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The Journal of Physical Chemistry Letters

Diffraction of CH4 from a Metal Surface

Amjad Al Taleb, Gloria Anemone, Linsen Zhou, Hua Guo, Daniel Farı́as

Published Mar 11, 2019• 16 citations
Publisher

Abstract

Diffraction with matter waves has been reported since the beginning of quantum mechanics. In free space, diffraction effects have been observed even with objects as large as C 60 molecules. However, in scattering from a solid surface, pure elastic diffraction features have never been observed with molecules larger than D 2 . Here we report the observation of pure molecular diffraction for CH 4 scattered off of an Ir(111) surface. These results prove that quantum coherence is preserved, despite the small separation between rotational levels and the interaction with surface phonons. Density functional theory calculations of the potential energy surface provide some clues to understand the larger corrugation sampled by CH 4 molecules in comparison to Ne atoms. Our results show that isotope separation of polyatomic molecules may be possible using gas–surface diffraction.

DOI
10.1021/acs.jpclett.9b00158

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Diffraction with matter waves has been reported since the beginning of quantum mechanics. In free space, diffraction effects have been observed even with objects as large as C 60 molecules. However, in scattering from a solid surface, pure elastic diffraction features have never been observed with molecules larger than D 2 . Here we report the observation of pure molecular diffraction for CH 4 scattered off of an Ir(111) surface. These results prove that quantum coherence is preserved, despite the small separation between rotational levels and the interaction with surface phonons. Density functional theory calculations of the potential energy surface provide some clues to understand the larger corrugation sampled by CH 4 molecules in comparison to Ne atoms. Our results show that isotope separation of polyatomic molecules may be possible using gas–surface diffraction.
The separation of isotopes in space and time by gas-surface atomic diffraction is presented as a new means for isotopic enrichment. A supersonic beam of natural abundance neon is scattered from a periodic surface of methyl-terminated silicon, with the ^{20}Ne and ^{22}Ne isotopes scattering into unique diffraction channels. Under the experimental conditions presented in this Letter, a single pass yields an enrichment factor 3.50±0.30 for the less abundant isotope, ^{22}Ne, with extension to multiple passes easily envisioned. The velocity distribution of the incident beam is demonstrated to be the determining factor in the degree of separation between the isotopes' diffraction peaks. In cases where there is incomplete angular separation, the difference in arrival times of the two isotopes at a given scattered angle can be exploited to achieve complete temporal separation of the isotopes. This study explores the novel application of supersonic molecular beam studies as a viable candidate for separation of isotopes without the need for ionization or laser excitation.
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.
Abstract Molecular beams of He and D2 are scattered from a ruled diffraction grating in conical‐mount geometry under grazing‐incidence conditions. Fully resolved diffraction patterns as a function of detection angle are recorded for different grating azimuth angles and for two different kinetic energies of the particle beams. Variations in diffraction peak widths are traced back to different velocity spreads of He and D2 determined by time‐of‐flight measurements. A comprehensive analysis of diffraction intensities confirms universal diffraction, that is, for identical de Broglie wavelengths, the relative diffraction intensities for He and D2 are the same. Universal diffraction results from peculiarities of quantum reflection of the atoms and molecules from the diffraction grating. In quantum reflection particles scatter many nanometers in front of the surface from the long‐range attractive branch of the particle–surface interaction potential without probing the potential well and the short‐range repulsive branch of the potential.
We develop a new method for the calculation of the atom scattering analog of the Debye-Waller factor. Unlike x-ray and neutron scattering, the properties of an atom scattered by a solid surface cannot be computer by perturbation theory, therefore the simple Debye-Waller theory cannot be applied. Nevertheless the Debye-Waller phenomenon has a close analog: the elastic intensity is depressed due to the uncorrelated part of the thermal motion of the lattice atoms. To compute this effect we develop a time dependent scattering theory in which the quantum properties of the scattered atom are described by propagating coherently an ensemble of wave packets and lattice motion is simulated by a classical Langevin equation. Applications are made to He and Ne scattering from a surface whose lattice dynamics mimics that of Pt(111) but whose corrugation was slightly increased to enrich the diffraction structure.
Diffraction and interference of matter waves are key phenomena in quantum mechanics. Here we present some results on particle diffraction in a wide variety of situations, ranging from simple slit experiments to more complicated cases such as atom scattering by corrugated metal surfaces and metal surfaces with simple and isolated adsorbates. The principal novelty of our study is the use of the so-called Bohmian formalism of quantum trajectories. These trajectories are able to satisfactorily reproduce the main features of the experimental results and, more importantly, they provide a causal intuitive interpretation of the underlying dynamics. In particular, we will focus our attention on: (a) a revision of the concepts of near and far field in undulatory optics; (b) the transition to the classical limit, where it is found that although the quantum and classical diffraction patterns tend to be quite similar, some quantum features are maintained even when the quantum potential goes to zero; and (c) a qualitative description of the scattering of atoms by metal surfaces in the presence of a single adsorbate.
We develop a new method for the calculation of the atom scattering analog of the Debye–Waller factor. Unlike x-ray and neutron scattering the properties of an atom scattered by a solid surface cannot be computed by perturbation theory; therefore the simple Debye–Waller theory cannot be applied. Nevertheless the Debye–Waller phenomenon has a close analog: the elastic intensity is depressed due to the uncorrelated part of the thermal motion of the lattice atoms. To compute this effect we develop a time dependent scattering theory in which the quantum properties of the scattered atom are described by propagating coherently an ensemble of wave packets and lattice motion is simulated by a classical Langevin equation. Applications are made to He and Ne scattering from a surface whose lattice dynamics mimics that of Pt(111) but whose corrugation was slightly increased to enrich the diffraction structure.