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The mean-square displacements of atoms in a face-centered cubic crystal have been calculated as a function of distance from a free surface using the harmonic approximation in the high-temperature limit. The procedure is based on the inversion of the dynamical matrix. Calculations have been made for the (100), (110), and (111) surfaces using a nearest-neighbor central-force model for crystals up to 30 layers thick. The force constants for surface atoms are assumed to be the same as those in the interior. The mean-square displacements increase monotonically from the middle of the crystal to the surface. Anisotropy of the meansquare displacement components is found for the surface atoms in each plane considered. The theoretical results are compared with recent low-energy electron-diffraction data on nickel single crystals.
Clark et al. (Mon,) studied this question.