A study of the effect of temperature on the stable crystal structures of potassium and sodium

Abstract

A nonlocal, optimized version of the Heine-Abarenkov model potential is used to calculate the structure-dependent part of the Helmholtz free energy for three different structures of sodium and potassium. It is found that, if a quasiharmonic approximation is used to describe the lattice vibrations, the hexagonal-close-packed (hcp) structure of sodium is preferred at temperatures below 99 K; above this temperature the body centred cubic phase has the lowest free energy. However, the model predicts incorrectly the hcp structure for potassium at 0 K. An approximate calculation of the anharmonic contributions to the free energy indicates that the phase stabilities of sodium and potassium are not significantly effected by these contributions. A calculation of the quasiharmonic free energy of potassium from an Ashcroft potential which is fitted to measured phonon frequencies also predicts an incorrect structure for this metal at 0 K. Possible reasons for this failure are discussed.