Temperature-dependent scattering of hyperthermal energy ${\mathrm{K}}^{+}$ ions

Extensive experimental and theoretical results are presented for the scattering of a beam of ${\mathrm{K}}^{+}$ ions incident on a Cu(001) surface along the ⟨100⟩ azimuth with incident energies of $50\text{to}154\mathrm{eV}$. Energy-resolved scattered intensity spectra reveal three distinct peaks whose widths and intensities vary with surface temperature. Using the results of a classical trajectory simulation, four distinct ionic trajectory types are assigned to these peaks. Using a classical mechanical theory that contains the correct equilibrium thermodynamics of the Cu crystal, general features of the ${\mathrm{K}}^{+}$ energy-resolved spectra are calculated for each trajectory type and compared with the experimental results. For the case of single ion-surface atom collisions, the dependence of the peak intensities and widths on the incident energy and surface temperature is well explained by the classical theory.

Figure 1

Energy-resolved intensity spectra as a function of the fractional final energy at the incident energy $E_i=154\mathrm{eV}$ and temperature $T_S=675\mathrm{K}$. The experimental data are shown as points. The solid curve is the sum of contributions from the four trajectories discussed in Sec. 3 of the text. The leftmost and rightmost peaks correspond to the SS and DF trajectories, respectively. The middle peak contains both DZZ (dashed curve) and TZZ (dotted curve) contributions.

Figure 2

Energy-resolved intensity spectra for an incident energy $E_i=154\mathrm{eV}$ and several different temperatures as marked. The experimental data are shown as points and the solid curves are the calculations with $M_c$ increased by 5% and with ${\theta }_{q,D}$, ${\theta }_{q,T}$, and ${\theta }_{r,T}$ each increased by 15%.

Figure 3

Single Scattering Trajectory: The (a) peak intensity and (b) mean-squared width plotted as a function of $T_S^{-1∕2}$ and $T_S$, respectively, for the three indicated incident energies. The symbols and lines correspond to the experimental data points and calculated results, respectively. The error associated with the experimental points is on the order of the displayed symbol sizes.

Figure 4

Double Forward Trajectory: The (a) peak intensity and (b) mean-squared width plotted as a function of $T_S^{-1∕2}$ and $T_S$, respectively, for the three indicated incident energies. The symbols and lines correspond to the experimental data points and calculated results, respectively. The error associated with the experimental points is on the order of the displayed symbol sizes.

Figure 5

Multiple Scattering Trajectory: The (a) peak intensity and (b) mean-squared width plotted as a function of $T_S^{-1∕2}$ and $T_S$, respectively, for the three indicated incident energies. The symbols and lines correspond to the experimental data points and calculated results, respectively. The error associated with the experimental points is on the order of the displayed symbol sizes.

Figure 6

Temperature dependence of the integrated peak intensity for the single scattering, double forward, and multiple scattering trajectory types at $E_i=99\mathrm{eV}$. The symbols and lines correspond to the experimental and calculated results, respectively. The error associated with the experimental points is on the order of the displayed symbol sizes.