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

Low-energy electron diffraction intensity vs voltage (LEED I-V) measurement s and analysis are used to determine the multilayer surface relaxation of W (110). Measurements and analysis are presented for both hat and vicinal sur faces, demonstrating that surface roughness leads to only small errors in L EED structure determinations. Flat, clean W(110) exhibits first-(d(12)) and second-(d(23)) layer relaxations of -3.0+/-1.3% and +0.2+/-1.3%, respectiv ely, relative to the bulk lattice spacing d(0)=2.237 Angstrom. This experim entally 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, I,. Hammer, K. Heinz, B: Kohler, and M. Scheffler, S urf. 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 d(12) when determined using standard (flat surface) LEED I-V methodology. However, for low step densities (<20 atoms/step) the appar ent change in d(12) is small compared to other sources of error, so it is u nlikely that surface roughness is a significant source of error in LEED str ucture determinations.