Evidence for longitudinal coherence in fast atom diffraction

Angular distributions for grazing scattering of keV H atoms from an Al${}_2$O${}_3$(11$\overline{2}$0) surface were recorded. These distributions reveal defined diffraction patterns which can be understood in terms of quantum scattering from well-ordered surfaces. From the observation of so-called Laue circles, we conclude a high degree of longitudinal coherence for fast atom diffraction at surfaces which allows one to resolve periodicity intervals of several 100 $\text{Å}$. We demonstrate this feature in scattering experiments from the reconstructed ($12\times 4$) phase of an Al${}_2$O${}_3$(11$\overline{2}$0) surface obtained after annealing at temperatures of about 2000 K.

Figure 1

Sketch of collision geometry for grazing scattering of fast atoms from crystal surface (surface plane). Angular distributions are recorded behind target normal to scattered beam (detection plane).

Figure 2

Angular distributions of scattered 300-eV H atoms as recorded with position-sensitive detector 0.66 m behind target. (a) ${\Phi }_{\text{in}}=0.{92}^{\circ }$, $\Gamma =0^{\circ }$; (b) ${\Phi }_{\text{in}}=0.{80}^{\circ }$, $\Gamma =3.6^{\circ }$; (c) ${\Phi }_{\text{in}}=0.{68}^{\circ }$, $\Gamma =8.1^{\circ }$; (d) calculated positions of diffraction spots for ${\Phi }_{\text{in}}=0.{68}^{\circ }$, $\Gamma =8.1^{\circ }$; $h$, $k$ denote diffraction orders, $\Gamma$ is azimuthal angle with respect to $\left[\overline{1}100\right]$.

Figure 3

Intensity projected on radius of Laue circle in terms of angle $\Omega$ for scattering of 300-eV H atoms from Al${}_2$O${}_3$(11$\overline{2}$0) surface. Upper left panel: ${\Phi }_{\text{in}}=0.{80}^{\circ }$, $\Gamma =3.6^{\circ }$; upper right panel: ${\Phi }_{\text{in}}=0.{69}^{\circ }$, $\Gamma =7.2^{\circ }$; lower left panel: ${\Phi }_{\text{in}}=0.{68}^{\circ }$, $\Gamma =8.1^{\circ }$; upper right panel: ${\Phi }_{\text{in}}=0.{63}^{\circ }$, $\Gamma =9.9^{\circ }$. $h$ denotes order of Laue circle.

Figure 4

Intensity projected on Laue circle of order $h=-1$ (left panel), $h=0$ (middle panel), and $h=+1$ (right panel) for scattering of 300-eV H atoms from Al${}_2$O${}_3$(11$\overline{2}$0) surface under ${\Phi }_{\text{in}}=0.{68}^{\circ }$ and $\Gamma =8.1^{\circ }$. $k$ denotes order of Bragg peaks.