Role of the image charge and electronic corrugation on charge-fraction azimuthal variations for keV Li and Na ions interacting with Cu(110) and Ag(110) under grazing incidence

The positive charge fraction resulting from charge exchange during the interaction of ${\mathrm{Li}}^{+}$ and ${\mathrm{Na}}^{+}$ ions on the Ag(110) and Cu(110) metal surfaces has been measured for different energies and incident azimuthal angles of the projectiles. Surprisingly, although metallic Cu and Ag are well described by the free-electron model, the positive charge fraction has been observed to vary significantly according to the azimuthal angle of incidence, for projectile energies lower than $4\mathrm{keV}$ and incidence angle below 5° with respect to the surface (grazing scattering conditions), and specifically around the low-index [001] and $\left[1\overline{1}0\right]$ directions. A detailed analysis of trajectory calculations for the $\mathrm{Li}∕\mathrm{Cu}\left(110\right)$ system allows one to distinguish between different types of trajectories (on tops, zigzags, and in rows), the relative importance of which varies rapidly with azimuthal angle. We obtain a good correlation between the observed azimuthal variation of the charge fraction and the mean value of the electronic density encountered by the projectile in the vicinity of the first atomic layers. We show that this short-range effect can be reflected on the observed variation of the charge fraction through the charge image effect on the trajectories. This effect is shown to be very sensitive to the electronic corrugation of the surface which is known to be low for Cu and Ag. Azimuthal experimental measurements thus appear to be a tool to characterize such low corrugations.

Figure 1

Comparison between experiment (line with circles) and simulation (thick line) of the number of Ar particles scattered off an Ag(110) surface as a function of the incidence azimuthal angle. Projectiles are $4\mathrm{keV}$ ${\mathrm{Ar}}^{+}$ ions under an incidence angle with respect to the surface $\alpha =15°$. The particles are detected in the specular scattering angle $\theta =30°$. The thin line added in the simulation view corresponds to a different collision geometry: $\alpha =3°$ (grazing angle) and $\theta =6°$.

Figure 2

The low-index crystallographic directions for an fcc (110) surface.

Figure 3

Left panel: Positive charge fraction as a function of the azimuthal angle of incidence for the scattering of $1.24\mathrm{keV}$ ${\mathrm{Li}}^{+}$ ions on Cu(110) (upper curve) and of $1.24\mathrm{keV}$ ${\mathrm{Na}}^{+}$ ions on Ag(110) (lower curve). The incidence angle is $\alpha =3°$ with respect to the surface and the scattering angle is $\theta =6°$ (specular reflection). The azimuthal angle is measured with respect to the $\left[1\overline{1}0\right]$ direction. Right panel: Sketch of energy diagrams for Li and Na atoms in front of Cu and Ag (110) surfaces.

Figure 4

Energy dependence of the azimuthal variations in the positive charge fraction, for grazing scattering from Cu(110) of $1.24\mathrm{keV}$ (lower curves) and $4\mathrm{keV}$ (upper curves) Li ions. The incidence angle is $\alpha =3°$ with respect to the surface and the scattering angle is $\theta =6°$ (specular reflection). Note the split of the horizontal azimuthal axis.

Figure 5

Positive charge fraction as a function of the azimuthal angle for scattering of $1.24\mathrm{keV}$ ${\mathrm{Li}}^{+}$ from Cu(110). The results correspond to three different angles of incidence: $\alpha =3°$ (full circles), $\alpha =4°$ (crosses), and $\alpha =5°$ (empty squares) and an exit angle in the specular direction.

Figure 6

Positive charge fraction as a function of the azimuthal angle for scattering of $2\mathrm{keV}$ ${\mathrm{Na}}^{+}$ from Ag(110). The results correspond to three different angles of incidence: $\alpha =3°$ (full circles), $\alpha =4°$ (crosses), and $\alpha =5°$ (empty squares) and an exit angle in the specular direction.

Figure 7

Calculated trajectories of 1.24 and $4\mathrm{keV}$ Li atoms scattered under grazing incidence from a Cu(110) surface. The incidence angle is $\alpha =3°$ with respect to the surface, the azimuthal angle is along the [001] direction, and the scattering angle is $\theta =6°$ (specular reflection). (a) and (c) are top views of the crystal surface; (b) and (d) are side views along the incidence direction. The gray scale allows one to distinguish between the different types of trajectories. Atoms of the first and second layers are represented by dots. The scale in the direction of incidence is shrunk; the lengths are expressed in unit of the lattice constant ($3.62\mathrm{\AA }$ for Cu). These simulations have been done without thermal effects in order to distinguish more clearly between the different trajectories. They have been performed with a modified Molière potential (adjustment of the screening length by a factor of 0.85).

Figure 8

Mean interaction potential (line with markers and left axis) and mean electronic density (dotted line and right axis) encountered by 1.24 and $4\mathrm{keV}$ Li projectiles impinging on Cu(110) with an $\alpha =3°$ grazing angle at different azimuthal angles.

Figure 9

Illustration of the image-charge effect on a projectile trajectory: case of an impinging positive ion which can be neutralized during scattering. In the case of a pure specular reflection, the exit angle of the projectile will be ${\beta }^0=\alpha +d\beta$ if scattered as a neutral and ${\beta }^{+}=\alpha$ if scattered as an ion.

Figure 10

Comparison of azimuthal variations of the charge fraction (bold line) and of the number of scattered positive ions (lines with markers) between experiment (top view) and two simulations (lower views). Experiment: $1.24\mathrm{keV}$ Li ions on Cu ($\alpha =3°$ and $\beta =3°$). Simulation 1: $\alpha =3°$ and $d\beta =0.3°$; simulation 2: $\alpha =1.3°$ and $d\beta =0.5°$ (see text).