  We report the pressure and temperature dependence of the phonon
density-of-states in superconducting Ca0.6Na0.4Fe2As2 (Tc=21 K) and the parent
compound CaFe2As2, using inelastic neutron scattering. We observe no
significant change in the phonon spectrum for Ca0.6Na0.4Fe2As2 at 295 K up to
pressures of 5 kbar. The phonon spectrum for CaFe2As2 shows softening of the
low-energy modes by about 1 meV when decreasing the temperature from 300 K to
180 K. There is no appreciable change in the phonon density of states across
the structural and anti-ferromagnetic phase transition at 172 K. These results,
combined with our earlier temperature dependent phonon density of states
measurements for Ca0.6Na0.4Fe2As2, indicate that the softening of low-energy
phonon modes in these compounds may be due to the interaction of phonons with
electron or short-range spin fluctuations in the normal state of the
superconducting compound as well as in the parent compound. The phonon spectra
are analyzed with ab-initio and empirical model calculations giving partial
densities of states and dispersion relations.
