Theory of Surface Atom Mean Square Displacements in Chrominum.

The temperature dependence of the mean square displacements for atoms on the 100 and 110 surfaces of chromium has been studied theoretically using the harmonic approximation. Calculations were carried out for crystals with periodic boundary conditions in two directions and free boundary conditions in the third direction using a Born-Von Karman model with central interactions up to third nearest neighbors and non-central angular stiffness interactions between nearest and next nearest neighbors. The values of the force constants were chosen to give good fits to the elastic constants and to the bulk phonon dispersion curves in the three major directions 100, 110 and 111. The ratio of the mean-square displacements at a surface to that in the bulk was calculated as a function of temperature for both the 100 and 100 surfaces. The theoretical results are compared with the available experimental data from low-energy electron diffraction. Author