Time-of-flight scattering and recoiling spectrometry. III. The structure of hydrogen on the W(211) surface

The technique of time-of-flight scattering and recoiling spectrometry (TOF-SARS) with detection of both neutrals and ions is applied to structural analysis of hydrogen adsorbed at saturation coverage on a W(211) surface in the temperature range 100 \ifmmode^\circ\else\textdegree\fi{}C to 200 \ifmmode^\circ\else\textdegree\fi{}C. Scattering and recoiling spectra, induced by pulsed ${\mathrm{Ne}}^{+}$ and ${\mathrm{Ar}}^{+}$ primary-ion beams, are monitored as a function of polar beam incident angle \ensuremath{\alpha}, surface azimuthal angle \ensuremath{\delta}, scattering angle \ensuremath{\theta}, recoiling angle \ensuremath{\varphi}, and ejection angle \ensuremath{\beta}. Plots of hydrogen recoil intensities in (\ensuremath{\alpha},\ensuremath{\delta}) space provide recoiling structural contour maps and recoiling structural plots which are representative of the recoil symmetry of hydrogen on the W(211) surface. Measurements of recoil (both direct and surface recoils) intensities as a function of \ensuremath{\alpha} and \ensuremath{\beta} along different azimuths \ensuremath{\delta} provide experimental values of the critical incident angle ${\ensuremath{\alpha}}_{c}$,sh for shadowing and the critical ejection angle ${\ensuremath{\beta}}_{c}$ (or ${\ensuremath{\alpha}}_{c}$,bl) for blocking by neighboring atoms.The hydrogen adsorption position is determined from analysis of the behavior of hydrogen surface recoiling peaks as a function of \ensuremath{\alpha} and from trajectory simulations and calculations of the shadowing and blocking cones obtained from interaction potentials calibrated for this system. The results show that hydrogen resides in a band that is located above the troughs along the [1 1\ifmmode\bar\else\textasciimacron\fi{} 1\ifmmode\bar\else\textasciimacron\fi{}] direction. The center of this band is located at 0.57\ifmmode\pm\else\textpm\fi{}0.20 A\r{} above the plane of the first-layer W atoms. Along the [001\ifmmode\bar\else\textasciimacron\fi{}] direction, i.e., perpendicular to the [1 1\ifmmode\bar\else\textasciimacron\fi{} 1\ifmmode\bar\else\textasciimacron\fi{}] troughs, the band is \ensuremath{\approxeq}1.0 A\r{} wide between two first-layer W atoms and \ensuremath{\approxeq}2.3 A\r{} wide at the short-bridge position between two first-layer W atoms.The average spacing between H atoms along the [1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1] azimuth is 2.7 A\r{}, which is equivalent to the W lattice spacing along this direction. Effective-medium-theory (EMT) calculations of the hydrogen-tungsten interaction are presented. They predict (i) that the H-atom probability distribution is finite throughout a broad region above the troughs and confined within a band that is 0.60 A\r{} above the first-layer W atom plane and (ii) that the H-atom probability distribution is maximum at the positions of the short-bridge and threefold trough site positions. This distribution is due to thermally activated vibrational motion. The ability to detect hydrogen by TOF-SARS within this band with approximately equal probabilities along all azimuths is in agreement with the EMT results, suggesting that H atoms can occupy an extensive region of this band.