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

Abstract

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-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 $V/V_0= 0.44$ ($V_0$ is the experimental volume of bcc-Cs with $a_0$=6.048Å), the linear-response calculations show soft intermediate wavelength $T_{[1\bar{1}0]}[ξξ0]$ 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 $T_{[1\bar{1}0]}[ξξ0]$ phonons results from a negative (110)-interplanar force-constant $Φ_{n=2}$. The frequencies of the $T_{[1\bar{1}0]}[ξξ0]$ phonons with $ξ$ around 1/3 become imaginary and the fcc structure becomes dynamically unstable for volumes below $0.41V_0$. It is suggested that superstructures corresponding to the $\mathbf{q}{\neq}0$ soft mode should be present as a precursor of tetragonal Cs-IV structure.