Phonon contribution in grazing-incidence fast atom diffraction from insulator surfaces

Abstract

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.

Polar inelastic profiles in fast-atom diffraction at surfaces

“…A major weakness of the QBCM is that surface vibration are treated only through the local Debye oscillator thus neglecting the phonons mode which are the genuine eigenstates of vibrations at surfaces. Only few authors have developed approaches where phonons are explicit, most are adapted to TEAS [34,[50][51][52] but also to grazing incidences [53,54].…”

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?…”

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

“…The interested reader can find the steps and assumptions involved in the derivation of the P0-SIVR approximation in the Appendix of Ref. [28].…”

“…To investigate thermal effects on GIFAD we make use of a recently developed semiquantum approach, named Phonon-Surface Initial Value Representation (P-SIVR) [28]. The P-SIVR approximation is based on the previous SIVR approach for grazing scattering from a rigid surface [26], incorporating lattice vibrations (i.e., phonon contributions) through a quantum description of the surface given by the harmonic crystal model [29].…”

“…The P-SIVR probability is expanded in terms of the number n of phonons exchanged between the crystal and the projectile during the collision. It gives rise to a series of partial Pn-SIVR probabilities involving the exchange of n phonons, where the first-order term -P0-SIVR -corresponds to the elastic scattering without net phonon exchange [28]. P0-SIVR projectile distributions for He-LiF(001) scattering under a fixed incidence condition are here investigated considering temperatures T in the 250 − 1000 K range.…”