Scattering of fast neutral atoms with keV kinetic energies at alkali-halide surfaces under grazing angles displays intriguing diffraction patterns. The surprisingly strong persistence of quantum coherence despite the impulsive interaction with an environment at solid state density and elevated temperatures raises fundamental questions such as to the suppression of decoherence and of the quantum-to-classical crossover. We present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the h110i direction and compare with recent experimental diffraction data. From the quantitative reconstruction of diffraction images the vertical LiF-surface reconstruction, or buckling, can be determined. DOI: 10.1103/PhysRevLett.101.253201 PACS numbers: 34.35.+a, 61.85.+p, 68.49.Bc, 79.20.Rf Diffraction of massive particles scattered at surfaces was one of the key experiments establishing the quantum wave nature. Coherent atom and molecule optics was initiated when Estermann and Stern [1] observed interference patterns of slow (''thermal'') helium atoms and H 2 molecules scattered off alkali-halide surfaces. Thermal atom scattering (TAS) [2,3] as well as low-energy electron diffraction (LEED) [4] are nowadays routinely employed to accurately probe properties of surfaces. These techniques exploit the fact that the de Broglie wavelength dB of the beam particles is comparable to the lattice constant a. More recently, probing the wave nature of massive objects has taken center stage in exploring the quantum-toclassical crossover [5,6]. One ingredient of the quantumto-classical transition is the limit of small de Broglie wave length dB ! 0, the other the ubiquitous presence of unobserved environmental degrees of freedom within the framework of decoherence theory [1], or alternatively, elements beyond standard unitary quantum dynamics, including the frequently involved ''collapse'' of the wave functions [7,8]. In matter-wave interferometry of large and complex biomolecules, de Broglie wavelengths as small as few picometer (10 À12 m) have been reached [6].Even shorter wavelengths have been accessed by recent fast-atom scattering studies at surfaces [9-11] with dB as small as % 200 femtometers. Persistence of quantum diffraction and the apparent suppression of decoherence is all the more remarkable, as thermal fluctuation amplitudes of the surface atoms are much larger than dB and, moreover, collisions with keV projectile energies would strongly suggest the dominance of dissipative and decohering processes. In this Letter we present an ab initio simulation of fast helium atom diffraction ( 4 He) at a LiF (100) surface. We analyze the suppression of decoherence in grazingincidence scattering within an open quantum system (OQS) approach and quantitatively reconstruct experimental diffraction images [9,10] in considerable detail. Fastatom diffraction has the potential to become a powerful tool to interrogate structural and dynamical properties of surfaces.Fast-atom scattering at surfaces under s...