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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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%% |
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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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is sufficient to explain the reconstructions observed on the Pt |
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systems and the lack of reconstruction of the Au systems. |
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|
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|
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The mechanism and dynamics of surface reconstructions of Pt(557) |
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and Au(557) exposed to various coverages of carbon monoxide (CO) |
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were investigated using molecular dynamics simulations. Metal-CO |
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interactions were parameterized from experimental data and plane-wave |
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Density Functional Theory (DFT) calculations. The large difference in |
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binding strengths of the Pt-CO and Au-CO interactions was found to play |
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a significant role in step-edge stability and adatom diffusion constants. |
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The energetics of CO adsorbed to the surface is sufficient to explain the |
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step-doubling reconstruction observed on Pt(557) and the lack of such |
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a reconstruction on the Au(557) surface. |
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\end{abstract} |
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|
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\newpage |
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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{Foiles86} 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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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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parameter sets. The glue model of Ercolessi {\it et al}.\cite{Ercolessi88} is among the |
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fastest of these density functional approaches. In |
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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$19~\AA~for Au. |
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The systems are arranged in a FCC crystal that have been cut |
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along the (557) plane so that they are periodic in the {\it x} and |
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{\it y} directions, and have been oriented to expose two aligned |
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1200~K were performed to confirm the relative |
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stability of the surfaces without a CO overlayer. |
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|
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The different bulk melting temperatures (1337~K for Au\cite{Au:melting} |
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and 2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
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The different bulk melting temperatures predicted by EAM (1345~$\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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|
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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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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 arises 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 and concentration |
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of adsorbates, as shown in this work, 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. |
| 455 |
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The amount of reconstruction is correlated to the amount of CO |
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propensity for reconstruction |
| 454 |
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because of the larger surface mobility and the greater extent of step wandering. |
| 455 |
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The amount of reconstruction was strongly correlated to the amount of CO |
| 456 |
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adsorbed upon the surface. This appears to be related to the |
| 457 |
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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 |
| 459 |
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step-edge wandering, only the 50\% Pt surface underwent the |
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doubling seen by Tao et al.\cite{Tao:2010} within the time scales studied here. |
| 461 |
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Over longer periods, (150~ns) two more double layers formed |
| 462 |
< |
on this interface. Although double layer formation did not occur |
| 463 |
< |
in the other Pt systems, they show more step-wandering and |
| 449 |
< |
general roughening compared to their Au counterparts. The |
| 458 |
> |
surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
| 459 |
> |
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
| 460 |
> |
Over a longer time scale (150~ns) two more double layers formed |
| 461 |
> |
on this surface. Although double layer formation did not occur |
| 462 |
> |
in the other Pt systems, they exhibited more step-wandering and |
| 463 |
> |
roughening compared to their Au counterparts. The |
| 464 |
|
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
| 465 |
< |
various times along the simulation showing the evolution of a step-edge. |
| 465 |
> |
various times along the simulation showing the evolution of a double layer step-edge. |
| 466 |
|
|
| 467 |
< |
The second reconstruction on the Pt(557) surface observed by |
| 468 |
< |
Tao involved the formation of triangular clusters that stretched |
| 469 |
< |
across the plateau between two step-edges. Neither system, within |
| 467 |
> |
The second reconstruction observed by |
| 468 |
> |
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
| 469 |
> |
across the plateau between two step-edges. Neither metal, within |
| 470 |
|
the 40~ns time scale or the extended simulation time of 150~ns for |
| 471 |
|
the 50\% Pt system, experienced this reconstruction. |
| 472 |
|
|
| 473 |
+ |
%Evolution of surface |
| 474 |
+ |
\begin{figure}[H] |
| 475 |
+ |
\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation.pdf} |
| 476 |
+ |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 477 |
+ |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 478 |
+ |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 479 |
+ |
doubling of the layers appears only after two adjacent step-edges |
| 480 |
+ |
touch. The circled spot in (b) nucleated the growth of the double |
| 481 |
+ |
step observed in the later configurations.} |
| 482 |
+ |
\label{fig:reconstruct} |
| 483 |
+ |
\end{figure} |
| 484 |
+ |
|
| 485 |
|
\subsection{Dynamics} |
| 486 |
< |
Previous atomistic simulations of stepped surfaces dealt largely |
| 487 |
< |
with the energetics and structures at different conditions |
| 488 |
< |
\cite{Williams:1991,Williams:1994}. Consequently, the most common |
| 489 |
< |
technique utilized to date has been Monte Carlo sampling. Monte Carlo gives an efficient |
| 490 |
< |
sampling of the equilibrium thermodynamic landscape at the expense |
| 491 |
< |
of ignoring the dynamics of the system. Previous experimental work by Pearl and |
| 492 |
< |
Sibener\cite{Pearl}, using STM, has been able to capture the coalescing |
| 493 |
< |
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. |
| 486 |
> |
Previous experimental work by Pearl and Sibener\cite{Pearl}, |
| 487 |
> |
using STM, has been able to capture the coalescence of steps |
| 488 |
> |
on Ni(977). The time scale of the image acquisition, $\sim$70~s/image, |
| 489 |
> |
provides an upper bound for the time required for the doubling |
| 490 |
> |
to occur. By utilizing Molecular Dynamics we are able to probe |
| 491 |
> |
the dynamics of these reconstructions at elevated temperatures |
| 492 |
> |
and in this section we provide data on the timescales for transport |
| 493 |
> |
properties, e.g. diffusion and layer formation time. |
| 494 |
|
|
| 495 |
|
|
| 496 |
|
\subsubsection{Transport of surface metal atoms} |
| 497 |
|
%forcedSystems/stepSeparation |
| 498 |
< |
The movement or wandering of a step-edge is a cooperative effect |
| 498 |
> |
The wandering of a step-edge is a cooperative effect |
| 499 |
|
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
| 500 |
|
displaying a low index facet, (111) or (100), is unlikely to experience |
| 501 |
|
much surface diffusion because of the large energetic barrier that must |
| 502 |
|
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
| 503 |
< |
on higher-index facets provide a lower energy source for mobile metal atoms. |
| 504 |
< |
Breaking away from the step-edge on a clean surface still imposes an |
| 505 |
< |
energetic penalty around $\sim$~40 kcal/mol, but this is significantly easier than lifting |
| 503 |
> |
on higher-index facets provides a lower energy source for mobile metal atoms. |
| 504 |
> |
Single-atom break-away from a step-edge on a clean surface still imposes an |
| 505 |
> |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
| 506 |
|
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 507 |
|
The penalty lowers significantly when CO is present in sufficient quantities |
| 508 |
< |
on the surface. For certain distributions of CO, the penalty can fall as low as |
| 508 |
> |
on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as |
| 509 |
|
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 510 |
< |
diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are |
| 511 |
< |
able to explore the terrace before rejoining either the original step-edge or |
| 512 |
< |
becoming a part of a different edge. It is a more difficult process for an atom |
| 510 |
> |
diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then |
| 511 |
> |
able to explore the terrace before rejoining either their original step-edge or |
| 512 |
> |
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom |
| 513 |
|
to traverse to a separate terrace although the presence of CO can lower the |
| 514 |
< |
energy barrier required to lift or lower the adatom. By tracking the mobility of individual |
| 514 |
> |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
| 515 |
|
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 516 |
|
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 517 |
|
observation of the mobile metal atoms showed that they were typically in |
| 518 |
< |
equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. |
| 518 |
> |
equilibrium with the step-edges. |
| 519 |
|
At times, their motion was concerted and two or more adatoms would be |
| 520 |
|
observed moving together across the surfaces. |
| 521 |
|
|
| 522 |
|
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 523 |
< |
between saved configurations of the system (typically 10-100 ps). An atom that was |
| 524 |
< |
truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 523 |
> |
between saved configurations of the system (typically 10-100 ps). A mobile atom |
| 524 |
> |
would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 525 |
|
was used to prevent swamping the diffusion data with the in-place vibrational |
| 526 |
|
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 527 |
|
local structures and in this work, the presence of single and double layer |
| 528 |
< |
step-edges causes the diffusion parallel to the step-edges to be different |
| 529 |
< |
from the diffusion perpendicular to these edges. Parallel and perpendicular |
| 528 |
> |
step-edges causes the diffusion parallel to the step-edges to be larger than |
| 529 |
> |
the diffusion perpendicular to these edges. Parallel and perpendicular |
| 530 |
|
diffusion constants are shown in Figure \ref{fig:diff}. |
| 508 |
– |
|
| 509 |
– |
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$40~ns was necessary for the layer to completely straighten. |
| 554 |
– |
The other two layers in this simulation formed over periods of |
| 555 |
– |
22~ns and 42~ns respectively. Comparing this to the upper |
| 556 |
– |
bounds of the image scan, it is likely that most aspects of this |
| 557 |
– |
reconstruction occur very rapidly. A possible explanation |
| 558 |
– |
for this rapid reconstruction is the elevated temperatures |
| 559 |
– |
under which our systems were simulated. It is probable that the process would |
| 560 |
– |
take longer at lower temperatures. |
| 561 |
– |
|
| 562 |
– |
%Evolution of surface |
| 563 |
– |
\begin{figure}[H] |
| 564 |
– |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 565 |
– |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 566 |
– |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 567 |
– |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 568 |
– |
doubling of the layers appears only after two adjacent step-edges |
| 569 |
– |
touch. The circled spot in (b) nucleated the growth of the double |
| 570 |
– |
step observed in the later configurations.} |
| 571 |
– |
\label{fig:reconstruct} |
| 572 |
– |
\end{figure} |
| 531 |
|
|
| 532 |
+ |
%Diffusion graph |
| 533 |
|
\begin{figure}[H] |
| 534 |
< |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
| 534 |
> |
\includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1.pdf} |
| 535 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
| 536 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 537 |
|
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 538 |
|
surface coverage. Diffusion parallel to the step-edge is higher |
| 539 |
|
than that perpendicular to the edge because of the lower energy |
| 540 |
|
barrier associated with traversing along the edge as compared to |
| 541 |
< |
completely breaking away. Additionally, the observed |
| 542 |
< |
maximum and subsequent decrease for the Pt system suggests that the |
| 543 |
< |
CO self-interactions are playing a significant role with regards to |
| 544 |
< |
movement of the Pt atoms around and across the surface. } |
| 541 |
> |
completely breaking away. The two reported diffusion constants for |
| 542 |
> |
the 50\% Pt system arise from different sample sets. The lower values |
| 543 |
> |
correspond to the same 40~ns amount that all of the other systems were |
| 544 |
> |
examined at, while the larger values correspond to a 20~ns period } |
| 545 |
|
\label{fig:diff} |
| 546 |
|
\end{figure} |
| 547 |
|
|
| 548 |
+ |
The weaker Au-CO interaction is evident in the weak CO-coverage |
| 549 |
+ |
dependance of Au diffusion. This weak interaction leads to lower |
| 550 |
+ |
observed coverages when compared to dosage amounts. This further |
| 551 |
+ |
limits the effect the CO can have on surface diffusion. The correlation |
| 552 |
+ |
between coverage and Pt diffusion rates shows a near linear relationship |
| 553 |
+ |
at the earliest times in the simulations. Following double layer formation, |
| 554 |
+ |
however, there is a precipitous drop in adatom diffusion. As the double |
| 555 |
+ |
layer forms, many atoms that had been tracked for mobility data have |
| 556 |
+ |
now been buried resulting in a smaller reported diffusion constant. A |
| 557 |
+ |
secondary effect of higher coverages is CO-CO cross interactions that |
| 558 |
+ |
lower the effective mobility of the Pt adatoms that are bound to each CO. |
| 559 |
+ |
This effect would become evident only at higher coverages. A detailed |
| 560 |
+ |
account of Pt adatom energetics follows in the Discussion. |
| 561 |
+ |
|
| 562 |
|
|
| 563 |
+ |
\subsubsection{Dynamics of double layer formation} |
| 564 |
+ |
The increased diffusion on Pt at the higher CO coverages is the primary |
| 565 |
+ |
contributor to double layer formation. However, this is not a complete |
| 566 |
+ |
explanation -- the 33\%~Pt system has higher diffusion constants, but |
| 567 |
+ |
did not show any signs of edge doubling in 40~ns. On the 50\%~Pt |
| 568 |
+ |
system, one double layer formed within the first 40~ns of simulation time, |
| 569 |
+ |
while two more were formed as the system was allowed to run for an |
| 570 |
+ |
additional 110~ns (150~ns total). This suggests that this reconstruction |
| 571 |
+ |
is a rapid process and that the previously mentioned upper bound is a |
| 572 |
+ |
very large overestimate.\cite{Williams:1991,Pearl} In this system the first |
| 573 |
+ |
appearance of a double layer appears at 19~ns into the simulation. |
| 574 |
+ |
Within 12~ns of this nucleation event, nearly half of the step has formed |
| 575 |
+ |
the double layer and by 86~ns the complete layer has flattened out. |
| 576 |
+ |
From the appearance of the first nucleation event to the first observed |
| 577 |
+ |
double layer, the process took $\sim$20~ns. Another $\sim$40~ns was |
| 578 |
+ |
necessary for the layer to completely straighten. The other two layers in |
| 579 |
+ |
this simulation formed over periods of 22~ns and 42~ns respectively. |
| 580 |
+ |
A possible explanation for this rapid reconstruction is the elevated |
| 581 |
+ |
temperatures under which our systems were simulated. The process |
| 582 |
+ |
would almost certainly take longer at lower temperatures. Additionally, |
| 583 |
+ |
our measured times for completion of the doubling after the appearance |
| 584 |
+ |
of a nucleation site are likely affected by our periodic boxes. A longer |
| 585 |
+ |
step-edge will likely take longer to ``zipper''. |
| 586 |
|
|
| 587 |
|
|
| 588 |
|
%Discussion |
| 589 |
|
\section{Discussion} |
| 590 |
< |
We have shown that the classical potential models are able to model the initial reconstruction of the |
| 591 |
< |
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 592 |
< |
were able to observe features of the dynamic processes necessary for this reconstruction. |
| 590 |
> |
We have shown that a classical potential model is able to model the |
| 591 |
> |
initial reconstruction of the Pt(557) surface upon CO adsorption as |
| 592 |
> |
shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were |
| 593 |
> |
able to observe features of the dynamic processes necessary for |
| 594 |
> |
this reconstruction. Here we discuss the features of the model that |
| 595 |
> |
give rise to the observed dynamical properties of the (557) reconstruction. |
| 596 |
|
|
| 597 |
+ |
\subsection{Diffusion} |
| 598 |
+ |
The perpendicular diffusion constant |
| 599 |
+ |
appears to be the most important indicator of double layer |
| 600 |
+ |
formation. As highlighted in Figure \ref{fig:reconstruct}, the |
| 601 |
+ |
formation of the double layer did not begin until a nucleation |
| 602 |
+ |
site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994}, |
| 603 |
+ |
the inability for edges to cross leads to an effective edge-edge repulsion that |
| 604 |
+ |
must be overcome to allow step coalescence. |
| 605 |
+ |
A greater $\textbf{D}_\perp$ implies more step-wandering |
| 606 |
+ |
and a larger chance for the stochastic meeting of two edges |
| 607 |
+ |
to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double |
| 608 |
+ |
layer. This helps explain why the time scale for formation after |
| 609 |
+ |
the appearance of a nucleation site was rapid, while the initial |
| 610 |
+ |
appearance of the nucleation site was unpredictable. |
| 611 |
+ |
|
| 612 |
|
\subsection{Mechanism for restructuring} |
| 613 |
< |
Since the Au surface showed no large scale restructuring throughout |
| 614 |
< |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 615 |
< |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 616 |
< |
Similarities of our results to those reported previously by |
| 617 |
< |
Tao et al.\cite{Tao:2010} are quite |
| 618 |
< |
strong. The simulated Pt |
| 619 |
< |
system exposed to a large dosage of CO readily restructures by doubling the terrace |
| 620 |
< |
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. |
| 621 |
< |
The adatoms either |
| 622 |
< |
break away from the step-edge and stay on the lower terrace or they lift |
| 623 |
< |
up onto a higher terrace. Once ``free'', they diffuse on the terrace |
| 624 |
< |
until reaching another step-edge or rejoining their original edge. |
| 625 |
< |
This combination of growth and decay of the step-edges is in a state of |
| 626 |
< |
dynamic equilibrium. However, once two previously separated edges |
| 627 |
< |
meet as shown in Figure 1.B, this nucleates the rest of the edge to meet up, forming a double layer. |
| 628 |
< |
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. |
| 613 |
> |
Since the Au surface showed no large scale restructuring in any of |
| 614 |
> |
our simulations, our discussion will focus on the 50\% Pt-CO system |
| 615 |
> |
which did exhibit doubling. A |
| 616 |
> |
number of possible mechanisms exist to explain the role of adsorbed |
| 617 |
> |
CO in restructuring the Pt surface. Quadrupolar repulsion between |
| 618 |
> |
adjacent CO molecules adsorbed on the surface is one possibility. |
| 619 |
> |
However, the quadrupole-quadrupole interaction is short-ranged and |
| 620 |
> |
is attractive for some orientations. If the CO molecules are ``locked'' in |
| 621 |
> |
a specific orientation relative to each other, through atop adsorption for |
| 622 |
> |
example, this explanation would gain credence. The calculated energetic repulsion |
| 623 |
> |
between two CO molecules located a distance of 2.77~\AA~apart |
| 624 |
> |
(nearest-neighbor distance of Pt) and both in a vertical orientation, |
| 625 |
> |
is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance |
| 626 |
> |
of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away |
| 627 |
> |
from a purely vertical orientation also lowers the repulsion. When the |
| 628 |
> |
carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is |
| 629 |
> |
reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}. |
| 630 |
> |
The calculated barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
| 631 |
> |
repulsion between adjacent CO molecules bound to Pt could increase the surface |
| 632 |
> |
diffusion. However, the residence time of CO on Pt suggests that these |
| 633 |
> |
molecules are extremely mobile, with diffusion constants 40 to 2500 times |
| 634 |
> |
larger than surface Pt atoms. This mobility suggests that the CO molecules jump |
| 635 |
> |
between different Pt atoms throughout the simulation, but will stay bound for |
| 636 |
> |
significant periods of time. |
| 637 |
|
|
| 638 |
< |
A number of possible mechanisms exist to explain the role of adsorbed |
| 639 |
< |
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 640 |
< |
CO molecules adsorbed on the surface is one possibility. However, |
| 641 |
< |
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 642 |
< |
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 643 |
< |
relative to each other, through atop adsorption for example, this explanation |
| 644 |
< |
gains some credence. The energetic repulsion between two CO located a |
| 645 |
< |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in |
| 646 |
< |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 647 |
< |
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 648 |
< |
nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation |
| 649 |
< |
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. |
| 650 |
< |
As mentioned above, the energy barrier for surface diffusion |
| 651 |
< |
of a Pt adatom is only 4 kcal/mol. So this repulsion between neighboring CO molecules can |
| 652 |
< |
increase the surface diffusion. However, the residence time of CO on Pt was |
| 653 |
< |
examined and while the majority of the CO is on or near the surface throughout |
| 654 |
< |
the run, most molecules are mobile. This mobility suggests that the CO are more |
| 655 |
< |
likely to shift their positions without necessarily the Pt along with them. |
| 638 |
> |
A different interpretation of the above mechanism, taking into account the large |
| 639 |
> |
mobility of the CO, looks at how instantaneous and short-lived configurations of |
| 640 |
> |
CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge |
| 641 |
> |
breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach |
| 642 |
> |
an edge atom is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures |
| 643 |
> |
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases |
| 644 |
> |
(e), (g), and (h), the barrier can be lowered to $\sim$23~kcal/mole. In these instances, |
| 645 |
> |
it becomes quite energetically favorable to roughen the edge by introducing a small |
| 646 |
> |
separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in |
| 647 |
> |
simulations with significant CO populations. The roughening is present to a lesser extent |
| 648 |
> |
on lower coverage surfaces and even on the bare surfaces, although in these cases it is likely |
| 649 |
> |
due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism |
| 650 |
> |
of step-edge breakup suggested by these energy curves is one of the most difficult |
| 651 |
> |
processes, a complete break-away from the step-edge in one unbroken movement. |
| 652 |
> |
Easier multistep mechanisms likely exist where an adatom moves laterally on the surface |
| 653 |
> |
after being ejected so it ends up alongside the ledge. This provides the atom with 5 nearest |
| 654 |
> |
neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher |
| 655 |
> |
than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO |
| 656 |
> |
quadrupolar repulsion is still playing a primary role, but for its importance in roughening |
| 657 |
> |
the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not |
| 658 |
> |
born out by their mobility data. The requirement for a large density of CO on the surface |
| 659 |
> |
for some of the more favorable suggested configurations in Figure \ref{fig:SketchGraphic} |
| 660 |
> |
correspond well with the increased mobility seen on higher coverage surfaces. |
| 661 |
|
|
| 662 |
< |
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:rxcoord} 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. |
| 650 |
< |
|
| 651 |
< |
%lambda progression of Pt -> shoving its way into the step |
| 662 |
> |
%Sketch graphic of different configurations |
| 663 |
|
\begin{figure}[H] |
| 664 |
< |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
| 665 |
< |
\caption{A model system of the Pt(557) surface was used as the framework |
| 666 |
< |
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 667 |
< |
placements, and rotations of CO were examined as they affect Pt movement. |
| 668 |
< |
The coordinate displayed in this Figure was a representative run. As shown |
| 669 |
< |
in Table \ref{tab:rxcoord}, relative to the energy of the system at 0\%, there |
| 670 |
< |
is a slight decrease upon insertion of the Pt atom into the step-edge along |
| 660 |
< |
with the resultant lifting of the other Pt atom when CO is present at certain positions.} |
| 661 |
< |
\label{fig:lambda} |
| 664 |
> |
\includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf} |
| 665 |
> |
\caption{The dark grey atoms refer to the upper ledge, while the white atoms are |
| 666 |
> |
the lower terrace. The blue highlighted atoms had a CO in a vertical atop position |
| 667 |
> |
upon them. These are a sampling of the configurations examined to gain a more |
| 668 |
> |
complete understanding of the effects CO has on surface diffusion and edge breakup. |
| 669 |
> |
Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.} |
| 670 |
> |
\label{fig:SketchGraphic} |
| 671 |
|
\end{figure} |
| 672 |
|
|
| 673 |
+ |
%energy graph corresponding to sketch graphic |
| 674 |
|
\begin{figure}[H] |
| 675 |
< |
\includegraphics[totalheight=0.9\textheight]{lambdaTable.png} |
| 676 |
< |
\caption{} |
| 677 |
< |
\label{fig:lambdaTable} |
| 675 |
> |
\includegraphics[width=\linewidth]{Portrait_SeparationComparison.pdf} |
| 676 |
> |
\caption{The energy curves directly correspond to the labeled model |
| 677 |
> |
surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative |
| 678 |
> |
to their initial configuration so the energy of a and h do not have the |
| 679 |
> |
same zero value. As is seen, certain arrangements of CO can lower |
| 680 |
> |
the energetic barrier that must be overcome to create an adatom. |
| 681 |
> |
However, it is the highest coverages where these higher-energy |
| 682 |
> |
configurations of CO will be more likely. } |
| 683 |
> |
\label{fig:SketchEnergies} |
| 684 |
|
\end{figure} |
| 685 |
|
|
| 686 |
+ |
While configurations of CO on the surface are able to increase diffusion, |
| 687 |
+ |
this does not immediately provide an explanation for the formation of double |
| 688 |
+ |
layers. If adatoms were constrained to their terrace then doubling would be |
| 689 |
+ |
much less likely to occur. Nucleation sites could still potentially form, but there |
| 690 |
+ |
would not be enough atoms to finish the doubling. For a non-simulated metal surface, where the |
| 691 |
+ |
step lengths can be assumed to be infinite relative to atomic sizes, local doubling would be possible, but in |
| 692 |
+ |
our simulations with our periodic treatment of the system, the system is not large enough to experience this effect. |
| 693 |
+ |
Thus, there must be a mechanism that explains how adatoms are able to move |
| 694 |
+ |
amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate |
| 695 |
+ |
where an adatom along the step-edge with an adsorbed CO ``burrows'' into the |
| 696 |
+ |
edge displacing an atom onto the higher terrace. This mechanism was chosen |
| 697 |
+ |
because of similar events that were observed during the simulations. The barrier |
| 698 |
+ |
heights we obtained are only approximations because we constrained the movement |
| 699 |
+ |
of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s |
| 700 |
+ |
are provide a strong energetic support for this modeled lifting mechanism. When CO is not present and |
| 701 |
+ |
this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown |
| 702 |
+ |
in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol. |
| 703 |
+ |
While the barrier height is comparable for both cases, there is nearly a 20~kcal/mol |
| 704 |
+ |
difference in energies and makes the process energetically favorable. |
| 705 |
|
|
| 706 |
+ |
%lambda progression of Pt -> shoving its way into the step |
| 707 |
+ |
\begin{figure}[H] |
| 708 |
+ |
\includegraphics[width=\linewidth]{EPS_rxnCoord.pdf} |
| 709 |
+ |
\caption{ Various points along a reaction coordinate are displayed in the figure. |
| 710 |
+ |
The mechanism of edge traversal is examined in the presence of CO. The approximate |
| 711 |
+ |
barrier for the displayed process is 20~kcal/mol. However, the $\Delta E$ of this process |
| 712 |
+ |
is -15~kcal/mol making it an energetically favorable process.} |
| 713 |
+ |
\label{fig:lambda} |
| 714 |
+ |
\end{figure} |
| 715 |
|
|
| 716 |
< |
\begin{table}[H] |
| 717 |
< |
\caption{} |
| 718 |
< |
\centering |
| 719 |
< |
\begin{tabular}{| c || c | c | c | c |} |
| 720 |
< |
\hline |
| 721 |
< |
\textbf{System} & 0.5~\AA & 2~\AA & 4~\AA & 6~\AA \\ |
| 722 |
< |
\hline |
| 723 |
< |
A & 6.38 & 38.34 & 44.65 & 47.60 \\ |
| 724 |
< |
B & -20.72 & 0.67 & 17.33 & 24.28 \\ |
| 681 |
< |
C & 4.92 & 27.02 & 41.05 & 47.43 \\ |
| 682 |
< |
D & -16.97 & 21.21 & 35.87 & 40.93 \\ |
| 683 |
< |
E & 5.92 & 30.96 & 43.69 & 49.23 \\ |
| 684 |
< |
F & 8.53 & 46.23 & 53.98 & 65.55 \\ |
| 685 |
< |
\hline |
| 686 |
< |
\end{tabular} |
| 687 |
< |
\label{tab:rxcoord} |
| 688 |
< |
\end{table} |
| 716 |
> |
The mechanism for doubling on this surface appears to require the cooperation of at least |
| 717 |
> |
these two described processes. For complete doubling of a layer to occur there must |
| 718 |
> |
be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from |
| 719 |
> |
that terrace they must either rise up on the ledge above them or drop to the ledge below |
| 720 |
> |
them. The presence of CO helps with the energetics of both of these situations. There must be sufficient |
| 721 |
> |
breakage of the step-edge to increase the concentration of adatoms on the surface and |
| 722 |
> |
these adatoms must then undergo the burrowing highlighted above or some comparable |
| 723 |
> |
mechanism to traverse the step-edge. Over time, these mechanisms working in concert |
| 724 |
> |
lead to the formation of a double layer. |
| 725 |
|
|
| 726 |
+ |
\subsection{CO Removal and double layer stability} |
| 727 |
+ |
Once a double layer had formed on the 50\%~Pt system it |
| 728 |
+ |
remained for the rest of the simulation time with minimal |
| 729 |
+ |
movement. There were configurations that showed small |
| 730 |
+ |
wells or peaks forming, but typically within a few nanoseconds |
| 731 |
+ |
the feature would smooth away. Within our simulation time, |
| 732 |
+ |
the formation of the double layer was irreversible and a double |
| 733 |
+ |
layer was never observed to split back into two single layer |
| 734 |
+ |
step-edges while CO was present. To further gauge the effect |
| 735 |
+ |
CO had on this system, additional simulations were run starting |
| 736 |
+ |
from a late configuration of the 50\%~Pt system that had formed |
| 737 |
+ |
double layers. These simulations then had their CO removed. |
| 738 |
+ |
The double layer breaks rapidly in these simulations, already |
| 739 |
+ |
showing a well-defined splitting after 100~ps. Configurations of |
| 740 |
+ |
this system are shown in Figure \ref{fig:breaking}. The coloring |
| 741 |
+ |
of the top and bottom layers helps to exhibit how much mixing |
| 742 |
+ |
the edges experience as they split. These systems were only |
| 743 |
+ |
examined briefly, 10~ns, and within that time despite the initial |
| 744 |
+ |
rapid splitting, the edges only moved another few \AA~apart. |
| 745 |
+ |
It is possible with longer simulation times that the |
| 746 |
+ |
(557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010} |
| 747 |
|
|
| 691 |
– |
\subsection{Diffusion} |
| 692 |
– |
The diffusion parallel to the step-edge tends to be |
| 693 |
– |
much larger than that perpendicular to the step-edge. The dynamic |
| 694 |
– |
equilibrium that is established between the step-edge and adatom interface. The coverage |
| 695 |
– |
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}. |
| 696 |
– |
The |
| 697 |
– |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
| 698 |
– |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
| 699 |
– |
appears, parallel diffusion, along the now slightly angled step-edge, will allow for |
| 700 |
– |
a faster formation of the double layer than if the entire process were dependent on |
| 701 |
– |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
| 702 |
– |
more likely a growth point is to be formed. |
| 703 |
– |
\\ |
| 748 |
|
|
| 749 |
|
|
| 750 |
|
%breaking of the double layer upon removal of CO |
| 751 |
|
\begin{figure}[H] |
| 752 |
< |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 752 |
> |
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking.pdf} |
| 753 |
|
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
| 754 |
< |
helped maintain the stability of the double layer and upon removal the two layers break |
| 755 |
< |
and begin separating. The separation is not a simple pulling apart however, rather |
| 756 |
< |
there is a mixing of the lower and upper atoms at the edge.} |
| 754 |
> |
helped maintain the stability of the double layer and its microfaceting of the double layer |
| 755 |
> |
into a (111) configuration. This microfacet immediately reverts to the original (100) step |
| 756 |
> |
edge which is a hallmark of the (557) surface. The separation is not a simple sliding apart, rather |
| 757 |
> |
there is a mixing of the lower and upper atoms at the edge.} |
| 758 |
|
\label{fig:breaking} |
| 759 |
|
\end{figure} |
| 760 |
|
|
| 782 |
|
|
| 783 |
|
|
| 784 |
|
\section{Conclusion} |
| 785 |
< |
In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in less than a $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems. |
| 785 |
> |
The strength of the Pt-CO binding interaction as well as the large |
| 786 |
> |
quadrupolar repulsion between CO molecules are sufficient to |
| 787 |
> |
explain the observed increase in surface mobility and the resultant |
| 788 |
> |
reconstructions at the highest simulated coverage. The weaker |
| 789 |
> |
Au-CO interaction results in lower diffusion constants, less step-wandering, |
| 790 |
> |
and a lack of the double layer reconstruction. An in-depth examination |
| 791 |
> |
of the energetics shows the important role CO plays in increasing |
| 792 |
> |
step-breakup and in facilitating edge traversal which are both |
| 793 |
> |
necessary for double layer formation. |
| 794 |
|
|
| 795 |
+ |
|
| 796 |
+ |
|
| 797 |
|
%Things I am not ready to remove yet |
| 798 |
|
|
| 799 |
|
%Table of Diffusion Constants |
| 816 |
|
% \end{tabular} |
| 817 |
|
% \end{table} |
| 818 |
|
|
| 819 |
< |
\section{Acknowledgments} |
| 819 |
> |
\begin{acknowledgement} |
| 820 |
|
Support for this project was provided by the National Science |
| 821 |
|
Foundation under grant CHE-0848243 and by the Center for Sustainable |
| 822 |
|
Energy at Notre Dame (cSEND). Computational time was provided by the |
| 823 |
|
Center for Research Computing (CRC) at the University of Notre Dame. |
| 824 |
< |
|
| 824 |
> |
\end{acknowledgement} |
| 825 |
|
\newpage |
| 826 |
|
\bibliography{firstTryBibliography} |
| 827 |
< |
\end{doublespace} |
| 827 |
> |
%\end{doublespace} |
| 828 |
> |
|
| 829 |
> |
\begin{tocentry} |
| 830 |
> |
%\includegraphics[height=3.5cm]{timelapse} |
| 831 |
> |
\end{tocentry} |
| 832 |
> |
|
| 833 |
|
\end{document} |
