Abstract:
We have presented a Green's function method for the calculation
of the atomic mean square displacement (MSD) for an anharmonic
Hamil toni an . This method effectively sums a whole class of
anharmonic contributions to MSD in the perturbation expansion in
the high temperature limit.
Using this formalism we have calculated the MSD for a nearest
neighbour fcc Lennard Jones solid. The results show an improvement
over the lowest order perturbation theory results, the difference
with Monte Carlo calculations at temperatures close to melting is
reduced from 11% to 3%.
We also calculated the MSD for the Alkali metals Nat K/ Cs
where a sixth neighbour interaction potential derived from the
pseudopotential theory was employed in the calculations. The MSD
by this method increases by 2.5% to 3.5% over the respective
perturbation theory results.
The MSD was calculated for Aluminum where different pseudopotential
functions and a phenomenological Morse potential were
used. The results show that the pseudopotentials provide better
agreement with experimental data than the Morse potential. An
excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential
with Hubbard-Sham screening function.
We have calculated the thermodynamic properties of solid Kr
by minimizing the total energy consisting of static and vibrational
components, employing different schemes: The quasiharmonic theory
(QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the
improved self consistent phonon theory (ISC), the ring diagrams up
to o ().4) (RING), the iteration scheme (ITER) derived from the
Greens's function method and a scheme consisting of ITER plus the
remaining contributions of 0 ().4) which are not included in ITER
which we call E(FULL). We have calculated the lattice constant,
the volume expansion, the isothermal and adiabatic bulk modulus,
the specific heat at constant volume and at constant pressure, and
the Gruneisen parameter from two different potential functions:
Lennard-Jones and Aziz.
The Aziz potential gives generally a better agreement with
experimental data than the LJ potential for the QH, ).2, ).4 and
E(FULL) schemes. When only a partial sum of the).4 diagrams is
used in the calculations (e.g. RING and ISC) the LJ results are in
better agreement with experiment. The iteration scheme brings a
definitive improvement over the).2 PT for both potentials.
