Impact of random nanoscale roughness on gas-scattering dynamics

The impact of nanoscale wall roughness on rarefied gas transport is widely acknowledged, yet the associated scattering dynamics largely remain elusive. In this paper, we develop a scattering kernel for surfaces having nanoscale roughness that distinctly characterizes the two major types of interactions between gas molecules and rough surfaces. Namely these are (a) the weak perturbations arising from the thermal motion of wall atoms, essentially gas-phonon collisions, which are captured by the well-established Cercignani-Lampis model, and (b) the hard collisions owing to the irregularities of the rough, static potential energy surface, which are generally described by the fully diffuse model. Drawing an analogy between wave-surface and gas-surface scattering, a pseudo Debye-Waller factor is incorporated into the modeling as a weighting coefficient to allow the transition between smooth and rough surface conditions. The proposed scattering kernel is validated through high-fidelity molecular dynamics simulations that are performed for systems with varying roughness, temperature, and gas-surface combinations. The results indicate that the model well captures the scattering dynamics of gas molecular beams impinging on surfaces at different velocities, specifically for the accommodation coefficients and reflection patterns. Additionally, in flow and heat transport cases, it accurately predicts macroscopic quantities such as velocity slip and temperature jumps across the range of tested conditions.

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.

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.

Quantum scattering of neon from a nanotextured surface

Phonon exchange is the usual cause of decoherence in atom-surface scattering. By including quantum effects in the treatment of Debye-Waller scattering, we show that phonon exchange becomes ineffective when the relevant phonon frequencies are high. The result explains the surprising observation of strong elastic scattering of Ne from a Cu(100) surface nanotextured with a c(2 × 2) Li adsorbate structure. We extend a previous model to describe the phonon spectra by an Einstein oscillator component with an admixture of a Debye spectrum. The Einstein oscillator represents the dominant, high frequency vibration of the adsorbate, normal to the surface, while the Debye spectrum represents the substrate contribution. Neon scattering is so slow that exciting the adsorbate mode has a low probability and is impossible if the incident energy is below the threshold. Thus, adsorbate vibrations are averaged out. A theoretical discussion and calculation shows that under such circumstances the vibrations of a light adsorbate do not contribute to the Debye-Waller effect, with the result that Ne scattering at thermal energies is quantum mechanical and largely elastic, explaining the high reflectivity and the diffraction peaks observed experimentally.

Simulation of thermal diffuse scattering including a detailed phonon dispersion curve

Thermal vibration of the atoms in a crystal give rise to a diffuse background in the diffraction pattern (in between the normal allowed Bragg reflections). The Einstein model for phonon vibrations in a crystal leads to Gaussian statistics for the phonons. However, the Einstein model ignores the possibility of correlation between the atoms. An accurate model of the phonon dispersion curves for silicon is used to generate a set of more accurate random atomic displacements. These displacements are used in a multislice-style simulation to gauge the validity of the Einstein approximation. The phonon dispersion curve yields a small additional oscillatory structure in the thermal diffuse scattering (TDS) pattern. This does not produce significant changes in the annular dark field scanning transmission electron microscope (ADF-STEM) image signal, but could have a large impact on convergent beam measurements of bond charges.