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The Journal of Chemical Physics

Scattering of He and Ne atoms from a (001) surface of sodium fluoride

B. Wood, B.F. Mason, Brian R. Williams

Published Aug 15, 1974• 48 citations
Publisher

Abstract

The scattering of He and Ne atoms from a cleaved (001) surface of NaF has been studied at different surface temperatures and incident beam energies. The geometric peak shape expected for the beam detector arrangement was compared to the experimentally observed peaks under different conditions of surface temperature and incident energy. The (00) peak height was followed as a function of surface temperature for two values of the incident momentum, in order to extract some information about the role of the attractive part of the interaction potential during a collision. Finally, the peak heights of several diffraction peaks were determined as a function of the incident energy. Several minima were observed in the scattering pattern, which can be associated with bound state resonances and which have been the subject of considerable interest recently. In this case, several maxima were found which can also be associated with bound state resonances. The (00) peak, observed in the scattering of Ne atoms, also showed maxima and minima when the height was monitored, as a function of the incident energy.

DOI
10.1063/1.1682071

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The scattering of He and Ne atoms from a cleaved (001) surface of NaF has been studied at different surface temperatures and incident beam energies. The geometric peak shape expected for the beam detector arrangement was compared to the experimentally observed peaks under different conditions of surface temperature and incident energy. The (00) peak height was followed as a function of surface temperature for two values of the incident momentum, in order to extract some information about the role of the attractive part of the interaction potential during a collision. Finally, the peak heights of several diffraction peaks were determined as a function of the incident energy. Several minima were observed in the scattering pattern, which can be associated with bound state resonances and which have been the subject of considerable interest recently. In this case, several maxima were found which can also be associated with bound state resonances. The (00) peak, observed in the scattering of Ne atoms, also showed maxima and minima when the height was monitored, as a function of the incident energy.
The conventional notion of elastic, coherent atom-surface scattering originates from the scattering particles acting as a quantum-mechanical matter wave, which coherently interfere to produce distinct Bragg peaks which persist at finite temperature. If we introduce inelastic scattering to this scenario, the result is that the surface particles become displaced by the scattering atoms, resulting in emission or absorption of phonons that shift the final energy and momentum of the scatterer. As the lowest-lying phonons are gapless excitations, the ability to measure these phonons is very difficult and this difficulty is exacerbated by the roughly 1-eV resolution found in high-energy helium scattering experiments. Even though the surface has in effect measured the presence of the scatterer which decoheres the particle, we retain the diffraction spots which are referred to as coherent scattering. How do we reconcile these disparate viewpoints? We propose an experiment to more precisely examine the question of coherence in atom-surface scattering. We begin with an initially coherent superposition of helium particles with equal probabilities of interacting with the surface or not interacting with the surface. The beams are directed so that after the scattering event, the atoms are recombined so that we can observe the resulting interference pattern. The degree to which phonons are excited in the lattice by the scattering process dictates the fringe contrast of the interference pattern of the resulting beams. We use semiclassical techniques to simulate and test the viability of this experiment and show that for a wide range of conditions, despite the massive change in the momentum perpendicular to the surface, we can still expect to have coherent (in the superposition sense) scattering.
Diffraction of fast helium atoms at alkali-halide surfaces under grazing angles of incidence shows intriguing diffraction patterns. The persistence of quantum coherence is remarkably strong, even though high surface temperatures and high (keV) kinetic energies of the incident atoms would strongly suggest the dominance of dissipative and decohering processes. The main source of decoherence is the excitation or absorption of surface vibrations upon impact. The momentum transfer between the surface and the incident helium atom depends on the amplitude of the thermal vibrations of the surface atoms and the energy of the incident particle. We present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the (110) direction, and compare with recent experimental diffraction data.
Using nozzle beams of He, Ne, and Ar, we have measured diffractive selective adsorption resonances from a Cu(110) surface kept at 20 K. Bound state energies of the atom-surface potentials have been determined from plots of the measured resonance energies versus incident angle and their fits to calculated kinematical dispersion relations. For 3He and 4He we have found a unique level assignment that is compatible with a single gas-surface potential curve with a well depth of 6.05 meV of the He-Cu(110) potential. This value is about 10% larger than the prediction of 5.55 meV from the current physisorption theory. The Ne and Ar data reveal a large number of closely spaced levels with level separations and estimated van der Waals coefficients that are compatible with available theoretical data.
Scattering of fast neutral atoms with keV kinetic energies at alkali-halide surfaces under grazing angles displays intriguing diffraction patterns (Schuller, Wethekam and Winter 2007, Roisseau et al. 2007). In spite of the impulsive interaction with a surface at elevated temperature, which results in phonon excitation, quantum coherence evidently persists. To quantitatively study this remarkable survival of coherence, we present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the 〈110〉 direction and compare with recent experimental diffraction data. Decoherence is analyzed employing a quantum trajectory Monte Carlo method (Minami, Reinhold and Burgdorfer 2003), calculating the ensemble average over solutions of a stochastic linear Schrodinger equation. The evolution of the atomic wavepacket is governed by a sequence of stochastic collisions and continuous propagation in the He-LiF surface potential. We find near-perfect agreement between the resulting diffraction patterns and experimental results (Schuller, Wethekam and Winter 2007) without using any adjustable parameters. The question, whether the LiF surface features “buckling”, (i.e. vertical surface reconstruction where the F atoms are displaced relative to the Li atoms) has been addressed in the past (de Wette, Kress and Schroder 1985). However, experimental uncertainties were of the same order as the displacement amplitude itself. In atom-surface diffraction at a grazing angle, surface reconstruction drastically changes the diffraction patterns. By comparison of numerical and experimental results, the buckling amplitude can be determined with unprecedented accuracy.
The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ℏ the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics of the beam of incoming particles. Necessary conditions for observation of quantum diffraction are derived for the angular width of the incoming beam. An analytic expression for the angular distribution as a function of the angular and momentum variance of the incoming beam is obtained. We show both analytically and through some numerical results that increasing the angular width of the incident beam leads to decoherence of the quantum diffraction peaks and one approaches the classical limit. However, the incoherence of the beam in the parallel direction does not destroy the diffraction pattern. We consider the specific example of Ar atoms scattered from a rigid LiF(100) surface.
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 110 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.