In a crystal with a free surface, the force constants associated with the coupling of surface atoms to their neighbors need not be the same as those associated with the coupling of interior atoms. A theoretical investigation has been made of the effect on the atomic mean square displacements of varying the force constants for surface atoms on the (110) surface of a face-centered cubic crystal. The bonds coupling atoms on such a surface to their nearest neighbors may be grouped into three classes, depending on the angle between the bond and the normal to the surface. The force constants for each of these three types of surface bonds have been varied independently, and the mean square displacements have been evaluated in the high-temperature limit of the harmonic approximation, using the nearest-neighbor central force model for crystals up to thirty layers thick. A comparison is given between the theoretical results and experimental low-energy electron diffraction data for the (110) surface of nickel.

• Received 20 November 1967

DOI:https://doi.org/10.1103/PhysRev.167.652