Theoretical Temperature Dependence of the Mean-Square Displacements and Velocities of Surface Atoms of Face-Centered Cubic Crystals

A theoretical investigation has been made of the temperature dependence of the mean-square displacements and velocities of surface atoms at a (110) free surface of a face-centered cubic crystal. A nearest-neighbor central-force model which provides a reasonable representation of nickel was used in the harmonic approximation. It was found that the mean-square displacements and velocities are essentially linear functions of temperature down to 200^∘{}K, or about one-half the bulk Debye temperature. Below 200^∘{}K, quantum-mechanical effects appear. Particular attention was paid to the temperature dependence of the anisotropy of the displacements and velocities associated with the (110) surface. Changes in the surface force constants were taken into acount.