Rumpling of LiF(001) surface from fast atom diffraction

Quantum diffraction of fast atoms scattered from the topmost layer of surfaces under grazing angles of incidence can be employed for the analysis of detailed structural properties of insulator surfaces. From comparison of measured and calculated diffraction patterns we deduce the rumpling of the topmost surface layer of LiF(001) (i.e., an inward shift of Li${}^{+}$ ions with respect to ${\mathrm{F}}^{-}$ ions). The effect of thermal vibrations on the measurement of rumpling is accounted for by ab initio calculations of the mean-square vibrational amplitudes of surface ions. At room temperature this leads to a reduction of the apparent rumpling by 0.008 Å. We then obtain a rumpling of ($0.05\pm 0.04$) Å, which improves its accuracy achieved in previous work.

Figure 1

Sketch for scattering of fast atoms from the LiF(001) surface under the grazing angle of incidence ${\Phi }_{\mathrm{in}}$ along a $\langle 110\rangle$ direction.

Figure 2

Equipotential lines of potential between the He atom and LiF(001) surface averaged along strings of Li${}^{+}$ and ${\mathrm{F}}^{-}$ ions of a $\langle 110\rangle$ direction. $\delta z$, vertical displacement between ${\mathrm{F}}^{-}$ and Li${}^{+}$ in the topmost surface layer, so-called “rumpling”.

Figure 3

Diffraction pattern as recorded with position-sensitive channel plate detector for ${}^3\mathrm{He}$ atoms scattered from the LiF(001) surface along $\langle 110\rangle$ under ${\Phi }_{\mathrm{in}}$ $=$ 0.99${}^{°}$ with energies of 0.65 keV (top panel), 0.85 keV (middle panel), and 1.00 keV (bottom panel). Color code is as follows: red (dark gray) indicates high intensity, light blue (light gray) indicates low intensity. Circle of radius ${\Phi }_{\mathrm{in}}$ indicates positions for elastic scattering.

Figure 4

Intensity within a narrow interval of angles centered around the circle of radius ${\Phi }_{\mathrm{in}}$ in Fig. 3 as a function of the deflection angle $\Theta$. Numbers denote diffraction order $n$ with $n=0$ being highlighted in red (center) and $n=1$ in blue (just right of center).

Figure 5

Three-dimensional plots of experimentally deduced intensities as function of deflection angle $\Theta$ and normal de Broglie wavelength ${\lambda }_{\mathrm{dB}\perp }$ for scattering of ${}^3\mathrm{He}$ atoms from LiF(001) along a $\langle 110\rangle$ direction. Projections of intensity distributions as shown in Fig. 4 are highlighted as black curves in upper panel. The same data are shown as two-dimensional diffraction chart in Fig. 8.

Figure 6

Interaction potential, averaged along a $\langle 110\rangle$ direction, between a He projectile and a LiF surface as a function of the distance $z$ to surface. Left solid curve, incidence on top of Li ions; right solid curve, incidence on top of F ions; dashed curves, potentials including an average over thermal displacements (see text).

Figure 7

(a) Phonon dispersion relation of bulk LiF. Solid lines, our ab initio calculations; circles, neutron diffraction data ($T$ $=$ 295 K) from Ref. [37]. (b) Phonon dispersion relation of a five-layer LiF slab. Circles, measurement of the Rayleigh mode by high-resolution helium time-of-flight studies from Ref. [38] (solid circles) and Ref. [39] (open circles).

Figure 8

“Diffraction charts” constructed from a series of diffraction patterns for scattering of ${}^3\mathrm{He}$ atoms from LiF(001) along a $\langle 110\rangle$ direction. Experimental data (left) are in accord with theoretical results from wave-packet simulations taking into account a rumpling of $\delta z=0.05$ Å (right). Red (dark oval shapes), high intensity; blue (background), low intensity.

Figure 9

Normalized relative intensity of diffraction order $n=0$ (top) and $n=1$ (bottom) for scattering of ${}^3\mathrm{He}$ atoms from LiF(001) along a $\langle 110\rangle$ direction under angle of incidence ${\Phi }_{\mathrm{in}}=0.{61}^{°}$ (circles), $0.{81}^{°}$ (squares), $0.{99}^{°}$ (triangles) as a function of normal energy $E_{\perp }$. (Curves) Wave-packet simulations based on He-LiF(001) interaction potential taking into account no rumpling (dash-dotted), a rumpling of $\delta z=0.042$ Å (solid curve), and $\delta z=0.084$ Å (dashed).

Figure 10

Mean-square deviation of measured and calculated relative intensities of diffraction order $n=0$ (circles) and $n=1$ (diamonds) as shown in Fig. 9 as a function of rumpling $\delta z$.

Figure 11

Surface rumpling of LiF(001). (Squares) Experimental values deduced by LEED from Laramore and Switendick [15], Vogt and Weiss [19, 20], and Roberts et al. [18], by HAS from Garcia [16], and by FAD from this work (black error bar, uncertainty based on present interaction potential; gray error bar, estimation on possible results with other interaction potentials from different approximations within the DFT). (Circles) Theoretical values from shell-model calculations from Benson and Claxton [14], Welton-Cook and Prutton [12], and de Wette et al. [13], from Hartree-Fock calculations by Wirtz reported in Ref. [11], and from DFT calculations by Wang et al. [21], Vogt [23], Pruneda reported in Ref. [22], and Wirtz (this work).