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\begin{document} |
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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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\author{Joseph R. Michalka} |
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\author{Patrick W. McIntyre} |
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\author{J. Daniel Gezelter} |
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\email{gezelter@nd.edu} |
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\affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\ |
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Department of Chemistry and Biochemistry\\ University of Notre |
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Dame\\ Notre Dame, Indiana 46556} |
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\keywords{} |
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\begin{document} |
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%% |
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%Introduction |
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% Experimental observations |
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%Summary |
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%% |
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|
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%Title |
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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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|
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\author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel |
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Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\ |
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Department of Chemistry and Biochemistry,\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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|
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%Date |
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\date{Mar 5, 2013} |
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%authors |
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% make the title |
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\maketitle |
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\begin{doublespace} |
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\begin{abstract} |
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We examine surface reconstructions of Pt and Au(557) under |
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various CO coverages using molecular dynamics in order to |
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reversible restructuring under exposure to moderate pressures of |
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carbon monoxide.\cite{Tao:2010} |
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|
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This work is an investigation into the mechanism and timescale for |
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This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557) |
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surface restructuring using molecular simulations. Since the dynamics |
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of the process are of particular interest, we employ classical force |
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fields that represent a compromise between chemical accuracy and the |
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catalyst with adsorbates, in this work, two metal systems exposed |
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to carbon monoxide were examined. The Pt(557) surface has already been shown |
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to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010} |
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The Au(557) surface, because of a weaker interaction with CO, is seen as less |
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likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000} |
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and Piccolo et al.\cite{Piccolo:2004} have both observed CO-induced |
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reconstruction of a Au(111) surface. Peters et al. saw a relaxation to the |
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The Au(557) surface, because of a weaker interaction with CO, is less |
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likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000} |
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and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced |
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reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the |
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22 x $\sqrt{3}$ cell. They argued that only a few Au atoms |
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become adatoms, limiting the stress of this reconstruction while |
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become adatoms, limiting the stress of this reconstruction, while |
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allowing the rest to relax and approach the ideal (111) |
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configuration. They did not see the usual herringbone pattern being greatly |
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affected by this relaxation. Piccolo et al. on the other hand, did see a |
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configuration. They did not see the usual herringbone pattern on Au(111) being greatly |
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affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a |
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disruption of the herringbone pattern as CO was adsorbed to the |
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surface. Both groups suggested that the preference CO shows for |
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low-coordinated Au atoms was the primary driving force for the reconstruction. |
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development of a sufficiently general yet computationally tractable |
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model of the chemical interactions between the surface atoms and |
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adsorbates. Since the interfaces involved are quite large (10$^3$ - |
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10$^6$ atoms) and respond slowly to perturbations, {\it ab initio} |
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10$^4$ atoms) and respond slowly to perturbations, {\it ab initio} |
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molecular dynamics |
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(AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello |
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methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum |
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Coulomb potential. For this work, we have used classical molecular |
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dynamics with potential energy surfaces that are specifically tuned |
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for transition metals. In particular, we used the EAM potential for |
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Au-Au and Pt-Pt interactions\cite{EAM}. The CO was modeled using a rigid |
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Au-Au and Pt-Pt interactions.\cite{EAM} The CO was modeled using a rigid |
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three-site model developed by Straub and Karplus for studying |
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photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
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Pt-CO cross interactions were parameterized as part of this work. |
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methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98} |
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but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and |
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the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
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parameter sets. The glue model of Ercolessi et al. is among the |
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parameter sets. The glue model of Ercolessi {\it et al}. is among the |
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fastest of these density functional approaches.\cite{Ercolessi88} In |
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all of these models, atoms are conceptualized as a positively charged |
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all of these models, atoms are treated as a positively charged |
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core with a radially-decaying valence electron distribution. To |
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calculate the energy for embedding the core at a particular location, |
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the electron density due to the valence electrons at all of the other |
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propagation,\cite{BECQUART:1993rg} and alloying |
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dynamics.\cite{Shibata:2002hh} One of EAM's strengths |
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is its sensitivity to small changes in structure. This arises |
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from the original parameterization, where the interactions |
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up to the third nearest neighbor were taken into account.\cite{Voter95a} |
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Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88} |
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because interactions |
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up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a} |
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Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88} |
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which is only parameterized up to the nearest-neighbor |
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interactions, EAM is a suitable choice for systems where |
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the bulk properties are of secondary importance to low-index |
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surface structures. Additionally, the similarity of EAMs functional |
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surface structures. Additionally, the similarity of EAM's functional |
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treatment of the embedding energy to standard density functional |
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theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier. |
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\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
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position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}. |
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The modified parameters yield binding energies that are slightly higher |
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than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
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et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
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Lennard-Jones interaction to mimic strong, but short-ranged partial |
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{\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
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Lennard-Jones interaction to mimic strong, but short-ranged, partial |
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binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
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Pt-O interaction was modeled with a Morse potential with a large |
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equilibrium distance, ($r_o$). These choices ensure that the C is preferred |
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over O as the surface-binding atom. In most cases, the Pt-O parameterization contributes a weak |
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over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak |
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repulsion which favors the atop site. The resulting potential-energy |
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surface suitably recovers the calculated Pt-C separation length |
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(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
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performed until the energy difference between subsequent steps |
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was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
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were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
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zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was |
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zone.\cite{Monkhorst:1976} The relaxed gold slab was |
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then used in numerous single point calculations with CO at various |
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heights (and angles relative to the surface) to allow fitting of the |
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empirical force field. |
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The parameters employed for the metal-CO cross-interactions in this work |
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are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
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(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
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and polarization are neglected in this model, although these effects are likely to |
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affect binding energies and binding site preferences, and will be addressed in |
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future work. |
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and polarization are neglected in this model, although these effects could have |
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an effect on binding energies and binding site preferences. |
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|
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%Table of Parameters |
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%Pt Parameter Set 9 |
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\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
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(Ref. \protect\cite{Kelemen:1979}) \\ |
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& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
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\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPD_Gold}) \\ |
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\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPDGold}) \\ |
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\hline |
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\end{tabular} |
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\label{tab:co_energies} |
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\subsection{Pt(557) and Au(557) metal interfaces} |
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Our Pt system is an orthorhombic periodic box of dimensions |
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54.482~x~50.046~x~120.88~\AA~while our Au system has |
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dimensions of 57.4~x~51.9285~x~100~\AA. |
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dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs |
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are 9 and 8 atoms deep respectively, corresponding to a slab |
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thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au. |
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The systems are arranged in a FCC crystal that have been cut |
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along the (557) plane so that they are periodic in the {\it x} and |
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{\it y} directions, and have been oriented to expose two aligned |
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1200~K were performed to confirm the relative |
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stability of the surfaces without a CO overlayer. |
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|
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The different bulk melting temperatures (1337~K for Au |
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and 2045~K for Pt) suggest that any possible reconstruction should happen at |
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The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting} |
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and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
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different temperatures for the two metals. The bare Au and Pt surfaces were |
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initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
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respectively for 100 ps. The two surfaces were relatively stable at these |
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% |
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\section{Results} |
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\subsection{Structural remodeling} |
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The surfaces of both systems, upon dosage of CO, began |
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to undergo remodeling that was not observed in the bare |
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metal system. The surfaces which were not exposed to CO |
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did experience minor roughening of the step-edge because |
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of the elevated temperatures, but the |
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(557) lattice was well-maintained throughout the simulation |
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time. The Au systems were limited to greater amounts of |
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roughening, i.e. breakup of the step-edge, and some step |
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wandering. The lower coverage Pt systems experienced |
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similar restructuring but to a greater extent when |
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compared to the Au systems. The 50\% coverage |
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Pt system was unique among our simulations in that it |
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formed numerous double layers through step coalescence, |
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similar to results reported by Tao et al.\cite{Tao:2010} |
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The bare metal surfaces experienced minor roughening of the |
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step-edge because of the elevated temperatures, but the (557) |
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face was stable throughout the simulations. The surface of both |
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systems, upon dosage of CO, began to undergo extensive remodeling |
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that was not observed in the bare systems. Reconstructions of |
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the Au systems were limited to breakup of the step-edges and |
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some step wandering. The lower coverage Pt systems experienced |
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similar restructuring but to a greater extent. The 50\% coverage |
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Pt system was unique among our simulations in that it formed |
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well-defined and stable double layers through step coalescence, |
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similar to results reported by Tao {\it et al}.\cite{Tao:2010} |
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\subsubsection{Step wandering} |
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The 0\% coverage surfaces for both metals showed minimal |
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movement at their respective run temperatures. As the CO |
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coverage increased however, the mobility of the surface, |
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adatoms and step-edges alike, also increased. Additionally, |
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at the higher coverages on both metals, there was more |
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step-wandering. Except for the 50\% Pt system, the step-edges |
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did not coalesce in any of the other simulations, instead preferring |
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to keep nearly the same distance between steps as in the |
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original (557) lattice. Previous work by Williams et al.\cite{Williams:1991, Williams:1994} |
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step-wandering at their respective temperatures. As the CO |
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coverage increased however, the mobility of the surface atoms, |
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described through adatom diffusion and step-edge wandering, |
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also increased. Except for the 50\% Pt system where step |
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coalescence occurred, the step-edges in the other simulations |
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preferred to keep nearly the same distance between steps as in |
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the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au. |
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Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994} |
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highlights the repulsion that exists between step-edges even |
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when no direct interactions are present in the system. This |
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repulsion exists because the entropy of the step-edges is constrained |
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since step-edge crossing is not allowed. This entropic repulsion |
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does not completely define the interactions between steps, |
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which is why some surfaces will undergo step coalescence, |
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where additional attractive interactions can overcome the |
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repulsion\cite{Williams:1991} and others will not. The presence |
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of adsorbates can affect these step interactions, potentially |
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leading to a new surface structure as the thermodynamic minimum. |
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repulsion is caused by an entropic barrier that arises from |
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the fact that steps cannot cross over one another. This entropic |
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repulsion does not completely define the interactions between |
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steps, however, so it is possible to observe step coalescence |
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on some surfaces.\cite{Williams:1991} The presence and |
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concentration of adsorbates, as shown in this work, can |
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affect step-step interactions, potentially leading to a new |
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surface structure as the thermodynamic equilibrium. |
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|
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\subsubsection{Double layers} |
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Tao et al. have shown experimentally that the Pt(557) surface |
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undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} |
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Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
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undergoes two separate reconstructions upon CO adsorption. |
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The first involves a doubling of the step height and plateau length. |
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Similar behavior has been seen to occur on numerous surfaces |
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at varying conditions: Ni(977), Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
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Similar behavior has been seen on a number of surfaces |
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at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
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Of the two systems we examined, the Pt system showed a greater |
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propensity for reconstruction when compared to the Au system |
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because of the larger surface mobility and extent of step wandering. |
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The amount of reconstruction is correlated to the amount of CO |
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propensity for reconstruction |
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because of the larger surface mobility and the greater extent of step wandering. |
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The amount of reconstruction was strongly correlated to the amount of CO |
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adsorbed upon the surface. This appears to be related to the |
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effect that adsorbate coverage has on edge breakup and on the |
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surface diffusion of metal adatoms. While both systems displayed |
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step-edge wandering, only the 50\% Pt surface underwent the |
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doubling seen by Tao et al. within the time scales studied here. |
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Over longer periods (150~ns) two more double layers formed |
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on this interface. Although double layer formation did not occur |
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in the other Pt systems, they show more step-wandering and |
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general roughening compared to their Au counterparts. The |
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surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
| 447 |
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doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
| 448 |
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Over a longer time scale (150~ns) two more double layers formed |
| 449 |
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on this surface. Although double layer formation did not occur |
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in the other Pt systems, they exhibited more step-wandering and |
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roughening compared to their Au counterparts. The |
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50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
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various times along the simulation showing the evolution of a step-edge. |
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various times along the simulation showing the evolution of a double layer step-edge. |
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|
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The second reconstruction on the Pt(557) surface observed by |
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Tao involved the formation of triangular clusters that stretched |
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across the plateau between two step-edges. Neither system, within |
| 455 |
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The second reconstruction observed by |
| 456 |
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Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
| 457 |
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across the plateau between two step-edges. Neither metal, within |
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the 40~ns time scale or the extended simulation time of 150~ns for |
| 459 |
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the 50\% Pt system, experienced this reconstruction. |
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|
| 461 |
+ |
%Evolution of surface |
| 462 |
+ |
\begin{figure}[H] |
| 463 |
+ |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 464 |
+ |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 465 |
+ |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 466 |
+ |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 467 |
+ |
doubling of the layers appears only after two adjacent step-edges |
| 468 |
+ |
touch. The circled spot in (b) nucleated the growth of the double |
| 469 |
+ |
step observed in the later configurations.} |
| 470 |
+ |
\label{fig:reconstruct} |
| 471 |
+ |
\end{figure} |
| 472 |
+ |
|
| 473 |
|
\subsection{Dynamics} |
| 474 |
< |
Previous atomistic simulations of stepped surfaces dealt largely |
| 475 |
< |
with the energetics and structures at different conditions |
| 476 |
< |
\cite{Williams:1991,Williams:1994}. Consequently, the most common |
| 477 |
< |
technique utilized to date has been Monte Carlo sampling. Monte Carlo gives an efficient |
| 478 |
< |
sampling of the equilibrium thermodynamic landscape at the expense |
| 479 |
< |
of ignoring the dynamics of the system. Previous experimental work by Pearl and |
| 480 |
< |
Sibener\cite{Pearl}, using STM, has been able to capture the coalescing |
| 481 |
< |
of steps on Ni(977). The time scale of the image acquisition, |
| 468 |
< |
$\sim$70 s/image provides an upper bound for the time required for |
| 469 |
< |
the doubling to occur. In this section we give data on dynamic and |
| 470 |
< |
transport properties, e.g. diffusion, layer formation time, etc. |
| 474 |
> |
Previous experimental work by Pearl and Sibener\cite{Pearl}, |
| 475 |
> |
using STM, has been able to capture the coalescence of steps |
| 476 |
> |
on Ni(977). The time scale of the image acquisition, $\sim$70~s/image, |
| 477 |
> |
provides an upper bound for the time required for the doubling |
| 478 |
> |
to occur. By utilizing Molecular Dynamics we are able to probe |
| 479 |
> |
the dynamics of these reconstructions at elevated temperatures |
| 480 |
> |
and in this section we provide data on the timescales for transport |
| 481 |
> |
properties, e.g. diffusion and layer formation time. |
| 482 |
|
|
| 483 |
|
|
| 484 |
|
\subsubsection{Transport of surface metal atoms} |
| 485 |
|
%forcedSystems/stepSeparation |
| 486 |
< |
The movement or wandering of a step-edge is a cooperative effect |
| 486 |
> |
The wandering of a step-edge is a cooperative effect |
| 487 |
|
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
| 488 |
|
displaying a low index facet, (111) or (100), is unlikely to experience |
| 489 |
|
much surface diffusion because of the large energetic barrier that must |
| 490 |
|
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
| 491 |
< |
on higher-index facets provide a lower energy source for mobile metal atoms. |
| 492 |
< |
Breaking away from the step-edge on a clean surface still imposes an |
| 493 |
< |
energetic penalty around $\sim$~40 kcal/mol, but this is significantly easier than lifting |
| 491 |
> |
on higher-index facets provides a lower energy source for mobile metal atoms. |
| 492 |
> |
Single-atom break-away from a step-edge on a clean surface still imposes an |
| 493 |
> |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
| 494 |
|
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 495 |
|
The penalty lowers significantly when CO is present in sufficient quantities |
| 496 |
< |
on the surface. For certain distributions of CO, the penalty can fall as low as |
| 496 |
> |
on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as |
| 497 |
|
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 498 |
< |
diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are |
| 499 |
< |
able to explore the terrace before rejoining either the original step-edge or |
| 500 |
< |
becoming a part of a different edge. It is a more difficult process for an atom |
| 498 |
> |
diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then |
| 499 |
> |
able to explore the terrace before rejoining either their original step-edge or |
| 500 |
> |
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom |
| 501 |
|
to traverse to a separate terrace although the presence of CO can lower the |
| 502 |
< |
energy barrier required to lift or lower the adatom. By tracking the mobility of individual |
| 502 |
> |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
| 503 |
|
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 504 |
|
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 505 |
|
observation of the mobile metal atoms showed that they were typically in |
| 506 |
< |
equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. |
| 506 |
> |
equilibrium with the step-edges. |
| 507 |
|
At times, their motion was concerted and two or more adatoms would be |
| 508 |
|
observed moving together across the surfaces. |
| 509 |
|
|
| 510 |
|
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 511 |
< |
between saved configurations of the system (typically 10-100 ps). An atom that was |
| 512 |
< |
truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 511 |
> |
between saved configurations of the system (typically 10-100 ps). A mobile atom |
| 512 |
> |
would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 513 |
|
was used to prevent swamping the diffusion data with the in-place vibrational |
| 514 |
|
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 515 |
|
local structures and in this work, the presence of single and double layer |
| 516 |
< |
step-edges causes the diffusion parallel to the step-edges to be different |
| 517 |
< |
from the diffusion perpendicular to these edges. Parallel and perpendicular |
| 516 |
> |
step-edges causes the diffusion parallel to the step-edges to be larger than |
| 517 |
> |
the diffusion perpendicular to these edges. Parallel and perpendicular |
| 518 |
|
diffusion constants are shown in Figure \ref{fig:diff}. |
| 519 |
|
|
| 520 |
< |
The lack of a definite trend in the Au diffusion data is likely due |
| 510 |
< |
to the weaker bonding between Au and CO. This leads to a lower |
| 511 |
< |
coverage ({\it x}-axis) when compared to dosage amount, which |
| 512 |
< |
then further limits the affects of the surface diffusion. The correlation |
| 513 |
< |
between coverage and Pt diffusion rates conversely shows a |
| 514 |
< |
definite trend marred by the highest coverage surface. Two |
| 515 |
< |
explanations arise for this drop. First, upon a visual inspection of |
| 516 |
< |
the system, after a double layer has been formed, it maintains its |
| 517 |
< |
stability strongly and is no longer a good source for adatoms. By |
| 518 |
< |
performing the same diffusion calculation but on a shorter run time |
| 519 |
< |
(20~ns), only including data before the formation of the double layer, |
| 520 |
< |
provides a $\mathbf{D}_{\perp}$ diffusion constant of $1.69~\pm~0.08$ |
| 521 |
< |
and a $\mathbf{D}_{\parallel}$ diffusion constant of $6.30~\pm~0.08$. |
| 522 |
< |
This places the parallel diffusion constant more closely in line with the |
| 523 |
< |
expected trend, while the perpendicular diffusion constant does not |
| 524 |
< |
drop as far. A secondary explanation arising from our analysis of the |
| 525 |
< |
mechanism of double layer formation show the affect that CO on the |
| 526 |
< |
surface has with respect to overcoming surface diffusion of Pt. If the |
| 527 |
< |
coverage is too sparse, the Pt engages in minimal interactions and |
| 528 |
< |
thus minimal diffusion. As coverage increases, there are more favorable |
| 529 |
< |
arrangements of CO on the surface allowing the formation of a path, |
| 530 |
< |
a minimum energy trajectory, for the adatom to explore the surface. |
| 531 |
< |
As the CO is constantly moving on the surface, this path is constantly |
| 532 |
< |
changing. If the coverage becomes too great, the paths could |
| 533 |
< |
potentially be clogged leading to a decrease in diffusion despite |
| 534 |
< |
their being more adatoms and step-wandering. |
| 535 |
< |
|
| 536 |
< |
\subsubsection{Dynamics of double layer formation} |
| 537 |
< |
The increased diffusion on Pt at the higher |
| 538 |
< |
CO coverages plays a primary role in double layer formation. However, this is not |
| 539 |
< |
a complete explanation -- the 33\%~Pt system |
| 540 |
< |
has higher diffusion constants but did not show |
| 541 |
< |
any signs of edge doubling in the observed run time. On the |
| 542 |
< |
50\%~Pt system, one layer formed within the first 40~ns of simulation time, while two more were formed as the system was run for an additional |
| 543 |
< |
110~ns (150~ns total). Previous experimental |
| 544 |
< |
work gives insight into the upper bounds of the |
| 545 |
< |
time required for step coalescence.\cite{Williams:1991,Pearl} |
| 546 |
< |
In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 547 |
< |
appearance of a double layer, appears at 19~ns |
| 548 |
< |
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
| 549 |
< |
formed the double layer and by 86~ns, the complete layer |
| 550 |
< |
has been flattened out. The double layer could be considered |
| 551 |
< |
``complete" by 37~ns but remains a bit rough. From the |
| 552 |
< |
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
| 553 |
< |
$\sim$40~ns was necessary for the layer to completely straighten. |
| 554 |
< |
The other two layers in this simulation formed over periods of |
| 555 |
< |
22~ns and 42~ns respectively. Comparing this to the upper |
| 556 |
< |
bounds of the image scan, it is likely that most aspects of this |
| 557 |
< |
reconstruction occur very rapidly. A possible explanation |
| 558 |
< |
for this rapid reconstruction is the elevated temperatures |
| 559 |
< |
under which our systems were simulated. It is probable that the process would |
| 560 |
< |
take longer at lower temperatures. |
| 561 |
< |
|
| 562 |
< |
%Evolution of surface |
| 520 |
> |
%Diffusion graph |
| 521 |
|
\begin{figure}[H] |
| 522 |
< |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 565 |
< |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 566 |
< |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 567 |
< |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 568 |
< |
doubling of the layers appears only after two adjacent step-edges |
| 569 |
< |
touch. The circled spot in (b) nucleated the growth of the double |
| 570 |
< |
step observed in the later configurations.} |
| 571 |
< |
\label{fig:reconstruct} |
| 572 |
< |
\end{figure} |
| 573 |
< |
|
| 574 |
< |
\begin{figure}[H] |
| 575 |
< |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
| 522 |
> |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf} |
| 523 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
| 524 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 525 |
|
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 526 |
|
surface coverage. Diffusion parallel to the step-edge is higher |
| 527 |
|
than that perpendicular to the edge because of the lower energy |
| 528 |
|
barrier associated with traversing along the edge as compared to |
| 529 |
< |
completely breaking away. Additionally, the observed |
| 530 |
< |
maximum and subsequent decrease for the Pt system suggests that the |
| 531 |
< |
CO self-interactions are playing a significant role with regards to |
| 532 |
< |
movement of the Pt atoms around and across the surface. } |
| 529 |
> |
completely breaking away. The two reported diffusion constants for |
| 530 |
> |
the 50\% Pt system arise from different sample sets. The lower values |
| 531 |
> |
correspond to the same 40~ns amount that all of the other systems were |
| 532 |
> |
examined at, while the larger values correspond to a 20~ns period } |
| 533 |
|
\label{fig:diff} |
| 534 |
|
\end{figure} |
| 535 |
|
|
| 536 |
+ |
The weaker Au-CO interaction is evident in the weak CO-coverage |
| 537 |
+ |
dependance of Au diffusion. This weak interaction leads to lower |
| 538 |
+ |
observed coverages when compared to dosage amounts. This further |
| 539 |
+ |
limits the effect the CO can have on surface diffusion. The correlation |
| 540 |
+ |
between coverage and Pt diffusion rates shows a near linear relationship |
| 541 |
+ |
at the earliest times in the simulations. Following double layer formation, |
| 542 |
+ |
however, there is a precipitous drop in adatom diffusion. As the double |
| 543 |
+ |
layer forms, many atoms that had been tracked for mobility data have |
| 544 |
+ |
now been buried resulting in a smaller reported diffusion constant. A |
| 545 |
+ |
secondary effect of higher coverages is CO-CO cross interactions that |
| 546 |
+ |
lower the effective mobility of the Pt adatoms that are bound to each CO. |
| 547 |
+ |
This effect would become evident only at higher coverages. A detailed |
| 548 |
+ |
account of Pt adatom energetics follows in the Discussion. |
| 549 |
+ |
|
| 550 |
|
|
| 551 |
+ |
\subsubsection{Dynamics of double layer formation} |
| 552 |
+ |
The increased diffusion on Pt at the higher CO coverages is the primary |
| 553 |
+ |
contributor to double layer formation. However, this is not a complete |
| 554 |
+ |
explanation -- the 33\%~Pt system has higher diffusion constants, but |
| 555 |
+ |
did not show any signs of edge doubling in 40~ns. On the 50\%~Pt |
| 556 |
+ |
system, one double layer formed within the first 40~ns of simulation time, |
| 557 |
+ |
while two more were formed as the system was allowed to run for an |
| 558 |
+ |
additional 110~ns (150~ns total). This suggests that this reconstruction |
| 559 |
+ |
is a rapid process and that the previously mentioned upper bound is a |
| 560 |
+ |
very large overestimate.\cite{Williams:1991,Pearl} In this system the first |
| 561 |
+ |
appearance of a double layer appears at 19~ns into the simulation. |
| 562 |
+ |
Within 12~ns of this nucleation event, nearly half of the step has formed |
| 563 |
+ |
the double layer and by 86~ns the complete layer has flattened out. |
| 564 |
+ |
From the appearance of the first nucleation event to the first observed |
| 565 |
+ |
double layer, the process took $\sim$20~ns. Another $\sim$40~ns was |
| 566 |
+ |
necessary for the layer to completely straighten. The other two layers in |
| 567 |
+ |
this simulation formed over periods of 22~ns and 42~ns respectively. |
| 568 |
+ |
A possible explanation for this rapid reconstruction is the elevated |
| 569 |
+ |
temperatures under which our systems were simulated. The process |
| 570 |
+ |
would almost certainly take longer at lower temperatures. Additionally, |
| 571 |
+ |
our measured times for completion of the doubling after the appearance |
| 572 |
+ |
of a nucleation site are likely affected by our periodic boxes. A longer |
| 573 |
+ |
step-edge will likely take longer to ``zipper''. |
| 574 |
|
|
| 575 |
|
|
| 576 |
|
%Discussion |
| 577 |
|
\section{Discussion} |
| 578 |
< |
We have shown that the classical potential models are able to model the initial reconstruction of the |
| 579 |
< |
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 580 |
< |
were able to observe features of the dynamic processes necessary for this reconstruction. |
| 578 |
> |
We have shown that a classical potential model is able to model the |
| 579 |
> |
initial reconstruction of the Pt(557) surface upon CO adsorption as |
| 580 |
> |
shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were |
| 581 |
> |
able to observe features of the dynamic processes necessary for |
| 582 |
> |
this reconstruction. Here we discuss the features of the model that |
| 583 |
> |
give rise to the observed dynamical properties of the (557) reconstruction. |
| 584 |
|
|
| 585 |
+ |
\subsection{Diffusion} |
| 586 |
+ |
The perpendicular diffusion constant |
| 587 |
+ |
appears to be the most important indicator of double layer |
| 588 |
+ |
formation. As highlighted in Figure \ref{fig:reconstruct}, the |
| 589 |
+ |
formation of the double layer did not begin until a nucleation |
| 590 |
+ |
site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994}, |
| 591 |
+ |
the inability for edges to cross leads to an effective edge-edge repulsion that |
| 592 |
+ |
must be overcome to allow step coalescence. |
| 593 |
+ |
A greater $\textbf{D}_\perp$ implies more step-wandering |
| 594 |
+ |
and a larger chance for the stochastic meeting of two edges |
| 595 |
+ |
to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double |
| 596 |
+ |
layer. This helps explain why the time scale for formation after |
| 597 |
+ |
the appearance of a nucleation site was rapid, while the initial |
| 598 |
+ |
appearance of the nucleation site was unpredictable. |
| 599 |
+ |
|
| 600 |
|
\subsection{Mechanism for restructuring} |
| 601 |
< |
Since the Au surface showed no large scale restructuring throughout |
| 602 |
< |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 603 |
< |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 604 |
< |
Similarities of our results to those reported previously by |
| 605 |
< |
Tao et al.\cite{Tao:2010} are quite |
| 606 |
< |
strong. The simulated Pt |
| 607 |
< |
system exposed to a large dosage of CO readily restructures by doubling the terrace |
| 608 |
< |
widths and step heights. The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a time, but is rapid on experimental timescales. |
| 609 |
< |
The adatoms either |
| 610 |
< |
break away from the step-edge and stay on the lower terrace or they lift |
| 611 |
< |
up onto a higher terrace. Once ``free'', they diffuse on the terrace |
| 612 |
< |
until reaching another step-edge or rejoining their original edge. |
| 613 |
< |
This combination of growth and decay of the step-edges is in a state of |
| 614 |
< |
dynamic equilibrium. However, once two previously separated edges |
| 615 |
< |
meet as shown in Figure 1.B, this nucleates the rest of the edge to meet up, forming a double layer. |
| 616 |
< |
From simulations which exhibit a double layer, the time delay from the initial appearance of a nucleation point to a fully formed double layer is $\sim$35~ns. |
| 601 |
> |
Since the Au surface showed no large scale restructuring in any of |
| 602 |
> |
our simulations, our discussion will focus on the 50\% Pt-CO system |
| 603 |
> |
which did exhibit doubling featured in Figure \ref{fig:reconstruct}. A |
| 604 |
> |
number of possible mechanisms exist to explain the role of adsorbed |
| 605 |
> |
CO in restructuring the Pt surface. Quadrupolar repulsion between |
| 606 |
> |
adjacent CO molecules adsorbed on the surface is one possibility. |
| 607 |
> |
However, the quadrupole-quadrupole interaction is short-ranged and |
| 608 |
> |
is attractive for some orientations. If the CO molecules are ``locked'' in |
| 609 |
> |
a specific orientation relative to each other, through atop adsorption for |
| 610 |
> |
example, this explanation would gain credence. The energetic repulsion |
| 611 |
> |
between two CO molecules located a distance of 2.77~\AA~apart |
| 612 |
> |
(nearest-neighbor distance of Pt) and both in a vertical orientation, |
| 613 |
> |
is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance |
| 614 |
> |
of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away |
| 615 |
> |
from a purely vertical orientation also lowers the repulsion. When the |
| 616 |
> |
carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is |
| 617 |
> |
reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}. |
| 618 |
> |
The barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
| 619 |
> |
repulsion between adjacent CO molecules could increase the surface |
| 620 |
> |
diffusion. However, the residence time of CO on Pt suggests that these |
| 621 |
> |
molecules are extremely mobile, with diffusion constants 40 to 2500 times |
| 622 |
> |
larger than surface Pt atoms. This mobility suggests that the CO are more |
| 623 |
> |
likely to shift their positions without dragging the Pt along with them. |
| 624 |
|
|
| 625 |
< |
A number of possible mechanisms exist to explain the role of adsorbed |
| 617 |
< |
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 618 |
< |
CO molecules adsorbed on the surface is one possibility. However, |
| 619 |
< |
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 620 |
< |
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 621 |
< |
relative to each other, through atop adsorption for example, this explanation |
| 622 |
< |
gains some credence. The energetic repulsion between two CO located a |
| 623 |
< |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in |
| 624 |
< |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 625 |
< |
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 626 |
< |
nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation |
| 627 |
< |
also quickly drops the repulsion, a minimum of 6.2 kcal/mol is reached at $\sim$24 degrees between the 2 CO when the carbons are locked at a distance of 2.77 \AA apart. |
| 628 |
< |
As mentioned above, the energy barrier for surface diffusion |
| 629 |
< |
of a Pt adatom is only 4 kcal/mol. So this repulsion between neighboring CO molecules can |
| 630 |
< |
increase the surface diffusion. However, the residence time of CO on Pt was |
| 631 |
< |
examined and while the majority of the CO is on or near the surface throughout |
| 632 |
< |
the run, most molecules are mobile. This mobility suggests that the CO are more |
| 633 |
< |
likely to shift their positions without necessarily the Pt along with them. |
| 625 |
> |
Another possible mechanism for the restructuring is in the destabilization of strong Pt-Pt interactions by CO adsorbed on surface Pt atoms. To test this hypothesis, a number of configurations of CO in varying quantities were arranged on the upper plateaus around a step on an otherwise clean Pt(557) surface. A few sample configurations are displayed in Figure \ref{fig:SketchGraphic}, with energy curves corresponding to each configuration in Figure \ref{fig:SketchEnergies}. Certain configurations of CO, cases (e), (g) and (h) for example, can provide significant energetic pushes for Pt atoms to break away from the step-edge. |
| 626 |
|
|
| 635 |
– |
Another possible and more likely mechanism for the restructuring is in the |
| 636 |
– |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 637 |
– |
Pt atoms. This would then have the effect of increasing surface mobility |
| 638 |
– |
of these atoms. To test this hypothesis, numerous configurations of |
| 639 |
– |
CO in varying quantities were arranged on the higher and lower plateaus |
| 640 |
– |
around a step on a otherwise clean Pt(557) surface. One representative |
| 641 |
– |
configuration is displayed in Figure \ref{fig:lambda}. Single or concerted movement |
| 642 |
– |
of Pt atoms was then examined to determine possible barriers. Because |
| 643 |
– |
the movement was forced along a pre-defined reaction coordinate that may differ |
| 644 |
– |
from the true minimum of this path, only the beginning and ending energies |
| 645 |
– |
are displayed in Table \ref{tab:energies} with the corresponding beginning and ending reaction coordinates in Figure \ref{fig:lambdaTable}. These values suggest that the presence of CO at suitable |
| 646 |
– |
locations can lead to lowered barriers for Pt breaking apart from the step-edge. |
| 647 |
– |
Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the |
| 648 |
– |
burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral |
| 649 |
– |
in terms of energetics. |
| 627 |
|
|
| 628 |
+ |
%Sketch graphic of different configurations |
| 629 |
+ |
\begin{figure}[H] |
| 630 |
+ |
\includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf} |
| 631 |
+ |
\caption{The dark grey atoms refer to the upper ledge, while the white atoms are |
| 632 |
+ |
the lower terrace. The blue highlighted atoms had a CO in a vertical atop position |
| 633 |
+ |
upon them. These are a sampling of the configurations examined to gain a more |
| 634 |
+ |
complete understanding of the effects CO has on surface diffusion and edge breakup. |
| 635 |
+ |
Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.} |
| 636 |
+ |
\label{fig:SketchGraphic} |
| 637 |
+ |
\end{figure} |
| 638 |
+ |
|
| 639 |
+ |
%energy graph corresponding to sketch graphic |
| 640 |
+ |
\begin{figure}[H] |
| 641 |
+ |
\includegraphics[width=\linewidth]{stepSeparationComparison.pdf} |
| 642 |
+ |
\caption{The energy curves directly correspond to the labeled model |
| 643 |
+ |
surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative |
| 644 |
+ |
to their initial configuration so the energy of a and h do not have the |
| 645 |
+ |
same zero value. As is seen, certain arrangements of CO can lower |
| 646 |
+ |
the energetic barrier that must be overcome to create an adatom. |
| 647 |
+ |
However, it is the highest coverages where these higher-energy |
| 648 |
+ |
configurations of CO will be more likely. } |
| 649 |
+ |
\label{fig:SketchEnergies} |
| 650 |
+ |
\end{figure} |
| 651 |
+ |
|
| 652 |
+ |
|
| 653 |
+ |
|
| 654 |
|
%lambda progression of Pt -> shoving its way into the step |
| 655 |
|
\begin{figure}[H] |
| 656 |
|
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
| 657 |
|
\caption{A model system of the Pt(557) surface was used as the framework |
| 658 |
|
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 659 |
|
placements, and rotations of CO were examined as they affect Pt movement. |
| 660 |
< |
The coordinate displayed in this Figure was a representative run. As shown |
| 658 |
< |
in Table \ref{tab:rxcoord}, relative to the energy of the system at 0\%, there |
| 660 |
> |
The coordinate displayed in this Figure was a representative run. relative to the energy of the system at 0\%, there |
| 661 |
|
is a slight decrease upon insertion of the Pt atom into the step-edge along |
| 662 |
|
with the resultant lifting of the other Pt atom when CO is present at certain positions.} |
| 663 |
|
\label{fig:lambda} |
| 664 |
|
\end{figure} |
| 665 |
|
|
| 666 |
< |
\begin{figure}[H] |
| 667 |
< |
\includegraphics[totalheight=0.9\textheight]{lambdaTable.png} |
| 668 |
< |
\caption{} |
| 669 |
< |
\label{fig:lambdaTable} |
| 670 |
< |
\end{figure} |
| 666 |
> |
\subsection{CO Removal and double layer stability} |
| 667 |
> |
Once a double layer had formed on the 50\%~Pt system it |
| 668 |
> |
remained for the rest of the simulation time with minimal |
| 669 |
> |
movement. There were configurations that showed small |
| 670 |
> |
wells or peaks forming, but typically within a few nanoseconds |
| 671 |
> |
the feature would smooth away. Within our simulation time, |
| 672 |
> |
the formation of the double layer was irreversible and a double |
| 673 |
> |
layer was never observed to split back into two single layer |
| 674 |
> |
step-edges while CO was present. To further gauge the effect |
| 675 |
> |
CO had on this system, additional simulations were run starting |
| 676 |
> |
from a late configuration of the 50\%~Pt system that had formed |
| 677 |
> |
double layers. These simulations then had their CO removed. |
| 678 |
> |
The double layer breaks rapidly in these simulations, already |
| 679 |
> |
showing a well-defined splitting after 100~ps. Configurations of |
| 680 |
> |
this system are shown in Figure \ref{fig:breaking}. The coloring |
| 681 |
> |
of the top and bottom layers helps to exhibit how much mixing |
| 682 |
> |
the edges experience as they split. These systems were only |
| 683 |
> |
examined briefly, 10~ns, and within that time despite the initial |
| 684 |
> |
rapid splitting, the edges only moved another few \AA~apart. |
| 685 |
> |
It is possible with longer simulation times that the |
| 686 |
> |
(557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010} |
| 687 |
|
|
| 688 |
|
|
| 671 |
– |
\subsection{Diffusion} |
| 672 |
– |
The diffusion parallel to the step-edge tends to be |
| 673 |
– |
much larger than that perpendicular to the step-edge. The dynamic |
| 674 |
– |
equilibrium that is established between the step-edge and adatom interface. The coverage |
| 675 |
– |
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}. |
| 676 |
– |
The |
| 677 |
– |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
| 678 |
– |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
| 679 |
– |
appears, parallel diffusion, along the now slightly angled step-edge, will allow for |
| 680 |
– |
a faster formation of the double layer than if the entire process were dependent on |
| 681 |
– |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
| 682 |
– |
more likely a growth point is to be formed. |
| 683 |
– |
\\ |
| 689 |
|
|
| 690 |
|
|
| 691 |
+ |
|
| 692 |
+ |
|
| 693 |
|
%breaking of the double layer upon removal of CO |
| 694 |
|
\begin{figure}[H] |
| 695 |
|
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 748 |
|
% \end{tabular} |
| 749 |
|
% \end{table} |
| 750 |
|
|
| 751 |
< |
\section{Acknowledgments} |
| 751 |
> |
\begin{acknowledgement} |
| 752 |
|
Support for this project was provided by the National Science |
| 753 |
|
Foundation under grant CHE-0848243 and by the Center for Sustainable |
| 754 |
|
Energy at Notre Dame (cSEND). Computational time was provided by the |
| 755 |
|
Center for Research Computing (CRC) at the University of Notre Dame. |
| 756 |
< |
|
| 756 |
> |
\end{acknowledgement} |
| 757 |
|
\newpage |
| 758 |
|
\bibliography{firstTryBibliography} |
| 759 |
< |
\end{doublespace} |
| 759 |
> |
%\end{doublespace} |
| 760 |
> |
|
| 761 |
> |
\begin{tocentry} |
| 762 |
> |
%\includegraphics[height=3.5cm]{timelapse} |
| 763 |
> |
\end{tocentry} |
| 764 |
> |
|
| 765 |
|
\end{document} |
