Electrostatic stability of Wigner and Wigner-Dyson lattices

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Abstract
The local electrostatic stability against homogeneous deformations of uniformly charge-compensated lattices of point charges of the Wigner (unary or single charge species) and Dyson (binary or two charge species in equal concentration) types is explored. Within the scope of these calculations only the bcc, fcc, and hcp unary lattices are found to be locally stable with the bcc having the lowest energy of the three. Among binary lattices, locally stable lattices at various charge ratios of the two species are found to be the CsCl, NaCl, sphalerite (ZnS), tungsten carbide (WC), and the 1:1 gold-copper (AuCu). At very large charge ratio a lattice here dubbed almost bcc is found to be locally and possibly globally stable. Parameters and energies for the above lattices plus that of some locally unstable lattices are given as well as the energies of segregated unary lattices of the two species for all values of the charge ratio. This allows the most-stable lattice at each charge ratio to be determined. It is further conjectured that among binary lattices with a basis of more than two atoms, the wurtzite (ZnS) structure is probably also locally stable over some charge-ratio range. No simple correlation between structure and electrostatic energy has become apparent, but the energies of all locally stable forms differ by 0.1% or less. Some implications are briefly discussed.

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