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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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\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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\maketitle |
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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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%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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%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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& 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} \\ |
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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 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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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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%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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