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\begin{document} |
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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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\author{Joseph R. Michalka} |
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\author{Patrick W. McIntyre} |
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\author{J. Daniel Gezelter} |
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\email{gezelter@nd.edu} |
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\affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\ |
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Department of Chemistry and Biochemistry\\ University of Notre |
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Dame\\ Notre Dame, Indiana 46556} |
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\keywords{} |
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\begin{document} |
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%% |
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%Introduction |
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% Experimental observations |
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%Summary |
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%% |
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|
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%Title |
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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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|
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\author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel |
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Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\ |
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Department of Chemistry and Biochemistry,\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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|
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%Date |
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\date{Mar 5, 2013} |
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%authors |
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% make the title |
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\maketitle |
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\begin{doublespace} |
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\begin{abstract} |
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We examine surface reconstructions of Pt and Au(557) under |
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various CO coverages using molecular dynamics in order to |
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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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\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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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 (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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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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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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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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\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 to which no CO was exposed |
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did experience minor roughening of the step-edge, but the |
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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 formed double layers at numerous spots upon its surface. |
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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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|
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|
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\subsubsection{Step wandering} |
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The 0\% coverage surfaces for both metals showed |
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minimal movement at their respective run temperatures. |
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As the coverage increased, the mobility of the surface |
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also increased. Additionally, at the higher coverages |
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on both metals, there was a large increase in the amount |
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of observed step-wandering. Previous work by |
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Williams\cite{Williams:1993} highlighted the entropic |
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contribution to the repulsion felt between step-edges, |
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and situations were that repulsion could be negated, or |
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overcome, to allow for step coalescence or facet formation. |
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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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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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|
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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 |
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we examined, the Pt system showed a greater propensity for |
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reconstruction when compared to the Au system. The amount |
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of reconstruction is correlated to the amount of CO |
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undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} |
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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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Of the two systems we examined, the Pt system showed a greater |
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propensity for reconstruction when compared to the Au system |
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because of the larger surface mobility and extent of step wandering. |
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The amount of reconstruction is correlated to the amount of CO |
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adsorbed upon the surface. This appears to be related to the |
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effect that adsorbate coverage has on edge breakup and on the surface |
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diffusion of metal adatoms. While both systems displayed step-edge |
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wandering, only the Pt surface underwent the doubling seen by |
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Tao et al. within the time scales studied here. |
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Only the 50\% coverage Pt system exhibited |
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a complete doubling in the time scales we |
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were able to monitor. Over longer periods (150~ns) two more double layers formed on this interface. |
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Although double layer formation did not occur in the other Pt systems, they show |
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more lateral movement of the step-edges |
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compared to their Au counterparts. The 50\% Pt system is highlighted |
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in Figure \ref{fig:reconstruct} at various times along the simulation |
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showing the evolution of a step-edge. |
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effect that adsorbate coverage has on edge breakup and on the |
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surface diffusion of metal adatoms. While both systems displayed |
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step-edge wandering, only the 50\% Pt surface underwent the |
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doubling seen by Tao et al.\cite{Tao:2010} within the time scales studied here. |
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Over longer periods, (150~ns) two more double layers formed |
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on this interface. Although double layer formation did not occur |
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in the other Pt systems, they show more step-wandering and |
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general roughening compared to their Au counterparts. The |
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50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
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various times along the simulation showing the evolution of a step-edge. |
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|
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The second reconstruction on the Pt(557) surface observed by |
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Tao involved the formation of triangular clusters that stretched |
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across the plateau between two step-edges. Neither system, within |
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the 40~ns time scale, experienced this reconstruction. |
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the 40~ns time scale or the extended simulation time of 150~ns for |
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the 50\% Pt system, experienced this reconstruction. |
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|
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\subsection{Dynamics} |
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Previous atomistic simulations of stepped surfaces dealt largely |
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\cite{Williams:1991,Williams:1994}. Consequently, the most common |
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technique utilized to date has been Monte Carlo sampling. Monte Carlo gives an efficient |
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sampling of the equilibrium thermodynamic landscape at the expense |
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of ignoring the dynamics of the system. Previous work by Pearl and |
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Sibener\cite{Pearl}, using STM, has been able to show the coalescing |
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of ignoring the dynamics of the system. Previous experimental work by Pearl and |
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Sibener\cite{Pearl}, using STM, has been able to capture the coalescing |
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of steps on Ni(977). The time scale of the image acquisition, |
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$\sim$70 s/image provides an upper bound for the time required for |
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$\sim$70~s/image provides an upper bound for the time required for |
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the doubling to occur. In this section we give data on dynamic and |
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transport properties, e.g. diffusion, layer formation time, etc. |
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|
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\subsubsection{Transport of surface metal atoms} |
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%forcedSystems/stepSeparation |
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The movement or wandering of a step-edge is a cooperative effect |
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arising from the individual movements, primarily through surface |
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diffusion, of the atoms making up the steps. An ideal metal surface |
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arising from the individual movements of the atoms making up the steps. An ideal metal surface |
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displaying a low index facet, (111) or (100), is unlikely to experience |
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much surface diffusion because of the large energetic barrier that must |
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be overcome to lift an atom out of the surface. The presence of step-edges |
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on higher-index surfaces provide a source for mobile metal atoms. |
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be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
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on higher-index facets provide a lower energy source for mobile metal atoms. |
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Breaking away from the step-edge on a clean surface still imposes an |
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energetic penalty around $\sim$~40 kcal/mol, but this is significantly easier than lifting |
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the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
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The penalty lowers significantly when CO is present in sufficient quantities |
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on the surface. For certain distributions of CO, the penalty can fall as low as |
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$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
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diffusion is negligible ( \textless~4 kcal/mol) and these adatoms are |
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diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are |
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able to explore the terrace before rejoining either the original step-edge or |
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becoming a part of a different edge. It is a more difficult process for an atom |
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to traverse to a separate terrace although the presence of CO can lower the |
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between saved configurations of the system (typically 10-100 ps). An atom that was |
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truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff |
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was used to prevent swamping the diffusion data with the in-place vibrational |
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movement of buried atoms. Diffusion on a surface is strongly affected by |
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movement of buried atoms. Diffusion on a surface is strongly affected by |
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local structures and in this work, the presence of single and double layer |
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step-edges causes the diffusion parallel to the step-edges to be different |
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from the diffusion perpendicular to these edges. Parallel and perpendicular |
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diffusion constants are shown in Figure \ref{fig:diff}. |
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|
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The lack of a definite trend in the Au diffusion data is likely due |
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to the weaker bonding between Au and CO. This leads to a lower |
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coverage ({\it x}-axis) when compared to dosage amount, which |
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then further limits the affects of the surface diffusion. The correlation |
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between coverage and Pt diffusion rates conversely shows a |
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definite trend marred by the highest coverage surface. Two |
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explanations arise for this drop. First, upon a visual inspection of |
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the system, after a double layer has been formed, it maintains its |
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stability strongly and is no longer a good source for adatoms. By |
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performing the same diffusion calculation but on a shorter run time |
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(20~ns), only including data before the formation of the double layer, |
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provides a $\mathbf{D}_{\perp}$ diffusion constant of $1.69~\pm~0.08$ |
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and a $\mathbf{D}_{\parallel}$ diffusion constant of $6.30~\pm~0.08$. |
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This places the parallel diffusion constant more closely in line with the |
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expected trend, while the perpendicular diffusion constant does not |
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drop as far. A secondary explanation arising from our analysis of the |
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mechanism of double layer formation show the affect that CO on the |
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surface has with respect to overcoming surface diffusion of Pt. If the |
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coverage is too sparse, the Pt engages in minimal interactions and |
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thus minimal diffusion. As coverage increases, there are more favorable |
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arrangements of CO on the surface allowing the formation of a path, |
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a minimum energy trajectory, for the adatom to explore the surface. |
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As the CO is constantly moving on the surface, this path is constantly |
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changing. If the coverage becomes too great, the paths could |
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potentially be clogged leading to a decrease in diffusion despite |
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their being more adatoms and step-wandering. |
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|
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\subsubsection{Dynamics of double layer formation} |
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The increased diffusion on Pt at the higher |
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CO coverages plays a primary role in double layer formation. However, this is not |
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a complete explanation -- the 33\%~Pt system |
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has higher diffusion constants but did not show |
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any signs of edge doubling. On the |
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50\%~Pt system, three separate layers were formed over |
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150~ns of simulation time. Previous experimental |
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any signs of edge doubling in the observed run time. On the |
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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 |
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110~ns (150~ns total). Previous experimental |
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work gives insight into the upper bounds of the |
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time required for step coalescence.\cite{Williams:1991,Pearl} |
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In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 552 |
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appearance of a double layer, appears at 19~ns |
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into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
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formed the double layer and by 86 ns, the complete layer |
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formed the double layer and by 86~ns, the complete layer |
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has been flattened out. The double layer could be considered |
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``complete" by 37~ns but remains a bit rough. From the |
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appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
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\begin{figure}[H] |
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\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
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\caption{The Pt(557) / 50\% CO system at a sequence of times after |
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initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
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(d) 86.1 ns. Disruption of the (557) step-edges occurs quickly. The |
| 571 |
> |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 572 |
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(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 573 |
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doubling of the layers appears only after two adjacent step-edges |
| 574 |
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touch. The circled spot in (b) nucleated the growth of the double |
| 575 |
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step observed in the later configurations.} |
| 616 |
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This combination of growth and decay of the step-edges is in a state of |
| 617 |
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dynamic equilibrium. However, once two previously separated edges |
| 618 |
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meet as shown in Figure 1.B, this nucleates the rest of the edge to meet up, forming a double layer. |
| 619 |
< |
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. |
| 619 |
> |
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. |
| 620 |
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|
| 621 |
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A number of possible mechanisms exist to explain the role of adsorbed |
| 622 |
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CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 647 |
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of Pt atoms was then examined to determine possible barriers. Because |
| 648 |
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the movement was forced along a pre-defined reaction coordinate that may differ |
| 649 |
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from the true minimum of this path, only the beginning and ending energies |
| 650 |
< |
are displayed in Table \ref{tab:energies}. These values suggest that the presence of CO at suitable |
| 650 |
> |
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 |
| 651 |
|
locations can lead to lowered barriers for Pt breaking apart from the step-edge. |
| 652 |
|
Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the |
| 653 |
|
burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral |
| 655 |
|
|
| 656 |
|
%lambda progression of Pt -> shoving its way into the step |
| 657 |
|
\begin{figure}[H] |
| 658 |
< |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO.png} |
| 658 |
> |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
| 659 |
|
\caption{A model system of the Pt(557) surface was used as the framework |
| 660 |
|
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 661 |
|
placements, and rotations of CO were examined as they affect Pt movement. |
| 666 |
|
\label{fig:lambda} |
| 667 |
|
\end{figure} |
| 668 |
|
|
| 669 |
+ |
\begin{figure}[H] |
| 670 |
+ |
\includegraphics[totalheight=0.9\textheight]{lambdaTable.png} |
| 671 |
+ |
\caption{} |
| 672 |
+ |
\label{fig:lambdaTable} |
| 673 |
+ |
\end{figure} |
| 674 |
|
|
| 675 |
|
|
| 676 |
+ |
|
| 677 |
+ |
\begin{table}[H] |
| 678 |
+ |
\caption{} |
| 679 |
+ |
\centering |
| 680 |
+ |
\begin{tabular}{| c || c | c | c | c |} |
| 681 |
+ |
\hline |
| 682 |
+ |
\textbf{System} & 0.5~\AA & 2~\AA & 4~\AA & 6~\AA \\ |
| 683 |
+ |
\hline |
| 684 |
+ |
A & 6.38 & 38.34 & 44.65 & 47.60 \\ |
| 685 |
+ |
B & -20.72 & 0.67 & 17.33 & 24.28 \\ |
| 686 |
+ |
C & 4.92 & 27.02 & 41.05 & 47.43 \\ |
| 687 |
+ |
D & -16.97 & 21.21 & 35.87 & 40.93 \\ |
| 688 |
+ |
E & 5.92 & 30.96 & 43.69 & 49.23 \\ |
| 689 |
+ |
F & 8.53 & 46.23 & 53.98 & 65.55 \\ |
| 690 |
+ |
\hline |
| 691 |
+ |
\end{tabular} |
| 692 |
+ |
\label{tab:rxcoord} |
| 693 |
+ |
\end{table} |
| 694 |
+ |
|
| 695 |
+ |
|
| 696 |
|
\subsection{Diffusion} |
| 697 |
|
The diffusion parallel to the step-edge tends to be |
| 698 |
|
much larger than that perpendicular to the step-edge. The dynamic |
| 711 |
|
%breaking of the double layer upon removal of CO |
| 712 |
|
\begin{figure}[H] |
| 713 |
|
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 714 |
< |
%: |
| 648 |
< |
\caption{(A) 0 ps, (B) 100 ps, (C) 1 ns, after the removal of CO. The presence of the CO |
| 714 |
> |
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
| 715 |
|
helped maintain the stability of the double layer and upon removal the two layers break |
| 716 |
|
and begin separating. The separation is not a simple pulling apart however, rather |
| 717 |
|
there is a mixing of the lower and upper atoms at the edge.} |
| 766 |
|
% \end{tabular} |
| 767 |
|
% \end{table} |
| 768 |
|
|
| 769 |
< |
\section{Acknowledgments} |
| 769 |
> |
\begin{acknowledgement} |
| 770 |
|
Support for this project was provided by the National Science |
| 771 |
|
Foundation under grant CHE-0848243 and by the Center for Sustainable |
| 772 |
|
Energy at Notre Dame (cSEND). Computational time was provided by the |
| 773 |
|
Center for Research Computing (CRC) at the University of Notre Dame. |
| 774 |
< |
|
| 774 |
> |
\end{acknowledgement} |
| 775 |
|
\newpage |
| 776 |
|
\bibliography{firstTryBibliography} |
| 777 |
< |
\end{doublespace} |
| 777 |
> |
%\end{doublespace} |
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> |
|
| 779 |
> |
\begin{tocentry} |
| 780 |
> |
%\includegraphics[height=3.5cm]{timelapse} |
| 781 |
> |
\end{tocentry} |
| 782 |
> |
|
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|
\end{document} |
