Pseudopotential Calculation of the Thermal Expansion Coefficient of Sodium and Potassium

The total adiabatic potential is represented by a model based on electrostatic interactions among the ions and conduction electrons, Born-Mayer repulsion between the ions, a local pseudopotential interaction between ion cores and conduction electrons, and conduction-electron kinetic, exchange, and correlation energies. The three model parameters are determined for sodium and potassium by requiring agreement with the crystal binding energy and its first two volume derivatives at zero temperature and pressure. The phonon frequencies and Gr\"uneisen parameters, the bulk-modulus pressure derivative, and the thermal expansion coefficient as a function of temperature are then calculated. These calculations are in good qualitative agreement with experimental results.