A study of the arsenic, black phosphorus, and other structures derived from rock salt by bond-breaking processes. I. Structural enumeration

The structures of arsenic and black phosphorus can be regarded as distortions of the simple cubic or NaCl structure. The presence of more than four electrons per site results in the breaking of three of the six linkages around each atom in the NaCl structure. A generalization of Pólya’s enumeration theorem is proven which allows counting of the 36 possible ways of breaking bonds to produce structures containing trigonal pyramidal coordination at each site and having the same size unit cell as NaCl. Larger cells are considered briefly.