Anharmonic Lattice Dynamics in K

Abstract

The lattice dynamics of K at $T=9,99,215, \mathrm{and} 299$ \ifmmode^\circ\else\textdegree\fi{}K is studied employing an effective pair ion-ion potential and the self-consistent (SC) theory for anharmonic crystals. The effective potential was derived from first principles following the method that Geldart et al. developed successfully for Na. The purpose of the present paper is (i) to test whether the potential derivation can be extended successfully to K and (ii) to compare the SC anharmonic theory with experiment and the standard anharmonic perturbation theory used by Buyers and Cowley. For all the symmetry directions except the ${\ensuremath{\Delta}}_{1}$ branch, the phonon frequencies computed here at 9 \ifmmode^\circ\else\textdegree\fi{}K lie within 2% of the observed frequencies verifying the validity of the K ion-ion potential. The total anharmonic shifts in frequency (quasiharmonic + anharmonic) with temperature are comparable but $\ensuremath{\sim}$ 20% greater than those computed by Buyers and Cowley. Given the scatter in the observed shifts, both calculations agree equally well with experiment.