Analysis of low-energy-electron-diffraction intensity spectra for (001), (110), and (111) nickel

Elastic low-energy-electron-diffraction intensity-energy spectra are calculated for Ni (001), (110), and (111) surfaces between 10 and 220 eV by the layer-Korringa-Kohn-Rostoker method and compared with recent room-temperature experimental results. The calculation uses the Wakoh self-consistent muffin-tin potential, retains eight phase shifts, and includes finite temperature effects (assuming a Debye spectrum). An effective Debye temperature of 335°K is found from the temperature dependence of spectral intensities, an energy-dependent imaginary potential roughly of the form $\beta =0.85\mathrm{}{E}^{\frac{1}{3}}$ for electron energy $E$ (in eV) is determined by matching features of the calculated spectra to experiment, and the best values of the first interlayer spacing are found to be 1.76 Å (the bulk spacing) +0.02 ± 0.02 Å on the (001) surface, 1.24 - (0.06±0.02) Å on the (110) surface, and 2.03 - (0.025±0.025) Å on the (111) surface. With these parameters, excellent agreement with observed spectra is obtained in positions and shapes of peaks for several beams and a large number of incident angles. For all faces a small systematic deviation in peak positions is found with a constant 11-eV inner potential, suggesting an inner potential varying from the expected static value of 13.5 at low energies to about 9 eV near 220 eV. Comparison of relative intensities between calculation with the above $\beta \mathrm{}\left(E\right)\mathrm{}$ and experiment suggests that excitation of $3p$ electrons from Ni significantly enhances electron absorption above 65 eV.