Lattice vibrations and structural instability in Cesium near the cubic to tetragonal transition

Under pressure cesium undergoes a transition from a high-pressure fcc phase (Cs-II) to a collapsed fcc phase (Cs-III) near 4.2GPa. At 4.4GPa there follows a transition to the tetragonal Cs-IV phase. In order to investigate the lattice vibrations in the fcc phase and seek a possible dynamical instability of the lattice, the phonon spectra of fcc-Cs at volumes near the III to IV transition are calculated using Savrasov’s density functional linear-response LMTO method. Compared with quasiharmonic model calculations including non-central interatomic forces up to second neighbours, at the volume V/V0 = 0.44 (V0 is the experimental volume of bcc-Cs with a0=6.048Å), the linear-response calculations show soft intermediate wavelength T[11̄0][ξξ0] phonons. Similar softening is also observed for short wavelength L[ξξξ] and L[00ξ] phonons and intermediate wavelength L[ξξξ] phonons. The Born-von Kármán analysis of dispersion curves indicates that the interplanar force constants exhibit oscillating behaviours against plane spacing n and the large softening of intermediate wavelength T[11̄0][ξξ0] phonons results from a negative (110)-interplanar force-constant Φn=2. The calculated frequencies for high-symmetry K and W phonons and longitudinal X and L phonons decrease with volume compression. In particular, the frequencies of the T[11̄0][ξξ0] phonons with ξ around 1 3 become imaginary and the fcc structure becomes dynamically unstable for volumes below 0.41V0. It is suggested that superstructures corresponding to the q6=0 soft mode should be present as a precursor of tetragonal Cs-IV structure.