## Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

##### Abstract

We have calculated the thermodynamic properties of monatomic fcc
crystals from the high temperature limit of the Helmholtz free energy.
This equation of state included the static and vibrational energy
components. The latter contribution was calculated to order A4 of perturbation
theory, for a range of crystal volumes, in which a nearest
neighbour central force model was used. We have calculated the lattice
constant, the coefficient of volume expansion, the specific heat at
constant volume and at constant pressure, the adiabatic and the isothermal
bulk modulus, and the Gruneisen parameter, for two of the rare gas solids,
Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones
and the Morse potential were each used to represent the atomic
interactions for the rare gas solids, and only the Morse potential was
used for the fcc metals. The thermodynamic properties obtained from the
A4 equation of state with the Lennard-Jones potential, seem to be in
reasonable agreement with experiment for temperatures up to about threequarters
of the melting temperature. However, for the higher temperatures,
the results are less than satisfactory. For Xe and Kr, the thermodynamic
properties calculated from the A2 equation of state with the Morse potential,
are qualitatively similar to the A
2 results obtained with the Lennard-Jones
potential, however, the properties obtained from the A4 equation of state
are in good agreement with experiment, since the contribution from the A4
terms seem to be small.
The lattice contribution to the thermal properties of the fcc metals
was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation
of state. In order to compare the calculated specific heats and bulk
moduli results with experiment~ the electronic contribution to thermal
properties was taken into account~ by using the free electron model.
We found that the results varied significantly with the value chosen for
the number of free electrons per atom.