Thermal effects on helium scattering from LiF(001) at grazing incidence

Abstract

Grazing-incidence fast atom diffraction (GIFAD) is an exceptionally sensitive method for surface analysis, which can be applied not only at room temperature but also at higher temperatures. In this work we use the He-LiF( 001) system as a benchmark to study the influence of temperature on GIFAD patterns from insulator surfaces. Our theoretical description is based on the phonon-surface initial value representation (P0-SIVR) approximation, which is a semiquantum approach that includes the phonon contribution to the elastic scattering. Within the P0-SIVR approach the main features introduced by thermal lattice vibrations on the angular distributions of scattered projectiles are investigated as a function of the crystal temperature. We found that azimuthal and polar spectra are strongly affected by thermal fluctuations, which modify the relative intensities and the polar spread of the interference structures. These findings are relevant for the use of GIFAD in surface research. Moreover, the present results are contrasted with available experimental data at room temperature.

Polar inelastic profiles in fast-atom diffraction at surfaces

“…The corresponding dashed line in Fig. 10 indicates a moderate increase of w at low values of E ⊥ but only for values of E ⊥ close to D. The value of σ z = 0.098 Å considered here for data recorded at 300 K, is taken from ab initio extensive calculations [2,18] of the LiF crystal and corresponds to a Debye temperature T D =550 K at the surface, very close to the recommended value derived from TEAS measurements [46].…”

“…This log-normal profile (1) was empirically adopted as a data-reduction procedure [14] because it was found to reproduce the asymmetry of the scattering profile in the classical scattering regime [15,16] when diffraction was not considered. It was also observed in quantum Monte Carlo [17] or semi-classical [18] and classical [15] approaches of scattering or inelastic diffraction. In the present context the adjustment has also the effect of rejecting the intensity observed far from the specular angle which is believed to be dominated by surface defects [19], see e.g.…”

Temperature dependence in fast-atom diffraction at surfaces

“…We have shown here that the width w of the scattering profile can be understood qualitatively in terms of a classical model using an effective stiffness G eff (E > ) and a thermal amplitude s z (T). This suggests that classical scattering simulation in grazing incidence, in general 57 and in the context of GIFAD 8,9 should produce a fair estimate of the inelastic profile. However, In fine, a quantum inelastic treatment as developed in TEAS 58 and recent attempts to encompass both elastic and inelastic aspects under grazing incidence 59 should help connecting to the real world of surface phonons and their possible specific coupling to the multiple collision regime.…”

“…with the vibration of the surface atoms or phonons, breaking the exact translation symmetry of the ideal surface and requiring a priori to abandon the ASCA for a full 3D representation. 8,9 In TEAS, X-ray or neutron diffraction, this situation is described by the Debye-Waller factor DWF = I e /I 0 = e Àsj 2 where s j 2 is the variance of the phase distribution induced the thermal displacement s z of surface atoms. In a Debye model of solids, each atom is described by a local harmonic oscillator with frequency o D and the thermal amplitude is Gaussian s z (T) resulting in a phase coherence e Àsj 2 = e Àq 2 sz 2 where q is the projectile momentum.…”

Grazing incidence fast atom diffraction, similarities and differences with thermal energy atom scattering (TEAS)

“…inelastic diffraction but this theory was not readily adapted to GIFAD and early models trying to reproduce thermal effects could qualitatively explain the inelastic scattering profiles but did not account for elastic diffraction, 31,81,107 leaving some open questions: What is the modified DWF? What are the inelastic polar and azimuthal profiles?…”