Surface mean-square displacements for NaCl

The mean-square displacements and mean-square velocities have been calculated for the (001) surface of a 15-layer NaCl crystal slab with the Kellermann rigid-ion and deformation-dipole models. Comparison of the two models shows that the inclusion of polarization effects results in an increase in the room-temperature value of $〈{\mu }_z^2\left({\mathrm{Cl}}^{-}\right)〉$ at the surface (the $z$ direction being perpendicular to the surface) and causes the room-temperature value of $\frac{〈{\mu }_z^2\left({\mathrm{Na}}^{+}\right)〉}{〈{\mu }_z^2\left({\mathrm{Cl}}^{-}\right)〉}$ at the surface to depart considerably from the corresponding bulk value. The calculation of various limiting values can be determined more efficiently using Gaussian quadrature numerical integration.