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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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%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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%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 attempt to understand the mechanism and timescale for |
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surface restructuring by using molecular simulations. Since the dynamics |
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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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computational efficiency necessary to simulate the process of interest. |
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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 relaxing of the |
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22 x $\sqrt{3}$ cell. They argued that a very small number of Au atoms |
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would become adatoms, limiting the stress of this reconstruction while |
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allowing the rest of the row to relax and approach the ideal (111) |
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configuration. They did not see the ``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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disruption of the ``herringbone'' pattern as CO was adsorbed 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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allowing the rest to relax and approach the ideal (111) |
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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 particles was the primary driving force for these reconstructions. |
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low-coordinated Au atoms was the primary driving force for the reconstruction. |
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|
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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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which only parameterized up to the nearest-neighbor |
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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) approaches gives EAM, and conclusions derived, a firm theoretical footing. |
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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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|
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|
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We used a model first proposed by Karplus and Straub to study |
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the photodissociation of CO from myoglobin because it reproduces |
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the quadrupole moment well.\cite{Straub} The Straub and |
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Karplus model, treats CO as a rigid three site molecule with a massless M |
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Karplus model treats CO as a rigid three site molecule with a massless M |
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site at the molecular center of mass. The geometry and interaction |
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parameters are reproduced in Table~\ref{tab:CO}. The effective |
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dipole moment, calculated from the assigned charges, is still |
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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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a future work.\cite{Deshlahra:2012,StreitzMintmire:1994} |
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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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\end{table} |
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|
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\subsection{Pt(557) and Au(557) metal interfaces} |
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Our Pt system has dimensions of 18~x~24~x~9 in a box of size |
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54.482~x~50.046~x~120.88~\AA while our Au system has |
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dimensions of 18~x~24~x~8 in a box of size 57.4~x~51.9285~x~100~\AA. |
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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. 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$19~\AA~for Au. |
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The systems are arranged in a FCC crystal that have been cut |
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along the (557) plane so that they are periodic in the {\it x} and |
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{\it y} directions, and have been oriented to expose two aligned |
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(557) cuts along the extended {\it z}-axis. Simulations of the |
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bare metal interfaces at temperatures ranging from 300~K to |
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1200~K were performed to observe the relative |
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1200~K were performed to confirm the relative |
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stability of the surfaces without a CO overlayer. |
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|
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The different bulk melting temperatures (1337~K for Au |
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and 2045~K for Pt) suggest that any possible reconstruction should happen at |
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The different bulk melting temperatures predicted by EAM (1345~$\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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mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
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that was initially placed in the vacuum region. Upon full adsorption, |
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these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
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coverage. Higher coverages resulted in CO double layer formation, which introduces artifacts that are not relevant to (557) reconstruction. |
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coverage. Higher coverages resulted in the formation of a double layer of CO, |
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which introduces artifacts that are not relevant to (557) reconstruction. |
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Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
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the Au surfaces often had a significant CO population in the gas |
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phase. These systems were allowed to reach thermal equilibrium (over |
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5 ns) before being run in the microcanonical (NVE) ensemble for |
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data collection. All of the systems examined had at least 40 ns in the |
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data collection stage, although simulation times for some of the |
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systems exceeded 200~ns. Simulations were run using the open |
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5~ns) before being run in the microcanonical (NVE) ensemble for |
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data collection. All of the systems examined had at least 40~ns in the |
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data collection stage, although simulation times for some Pt of the |
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systems exceeded 200~ns. Simulations were carried out using the open |
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source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} |
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|
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% Just results, leave discussion for discussion section |
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% structure |
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% Pt: step wandering, double layers, no triangular motifs |
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% Au: step wandering, no double layers |
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% dynamics |
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% diffusion |
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% time scale, formation, breakage |
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|
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|
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|
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% RESULTS |
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% |
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\section{Results} |
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\subsection{Structural remodeling} |
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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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|
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|
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\subsubsection{Step wandering} |
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The 0\% coverage surfaces for both metals showed minimal |
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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 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 |
| 432 |
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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 |
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adsorption.\cite{Tao:2010} The first involves a doubling of |
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the step height and plateau length. Similar behavior has been |
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seen to occur on numerous surfaces at varying conditions: Ni(977), Si(111). |
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\cite{Williams:1994,Williams:1991,Pearl} Of the two systems |
| 441 |
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we examined, the Pt system showed a larger amount of |
| 442 |
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reconstruction when compared to the Au system. The amount |
| 443 |
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of reconstruction is correlated to the amount of CO |
| 435 |
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Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
| 436 |
> |
undergoes two separate reconstructions upon CO adsorption. |
| 437 |
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The first involves a doubling of the step height and plateau length. |
| 438 |
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Similar behavior has been seen on a number of surfaces |
| 439 |
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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 |
| 441 |
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propensity for reconstruction |
| 442 |
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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 |
| 444 |
|
adsorbed upon the surface. This appears to be related to the |
| 445 |
< |
effect that adsorbate coverage has on edge breakup and on the surface |
| 446 |
< |
diffusion of metal adatoms. While both systems displayed step-edge |
| 447 |
< |
wandering, only the Pt surface underwent the doubling seen by |
| 448 |
< |
Tao et al. within the time scales studied here. |
| 449 |
< |
Only the 50\% coverage Pt system exhibited |
| 450 |
< |
a complete doubling in the time scales we |
| 451 |
< |
were able to monitor. Over longer periods (150~ns) two more double layers formed on this interface. |
| 452 |
< |
Although double layer formation did not occur in the other Pt systems, they show |
| 453 |
< |
more lateral movement of the step-edges |
| 416 |
< |
compared to their Au counterparts. The 50\% Pt system is highlighted |
| 417 |
< |
in Figure \ref{fig:reconstruct} at various times along the simulation |
| 418 |
< |
showing the evolution of a step-edge. |
| 445 |
> |
effect that adsorbate coverage has on edge breakup and on the |
| 446 |
> |
surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
| 447 |
> |
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
| 448 |
> |
Over a longer time scale (150~ns) two more double layers formed |
| 449 |
> |
on this surface. Although double layer formation did not occur |
| 450 |
> |
in the other Pt systems, they exhibited more step-wandering and |
| 451 |
> |
roughening compared to their Au counterparts. The |
| 452 |
> |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
| 453 |
> |
various times along the simulation showing the evolution of a double layer step-edge. |
| 454 |
|
|
| 455 |
< |
The second reconstruction on the Pt(557) surface observed by |
| 456 |
< |
Tao involved the formation of triangular clusters that stretched |
| 457 |
< |
across the plateau between two step-edges. Neither system, within |
| 458 |
< |
the 40~ns time scale, experienced this reconstruction. |
| 455 |
> |
The second reconstruction observed by |
| 456 |
> |
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
| 457 |
> |
across the plateau between two step-edges. Neither metal, within |
| 458 |
> |
the 40~ns time scale or the extended simulation time of 150~ns for |
| 459 |
> |
the 50\% Pt system, experienced this reconstruction. |
| 460 |
|
|
| 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 were largely |
| 475 |
< |
concerned with the energetics and structures at different conditions |
| 476 |
< |
\cite{Williams:1991,Williams:1994}. Consequently, the most common |
| 477 |
< |
technique has been Monte Carlo. Monte Carlo gives an efficient |
| 478 |
< |
sampling of the equilibrium thermodynamic landscape at the expense |
| 479 |
< |
of ignoring the dynamics of the system. Previous work by Pearl and |
| 480 |
< |
Sibener\cite{Pearl}, using STM, has been able to show the coalescing |
| 481 |
< |
of steps on Ni(977). The time scale of the image acquisition, |
| 434 |
< |
$\sim$70 s/image provides an upper bound for the time required for |
| 435 |
< |
the doubling to occur. In this section we give data on dynamic and |
| 436 |
< |
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 |
| 487 |
< |
arising from the individual movements, primarily through surface |
| 488 |
< |
diffusion, of the atoms making up the steps An ideal metal surface |
| 444 |
< |
displaying a low index facet, (111) or (100) is unlikely to experience |
| 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 |
| 491 |
< |
on higher-index surfaces provide a 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 is much less than lifting |
| 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 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 be 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) and these adatoms are well |
| 499 |
< |
able to explore the terrace before rejoining either the original step-edge or becoming a part |
| 500 |
< |
of a different edge. Atoms traversing separate terraces is a more difficult |
| 501 |
< |
process, but can be overcome through a joining and lifting stage which is |
| 502 |
< |
examined in the discussion section. By tracking the mobility of individual |
| 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 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. The primary challenge in |
| 465 |
< |
quantifying the overall surface mobility was in defining ``mobile" vs. ``static" atoms. |
| 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 |
| 513 |
< |
was to prevent swamping the diffusion data with the in-place vibrational |
| 514 |
< |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 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). 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 |
< |
\subsubsection{Dynamics of double layer formation} |
| 478 |
< |
The increased amounts of diffusion on Pt at the higher CO coverages plays a primary role in the formation of the double layers observed on Pt. However, this is not a complete explanation as seen by the 33\% Pt system which has higher diffusion constants but did not show any signs of undergoing the doubling. This difference will be explored more fully in the discussion. On the 50\% Pt system, three separate layers were formed over the extended run time of this system. Previous experimental work has given some insight into the upper bounds of the time required for step coalescing.\cite{Williams:1991,Pearl} In this system, as seen in Figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into the simulation. Within 12 ns, nearly half of the step has formed the double layer and by 86 ns, the complete layer has been smoothed. The double layer could be considered ``complete" by 37 ns but is a bit rough or wavy. From the appearance of the first node to the first observed double layer, ignoring roughening, the process took $\sim$20 ns. Another $\sim$40 ns was necessary for the layer to completely straighten. The other two layers in this simulation form over a period of 22 ns and 42 ns respectively. Comparing this to the upper bounds of the image scan, it is likely that aspects of this reconstruction occur very quickly. A possible explanation for this rapid reconstruction is the elevated temperatures our systems were run at. It is likely that the process would take longer at lower temperatures and is an area of exploration for future work. |
| 479 |
< |
|
| 480 |
< |
%Evolution of surface |
| 520 |
> |
%Diffusion graph |
| 521 |
|
\begin{figure}[H] |
| 522 |
< |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 483 |
< |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 484 |
< |
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
| 485 |
< |
(d) 86.1 ns. Disruption of the (557) step-edges occurs quickly. The |
| 486 |
< |
doubling of the layers appears only after two adjacent step-edges |
| 487 |
< |
touch. The circled spot in (b) nucleated the growth of the double |
| 488 |
< |
step observed in the later configurations.} |
| 489 |
< |
\label{fig:reconstruct} |
| 490 |
< |
\end{figure} |
| 491 |
< |
|
| 492 |
< |
\begin{figure}[H] |
| 493 |
< |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
| 522 |
> |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf} |
| 523 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
| 524 |
|
parallel ($\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 |
< |
In this paper we have shown that we were able to accurately 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 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 |
< |
Comparing the results from this simulation to those reported previously by |
| 605 |
< |
Tao et al.\cite{Tao:2010} the similarities in the Pt-CO system are quite |
| 606 |
< |
strong. As shown in Figure \ref{fig:reconstruct}, the simulated Pt |
| 607 |
< |
system exposed to a large dosage of CO will restructure by doubling the terrace |
| 608 |
< |
widths and step heights. The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a time and as such is a fairly stochastic event. |
| 609 |
< |
Looking at individual configurations of the system, the adatoms either |
| 610 |
< |
break away from the step-edge and stay on the lower terrace or they lift |
| 611 |
< |
up onto the higher terrace. Once ``free'', they will 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 meeting point tends to act as a focus |
| 616 |
< |
or growth point for the rest of the edge to meet up, akin to that of a zipper. |
| 617 |
< |
From the handful of cases where a double layer was formed during the |
| 618 |
< |
simulation, measuring from the initial appearance of a growth point, the |
| 619 |
< |
double layer tends to be fully formed within $\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 |
| 538 |
< |
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 539 |
< |
CO molecules adsorbed on the surface is one likely possibility. However, |
| 540 |
< |
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 541 |
< |
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 542 |
< |
relative to each other, through atop adsorption for example, this explanation |
| 543 |
< |
gains some weight. The energetic repulsion between two CO located a |
| 544 |
< |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in |
| 545 |
< |
a vertical orientation is 8.62 kcal/mol. Moving the CO apart to the second |
| 546 |
< |
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 547 |
< |
nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation |
| 548 |
< |
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. |
| 549 |
< |
As mentioned above, the energy barrier for surface diffusion |
| 550 |
< |
of a Pt adatom is only 4 kcal/mol. So this repulsion between CO can help |
| 551 |
< |
increase the surface diffusion. However, the residence time of CO on Pt was |
| 552 |
< |
examined and while the majority of the CO is on or near the surface throughout |
| 553 |
< |
the run, it is extremely mobile. This mobility suggests that the CO are more |
| 554 |
< |
likely to shift their positions without necessarily dragging 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 |
|
|
| 556 |
– |
Another possible and more likely mechanism for the restructuring is in the |
| 557 |
– |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 558 |
– |
Pt atoms. This would then have the effect of increasing surface mobility |
| 559 |
– |
of these atoms. To test this hypothesis, numerous configurations of |
| 560 |
– |
CO in varying quantities were arranged on the higher and lower plateaus |
| 561 |
– |
around a step on a otherwise clean Pt(557) surface. One representative |
| 562 |
– |
configuration is displayed in Figure \ref{fig:lambda}. Single or concerted movement |
| 563 |
– |
of Pt atoms was then examined to determine possible barriers. Because |
| 564 |
– |
the movement was forced along a pre-defined reaction coordinate that may differ |
| 565 |
– |
from the true minimum of this path, only the beginning and ending energies |
| 566 |
– |
are displayed in Table \ref{tab:energies}. These values suggest that the presence of CO at suitable |
| 567 |
– |
locations can lead to lowered barriers for Pt breaking apart from the step-edge. |
| 568 |
– |
Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the |
| 569 |
– |
burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral |
| 570 |
– |
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.png} |
| 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 |
| 579 |
< |
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 |
+ |
\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 |
|
|
| 587 |
– |
\subsection{Diffusion} |
| 588 |
– |
As shown in the results section, the diffusion parallel to the step-edge tends to be |
| 589 |
– |
much larger than that perpendicular to the step-edge, likely because of the dynamic |
| 590 |
– |
equilibrium that is established between the step-edge and adatom interface. The coverage |
| 591 |
– |
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}. |
| 592 |
– |
The |
| 593 |
– |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
| 594 |
– |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
| 595 |
– |
appears, parallel diffusion, along the now slightly angled step-edge, will allow for |
| 596 |
– |
a faster formation of the double layer than if the entire process were dependent on |
| 597 |
– |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
| 598 |
– |
more likely a growth point is to be formed. |
| 599 |
– |
\\ |
| 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} |
| 696 |
< |
%: |
| 606 |
< |
\caption{(A) 0 ps, (B) 100 ps, (C) 1 ns, after the removal of CO. The presence of the CO |
| 696 |
> |
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
| 697 |
|
helped maintain the stability of the double layer and upon removal the two layers break |
| 698 |
|
and begin separating. The separation is not a simple pulling apart however, rather |
| 699 |
|
there is a mixing of the lower and upper atoms at the edge.} |
| 704 |
|
|
| 705 |
|
|
| 706 |
|
%Peaks! |
| 707 |
< |
\begin{figure}[H] |
| 708 |
< |
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 709 |
< |
\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 710 |
< |
of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 711 |
< |
aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 712 |
< |
\label{fig:peaks} |
| 713 |
< |
\end{figure} |
| 707 |
> |
%\begin{figure}[H] |
| 708 |
> |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 709 |
> |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 710 |
> |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 711 |
> |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 712 |
> |
%\label{fig:peaks} |
| 713 |
> |
%\end{figure} |
| 714 |
|
|
| 715 |
|
|
| 716 |
|
%Don't think I need this |
| 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} |
