We study the effect of crystal lattice vibrations on grazing-incidence fast atom diffraction (GIFAD) from insulator surfaces. To describe the phonon contribution to GIFAD we introduce a semiquantum method, named Phonon-Surface Initial Value Representation (P-SIVR), which represents the surface with a harmonic crystal model, while the scattering process is described by means of the Surface Initial Value Representation approach, including phonon excitations. Expressions for the partial scattering probabilities involving zero-and one-phonon exchange are derived. In particular, the P-SIVR approach for zero-phonon scattering is applied to study the influence of thermal lattice vibrations on GIFAD patterns for Ne/LiF(001) at room temperature. It is found that the thermal lattice fluctuations introduce a polar-angle spread into the projectile distributions, which can affect the relative intensities of the interference maxima, even giving rise to interference sub-patterns depending on the incidence conditions. Present results are in agreement with the available experiments.

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.

Coherence properties of projectiles, found relevant in ion-atom collisions, are investigated by analyzing the influence of the degree of coherence of the atomic beam on interference patterns produced by grazing-incidence fast-atom diffraction (GIFAD or FAD). The transverse coherence length of the projectiles, which depends on the incidence conditions and the collimating setup, determines the overall characteristics of GIFAD distributions. We show that for atoms scattered from a LiF(001) surface after a given collimation, we can modify the interference signatures of the angular spectra by varying the total impact energy, while keeping the normal energy as a constant. Also, the role played by the geometry of the collimating aperture is analyzed, comparing results for square and circular openings. Furthermore, we study the spot-beam effect, which is due to different focus points of the impinging particles. We show that when a region narrower than a single crystallographic channel is coherently illuminated by the atomic beam, the spot-beam contribution strongly affects the visibility of the interference structures, contributing to the gradual quantum-classical transition of the projectile distributions.

Grazing incidence fast atom diffraction (GIFAD) is a sensitive tool for surface analysis, which strongly relies on the quantum coherence of the incident beam. In this article we study the spot-beam effect, due to contributions coming from different positions of the focus point of the incident particles, which affects the coherence of GIFAD spectra. We show that the influence of the spot-beam effect on GIFAD patterns depends on the width of the surface area that is coherently lighted by the atomic beam. While for extended illuminations the spot-beam contribution plays a minor role, when a narrow surface area is coherently lighted, the spot-beam effect allows projectiles to explore different zones of a single crystallographic channel, bringing to light intra-channel interference structures. In this last case the spot-beam effect gives also rise to a non-coherent background, which deteriorates the visibility of the interference structures. We found that by varying the impact energy, while keeping the same collimating setup, it is possible to switch gradually from quantum to classical projectile distributions. Present results are compared with available experimental data, making evident that the inclusion of focusing effects is necessary for the proper theoretical description of the experimental spectra.

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