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Chen Y, Gibelli L, Borg MK. Impact of random nanoscale roughness on gas-scattering dynamics. Phys Rev E 2024; 109:065308. [PMID: 39020882 DOI: 10.1103/physreve.109.065308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Accepted: 06/05/2024] [Indexed: 07/20/2024]
Abstract
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.
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OUP accepted manuscript. Microscopy (Oxf) 2022; 71:i174-i199. [DOI: 10.1093/jmicro/dfab050] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Revised: 11/20/2021] [Accepted: 01/28/2022] [Indexed: 11/14/2022] Open
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Affiliation(s)
- D. E. Parks
- General Atomic Division of General Dynamics Corporation, John Jay Hopkins Laboratory for Pure and Applied Science, San Diego, California
| | - J. R. Beyster
- General Atomic Division of General Dynamics Corporation, John Jay Hopkins Laboratory for Pure and Applied Science, San Diego, California
| | - N. F. Wikner
- General Atomic Division of General Dynamics Corporation, John Jay Hopkins Laboratory for Pure and Applied Science, San Diego, California
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Sobrino LD, Clark M. Comparison of the Wilkins Equation and Higher Order Approximations for Solid Moderators. NUCL SCI ENG 2017. [DOI: 10.13182/nse61-a15383] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Luis de Sobrino
- Massachusetts Institute of Technology, Cambridge, Massachusetts
| | - Melville Clark
- Massachusetts Institute of Technology, Cambridge, Massachusetts
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Affiliation(s)
- Mark Nelkin
- Knools Atomic Power Laboratory, Schenectady, New York
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Affiliation(s)
- Donald E. Parks
- John Jay Hopkins Laboratory for Pure and Applied Science, General Atomic Division of General Dynamics Corporation, San Diego, California
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Mapping vibrational surface and bulk modes in a single nanocube. Nature 2017; 543:529-532. [DOI: 10.1038/nature21699] [Citation(s) in RCA: 176] [Impact Index Per Article: 25.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2016] [Accepted: 02/09/2017] [Indexed: 12/25/2022]
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Hayes WW, Manson JR. Determination of the surface corrugation amplitude from classical atom scattering. PHYSICAL REVIEW LETTERS 2012; 109:063203. [PMID: 23006264 DOI: 10.1103/physrevlett.109.063203] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2012] [Indexed: 06/01/2023]
Abstract
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.
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Affiliation(s)
- W W Hayes
- Physical Sciences Department, Greenville Technical College, Greenville, South Carolina 29606, USA.
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Hayes WW, Manson JR. Relating temperature dependence of atom scattering spectra to surface corrugation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:484003. [PMID: 22085838 DOI: 10.1088/0953-8984/23/48/484003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
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.
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Affiliation(s)
- W W Hayes
- Physical Sciences Department, Greenville Technical College, Greenville, SC 29606, USA.
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Levi AC, Huang C, Allison W, Maclaren DA. Quantum scattering of neon from a nanotextured surface. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:225009. [PMID: 21715773 DOI: 10.1088/0953-8984/21/22/225009] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
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.
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Affiliation(s)
- A C Levi
- Dipartimento di Fisica and CNISM, Università di Genova, 16146 Genova, Italy
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MacLaren DA, Huang C, Levi AC, Allison W. Coverage-dependent quantum versus classical scattering of thermal neon atoms from Li/Cu(100). J Chem Phys 2008; 129:094706. [DOI: 10.1063/1.2976766] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Muller DA, Edwards B, Kirkland EJ, Silcox J. Simulation of thermal diffuse scattering including a detailed phonon dispersion curve. Ultramicroscopy 2001; 86:371-80. [PMID: 11281157 DOI: 10.1016/s0304-3991(00)00128-5] [Citation(s) in RCA: 105] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
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.
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Affiliation(s)
- D A Muller
- Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974, USA.
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Berry MV. Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/8/4/019] [Citation(s) in RCA: 93] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Alvarez F, Arbe A, Colmenero J. Methyl group dynamics above the glass transition temperature: a molecular dynamics simulation in polyisoprene. Chem Phys 2000. [DOI: 10.1016/s0301-0104(00)00225-1] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Balzer F, Gerlach R, Manson JR, Rubahn HG. Photodesorption of Na atoms from rough Na surfaces. J Chem Phys 1997. [DOI: 10.1063/1.473810] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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Bilic A, Gumhalter B. Quantum versus semiclassical treatment of multiphonon effects in He-atom scattering from surfaces. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:12307-12328. [PMID: 9980373 DOI: 10.1103/physrevb.52.12307] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Miret-Artes S, Micha DA. Multiphoton fragmentation of H2+ and D2+ with coherent and incoherent fields. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:2984-2993. [PMID: 9912585 DOI: 10.1103/physreva.52.2984] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Manson JR, Celli V, Himes D. Multiphonon scattering from surfaces. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:2782-2790. [PMID: 10011111 DOI: 10.1103/physrevb.49.2782] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Miret-Artés S, Micha DA. Multiphoton dissociation for coherent and incoherent fields. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:4059-4061. [PMID: 9910103 DOI: 10.1103/physreva.48.r4059] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Jiang QT, Gustafsson T, Häberle P, Zehner DM. Missing-row surface reconstruction of Au(113) induced by adsorbed calcium atoms. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:14256-14263. [PMID: 10001551 DOI: 10.1103/physrevb.45.14256] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Franchini A, Santoro G, Bortolani V, Maradudin AA, Wallis RF. Theory of the anharmonic linewidths of surface phonons in aluminum. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:11982-11988. [PMID: 10001216 DOI: 10.1103/physrevb.45.11982] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Manson JR. Inelastic scattering from surfaces. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:6924-6937. [PMID: 9998154 DOI: 10.1103/physrevb.43.6924] [Citation(s) in RCA: 85] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Chicault R, Joly Y. Model for phonon transmission through a NbN grain-size distribution: Comparison with tunneling-spectroscopy observations. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:11655-11664. [PMID: 9995469 DOI: 10.1103/physrevb.42.11655] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Zoli M, Santoro G, Bortolani V, Maradudin AA, Wallis RF. Anharmonic damping of phonon modes in the fcc metals. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:7507-7514. [PMID: 9993042 DOI: 10.1103/physrevb.41.7507] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Gibson KD, Sibener SJ. Inelastic helium scattering studies of ordered Ar, Kr, and Xe monolayers physisorbed on Ag(111): Dispersion curves, scattering cross sections, and excitation line shapes. J Chem Phys 1988. [DOI: 10.1063/1.454300] [Citation(s) in RCA: 55] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Yu C, Whaley KB, Hogg CS, Sibener SJ. Investigation of the spatially isotropic component of the laterally averaged molecular hydrogen/Ag(111) physisorption potential. J Chem Phys 1985. [DOI: 10.1063/1.449086] [Citation(s) in RCA: 70] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Tully JC. Dynamics of gas–surface interactions: 3D generalized Langevin model applied to fcc and bcc surfaces. J Chem Phys 1980. [DOI: 10.1063/1.440287] [Citation(s) in RCA: 364] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Morawitz H, Eisenthal KB. Relaxation Processes and Molecular Motion in Liquids and Gases. J Chem Phys 1971. [DOI: 10.1063/1.1676158] [Citation(s) in RCA: 31] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Campisano SU, Grasso F, Rimini E. Proton dechannelling in Ge probes the crystal scattering. ACTA ACUST UNITED AC 1971. [DOI: 10.1080/00337577108231044] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Brice DK. Channeling ofH+1,D+2, andHe++3Ions in Germanium: A Diffraction Calculation. ACTA ACUST UNITED AC 1968. [DOI: 10.1103/physrev.165.475] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Quantum Mechanics in Gas Crystal-Surface Van Der Waals Scattering. ADVANCES IN ATOMIC AND MOLECULAR PHYSICS VOLUME 3 1968. [DOI: 10.1016/s0065-2199(08)60174-8] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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Gadzuk IW. Single-Phonon Energy Transfer between Molecular Beams and Solid Surfaces. ACTA ACUST UNITED AC 1967. [DOI: 10.1103/physrev.153.759] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Shimizu H. Time‐Correlation Function of Molecular Random Motion and Shape of Spectral Bands. J Chem Phys 1965. [DOI: 10.1063/1.1697145] [Citation(s) in RCA: 107] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Reiner AS. Density Propagator for a Self-Bound Fermion System. II. Linear Response and Inelastic Electron Scattering. ACTA ACUST UNITED AC 1965. [DOI: 10.1103/physrev.138.b389] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Aamodt R, Case KM, Rosenbaum M, Zweifel PF. Quasi-Classical Treatment of Neutron Scattering. ACTA ACUST UNITED AC 1962. [DOI: 10.1103/physrev.126.1165] [Citation(s) in RCA: 46] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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