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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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|
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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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% Causes of 2_layer reordering in Pt |
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%Summary |
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%% |
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%Title |
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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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|
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\author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel |
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Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\ |
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Department of Chemistry and Biochemistry,\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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|
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%Date |
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\date{Mar 5, 2013} |
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|
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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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|
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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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Coulomb potential. For this work, we have used classical molecular |
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dynamics with potential energy surfaces that are specifically tuned |
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for transition metals. In particular, we used the EAM potential for |
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Au-Au and Pt-Pt interactions\cite{EAM}. The CO was modeled using a rigid |
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Au-Au and Pt-Pt interactions.\cite{EAM} The CO was modeled using a rigid |
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three-site model developed by Straub and Karplus for studying |
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photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
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Pt-CO cross interactions were parameterized as part of this work. |
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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 (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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\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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to undergo extensive remodeling that was not observed in the bare |
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systems. The bare metal surfaces |
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experienced 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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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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described through adatom diffusion and step-edge wandering, |
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also increased. Except for the 50\% Pt system, the step-edges |
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did not coalesce in any of the other simulations, instead |
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preferring to keep nearly the same distance between steps |
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as in the original (557) lattice, $\sim$13\AA for Pt and $\sim$14\AA for Au. |
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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 exists because the entropy of the step-edges is constrained |
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since step-edge crossing is not allowed. This entropic repulsion |
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does not completely define the interactions between steps, |
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which is why some surfaces will undergo step coalescence, |
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where additional attractive interactions can overcome the |
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repulsion\cite{Williams:1991} and others will not. The presence |
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of adsorbates can affect these step interactions, potentially |
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leading to a new surface structure as the thermodynamic minimum. |
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repulsion arises because step-edge crossing is not allowed |
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which constrains the entropy. This entropic repulsion does |
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not completely define the interactions between steps, which |
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is why some surfaces will undergo step coalescence, where |
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additional attractive interactions can overcome the repulsion.\cite{Williams:1991} |
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The presence and concentration of adsorbates, as shown in |
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this work, can affect these step interactions, potentially leading |
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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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Tao et al.\cite{Tao:2010} 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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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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Similar behavior has been seen 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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The amount of reconstruction is strongly correlated to the amount of CO |
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adsorbed upon the surface. This appears to be related to the |
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effect that adsorbate coverage has on edge breakup and on the |
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surface diffusion of metal adatoms. While both systems displayed |
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step-edge wandering, only the 50\% Pt surface underwent the |
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doubling seen by Tao et al. within the time scales studied here. |
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Over longer periods (150~ns) two more double layers formed |
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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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various times along the simulation showing the evolution of a double layer step-edge. |
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|
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The second reconstruction on the Pt(557) surface observed by |
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Tao involved the formation of triangular clusters that stretched |
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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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%Evolution of surface |
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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 |
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doubling of the layers appears only after two adjacent step-edges |
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touch. The circled spot in (b) nucleated the growth of the double |
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step observed in the later configurations.} |
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\label{fig:reconstruct} |
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\end{figure} |
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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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with the energetics and structures at different conditions |
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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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with the energetics and structures at different conditions. |
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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 approaches give 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 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$70 s/image provides an upper bound for the time required for |
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the doubling to occur. In this section we give data on dynamic and |
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$\sim$70~s/image provides an upper bound for the time required for |
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the doubling to occur. By utilizing Molecular Dynamics we were able to probe the dynamics of these reconstructions and 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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|
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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 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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on higher-index facets provides 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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energetic penalty around $\sim$~45 kcal/mol, but this is 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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on the surface. For certain distributions of CO, see Figures \ref{fig:SketchGraphic} and \ref{fig:SketchEnergies}, the penalty can fall to 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 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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diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are then |
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able to explore the terrace before rejoining either their original step-edge or |
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becoming a part of a different edge. It is a 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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energy barrier required to lift or lower the adatom. By tracking the mobility of individual |
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energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
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metal atoms on the Pt and Au surfaces we were able to determine the relative |
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diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
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observation of the mobile metal atoms showed that they were typically in |
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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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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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step-edges causes the diffusion parallel to the step-edges to be larger than |
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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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%Diffusion graph |
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\begin{figure}[H] |
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\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf} |
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\caption{Diffusion constants for mobile surface atoms along directions |
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parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
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($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
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surface coverage. Diffusion parallel to the step-edge is higher |
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than that perpendicular to the edge because of the lower energy |
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barrier associated with traversing along the edge as compared to |
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completely breaking away. The two reported diffusion constants for |
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the 50\% Pt system arise from different sample sets. The lower values |
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correspond to the same 40~ns amount that all of the other systems were |
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examined at, while the larger values correspond to a 20~ns period } |
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\label{fig:diff} |
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\end{figure} |
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|
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The lack of a definite trend in the Au diffusion data in Figure \ref{fig:diff} is likely due |
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to the weaker bonding between Au and CO. This leads to a lower observed |
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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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then further limits the effect the CO can have on 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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stability strongly and many atoms that had been tracked for mobility |
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data have now been buried. By performing the same diffusion |
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calculation but on a shorter run time (20~ns), only including data |
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before the formation of the first double layer, we obtain the larger |
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values for both $\mathbf{D}_{\parallel}$ and $\mathbf{D}_{\perp}$ |
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at the 50\% coverage as seen in Figure \ref{fig:diff}. |
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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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mechanism of double layer formation focuses on the effect 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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arrangements of CO on the surface allowing for 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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|
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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 |
| 576 |
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has higher diffusion constants but did not show |
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any signs of edge doubling in the observed run time. On the |
| 578 |
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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 |
| 580 |
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work gives insight into the upper bounds of the |
| 581 |
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time required for step coalescence.\cite{Williams:1991,Pearl} |
| 573 |
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The increased diffusion on Pt at the higher CO coverages |
| 574 |
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plays a primary role in double layer formation. However, |
| 575 |
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this is not a complete explanation -- the 33\%~Pt system |
| 576 |
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has higher diffusion constants but did not show any signs |
| 577 |
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of edge doubling in the observed run time. On the |
| 578 |
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50\%~Pt system, one layer formed within the first 40~ns |
| 579 |
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of simulation time, while two more were formed as the |
| 580 |
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system was allowed to run for an additional |
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110~ns (150~ns total). This suggests that this reconstruction is |
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a rapid process and that the previously mentioned upper bound |
| 583 |
> |
will be lowered as experimental techniques continue to improve.\cite{Williams:1991,Pearl} |
| 584 |
|
In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 585 |
|
appearance of a double layer, appears at 19~ns |
| 586 |
|
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
| 590 |
|
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
| 591 |
|
$\sim$40~ns was necessary for the layer to completely straighten. |
| 592 |
|
The other two layers in this simulation formed over periods of |
| 593 |
< |
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 |
| 593 |
> |
22~ns and 42~ns respectively. A possible explanation |
| 594 |
|
for this rapid reconstruction is the elevated temperatures |
| 595 |
|
under which our systems were simulated. It is probable that the process would |
| 596 |
< |
take longer at lower temperatures. |
| 596 |
> |
take longer at lower temperatures. Additionally, our measured times for completion |
| 597 |
> |
of the doubling after the appearance of a nucleation site are likely affected by our |
| 598 |
> |
constrained axes. A longer step-edge will likely take longer to ``zipper''. However, |
| 599 |
> |
the first appearance of a nucleation site will likely occur more quickly due to its stochastic nature. |
| 600 |
|
|
| 601 |
< |
%Evolution of surface |
| 601 |
> |
|
| 602 |
> |
|
| 603 |
> |
|
| 604 |
> |
|
| 605 |
> |
|
| 606 |
> |
%Sketch graphic of different configurations |
| 607 |
|
\begin{figure}[H] |
| 608 |
< |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 609 |
< |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 610 |
< |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 611 |
< |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 612 |
< |
doubling of the layers appears only after two adjacent step-edges |
| 613 |
< |
touch. The circled spot in (b) nucleated the growth of the double |
| 614 |
< |
step observed in the later configurations.} |
| 571 |
< |
\label{fig:reconstruct} |
| 608 |
> |
\includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf} |
| 609 |
> |
\caption{The dark grey atoms refer to the upper ledge, while the white atoms are |
| 610 |
> |
the lower terrace. The blue highlighted atoms had a CO in a vertical atop position |
| 611 |
> |
upon them. These are a sampling of the configurations examined to gain a more |
| 612 |
> |
complete understanding of the effects CO has on surface diffusion and edge breakup. |
| 613 |
> |
Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.} |
| 614 |
> |
\label{fig:SketchGraphic} |
| 615 |
|
\end{figure} |
| 616 |
|
|
| 617 |
+ |
%energy graph corresponding to sketch graphic |
| 618 |
|
\begin{figure}[H] |
| 619 |
< |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
| 620 |
< |
\caption{Diffusion constants for mobile surface atoms along directions |
| 621 |
< |
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 622 |
< |
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 623 |
< |
surface coverage. Diffusion parallel to the step-edge is higher |
| 624 |
< |
than that perpendicular to the edge because of the lower energy |
| 625 |
< |
barrier associated with traversing along the edge as compared to |
| 626 |
< |
completely breaking away. Additionally, the observed |
| 627 |
< |
maximum and subsequent decrease for the Pt system suggests that the |
| 584 |
< |
CO self-interactions are playing a significant role with regards to |
| 585 |
< |
movement of the Pt atoms around and across the surface. } |
| 586 |
< |
\label{fig:diff} |
| 619 |
> |
\includegraphics[width=\linewidth]{stepSeparationComparison.pdf} |
| 620 |
> |
\caption{The energy curves directly correspond to the labeled model |
| 621 |
> |
surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative |
| 622 |
> |
to their initial configuration so the energy of a and h do not have the |
| 623 |
> |
same zero value. As is seen, certain arrangements of CO can lower |
| 624 |
> |
the energetic barrier that must be overcome to create an adatom. |
| 625 |
> |
However, it is the highest coverages where these higher-energy |
| 626 |
> |
configurations of CO will be more likely. } |
| 627 |
> |
\label{fig:SketchEnergies} |
| 628 |
|
\end{figure} |
| 629 |
|
|
| 589 |
– |
|
| 590 |
– |
|
| 591 |
– |
|
| 630 |
|
%Discussion |
| 631 |
|
\section{Discussion} |
| 632 |
|
We have shown that the classical potential models are able to model the initial reconstruction of the |
| 633 |
|
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 634 |
|
were able to observe features of the dynamic processes necessary for this reconstruction. |
| 635 |
|
|
| 636 |
+ |
\subsection{Diffusion} |
| 637 |
+ |
As shown in Figure \ref{fig:diff}, for the Pt systems, there |
| 638 |
+ |
is a strong trend toward higher diffusion constants as |
| 639 |
+ |
surface coverage of CO increases. The drop for the 50\% |
| 640 |
+ |
case being explained as double layer formation already |
| 641 |
+ |
beginning to occur in the analyzed 40~ns, which lowered |
| 642 |
+ |
the calculated diffusion rates. Between the parallel and |
| 643 |
+ |
perpendicular rates, the perpendicular diffusion constant |
| 644 |
+ |
appears to be the most important indicator of double layer |
| 645 |
+ |
formation. As highlighted in Figure \ref{fig:reconstruct}, the |
| 646 |
+ |
formation of the double layer did not begin until a nucleation |
| 647 |
+ |
site appeared. And as mentioned by Williams et al.\cite{Williams:1991, Williams:1994}, |
| 648 |
+ |
the inability for edges to cross leads to an effective repulsion. |
| 649 |
+ |
This repulsion must be overcome to allow step coalescence. |
| 650 |
+ |
A greater $\textbf{D}_\perp$ implies more step-wandering |
| 651 |
+ |
and a larger chance for the stochastic meeting of two edges |
| 652 |
+ |
to form the nucleation point. Upon that appearance, parallel |
| 653 |
+ |
diffusion along the step-edge can help ``zipper'' up the double |
| 654 |
+ |
layer. This helps explain why the time scale for formation after |
| 655 |
+ |
the appearance of a nucleation site was rapid, while the initial |
| 656 |
+ |
appearance of said site was unpredictable. |
| 657 |
+ |
|
| 658 |
|
\subsection{Mechanism for restructuring} |
| 659 |
< |
Since the Au surface showed no large scale restructuring throughout |
| 660 |
< |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 661 |
< |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 662 |
< |
Similarities of our results to those reported previously by |
| 663 |
< |
Tao et al.\cite{Tao:2010} are quite |
| 664 |
< |
strong. The simulated Pt |
| 665 |
< |
system exposed to a large dosage of CO readily restructures by doubling the terrace |
| 666 |
< |
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. |
| 667 |
< |
The adatoms either |
| 668 |
< |
break away from the step-edge and stay on the lower terrace or they lift |
| 669 |
< |
up onto a higher terrace. Once ``free'', they diffuse on the terrace |
| 670 |
< |
until reaching another step-edge or rejoining their original edge. |
| 671 |
< |
This combination of growth and decay of the step-edges is in a state of |
| 672 |
< |
dynamic equilibrium. However, once two previously separated edges |
| 673 |
< |
meet as shown in Figure 1.B, this nucleates the rest of the edge to meet up, forming a double layer. |
| 674 |
< |
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. |
| 659 |
> |
Since the Au surface showed no large scale restructuring throughout |
| 660 |
> |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 661 |
> |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 662 |
> |
Similarities of our results to those reported previously by Tao et al.\cite{Tao:2010} |
| 663 |
> |
are quite strong. The simulated Pt system exposed to a large dosage |
| 664 |
> |
of CO readily restructures by doubling the terrace widths and step heights. |
| 665 |
> |
The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a |
| 666 |
> |
time, but is rapid on experimental timescales. The adatoms either break |
| 667 |
> |
away from the step-edge and stay on the lower terrace or they lift up onto |
| 668 |
> |
a higher terrace. Once ``free'', they diffuse on the terrace until reaching |
| 669 |
> |
another step-edge or rejoining their original edge. This combination of |
| 670 |
> |
growth and decay of the step-edges is in a state of dynamic equilibrium. |
| 671 |
> |
However, once two previously separated edges meet as shown in Figure 1.B, |
| 672 |
> |
this nucleates the rest of the edge to meet up, forming a double layer. |
| 673 |
> |
From simulations which exhibit a double layer, the time delay from the |
| 674 |
> |
initial appearance of a nucleation point to a fully formed double layer is $\sim$35~ns. |
| 675 |
|
|
| 676 |
|
A number of possible mechanisms exist to explain the role of adsorbed |
| 677 |
|
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 679 |
|
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 680 |
|
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 681 |
|
relative to each other, through atop adsorption for example, this explanation |
| 682 |
< |
gains some credence. The energetic repulsion between two CO located a |
| 682 |
> |
gains some credence. The energetic repulsion between two CO located a |
| 683 |
|
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in |
| 684 |
< |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 684 |
> |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 685 |
|
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 686 |
< |
nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation |
| 687 |
< |
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. |
| 688 |
< |
As mentioned above, the energy barrier for surface diffusion |
| 689 |
< |
of a Pt adatom is only 4 kcal/mol. So this repulsion between neighboring CO molecules can |
| 690 |
< |
increase the surface diffusion. However, the residence time of CO on Pt was |
| 691 |
< |
examined and while the majority of the CO is on or near the surface throughout |
| 692 |
< |
the run, most molecules are mobile. This mobility suggests that the CO are more |
| 693 |
< |
likely to shift their positions without necessarily the Pt along with them. |
| 686 |
> |
nearly 0 kcal/mol. Allowing the CO to rotate away from a purely vertical orientation |
| 687 |
> |
also lowers the repulsion. A minimum of 6.2 kcal/mol is reached at when the |
| 688 |
> |
angle between the 2 CO is $\sim$24\textsuperscript{o}, when the carbons are |
| 689 |
> |
locked at a distance of 2.77 \AA apart. As mentioned above, the energy barrier |
| 690 |
> |
for surface diffusion of a Pt adatom is only 4 kcal/mol. So this repulsion between |
| 691 |
> |
neighboring CO molecules can increase the surface diffusion. However, the |
| 692 |
> |
residence time of CO on Pt was examined and while the majority of the CO is |
| 693 |
> |
on or near the surface throughout the run, the molecules are extremely mobile, |
| 694 |
> |
with diffusion constants 40 to 2500 times larger, depending on coverage. This |
| 695 |
> |
mobility suggests that the CO are more likely to shift their positions without |
| 696 |
> |
necessarily the Pt along with them. |
| 697 |
|
|
| 698 |
|
Another possible and more likely mechanism for the restructuring is in the |
| 699 |
|
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 700 |
< |
Pt atoms. This would then have the effect of increasing surface mobility |
| 638 |
< |
of these atoms. To test this hypothesis, numerous configurations of |
| 700 |
> |
Pt atoms. To test this hypothesis, numerous configurations of |
| 701 |
|
CO in varying quantities were arranged on the higher and lower plateaus |
| 702 |
< |
around a step on a otherwise clean Pt(557) surface. One representative |
| 703 |
< |
configuration is displayed in Figure \ref{fig:lambda}. Single or concerted movement |
| 704 |
< |
of Pt atoms was then examined to determine possible barriers. Because |
| 705 |
< |
the movement was forced along a pre-defined reaction coordinate that may differ |
| 706 |
< |
from the true minimum of this path, only the beginning and ending energies |
| 707 |
< |
are displayed in Table \ref{tab:energies} with the corresponding beginning and ending reaction coordinates in Figure \ref{fig:lambdaTable}. These values suggest that the presence of CO at suitable |
| 708 |
< |
locations can lead to lowered barriers for Pt breaking apart from the step-edge. |
| 709 |
< |
Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the |
| 710 |
< |
burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral |
| 711 |
< |
in terms of energetics. |
| 702 |
> |
around a step on a otherwise clean Pt(557) surface. A few sample |
| 703 |
> |
configurations are displayed in Figure \ref{fig:SketchGraphic}, with |
| 704 |
> |
energies at various positions along the path displayed in Table |
| 705 |
> |
NO TABLE. Certain configurations of CO, cases B and D for |
| 706 |
> |
example, can have quite strong energetic reasons for breaking |
| 707 |
> |
away from the step-edge. Although the packing of these configurations |
| 708 |
> |
is unlikely until CO coverage has reached a high enough value. |
| 709 |
> |
These examples are showing the most difficult cases, immediate |
| 710 |
> |
adatom formation through breakage away from the step-edge, which |
| 711 |
> |
is why their energies at large distances are relatively high. There are |
| 712 |
> |
mechanistic paths where an edge atom could get shifted to onto the |
| 713 |
> |
step-edge to form a small peak before fully breaking away. And again, |
| 714 |
> |
once the adatom is formed, the barrier for diffusion on the surface is |
| 715 |
> |
negligible. These sample configurations help explain CO's effect on |
| 716 |
> |
general surface mobility and step wandering, but they are lacking in |
| 717 |
> |
providing a mechanism for the formation of double layers. One possible |
| 718 |
> |
mechanism is elucidated in Figure \ref{fig:lambda}, where a burrowing |
| 719 |
> |
and lifting process of an adatom and step-edge atom respectively is |
| 720 |
> |
examined. The system, without CO present, is nearly energetically |
| 721 |
> |
neutral, whereas with CO present there is a $\sim$ 15 kcal/mol drop |
| 722 |
> |
in the energy of the system. |
| 723 |
|
|
| 724 |
|
%lambda progression of Pt -> shoving its way into the step |
| 725 |
|
\begin{figure}[H] |
| 727 |
|
\caption{A model system of the Pt(557) surface was used as the framework |
| 728 |
|
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 729 |
|
placements, and rotations of CO were examined as they affect Pt movement. |
| 730 |
< |
The coordinate displayed in this Figure was a representative run. As shown |
| 658 |
< |
in Table \ref{tab:rxcoord}, relative to the energy of the system at 0\%, there |
| 730 |
> |
The coordinate displayed in this Figure was a representative run. relative to the energy of the system at 0\%, there |
| 731 |
|
is a slight decrease upon insertion of the Pt atom into the step-edge along |
| 732 |
|
with the resultant lifting of the other Pt atom when CO is present at certain positions.} |
| 733 |
|
\label{fig:lambda} |
| 734 |
|
\end{figure} |
| 735 |
|
|
| 664 |
– |
\begin{figure}[H] |
| 665 |
– |
\includegraphics[totalheight=0.9\textheight]{lambdaTable.png} |
| 666 |
– |
\caption{} |
| 667 |
– |
\label{fig:lambdaTable} |
| 668 |
– |
\end{figure} |
| 736 |
|
|
| 737 |
|
|
| 671 |
– |
\subsection{Diffusion} |
| 672 |
– |
The diffusion parallel to the step-edge tends to be |
| 673 |
– |
much larger than that perpendicular to the step-edge. The dynamic |
| 674 |
– |
equilibrium that is established between the step-edge and adatom interface. The coverage |
| 675 |
– |
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}. |
| 676 |
– |
The |
| 677 |
– |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
| 678 |
– |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
| 679 |
– |
appears, parallel diffusion, along the now slightly angled step-edge, will allow for |
| 680 |
– |
a faster formation of the double layer than if the entire process were dependent on |
| 681 |
– |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
| 682 |
– |
more likely a growth point is to be formed. |
| 683 |
– |
\\ |
| 738 |
|
|
| 739 |
|
|
| 740 |
|
%breaking of the double layer upon removal of CO |
| 795 |
|
% \end{tabular} |
| 796 |
|
% \end{table} |
| 797 |
|
|
| 798 |
< |
\section{Acknowledgments} |
| 798 |
> |
\begin{acknowledgement} |
| 799 |
|
Support for this project was provided by the National Science |
| 800 |
|
Foundation under grant CHE-0848243 and by the Center for Sustainable |
| 801 |
|
Energy at Notre Dame (cSEND). Computational time was provided by the |
| 802 |
|
Center for Research Computing (CRC) at the University of Notre Dame. |
| 803 |
< |
|
| 803 |
> |
\end{acknowledgement} |
| 804 |
|
\newpage |
| 805 |
|
\bibliography{firstTryBibliography} |
| 806 |
< |
\end{doublespace} |
| 806 |
> |
%\end{doublespace} |
| 807 |
> |
|
| 808 |
> |
\begin{tocentry} |
| 809 |
> |
%\includegraphics[height=3.5cm]{timelapse} |
| 810 |
> |
\end{tocentry} |
| 811 |
> |
|
| 812 |
|
\end{document} |
