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Kattwinkel L, Magnussen OM. Measurement of Surface Diffusion at the Electrochemical Interface by In Situ Linear Optical Diffraction. ACS MEASUREMENT SCIENCE AU 2023; 3:98-102. [PMID: 37090255 PMCID: PMC10120029 DOI: 10.1021/acsmeasuresciau.2c00066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/18/2022] [Revised: 12/21/2022] [Accepted: 12/22/2022] [Indexed: 05/03/2023]
Abstract
A new in situ method for measuring the surface diffusion rates of adsorbates on electrode surfaces in electrolyte solution is presented. The method is based on the generation of a periodic spatial modulation of the adsorbate coverage via interfering laser pulses and subsequent monitoring of the diffusion-induced decay of this pattern using the optical diffraction signal of a second laser. Proof-of-principle measurements of the surface diffusion of adsorbed sulfur on Pt(111) electrodes in 0.1 M H2SO4 indicate potential- and coverage-dependent diffusion constants that are significantly higher than those of sulfur on Pt(111) under vacuum conditions.
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2
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Cheng YH, Zhu YC, Kang W, Li X, Fang W. Determination of concerted or stepwise mechanism of hydrogen tunneling from isotope effects: Departure between experiment and theory. J Chem Phys 2022; 156:124304. [DOI: 10.1063/5.0085010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Isotope substitution is an important experimental technique that offers deep insight into reaction mechanisms, as the measured kinetic isotope effects (KIEs) can be directly compared with theory. For multiple proton transfer processes, there are two types of mechanisms: stepwise transfer and concerted transfer. The Bell-Limbach model provides a simple theory to determine whether the proton transfer mechanism is stepwise or concerted from KIEs. Recent STM experiments have studied the proton switching process in water tetramers on NaCl(001). Theoretical studies predict that this process occurs via a concerted mechanism, however, the experimental KIEs resemble the Bell-Limbach model for stepwise tunneling, raising question on the underlying mechanism or the validity of the model. We study this system using ab initio instanton theory, and in addition to thermal rates, we also considered microcanonical rates, as well as tunneling splittings. Instanton theory predicts a concerted mechanism, and the KIEs for tunneling rates (both thermal and microcanonical) upon deuteration are consistent with the Bell-Limbach model for concerted tunneling, but could not explain the experiments. For tunneling splittings, partial and full deuteration changes the size of it in a similar fashion to how it changes the rates. We further examined the Bell-Limbach model in another system, porphycene, which has both stepwise and concerted tunneling pathways. The KIEs predicted by instanton theory are again consistent with the Bell-Limbach model. This study highlights differences between KIEs in stepwise and concerted tunneling, and the discrepancy between theory and recent STM experiments. New theory/experiments are desired to settle this problem.
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Affiliation(s)
| | | | - Wei Kang
- Center for Applied Physics and Technology, Peking University, China
| | | | - Wei Fang
- Dalian Institute of Chemical Physics, China
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3
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Fang W, Richardson JO, Chen J, Li XZ, Michaelides A. Simultaneous Deep Tunneling and Classical Hopping for Hydrogen Diffusion on Metals. PHYSICAL REVIEW LETTERS 2017; 119:126001. [PMID: 29341641 DOI: 10.1103/physrevlett.119.126001] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2017] [Indexed: 06/07/2023]
Abstract
Hydrogen diffusion on metals exhibits rich quantum behavior, which is not yet fully understood. Using simulations, we show that many hydrogen diffusion barriers can be categorized into those with parabolic tops and those with broad tops. With parabolic-top barriers, hydrogen diffusion evolves gradually from classical hopping, to shallow tunneling, to deep tunneling as the temperature (T) decreases, and noticeable quantum effects persist at moderate T. In contrast, with broad-top barriers quantum effects become important only at low T and the classical-to-quantum transition is sharp, at which classical hopping and deep tunneling both occur. This coexistence indicates that more than one mechanism contributes to the quantum reaction rate. The conventional definition of the classical-to-quantum crossover T is invalid for the broad tops, and we give a new definition. Extending this, we propose a model to predict the transition T for broad-top diffusion, providing a general guide for theory and experiment.
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Affiliation(s)
- Wei Fang
- Thomas Young Centre, London Centre for Nanotechnology and Department of Chemistry, University College London, London WC1E 6BT, United Kingdom
| | | | - Ji Chen
- Thomas Young Centre, London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Xin-Zheng Li
- School of Physics and the Collaborative Innovation Center of Quantum Matters, Peking University, Beijing 100871, People's Republic of China
| | - Angelos Michaelides
- Thomas Young Centre, London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
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4
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Bao JL, Truhlar DG. Variational transition state theory: theoretical framework and recent developments. Chem Soc Rev 2017; 46:7548-7596. [DOI: 10.1039/c7cs00602k] [Citation(s) in RCA: 207] [Impact Index Per Article: 29.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
This article reviews the fundamentals of variational transition state theory (VTST), its recent theoretical development, and some modern applications.
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Affiliation(s)
- Junwei Lucas Bao
- Department of Chemistry
- Chemical Theory Center, and Minnesota Supercomputing Institute
- University of Minnesota
- Minneapolis
- USA
| | - Donald G. Truhlar
- Department of Chemistry
- Chemical Theory Center, and Minnesota Supercomputing Institute
- University of Minnesota
- Minneapolis
- USA
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5
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Zhang Y, Rommel JB, Cvitaš MT, Althorpe SC. Shallow-tunnelling correction factor for use with Wigner–Eyring transition-state theory. Phys Chem Chem Phys 2014; 16:24292-300. [DOI: 10.1039/c4cp03235g] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We obtain a shallow-tunnelling correction factor for use with Wigner–Eyring transition-state theory (TST).
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Affiliation(s)
- Yanchuan Zhang
- Department of Chemistry
- University of Cambridge
- Cambridge CB2 1EW, UK
| | - Judith B. Rommel
- Department of Chemistry
- University of Cambridge
- Cambridge CB2 1EW, UK
| | - Marko T. Cvitaš
- Ruđer Bošković Institute
- Department of Physical Chemistry
- 10000 Zagreb, Croatia
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6
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Decoherence Mechanisms in Adsorbate Localization and Diffusion on Solid Surfaces. E-JOURNAL OF SURFACE SCIENCE AND NANOTECHNOLOGY 2010. [DOI: 10.1380/ejssnt.2010.6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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7
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Wang W, Zhao Y. Path integral evaluation of H diffusion on Ni(100) surface based on the quantum instanton approximation. J Chem Phys 2009; 130:114708. [DOI: 10.1063/1.3097132] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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8
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Martínez-Casado R, Sanz AS, Miret-Artés S. Quantum Markovian activated surface diffusion of interacting adsorbates. J Chem Phys 2008; 129:184704. [DOI: 10.1063/1.3009624] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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9
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Zheng CZ, Yeung CK, Loy MMT, Xiao X. Quantum diffusion of H on Pt(111): step effects. PHYSICAL REVIEW LETTERS 2006; 97:166101. [PMID: 17155414 DOI: 10.1103/physrevlett.97.166101] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2006] [Indexed: 05/12/2023]
Abstract
Using a linear optical diffraction technique, we have systematically investigated the defect effects on quantum surface diffusion of hydrogen on Pt(111) surfaces. The quantum tunneling effect was clearly observed for hydrogen diffusion at low temperatures as manifested by a leveling off of the diffusion coefficient on flat surfaces. The strong influence of surface defects on the quantum diffusion is in good agreement with the creation of an inhomogeneous surface with adsorption sites of different binding energies.
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Affiliation(s)
- C Z Zheng
- Department of Physics and Institute of Nano Science and Technology, Hong Kong University of Science & Technology, Hong Kong, China
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10
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Danziger IM, Asscher M. Collision-Induced Migration of Adsorbates on Solid Surfaces: An Experimental Approach. J Phys Chem A 2006; 110:8339-45. [PMID: 16821817 DOI: 10.1021/jp056839o] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Collision-induced migration (CIM) is a process in which energetic gas-phase atoms or molecules at the tail of the Boltzmann distribution enhance surface migration of adsorbates upon collision. It is believed to exist and play an important role in any realistic high pressure-high-temperature heterogeneous catalytic system. Combining supersonic beam-surface collision setup with in-situ optical second harmonic generation diffraction technique from a coverage grating, we have shown, for the first time, that indeed energetic collisions (Kr seeded in He) promote surface mobility of CO-K surface complex on Ru(001) with a threshold total kinetic energy of 3 eV. An average migration distance/collision of more than 30 adsorption sites was estimated from the experimental data at Kr total energy of 3.8 eV. This long-range migration distance per collision is understood in terms of a cascade migration mechanism, where adsorbed CO molecules collide and push their neighbors from high to low coverage areas, in a direction dictated by the collision momentum vector. A similar mechanism has recently been suggested to explain adsorbate mobility at high coverage induced by an STM tip.
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Affiliation(s)
- I M Danziger
- Department of Physical Chemistry and the Farkas Center for Light Induced Processes, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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11
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Kerner G, Horowitz Y, Asscher M. Diffusion of Buffer Layer Assisted Grown Gold Nanoclusters on Ru(100) and p(1 × 2)-O/Ru(100) Surfaces. J Phys Chem B 2005; 109:4545-53. [PMID: 16851531 DOI: 10.1021/jp045604u] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Patterning of metallic clusters on surfaces is demonstrated by utilizing a buffer layer assisted laser patterning technique (BLALP). This method has been employed in order to measure the diffusion of AFM and STM characterized size selected gold nanoclusters (5-10 nm diameter), over Ru(100) and p(1 x 2)-O/Ru(100) surfaces. Optical linear diffraction from gold cluster coverage gratings was utilized for the macroscopic diffusion measurements. The clusters were found to diffuse on the surface intact without significant coalescence or sintering. The barrier for metastable gold nanocluster diffusion on the surface is thought to be lower than the energy required for surface wetting. The apparent activation energy for diffusion was found to depend on the cluster size, increasing from 6.2 +/- 0.4 kcal/mol for 5 nm clusters to 10.6 +/- 0.5 kcal/mol for 9 nm clusters. The macroscopic diffusion of gold nanoclusters has been studied on the p(1 x 2)-O/Ru(100) surface as well, where surface diffusion was found to be rather insensitive to the clusters size with activation energy of 5.5 +/- 1 kcal/mol. The difference between the two surfaces is discussed in terms of a better commensurability (higher level of friction) of the gold facets at the contact area with the clean Ru(100) than in the case of the oxidized surface.
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Affiliation(s)
- Gabriel Kerner
- Department of Physical Chemistry, The Farkas Center for Light Induced Processes, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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12
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Danziger IM, Hallac B, Asscher M. Surface Diffusion of Potassium Coadsorbed with CO on Ru(001): A Coverage Grating−Optical Second Harmonic Diffraction Study. J Phys Chem B 2004. [DOI: 10.1021/jp040139m] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- I. M. Danziger
- Department of Physical Chemistry and the Farkas Center for Light Induced Processes, The Hebrew University, Jerusalem 91904, Israel
| | - B. Hallac
- Department of Physical Chemistry and the Farkas Center for Light Induced Processes, The Hebrew University, Jerusalem 91904, Israel
| | - M. Asscher
- Department of Physical Chemistry and the Farkas Center for Light Induced Processes, The Hebrew University, Jerusalem 91904, Israel
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13
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Martinazzo R, Assoni S, Marinoni G, Tantardini GF. Hot-atom versus Eley–Rideal dynamics in hydrogen recombination on Ni(100). I. The single-adsorbate case. J Chem Phys 2004; 120:8761-71. [PMID: 15267808 DOI: 10.1063/1.1695316] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We compare the efficiency of the Eley-Rideal (ER) reaction with the formation of hot-atom (HA) species in the simplest case, i.e., the scattering of a projectile off a single adsorbate, considering the Hydrogen and Hydrogen-on-Ni(100) system. We use classical mechanics and the accurate embedded diatomics-in-molecules potential to study the collision system over a wide range of collision energies (0.10-1.50 eV), both with a rigid and a nonrigid Ni substrate and for impact on the occupied and neighboring empty cells. In the rigid model metastable and truly bound hot-atoms occur and we find that the cross section for the formation of bound hot-atoms is considerably higher than that for the ER reaction over the whole range of collision energies examined. Metastable hot-atoms form because of the inefficient energy transfer to the adsorbate and have lifetimes of the order 0.1-0.7 ps, depending on the collision energy. When considering the effects of lattice vibrations we find, on average, a consistent energy transfer to the substrate, say 0.1-0.2 eV, which forced us to devise a two-step dynamical model to get rid of the problems associated with the use of periodic boundary conditions. Results for long-lived HA formation due to scattering on the occupied cell at a surface temperature of 120 K agree well with those of the rigid model, suggesting that in the above process the substrate plays only a secondary role and further calculations at surface temperatures of 50 and 300 K are in line with these findings. However, considerably high cross sections for formation of long-lived hot-atoms result also from scattering off the neighboring cells where the energy transfer to the lattice cannot be neglected. Metastable hot-atoms are reduced in number and have usually lifetimes shorter than those of the rigid-model, say less than 0.3 ps. In addition, ER cross sections are only slightly affected by the lattice motion and show a little temperature dependence. Finally, we find also that absorption and reflection strongly depend on the correct consideration of lattice vibrations and the occurrence of trapping.
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Affiliation(s)
- R Martinazzo
- Department of Physical Chemistry and Electrochemistry, University of Milan, V. Golgi 19, 20133 Milan, Italy
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14
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Haug K, Raibeck G. Kinetic Monte Carlo Study of Competing Hydrogen Pathways into Connected (100), (110), and (111) Ni Surfaces. J Phys Chem B 2003. [DOI: 10.1021/jp030596n] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Kenneth Haug
- Department of Chemistry, Lafayette College, Easton, Pennsylvania 18042
| | - Gretel Raibeck
- Department of Chemistry, Lafayette College, Easton, Pennsylvania 18042
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15
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Bae C, Freeman DL, Doll JD, Kresse G, Hafner J. Energetics of hydrogen chemisorbed on Cu(110): A first principles calculations study. J Chem Phys 2000. [DOI: 10.1063/1.1311293] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Pouthier V, Light JC. Surface self-diffusion of hydrogen on Cu(100): A quantum kinetic equation approach. J Chem Phys 2000. [DOI: 10.1063/1.481899] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Zhang DH, Light JC, Lee SY. Transition state wave packet study of hydrogen diffusion on Cu(100) surface. J Chem Phys 1999. [DOI: 10.1063/1.479870] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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18
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Romm L, Asscher M, Zeiri Y. Collision induced migration of adsorbates on surfaces. J Chem Phys 1999. [DOI: 10.1063/1.479038] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Zhu XD. Formation of adatom density gratings on a substrate by channeling of an atomic beam through a pulsed-laser standing wave under a completely off-resonant condition. OPTICS LETTERS 1997; 22:1890-1892. [PMID: 18188398 DOI: 10.1364/ol.22.001890] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We show that a transversely uncooled atomic beam can be focused by a microsecond laser standing wave to form adatom density gratings on a substrate with good contrast ratio under a completely off-resonant condition (D?/? ~ 1) .
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20
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Zhao W, Verhoef RW, Asscher M. Diffusion of potassium on Re(001) investigated by coverage grating-optical second-harmonic diffraction. J Chem Phys 1997. [DOI: 10.1063/1.474231] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Takagi N, Yasui Y, Takaoka T, Sawada M, Yanagita H, Aruga T, Nishijima M. Quantum delocalization of H on Pd(110): A vibrational study. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:13767-13771. [PMID: 9983130 DOI: 10.1103/physrevb.53.13767] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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22
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Westre ED, Brown DE, Kutzner J, George SM. Surface diffusion of carbon monoxide and potassium coadsorbed on Ru(001): Confirmation of a 1:1 CO:K trapping interaction. J Chem Phys 1996. [DOI: 10.1063/1.471398] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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Farbman I, Asscher M, Ben‐Shaul A. Effects of adsorbate lateral repulsion on desorption and diffusion kinetics studied by Monte Carlo simulations. J Chem Phys 1996. [DOI: 10.1063/1.471805] [Citation(s) in RCA: 16] [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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24
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Wonchoba SE, Hu WP, Truhlar DG. Surface diffusion of H on Ni(100): Interpretation of the transition temperature. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:9985-10002. [PMID: 9977674 DOI: 10.1103/physrevb.51.9985] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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25
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Wong A, Lee A, Zhu XD. Coverage dependence of quantum tunneling diffusion of hydrogen and deuterium on Ni(111). PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:4418-4425. [PMID: 9979286 DOI: 10.1103/physrevb.51.4418] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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26
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Mattsson TR, Wahnström G. Quantum Monte Carlo study of surface diffusion. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:1885-1896. [PMID: 9978912 DOI: 10.1103/physrevb.51.1885] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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27
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Chen LY, Ying SC. Theory of surface diffusion: Crossover from classical to quantum regime. PHYSICAL REVIEW LETTERS 1994; 73:700-703. [PMID: 10057515 DOI: 10.1103/physrevlett.73.700] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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28
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Zhu XD, Deng L. Phonon-assisted tunneling of adatoms on a solid surface: The influence of quadratic adatom-phonon couplings. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:17527-17532. [PMID: 10008367 DOI: 10.1103/physrevb.48.17527] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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29
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Rick SW, Lynch DL, Doll JD. The quantum dynamics of hydrogen and deuterium on the Pd(111) surface: A path integral transition state theory study. J Chem Phys 1993. [DOI: 10.1063/1.465645] [Citation(s) in RCA: 54] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Mattsson TR, Engberg U, Wahnström G. H diffusion on Ni(100): A quantum Monte Carlo simulation. PHYSICAL REVIEW LETTERS 1993; 71:2615-2618. [PMID: 10054726 DOI: 10.1103/physrevlett.71.2615] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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31
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Lee A, Zhu XD, Wong A, Deng L, Linke U. Observation of diffusion of H and D on Ni(111) from over-barrier hopping to nonactivated tunneling. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:11256-11259. [PMID: 10007434 DOI: 10.1103/physrevb.48.11256] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Rosenzweig Z, Farbman I, Asscher M. Diffusion of ammonia on Re(001): A monolayer grating optical second harmonic diffraction study. J Chem Phys 1993. [DOI: 10.1063/1.464533] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Reilly PD, Harris RA, Whaley KB. Quantum diffusion of light interstitials: One-phonon contribution to the impurity-lattice scattering. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:5721-5730. [PMID: 10004519 DOI: 10.1103/physrevb.47.5721] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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36
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Lee A, Zhu XD, Deng L, Linke U. Observation of a transition from over-barrier hopping to activated tunneling diffusion: H and D on Ni(100). PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:15472-15476. [PMID: 10003669 DOI: 10.1103/physrevb.46.15472] [Citation(s) in RCA: 30] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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37
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Reilly PD, Harris RA, Whaley KB. Multiple‐band theory of dynamics for interacting adsorbates coupled to phonons. II. Single adsorbate dynamics. J Chem Phys 1992. [DOI: 10.1063/1.463213] [Citation(s) in RCA: 13] [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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