Anharmonic free energy and specific heat at constant volume of sodium and potassium

Abstract

The lowest-order cubic ($F_3$) and quartic ($F_4$) anharmonic contributions to the Helmholtz free energy have been calculated at several temperatures and lattice spacings for sodium and potassium using interionic potentials developed by Taylor and co-workers. The effect of using either the Geldart-Taylor or Vashishta-Singwi screening on these calculations has been examined. $F_3$ and $F_4$ are not sensitive to the choice of screening. A method of calculating $F_3$ has been developed which is more suited to long-range potentials. At all temperatures the anharmonic specific heat at constant volume ($C_V^A$) is found to be positive for potassium. For sodium, $C_V^A$ is positive for $T<\mathrm{}293\mathrm{}$ °K at which temperature $F_3$ and $F_4$ appear to cancel each other; the sign of $C_V^A$ becomes negative at $T=361\mathrm{}$ °K.