Mean-square atomic displacement of alkali-metal atoms: A comparison of the lattice-dynamics and molecular-dynamics results

Molecular-dynamics (MD) calculations of the mean-square displacement (MSD) have been carried out for a sixth-neighbor-interaction model of the alkali metals Na, K, and Cs for several temperatures for the zero-pressure, zero-temperature volume as well as for the zero-pressure volume corresponding to each temperature. The lattice-dynamics (LD) calculations of the harmonic and the lowest-order anharmonic (cubic and quartic) contributions to the MSD were performed for the same model potential with interactions extending to six-neighbor shells as in the MD calculations. The Brillouin-zone (BZ) 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 fully converged with respect to the number of points in the BZ. The BZ sums arising in the cubic contribution to MSD were converged to about 5% accuracy. Excellent agreement between the MD and LD results was observed in the case of all the alkali metals, except for the zero-pressure case of Cs, where the difference is about 15% near the melting temperature ($T_M$). It is concluded that for the alkali metals, the lowest-order perturbation theory works well for MSD even at temperatures close to $T_M$.