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%Title |
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\title{Investigation of the Pt and Au 557 Surface Reconstructions |
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under a CO Atmosphere} |
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\author{Joseph R. Michalka, Patrick W. MacIntyre and J. Daniel |
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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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%authors |
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% make the title |
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\maketitle |
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\maketitle/ |
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\begin{doublespace} |
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\hline |
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\multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\ |
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\hline |
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& r & $\sigma$ & $\epsilon$ & q\\ |
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& {\it z} & $\sigma$ & $\epsilon$ & q\\ |
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\hline |
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\textbf{C} & 0.0 & 0.0262 & 3.83 & -0.75 \\ |
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\textbf{O} & 1.13 & 0.1591 & 3.12 & -0.85 \\ |
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\textbf{M} & 0.6457 & - & - & 1.6 \\ |
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\textbf{C} & -0.6457 & 0.0262 & 3.83 & -0.75 \\ |
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\textbf{O} & 0.4843 & 0.1591 & 3.12 & -0.85 \\ |
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\textbf{M} & 0.0 & - & - & 1.6 \\ |
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\hline |
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\end{tabular} |
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\end{table} |
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\subsection{Construction and Equilibration of 557 Metal interfaces} |
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Our model systems are composed of approximately 4000 metal atoms cut along the 557 plane so that they are periodic in the \it{x} and \it{y} directions exposing the 557 plane in the \it{z} direction. Runs at various temperatures ranging from 300~K to 1200~K were started with the intent of viewing relative stability of the surface when CO was not present in the system. Owing to the different melting points (1337~K for Au and 2045~K for Pt), the bare crystal systems were initially run in the Canonical ensemble for at 800~K and 1000~K respectively for 100 ps. Various amounts of CO were placed in the vacuum portion which upon full adsorption to the surface corresponded to 5\%, 25\%, 33\%, and 50\% coverages. These systems were again allowed to reach thermal equilibrium before being run in the micro canonical ensemble. All of the systems examined were run for at least 40 ns. A subset that were undergoing interesting effects have been allowed to continue running with one system approaching 200 ns.em |
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Our model systems are composed of approximately 4000 metal atoms |
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cut along the 557 plane so that they are periodic in the {\it x} and {\it y} |
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directions exposing the 557 plane in the {\it z} direction. Runs at various |
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temperatures ranging from 300~K to 1200~K were started with the intent |
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of viewing relative stability of the surface when CO was not present in the |
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system. Owing to the different melting points (1337~K for Au and 2045~K for Pt), |
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the bare crystal systems were initially run in the Canonical ensemble at |
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800~K and 1000~K respectively for 100 ps. Various amounts of CO were |
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placed in the vacuum region, which upon full adsorption to the surface |
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corresponded to 5\%, 25\%, 33\%, and 50\% coverages. Because of the |
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high temperature and the difference in binding energies, the platinum systems |
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very rarely had CO that was not adsorbed to the surface whereas the gold systems |
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often had a substantial minority of CO away from the surface. |
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These systems were again allowed to reach thermal equilibrium before being run in the |
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microcanonical ensemble. All of the systems examined in this work were |
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run for at least 40 ns. A subset that were undergoing interesting effects |
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have been allowed to continue running with one system approaching 200 ns. |
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All simulations were run using the open source molecular dynamics package, OpenMD. \cite{Ewald, OOPSE} |
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& Calc. & Exp. \\ |
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\hline |
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\textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\ |
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\textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\ |
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\textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold} \\ |
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\hline |
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\end{tabular} |
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\end{table} |
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% Just results, leave discussion for discussion section |
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\section{Results} |
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\subsection{Diffusion} |
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While an ideal metallic surface is unlikely to experience much surface diffusion, high-index surfaces have large numbers of low-coordinated atoms which have a much easier time overcoming the energetic barriers limiting diffusion, leading to easier surface reconstructions. Surface movement was divided between the parallel ($\parallel$) and perpendicular ($\perp$) directions relative to the step edge. We were then able to calculate diffusion constants as a function of CO coverage. As can be seen in Table 4, the presence and amount of CO directly affects the diffusion constants of surface platinum atoms. The presence of two 50\% coverage systems is to show how the diffusion process is affected by time. The majority of the systems were run for approximately 50 ns while the half monolayer system been running continuously. The lowered diffusion constant at longer run times will be examined in-depth in the discussion section. |
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While an ideal metallic surface is unlikely to experience much surface diffusion, high-index surfaces have large numbers of low-coordinated atoms which have a much easier time overcoming the energetic barriers limiting diffusion, leading to easier surface reconstructions. Surface movement was divided between the parallel ($\parallel$) and perpendicular ($\perp$) directions relative to the step edge. We were then able to calculate diffusion constants as a function of CO coverage. As can be seen in Table 4, the presence and amount of CO directly affects the diffusion constants of surface platinum atoms. The presence of two 50\% coverage systems is to show how the diffusion process is affected by time. The majority of the systems were run for approximately 50 ns while the half monolayer system has been running continuously. The lowered diffusion constant at longer run times will be examined in-depth in the discussion section. |
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\begin{figure}[H] |
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\includegraphics[scale=0.6]{DiffusionComparison_error.png} |
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\caption{Diffusion parallel to the step edge will always be higher than that perpendicular to the edge because of the lower energy barrier associated with going from approximately 7 nearest neighbors to 5, as compared to the 3 of an adatom. Additionally, the observed maximum and subsequent decrease for the Pt system suggests that the CO self-interactions are playing a significant role with regards to movement of the platinum atoms around and more importantly across the surface. } |
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\end{figure} |
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%Table of Diffusion Constants |
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%Add gold?M |
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\begin{table}[H] |
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\caption{Platinum diffusion constants parallel and perpendicular to the 557 step edge. As the coverage increases, the diffusion constants parallel and perpendicular to the step edge both initially increase and then decrease slightly. There were two approaches of analysis. One looking at the surface atoms that had moved more than a prescribed amount over the run time and the other looking at all surface atoms. Units are \AA\textsuperscript{2}/ns} |
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\caption{Platinum and gold diffusion constants parallel and perpendicular to the 557 step edge. As the coverage increases, the diffusion constants parallel and perpendicular to the step edge both initially increase and then decrease slightly. Units are \AA\textsuperscript{2}/ns} |
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\centering |
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\begin{tabular}{| c | ccc | ccc | c |} |
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\begin{tabular}{| c | cc | cc | c |} |
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\hline |
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\textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & \textbf{Time (ns)}\\ |
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\textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Time (ns)}\\ |
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\hline |
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&\multicolumn{3}{c|}{\textbf{Mobile}}&\multicolumn{3}{c|}{\textbf{Surface Atoms}} & \\ |
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&\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} & \\ |
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\hline |
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50\% & 3.74 & 0.89 & 497 & 2.05 & 0.49 & 912 & 116 \\ |
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50\% & 5.81 & 1.59 & 365 & 2.41 & 0.68 & 912 & 46 \\ |
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33\% & 6.73 & 2.47 & 332 & 2.51 & 0.93 & 912 & 46 \\ |
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25\% & 5.38 & 2.04 & 361 & 2.18 & 0.84 & 912 & 46 \\ |
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5\% & 5.54 & 0.63 & 230 & 1.44 & 0.19 & 912 & 46 \\ |
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0\% & 3.53 & 0.61 & 282 & 1.11 & 0.22 & 912 & 56 \\ |
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\hline |
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50\%-r & 6.91 & 2.00 & 198 & 2.23 & 0.68 & 925 & 25\\ |
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0\%-r & 4.73 & 0.27 & 128 & 0.72 & 0.05 & 925 & 43\\ |
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50\% & 4.32 $\pm$ 0.02 & 1.185 $\pm$ 0.008 & 1.72 $\pm$ 0.02 & 0.455 $\pm$ 0.006 & 40 \\ |
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33\% & 5.18 $\pm$ 0.03 & 1.999 $\pm$ 0.005 & 1.95 $\pm$ 0.02 & 0.337 $\pm$ 0.004 & 40 \\ |
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25\% & 5.01 $\pm$ 0.02 & 1.574 $\pm$ 0.004 & 1.26 $\pm$ 0.03 & 0.377 $\pm$ 0.006 & 40 \\ |
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5\% & 3.61 $\pm$ 0.02 & 0.355 $\pm$ 0.002 & 1.84 $\pm$ 0.03 & 0.169 $\pm$ 0.004 & 40 \\ |
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0\% & 3.27 $\pm$ 0.02 & 0.147 $\pm$ 0.004 & 1.50 $\pm$ 0.02 & 0.194 $\pm$ 0.002 & 40 \\ |
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\hline |
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\end{tabular} |
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\end{table} |
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%Discussion |
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\section{Discussion} |
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Comparing the results from simulation to those reported previously by Tao et al. the similarities in the platinum and CO system are quite strong. As shown in figure 1, the simulated platinum system under a CO atmosphere will restructure slightly by doubling the terrace heights. The restructuring appears to occur slowly, one to two platinum atoms at a time. Looking at individual snapshots, these adatoms tend to either rise on top of the plateau or break away from the step edge and then diffuse perpendicularly to the step direction until reaching another step edge. This combination of growth and decay of the step edges appears to be in somewhat of a state of dynamic equilibrium. However, once two previously separated edges meet as shown in figure 1.B, this point tends to act as a focus or growth point for the rest of the edge to meet up, akin to that of a zipper. From the handful of cases where a double layer was formed during the simulation. Measuring from the initial appearance of a growth point, the double layer tends to be fully formed within $\sim$~35 ns. |
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Comparing the results from simulation to those reported previously by Tao et al. the similarities in the platinum and CO system are quite strong. As shown in figure 1, the simulated platinum system under a CO atmosphere will restructure slightly by doubling the terrace heights. The restructuring appears to occur slowly, one to two platinum atoms at a time. Looking at individual snapshots, these adatoms tend to either rise on top of the plateau or break away from the step edge and then diffuse perpendicularly to the step direction until reaching another step edge. This combination of growth and decay of the step edges appears to be in somewhat of a state of dynamic equilibrium. However, once two previously separated edges meet as shown in figure 1.B, this point tends to act as a focus or growth point for the rest of the edge to meet up, akin to that of a zipper. From the handful of cases where a double layer was formed during the simulation, measuring from the initial appearance of a growth point, the double layer tends to be fully formed within $\sim$~35 ns. |
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|
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\subsection{Diffusion} |
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As shown in the results section, the diffusion parallel to the step edge tends to be much faster than that perpendicular to the step edge. Additionally, the coverage of CO appears to play a slight role in relative rates of diffusion, as shown in Table 4. Thus, the bottleneck of the double layer formation appears to be the initial formation of this growth point, which seems to be somewhat of a stochastic event. Once it appears, parallel diffusion, along the now slightly angled step edge, will allow for a faster formation of the double layer than if the entire process were dependent on only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the more likely a growth point is to be formed. One driving force behind this reconstruction appears to be the lowering of surface energy that occurs by doubling the terrace widths. (I'm not really proving this... I have the surface flatness to show it, but surface energy?) |
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%Peaks! |
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\begin{figure}[H] |
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\includegraphics[scale=0.25]{doublePeaks_noCO.png} |
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\caption{} |
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\end{figure} |
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\section{Conclusion} |
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