Stabilizing the Simple Hexagonal Structure -- Alloys of Tin*

Approximately thirty elements have ground state or room-temperature structures with only one atom in the unit cell: fcc (Cu, Ir, Pb, etc.), bct (Cr, Ta, W, etc.), bct (In), rhombohedral (Hg), and even simple cubic (Po) lattices. The simple hexagonal (sh) lattice is never seen, even though it has a higher symmetry than rhombohedral and the same number of near neighbors as the bcc lattice. Only element, tin, has even a relatively low-energy sh structure.

Experimentally, the sh structure is found in mercury-tin alloys. To understand this, we performed a series of Density Functional calculations on Hg_xSn_1-x and Cd_xSn_1-x structures by the virtual crystal approximation (VCA); supercell calculations with ordered placement of the Cd/Hg atom (e.g., one impurity atom per unit cell); and using high-throughput AFLOW calculations to sample larger supercells with random impurities.

Both Cd and Hg stabilize the simple hexagonal structure against α- and β-Sn. The success of the VCA suggests that this is a density of states effect, and we examine the effect of alloying on the density of states using all of our techniques.