Sub-resolution contrast in neutral helium microscopy through facet scattering for quantitative imaging of nanoscale topographies on macroscopic surfaces.

Nanoscale thin film coatings and surface treatments are ubiquitous across industry, science, and engineering; imbuing specific functional or mechanical properties (such as corrosion resistance, lubricity, catalytic activity and electronic behaviour). Non-destructive nanoscale imaging of thin film coatings across large (ca. centimetre) lateral length scales, crucial to a wide range of modern industry, remains a significant technical challenge. By harnessing the unique nature of the helium atom-surface interaction, neutral helium microscopy images these surfaces without altering the sample under investigation. Since the helium atom scatters exclusively from the outermost electronic corrugation of the sample, the technique is completely surface sensitive. Furthermore, with a cross-section that is orders of magnitude larger than that of electrons, neutrons and photons, the probe particle routinely interacts with features down to the scale of surface defects and small adsorbates (including hydrogen). Here, we highlight the capacity of neutral helium microscopy for sub-resolution contrast using an advanced facet scattering model based on nanoscale features. By replicating the observed scattered helium intensities, we demonstrate that sub-resolution contrast arises from the unique surface scattering of the incident probe. Consequently, it is now possible to extract quantitative information from the helium atom image, including localised ångström-scale variations in topography.

The role of high-energy phonons in electron-phonon interaction at conducting surfaces with helium-atom scattering.

In previous works it has been shown that the Debye-Waller (DW) exponent for Helium atom specular reflection from a conducting surface, when measured as a function of temperature in the linear high-temperature regime, allows for the determination of the surface electron-phonon coupling. However, there exist a number of experimental measurements that exhibit non-linearities in the DW exponent as a function of the surface temperature. Such non-linearities have been suggested as due to vibrational anharmonicity or a temperature dependence of the surface carrier concentration. In this work, it is suggested, on the basis of a few recent experimental data, that the deviations from linearity of the DW exponent temperature-dependence, as observed for conducting surfaces or supported metal overlayers with the present high-resolution He-atom scattering, permit to single out the specific role of high-energy phonons in the surface electron-phonon mass-enhancement factor.

Atom-surface scattering in the classical multiphonon regime.

Many experiments that utilize beams of incident atoms colliding with surfaces as a probe of surface properties are carried out at large energies, high temperatures and with large mass atoms. Under these conditions the scattering process does not exhibit quantum mechanical properties such as diffraction or single-phonon excitation, but rather can be treated with classical physics. This is a review of work carried out by the authors over a span of several years to develop theoretical frameworks using classical physics for describing the scattering interactions of atom with surfaces.

Erratum: Bending Rigidity of 2D Silica [Phys. Rev. Lett. 120, 226101 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.120.226101.

Temperature-Dependent Bending Rigidity of AB-Stacked Bilayer Graphene.

The change in bending rigidity with temperature κ(T) for 2D materials is highly debated: theoretical works predict both increase and decrease. Here we present measurements of κ(T), for a 2D material: AB-stacked bilayer graphene. We obtain κ(T) from phonon dispersion curves measured with helium atom scattering in the temperature range 320-400 K. We find that the bending rigidity increases with temperature. Assuming a linear dependence over the measured temperature region we obtain κ(T)=[(1.3±0.1)+(0.006±0.001)T/K] eV by fitting the data. We discuss this result in the context of existing predictions and room temperature measurements.

Origin of the Electron-Phonon Interaction of Topological Semimetal Surfaces Measured with Helium Atom Scattering.

He atom scattering has been demonstrated to be a sensitive probe of the electron-phonon interaction parameter λ at metal and metal-overlayer surfaces. Here it is shown that the theory linking λ to the thermal attenuation of atom scattering spectra (the Debye-Waller factor) can be applied to topological semimetal surfaces, such as the quasi-one-dimensional charge-density-wave system Bi(114) and the layered pnictogen chalcogenides. The electron-phonon coupling, as determined for several topological insulators belonging to the class of bismuth chalcogenides, suggests a dominant contribution of the surface quantum well states over the Dirac electrons in terms of λ.

Bending Rigidity of 2D Silica.

A chemically stable bilayers of SiO_{2} (2D silica) is a new, wide band gap 2D material. Up till now graphene has been the only 2D material where the bending rigidity has been measured. Here we present inelastic helium atom scattering data from 2D silica on Ru(0001) and extract the first bending rigidity, κ, measurements for a nonmonoatomic 2D material of definable thickness. We find a value of κ=8.8 eV±0.5 eV which is of the same order of magnitude as theoretical values in the literature for freestanding crystalline 2D silica.

Electron-Phonon Coupling Constant of Metallic Overlayers from Specular He Atom Scattering.

He atom scattering has been shown to be a sensitive probe of electron-phonon interaction properties at surfaces. Here it is shown that measurements of the thermal attenuation of the specular He atom diffraction peak (the Debye-Waller effect) can determine the electron-phonon coupling constant, λ, for ultrathin films of metal overlayers on various close-packed metal substrates. Values of λ obtained for single and multiple monolayers of alkali metals, and for Pb layers on Cu(111), extrapolated to large thicknesses, agree favorably with known bulk values. This demonstrates that He atom scattering can measure the electron-phonon coupling strength as a function of film thickness on a layer-by-layer basis.

Possible effect of static surface disorder on diffractive scattering of H2 from Ru(0001): Comparison between theory and experiment.

Specific features of diffractive scattering of H2 from metal surfaces can serve as fingerprints of the reactivity of the metal towards H2, and in principle theory-experiment comparisons for molecular diffraction can help with the validation of semi-empirical functionals fitted to experiments of sticking of H2 on metals. However, a recent comparison of calculated and Debye-Waller (DW) extrapolated experimental diffraction probabilities, in which the theory was done on the basis of a potential energy surface (PES) accurately describing sticking to Ru(0001), showed substantial discrepancies, with theoretical and experimental probabilities differing by factors of 2 and 3. We demonstrate that assuming a particular amount of random static disorder to be present in the positions of the surface atoms, which can be characterized through a single parameter, removes most of the discrepancies between experiment and theory. Further improvement might be achievable by improving the accuracy of the DW extrapolation, the model of the H2 rotational state distribution in the experimental beams, and by fine-tuning the PES. However, the question of whether the DW model is applicable to attenuation of diffractive scattering in the presence of a sizable van der Waals well (depth ≈ 50 meV) should also receive attention, in addition to the question of whether the amount of static surface disorder effectively assumed in the modeling by us could have been present in the experiments.

Electron-Phonon Coupling Strength at Metal Surfaces Directly Determined from the Helium Atom Scattering Debye-Waller Factor.

A new quantum-theoretical derivation of the elastic and inelastic scattering probability of He atoms from a metal surface, where the energy and momentum exchange with the phonon gas can occur only through the mediation of the surface free-electron density, shows that the Debye-Waller exponent is directly proportional to the electron-phonon mass coupling constant λ. The comparison between the values of λ extracted from existing data on the Debye-Waller factor for various metal surfaces and the λ values known from literature indicates a substantial agreement, which opens the possibility of directly extracting the electron-phonon coupling strength in quasi-2D conducting systems from the temperature or incident energy dependence of the elastic helium atom scattering intensities.

Temperature dependence of stream aeration coefficients and the effect of water turbulence: a critical review.

The gas transfer velocity (K(L)) and related gas transfer coefficient (k(2) = K(L)A/V, with A, area and V, volume) at the air-water interface are critical parameters in all gas flux studies such as green house gas emission, whole stream metabolism or industrial processes. So far, there is no theoretical model able to provide accurate estimation of gas transfer in streams. Hence, reaeration is often estimated with empirical equations. The gas transfer velocity need then to be corrected with a temperature coefficient θ = 1.0241. Yet several studies have long reported variation in θ with temperature and 'turbulence' of water (i.e. θ is not a constant). Here we re-investigate thoroughly a key theoretical model (Dobbins model) in detail after discovering important discrepancies. We then compare it with other theoretical models derived from a wide range of hydraulic behaviours (rigid to free continuous surface water, wave and waterfalls with bubbles). The results of the Dobbins model were found to hold, at least theoretically in the light of recent advances in hydraulics, although the more comprehensive results in this study highlighted a higher degree of complexity in θ's behaviour. According to the Dobbins model, the temperature coefficient θ, could vary from 1.005 to 1.042 within a temperature range of 0-35 °C and wide range of gas transfer velocities, i.e. 'turbulence' condition (0.005 < K(L) < 1.28 cm min(-1)). No other theoretical models showed any significant variability in θ with change in 'turbulence', and only modest variability in θ with change in temperature. However, the other theoretical models did not have the same temperature coefficient θ (with 1.000 < θ < 1.056 within 0-35 °C). A model integrating turbulence and bubble mediated gas transfer velocities suggested a lower temperature dependence for bubble (1.013<θ < 1.017) than turbulence (1.023<θ < 1.031) mediated processes. As it stands, the effect of turbulence on the temperature dependence of gas transfer at the air-water interface has still to be clarified, although many models simulate different flow conditions which may explain some of the observed discrepancies. We suggest that the temperature dependence curves produced by the Dobbins model may be used tentatively as a simple theoretical guide for streams with free surface water but not self-aerated flows encountered in whitewater rapids, cascades or weirs. Greater awareness of the different models and conditions of applications should help choosing an appropriate correction. Three case studies investigated the effect of the temperature coefficient on reaeration and stream metabolism (photosynthesis and respiration). In practice, the temperature correction may be an important parameter under constant turbulence conditions, but as the range in turbulence increases, the role of temperature may become negligible in determining K(L), whatever the temperature correction. The theoretical models reviewed here are also useful references to correct K(L) values determined using a reference tracer gas to a second species of interest.

Determination of the surface corrugation amplitude from classical atom scattering.

The energy landscape of an atomic or molecular projectile interacting with a surface is often described in terms of a corrugation function that gives the classical turning point as a function of position vector parallel to the surface. It is shown here that the relative height variation of the corrugation function for scattering of atoms under classical conditions can be determined by a measurement of the maximum intensity in energy-resolved scattering spectra as a function of surface temperature. This is demonstrated by developing a semiclassical quantum theory of atomic scattering from corrugated surfaces and then extending the theory to the classical limit of large incident energies and high surface temperatures. Comparisons of calculations with available data for Ar atom scattering determine the corrugation amplitude for a molten In surface to be about 29% of the mean interparticle spacing in the bulk liquid.

Scattering of CO and N2 molecules by a graphite surface.

Measurements of angular distributions for the scattering of well-defined incident beams of CO and N(2) molecules from a graphite surface are presented. The measurements were carried out over a range of graphite surface temperatures from 150 to 400 K and a range of incident translational energies from 275 to over 600 meV. The behavior of the widths, positions and relative intensities of the angular distributions for both CO and N(2) were found to be quite similar. The experimental measurements are discussed in comparison with calculations using a classical mechanical model that describes single collisions with a surface. Based on the behavior of the angular distributions as functions of temperature and incident translational energy, and the agreement between measured data and calculations of the single-collision model, it is concluded that the scattering process is predominantly a single collision with a collective surface for which the effective mass is significantly larger than that of a single carbon atom. This conclusion is consistent with that of earlier experiments for molecular beams of O(2) molecules and Xe atoms scattering from graphite. Further calculations are carried out with the theoretical molecular scattering model in order to predict translational and rotational energy transfers to and from the molecule during scattering events under similar initial conditions.

Scattering of O2 from a graphite surface.

Recently an extensive series of measurements has been presented for the angular distributions of oxygen molecules scattered from a graphite surface. Incident translational energies ranged from 291 to 614 meV with surface temperatures from 150 to 500 K. The measurements were taken with a fixed angle of 90° between the source beam and the detector and the angular distributions consisted of a single broad peak with the most probable intensity located at an angle slightly larger than the 45° specular position. Analysis with the hard cubes model for atom-surface scattering indicated that the scattering is primarily a single collision event with a surface having a collective effective mass much larger than a single carbon atom. Limited analysis with a classical diatomic molecular scattering theory was also presented. In this paper a more complete analysis using the classical diatomic molecular scattering theory is presented. The energy and temperature dependence of the observed angular distributions are well described as single collision events with a surface having an effective mass of 1.8 carbon graphite rings. In agreement with the earlier analysis and with other experiments, this suggests a large cooperative response of the carbon atoms in the outermost graphene layer.

Temperature dependence in atom­surface scattering.

It is shown that a straightforward measure of the temperature dependence of energy resolved atom­surface scattering spectra measured under classical conditions can be related to the strength of the surface corrugation. Using classical perturbation theory combined with a Langevin bath formalism for describing energy transfer, explicit expressions for the scattering probabilities are obtained for both two-dimensional, in-plane scattering and full three-dimensional scattering. For strong surface corrugations results expressed as analytic closed-form equations for the scattering probability are derived which demonstrate that the temperature dependence of the scattering probability weakens with increasing corrugation strength. The relationship to the inelastic rainbow is briefly discussed.

Relating temperature dependence of atom scattering spectra to surface corrugation.

It is suggested that a measurement of the temperature dependence of the most probable intensity of energy-resolved atom-surface scattering spectra can reveal the strength of the surface corrugation. To support this conjecture, a classical mechanical theory of atom scattering from a corrugated surface, valid in the weak corrugation limit, is developed. The general result for the scattering probability is expressed in terms of spatial integrals over the impact parameter within a surface unit cell. For the case of a one-dimensional corrugation, approximate expressions for the scattering probability are obtained in terms of analytic closed form expressions. As an indicator of its relation to experimental measurements, calculations using a one-dimensional corrugation model are compared with data for Ar scattering from a molten Ga surface and an approximate value of the corrugation height parameter is extracted.

Scattering of Xe from graphite.

Recently a series of experimental measurements for the scattering of Xe atoms from graphite has been reported for both energy-resolved spectra and angular distributions. This system is of fundamental interest because the projectile Xe atoms are considerably more massive than the carbon atoms making up the graphite surface. These measurements were initially analyzed using the hard cubes model and molecular dynamics simulations, and both treatments indicated that the scattering process was a single collision in which the incoming Xe atom interacted strongly with a large number of carbon atoms in the outermost graphite layer. In this work we analyze the data using a single scattering theory that has been shown to explain a number of other experiments on molecular beam scattering from surfaces. These calculations confirm that the scattering process is a single collision with an effective surface mass that is substantially larger than that of the basic graphite ring.

Angular intensity distribution of a molecular oxygen beam scattered from a graphite surface.

The scattering of the oxygen molecule from a graphite surface has been studied using a molecular beam scattering technique. The angular intensity distributions of scattered oxygen molecules were measured at incident energies from 291 to 614 meV with surface temperatures from 150 to 500 K. Every observed distribution has a single peak at a larger final angle than the specular angle of 45° which indicates that the normal component of the translation energy of the oxygen molecule is lost by the collision with the graphite surface. The amount of the energy loss by the collision has been roughly estimated as about 30-41% based on the assumption of the tangential momentum conservation during the collision. The distributions have also been analyzed with two theoretical models, the hard cubes model and the smooth surface model. These results indicate that the scattering is dominated by a single collision event of the particle with a flat surface having a large effective mass. The derived effective mass of the graphite surface for the incoming oxygen is 9-12 times heavier than that of a single carbon atom, suggesting a large cooperative motion of the carbon atoms in the topmost graphene layer.

Calculations of trapping and desorption in heavy atom collisions with surfaces.

Calculations are carried out for the scattering of heavy rare gas atoms with surfaces using a recently developed classical theory that can track particles trapped in the physisorption potential well and follow them until ultimate desorption. Comparisons are made with recent experimental data for xenon scattering from molten gallium and indium, systems for which the rare gas is heavier than the surface atoms. The good agreement with the data obtained for both time-of-flight energy-resolved spectra and for total scattered angular distributions yields an estimate of the physisorption well depths for the two systems.