Abstract:
Molec ul ar dynamics calculations of the mean sq ua re
displacement have been carried out for the alkali metals Na, K
and Cs and for an fcc nearest neighbour Lennard-Jones model
applicable to rare gas solids. The computations for the alkalis
were done for several temperatures for
temperature vol ume a swell as for
the
the
ze r 0 pressure ze ro
zero pressure volume
corresponding to each temperature. In the fcc case, results were
obtained for a wide range of both the temperature and density.
Lattice dynamics calculations of the harmonic and the lowe s t
order anharmonic (cubic and quartic) contributions to the mean
square displacement were performed for the same potential models
as in the molecular dynamics calculations. The Brillouin zone
sums arising in the harmonic and the quartic terms were computed
for very large numbers of points in q-space, and were
extrapolated to obtain results ful converged with respect to
the number of points in the Brillouin zone.An excellent agreement between the
lattice dynamics results was observed
molecular dynamics and
in the case of all the
alkali metals, e~ept for the zero pressure case of CSt where the
difference is about 15 % near the melting temperature. It was
concluded that for the alkalis, the lowest order perturbation
theory works well even at temperat ures close to the melting
temperat ure.
For the fcc nearest neighbour model it was found that the
number of particles (256) used for the molecular dynamics
calculations, produces a result which is somewhere between 10 and
20 % smaller than the value converged with respect to the number
of particles. However, the general temperature dependence of the
mean square displacement is the same in molecular dynamics and
lattice dynamics for all temperatures at the highest densities
examined, while at higher volumes and high temperatures the
results diverge. This indicates the importance of the higher
order (eg. ~* ) perturbation theory contributions in these cases.
