Mean Displacement of Surface Atoms in Palladium and Lead Single Crystals

The intensity of specularly reflected (00) reflection low-energy (5-500-eV) electrons has been measured as a function of temperature for the (100) and (111) faces of palladium and for the (111) face of lead in the temperature ranges 25°-600°C and 25°-225°C, respectively. From the data, the root-mean-square displacements, 〈u⊥〉, of surface atoms perpendicular to the surface planes and the surface Debye temperatures have been calculated. The mean vibrational amplitudes of surface atoms are 40%→100% larger than for bulk atoms. There is little difference between the surface mean displacements of different crystal orientations; 〈u⊥〉 appears to be relatively insensitive to changes of surface structure or surface density. The experimental results correlate well with those obtained for platinum and silver single-crystal surfaces. It is believed that all monatomic face-centered cubic crystal surfaces should have mean displacements markedly larger than those in the bulk.