The atomic mean square displacement (MSD) and the phonon dispersion
curves (PDC's) of a number of face-centred cubic (fcc) and body-centred
cubic (bcc) materials have been calclllated from the quasiharmonic (QH)
theory, the lowest order (A2
) perturbation theory (PT) and a recently proposed
Green's function (GF) method by Shukla and Hiibschle. The latter
method includes certain anharmonic effects to all orders of anharmonicity.
In order to determine the effect of the range of the interatomic interaction
upon the anharmonic contributions to the MSD we have carried out our
calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN)
and next-nearest neighbour (NNN) approximations. These results can be
presented in dimensionless units but if the NN and NNN results are to be
compared with each other they must be converted to that of a real solid.
When this is done for Xe, the QH MSD for the NN and NNN approximations
are found to differ from each other by about 2%. For the A2 and GF results
this difference amounts to 8% and 7% respectively. For the NN case we have
also compared our PT results, which have been calculated exactly, with PT
results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation.
We have calculated the MSD of five alkali metals, five bcc transition
metals and seven fcc transition metals. The model potentials we have used
include the Morse, modified Morse, and Rydberg potentials. In general the
results obtained from the Green's function method are in the best agreement
with experiment. However, this improvement is mostly qualitative and the
values of MSD calculated from the Green's function method are not in much
better agreement with the experimental data than those calculated from the
We have calculated the phonon dispersion curves (PDC's) of Na and Cu,
using the 4 parameter modified Morse potential. In the case of Na, our
results for the PDC's are in poor agreement with experiment. In the case of
eu, the agreement between the tlleory and experiment is much better and
in addition the results for the PDC's calclliated from the GF method are in
better agreement with experiment that those obtained from the QH theory.
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