  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.
