The thermal attenuation of elastic scattering of helium from copper single crystal surfaces

The dependence of diffraction peak intensities upon temperature for the scattering of helium from various copper surfaces: Cu (111), (100), (110), (113), (115) and (117), has been experimentally determined for two incident energies (21–63 meV) and a large range of incidence angles. For the close-packed faces (111) and (100), the data are consistent with a Debye-Waller formalism involving an effective surface mean square displacement <u²_eff〉. The quantitative fit with the data is good if anharmonic effects are properly taken into account. This result establishes that a generalized Debye-Waller formalism is, at least as a first approximation, relevant to the helium-surface diffraction. For the rougher surfaces the agreement remains good up to a threshold temperature above which the intensities are always lower than predicted by the model. It is proposed that this may be due to some kind of thermal roughening of the surface.