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

Under pressure, caesium undergoes a transition from a high-pressure fee (fa ce-centred cubic) phase (Cs-LI) to a collapsed fee phase (Cs-III) near 4.2 GPa. At 4.4 GPa there follows a transition to the tetragonal Cs-IV phase. I n order to investigate the lattice vibrations in the fee phase and seek a p ossible dynamical instability of the lattice, the phonon spectra of fee Cs at volumes near the III-to-IV transition are calculated using Savrasov's de nsity functional linear-response LMTO (linear muffin-tin orbital) method. C ompared with quasiharmonic model calculations including non-central interat omic forces up to second neighbours, at the volume V/V-0 = 0.44 (V-0 is the experimental volume of bcc Cs (bcc equivalent to body-centred cubic) with a(0) = 6.048 Angstrom), the linear-response calculations show soft intermed iate-wavelength T[(1 (1) over bar0)][xi xi0] phonons. Similar softening is also observed for short-wavelength L[xi xi xi] and L[00 xi] phonons and int ermediate-wavelength;th L[xi xi xi] phonons. The Born-von Karman analysis o f the dispersion curves indicates that the interplanar force constants exhi bit oscillating behaviours against plane spacing n and the large softening of intermediate wavelength T-[1 (1) over bar0][xi xi0] phonons results from a negative (110) interplanar force constant Phi (n=2). The calculated freq uencies for high-symmetry K and W and longitudinal X and L phonons decrease with volume compression. In particular, the frequencies of the T-[110] [xi xi0] phonons with xi around 1/3 become imaginary and the fee structure bec omes dynamically unstable for volumes below 0.41V(0). It is suggested that superstructures corresponding to the q not equal 0 soft mode should be pres ent as a precursor of tetragonal Cs-IV structure.