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Various surface properties have been calculated for the (100), (111), and (110) surfaces of noble-gas crystals through the method of molecular dynamics. This method takes complete account of anharmonic effects and mean displacements, both of which are found to be important for surface calculations at high temperatures. The results are compared with those obtained through lattice dynamics in the quasiharmonic approximation. The results for the displacements of the mean atomic positions (from the positions in the bulk) are in good agreement with these found through lattice dynamics. The results for the mean-square amplitudes are in good agreement for atoms a few layers beneath the surface, but indicate that anharmonicity causes a substantial increase in these quantities near the surface at about half the melting temperature (the temperature for which most of the calculations were performed). The Fourier transform of the velocity autocorrelation function is compared with the density-of-states function determined in the quasiharmonic approximation, and the presence of anharmonic effects is again indicated. The static displacements, determined by damping the motion of the atoms, are found to be the same for all atoms in a given plane, thus justifying the usual assumption made in calculating these quantities.
Allen et al. (Sat,) studied this question.