NaZn 13 structure type is investigated in detail using a combination of Monte Carlo simulated annealing and gradient optimizations. This paper shows that if distortions from the perfect icosahedral arrangement of Zn spheres are considered the binary packing density can exceed that of segregated spheres in close packed lattices and that the optimal packing fraction of 0.748431 occurs at a radius ratio of 0.578458. This accurately coincides with the size ratio observed in precious opal structures with this structure type. Atomic alloys with this structure type are also distorted but not in the same way as would be required for ideal binary sphere packing. Instead, they are broadly consistent with the distortions required for ideal packing of ternary sphere systems when the central sphere in the icosahedron of small spheres is permitted to take on a different size. This paper also presents an improved optimal ternary structure with a packing fraction of 0.77124, which also has relevance to lower pressure binary phase diagrams, and systems with a degree of polydispersity.