Effects of surface atom vibrations on the diffraction of proton and deuteron beams from the basal plane of graphite

The diffractive scattering of 1H and 2H beams from the basal plane of graphite has been studied as a function of the crystal temperature in the range 65-350 K. The data at low temperatures have been interpreted by using the hard corrugated wall (HCW) model which gives a peak-to-peak corrugation Epp = 0.090 A which is about a factor of 2 lower than the value reported in the literature for He-(0001)C. The agreement between the experimental probabilities and the predictions of the HCW model as a function of the incident angle is discussed. Furthermore, the temperature dependence of the experimental intensities of the (0,0) and (1,0) peaks have been studied at several incident angles in order to test the applicability of a Debye-Waller factor theory. Although the high-temperature range of the data seems to be well reproduced by a DWF theory when a Beeby correction is included, a comparison with recent accurate calculation of the surface mean square displacements shows that the Armand correction is needed to compare the theoretical results with the experiment. The present data are also compared with similar data obtained for He by Boato, G. et al. Surf. Sci. 1982, 114, 485