Surface roughness and LEED crystallography: Analysis of flat and vicinal W(110)

Low-energy electron diffraction intensity vs voltage (LEED I-V) measurements and analysis are used to determine the multilayer surface relaxation of W(110). Measurements and analysis are presented for both flat and vicinal surfaces, demonstrating that surface roughness leads to only small errors in LEED structure determinations. Flat, clean W(110) exhibits first-(d₁₂) and second-(d₂₃) layer relaxations of -3.0±1.3% and +0.2±1.3%, respectively, relative to the bulk lattice spacing d₀=2.237. This experimentally determined surface relaxation of W(110) is compatible with a recent combined density-functional theory calculation and LEED study [M. Arnold, G. Hupfauer, P. Bayer, L. Hammer, K. Heinz, B. Kohler, and M. Scheffler, Surf. Sci. 382, 288 (1997)]. Surface roughness (in the present case, uniform atomic height steps) is found to produce a small apparent increase in the measured value of d₁₂ when determined using standard (flat surface) LEED I-V methodology. However, for low step densities (20 atoms/step) the apparent change in d₁₂ is small compared to other sources of error, so it is unlikely that surface roughness is a significant source of error in LEED structure determinations.