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\begin{document} |
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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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\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, Patrick W. McIntyre and J. Daniel |
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Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\ |
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Department of Chemistry and Biochemistry,\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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%Date |
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\date{Dec 15, 2012} |
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\date{Dec 15, 2012} |
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%authors |
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% make the title |
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\section{Simulation Methods} |
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The challenge in modeling any solid/gas interface problem is the |
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development of a sufficiently general yet computationally tractable |
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mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}. |
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%CO Table |
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\begin{table}[H] |
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\caption{Positions, $\sigma$, $\epsilon$ and charges for CO geometry and self-interactions\cite{Straub}. Distances are in \AA~, energies are in kcal/mol, and charges are in $e$.} |
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\caption{Positions, $\sigma$, $\epsilon$ and charges for CO geometry |
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and self-interactions\cite{Straub}. Distances are in \AA~, energies are |
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in kcal/mol, and charges are in $e$.} |
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\centering |
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\begin{tabular}{| c | c | ccc |} |
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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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%where did you actually get the functionals for citation? |
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%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
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%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
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The Au-C and Au-O interaction parameters were also fit to a Lennard-Jones |
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and Morse potential respectively, to reproduce Au-CO binding energies. |
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These energies were obtained from quantum calculations carried out using |
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the PBE GGA exchange-correlation functionals\cite{Perdew_GGA} for gold, carbon, and oxygen |
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constructed by Rappe, Rabe, Kaxiras, and Joannopoulos. \cite{RRKJ_PP}. |
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All calculations were run using the {\sc Quantum ESPRESSO} package. \cite{QE-2009} |
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First, a four layer slab of gold comprised of 32 atoms displaying a (111) surface was |
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converged using a 4X4X4 grid of Monkhorst-Pack \emph{k}-points.\cite{Monkhorst:1976} |
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The kinetic energy of the wavefunctions were truncated at 20 Ry while the |
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cutoff for the charge density and potential was set at 80 Ry. This relaxed |
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gold slab was then used in numerous single point calculations with CO at various heights |
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to create a potential energy surface for the Au-CO interaction. |
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The Au-C and Au-O cross-interactions were fit using Lennard-Jones and |
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Morse potentials, respectively, to reproduce Au-CO binding energies. |
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The fits were refined against gas-surface calculations using DFT with |
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a periodic supercell plane-wave basis approach, as implemented in the |
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{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are |
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described with the projector augmented-wave (PAW) |
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method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
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included to an energy cutoff of 20 Ry. Electronic energies are |
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computed with the PBE implementation of the generalized gradient |
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approximation (GGA) for gold, carbon, and oxygen that was constructed |
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by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP} |
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Ionic relaxations were performed until the energy difference between |
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subsequent steps was less than 0.0001 eV. In testing the CO-Au |
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interaction, Au(111) supercells were constructed of four layers of 4 |
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Au x 2 Au surface planes and separated from vertical images by six |
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layers of vacuum space. The surface atoms were all allowed to relax. |
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Supercell calculations were performed nonspin-polarized, and energies |
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were converged to within 0.03 meV per Au atom with a 4 x 4 x 4 |
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Monkhorst-Pack\cite{Monkhorst:1976,PhysRevB.13.5188} {\bf k}-point |
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sampling of the first Brillouin zone. The relaxed gold slab was then |
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used in numerous single point calculations with CO at various heights |
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(and angles relative to the surface) to allow fitting of the empirical |
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force field. |
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|
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%Hint at future work |
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The fit parameter sets employed in this work are shown in Table 2 and their |
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reproduction of the binding energies are displayed in Table 3. Currently, |
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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 & -0.40~\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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An ideal metal surface displaying a low-energy facet, a (111) face for |
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instance, is unlikely to experience much surface diffusion because of |
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the large energy barrier associated with atoms 'lifting' from the top |
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layer to then be able to explore the surface. Rougher surfaces, those |
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that already contain numerous adatoms, step edges, and kinks, should |
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have concomitantly higher surface diffusion rates. Tao et al. showed |
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that the platinum 557 surface undergoes two separate reconstructions |
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upon CO adsorption. \cite{Tao:2010} The first reconstruction involves a |
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doubling of the step edge height which is accomplished by a doubling |
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of the plateau length. The second reconstruction led to the formation of |
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triangular motifs stretching across the lengthened plateaus. |
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As shown in Figure 2, over a period of approximately 100 ns, the surface |
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has reconstructed from a 557 surface by doubling the step height and |
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step length. Focusing on only the platinum, or gold, atoms that were |
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deemed mobile on the surface, an analysis of the surface diffusion was |
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performed. A particle was considered mobile once it had traveled more |
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than 2~\AA between snapshots. This immediately eliminates all of the |
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bulk metal and greatly limits the number of surface atoms examined. |
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Since diffusion on a surface is strongly affected by overcoming energy |
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barriers, the diffusion parallel to the step edge axis was determined |
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separately from the diffusion perpendicular to the step edge. The results |
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at various coverages on both platinum and gold are shown in Table 4. |
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|
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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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%Evolution of surface |
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\begin{figure}[H] |
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\includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
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\caption{Four snapshots at various times a) 258 ps b) 19 ns c) 31.2 ns d) 86.1 ns. Slight disruption of the surface occurs fairly quickly. However, the doubling of the layers seems to be very dependent on the initial linking of two separate step edges. The focal point in b, appears to be a growth spot for the rest of the double layer.} |
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\caption{Four snapshots of the $\frac{1}{2}$ monolayer system at various times a) 258 ps b) 19 ns c) 31.2 ns and d) 86.1 ns. Slight disruption of the surface occurs fairly quickly. However, the doubling of the layers seems to be very dependent on the initial linking of two separate step edges. The focal point in b, appears to be a growth spot for the rest of the double layer.} |
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\end{figure} |
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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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