New instabilities in Wigner-Dyson lattices

Binary NaCl and CsCl Wigner-Dyson lattices have been found to exhibit a new instability (mode-softening) at critical values of the charge ratio of the two species. These occur for transverse-acoustic vibrational modes with wave vector in the [110] direction in CsCl structure (and polarization in the [001] direction) at the first Brillouin-zone boundary and in the [100] direction in NaCl structure at the zone boundary (point $M$ for CsCl and point $X$ for NaCl in reciprocal-lattice space). These instabilities leave a gap in the charge-ratio parameter range in which the only currently known locally stable structure consists of segregated bcc lattices for the two species.