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\documentclass[a4paper,12pt]{article} |
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\usepackage{setspace} |
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\usepackage{float} |
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\usepackage{cite} |
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\usepackage[pdftex]{graphicx} |
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\usepackage[font=small,labelfont=bf]{caption} |
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%% |
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%Introduction |
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% Experimental observations |
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% Previous work on Pt, CO, etc. |
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% |
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%Simulation Methodology |
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% FF (fits and parameters) |
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% MD (setup, equilibration, collection) |
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% |
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% Analysis of trajectories!!! |
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%Discussion |
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% CO preferences for specific locales |
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% CO-CO interactions |
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% Differences between Au & Pt |
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% Causes of 2_layer reordering in Pt |
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%Summary |
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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 under a CO Atmosphere} |
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%Date |
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\date{Dec 15, 2012} |
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%authors |
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\author{Joseph R.~Michalka, Patrick W. McIntyre, \& J.~Daniel Gezelter} |
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% make the title |
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\maketitle |
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\doublespacing |
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\section{Introduction} |
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% Importance: catalytically active metals are important |
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% Sub: Knowledge of how their surface structure affects their ability to catalytically facilitate certain reactions is growing, but is more reactionary than predictive |
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% Sub: Designing catalysis is the future, and will play an important role in numerous processes (ones that are currently seen to be impractical, or at least inefficient) |
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% Theory can explore temperatures and pressures which are difficult to work with in experiments |
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% Sub: Also, easier to observe what is going on and provide reasons and explanations |
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% |
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jmichalk |
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High-index surfaces of catalytically active metals are an important area of exploration because they are typically more reactive than an ideal surface of the same metal. The greater number of low-coordinated surface atoms is likely responsible for this increased reactivity \cite{}. Additionally, the activity and specificity of many metals towards certain chemical processes has been shown to strongly depend on the structure of the surface \cite{}. Prior work has also shown that reaction conditions, such as high pressures and high temperatures are able to cause reconstructions of the metallic surface, either through changing the displayed surface facets or by changing the number and types of high-index sites available for reactions \cite{doi:10.1126/science.1197461,doi:10.1021/nn3015322, doi:10.1021/jp302379x}. A greater understanding of these high-index surfaces and the restructuring processes they undergo is needed as a prerequisite for more intelligent catalyst design. While current experimental work has started exploring systems at \emph{in situ} conditions, for a long time such experiments were limited to ideal surfaces in high vacuum. New techniques, such as ambient pressure XPS (AP-XPS) \cite{}, high-pressure XPS (HP-XPS) \cite{}, high-pressure STM \cite{}, environmental transmission electron microscopy (E-TEM) \cite{} and many others, are providing clearer pictures of the processes that are occurring on metal surfaces under these conditions. Nevertheless, all of these techniques still have limitations, especially in observing what is occurring at an atomic level. Theoretical models and simulations in combination with experiment have proven their worth in explaining the underlying reasons for some of these reconstructions \cite{}. |
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\\ |
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By examining two different metal-CO systems the effect that the metal and the metal-CO interaction plays can be elucidated. Our first system is composed of Platinum and CO and has been the subject of many experimental and theoretical studies primarily because of Platinum's strong reactivity toward CO oxidation. The focus has primarily been on adsorption energies, preferred adsorption sites, and catalytic activities. The second system we examined is composed of Gold and CO. The Gold-CO interaction is much weaker than the Platinum-CO interaction and it seems likely that this difference in attraction would lead to differences in any potential surface reconstructions. |
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%It has also been a good test for new quantum methods because of the difficulty with modeling the preference CO has for the atop binding site \cite{doi:10.1021/jp002302t}. |
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%Now that dynamic surface events are known to play a role in many catalytic systems, additional research is being done to more closely examine many systems. Recent work by Tao et al. \cite{doi:10.1126/science.1182122} shows that a high-index platinum surface undergoes surface reconstructions when exposed to a small amount of CO, $\sim$~1 torr. Unexpectedly, the reconstruction was metastable and reverted upon removal of the CO. Work by McCarthy et al. \cite{doi:10.1021/jp302379x} examined temperature programmed desorption's of CO from various Platinum samples and saw that species which had large amounts of low-coordinated surface atoms, highly sputtered surfaces or small nano particles, developed a higher temperature desorption peak, suggesting that binding of CO to the Platinum surface is strongly dependent on local geometry. |
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\section{Simulation Methods} |
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Our model systems are composed of approximately 4000 metal atoms cut along the 557 plane. This cut creates a stepped surface of 6x(111) surface plateaus separated by a single (100) atomic step height. The large number of low-coordination atoms along the step edges provide a suitable model for industrial catalysts which tend to have a prevalence of lower CN, i.e. more reactive, sites. Drawing from experimental conclusions, the reconstructions seen for the Pt 557 surface involve doubling of the step height and the formation of triangular motifs along the steps \cite{doi:10.1126/science.1182122}. To properly observe these changes, our system size needs to be greater than the periodic phenomena we are examining. The large size and the long time scales needed precluded us from using expensive quantum approaches. Thus, a forcefield describing the Metal-Metal, CO-CO, and CO-Metal interactions was parameterized. |
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%Metal |
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\subsection{Metal} |
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Recent metallic forcefields, inspired by density-functional theory, including EAM\cite{doi:10.1103/PhysRevB.29.6443, doi:10.1103/PhysRevB.33.7983} and QSC\cite{} have become very popular for modeling novel metallic systems. What makes these forcefields more suitable for metals than their pair-wise predecessors is that they work with the total electron density of the system in a manner akin to DFT. The energy contributed by a single atom is a function of the total background electron density at the point where the atom is to be embedded. The density at any given point is well-approximated by a linear superposition of the electron density as contributed by all the other atoms in the system. This description of the embedding energy allows this method to more accurately treat surfaces, alloys, and other non-bulk systems. The function describing the energy as related to the density is parameterized for each element, rather than by solving the Kohn-Sham equations which is what allows this method to be used for large systems. The embedding energy is completely enclosed within the functional $F_i[\rho_{h,i}]$ which is dependent on the host density $\rho_{h}$ at atom $i$. The density at $i$ is the sum of the density as generated by the rest of the metal. The $\phi_{ij}$ term is a purely repulsive pair-pair interaction parameterized from effective charge repulsions. |
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%Can I increase the \sum size, not sure how... |
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\begin{equation} |
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E_{tot} = \sum_i F_i[\rho_{h,i}] + \frac{1}{2}\sum_i\sum_{j(\ne i)} \phi_{ij}(R_{ij}) |
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\end{equation} |
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\begin{equation} |
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\rho_{h,i} = \sum_{j (\ne i)} \rho_j^a(R_{ij}) |
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\end{equation} |
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The EAM functional forms are used to model the Au and Pt self-interactions in all of our simulations. |
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%CO |
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\subsection{CO} |
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Our CO model was obtained from work done by Karplus and Straub\cite{}. In their description of the biological importance of CO they developed an accurate quadrupolar model of CO which we make use of in this work. It has been suggested that the strong electrostatic repulsion that arises from this linear quadrupole may play an important role in the restructuring of metal surfaces to which CO is bound\cite{}. |
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%CO Table |
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\begin{table}[H] |
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\caption{$\sigma$, $\epsilon$ and charges for CO self-interactions\cite{}. Distances are in \AA~, energies are in kcal/mol, and charges are in $e$.} |
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\centering |
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\begin{tabular}{| c | ccc |} |
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\hline |
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\multicolumn{4}{|c|}{\textbf{Self-Interactions}}\\ |
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\hline |
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& $\sigma$ & $\epsilon$ & q\\ |
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\hline |
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\textbf{C} & 0.0262 & 3.83 & -0.75 \\ |
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\textbf{O} & 0.1591 & 3.12 & -0.85 \\ |
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\textbf{M} & - & - & 1.6 \\ |
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\hline |
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\end{tabular} |
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\end{table} |
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%Cross |
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\subsection{Cross-Interactions} |
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To finish the forcefield, the cross-interactions between the metals and the CO needed to be parameterized. Previous attempts at parameterization have used two different functional forms to model these interactions\cite{}. A LJ model was fit for the Metal-Carbon interaction and a Morse potential was parameterized for the Metal-Oxygen interaction. The parameter sets chosen, as shown in Table 2, did a suitable job at reproducing experimental adsorption energies as shown in Table 3, but more importantly, they were able to capture the binding site preference. The Pt-CO parameters show a slight preference for the atop binding site which matches the experimental observations. |
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%\subsection{System} |
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%Once equilibration was reached, the systems were exposed to various sub-monolayer coverage of CO: $0, \frac{1}{10}, \frac{1}{4}, \frac{1}{3},\frac{1}{2}$. The CO was started many \AA~above the surface with random velocity and rotational velocity vectors sampling from a Gaussian distribution centered on the temperature of the equilibrated metal block. Full adsorption occurred over the period of approximately 10 ps for Pt, while the binding energy between Au and CO is smaller and led to an incomplete adsorption. The metal-metal interactions were treated using the Embedded Atom Method while the Pt-CO and Au-CO interactions were fit to experimental data and quantum calculations. The raised temperature helped shorten the length of the simulations by allowing the activation barrier of reconstruction to be more easily overcome. A few runs at lower temperatures showed the very beginnings of reconstructions, but their simulation lengths limited their usefulness. |
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%Table of Parameters |
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%Pt Parameter Set 9 |
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%Au Parameter Set 35 |
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\begin{table}[H] |
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\caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol} |
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\centering |
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\begin{tabular}{| c | cc | c | ccc |} |
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\hline |
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\multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\ |
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\hline |
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& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\ |
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\hline |
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\textbf{Pt-C} & 1.3 & 15 & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\ |
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\textbf{Au-C} & 1.9 & 6.5 & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\ |
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\hline |
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\end{tabular} |
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\end{table} |
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%Table of energies |
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\begin{table}[H] |
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\caption{Adsorption energies in eV} |
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\centering |
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\begin{tabular}{| c | cc |} |
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\hline |
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& Calc. & Exp. \\ |
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\hline |
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\textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen}-- -1.9~\cite{Yeo} \\ |
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\textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\ |
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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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%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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\centering |
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\begin{tabular}{| c | ccc | ccc | 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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\hline |
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&\multicolumn{3}{c|}{\textbf{Mobile}}&\multicolumn{3}{c|}{\textbf{Surface Atoms}} & \\ |
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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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\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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\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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\end{figure} |
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%Peaks! |
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\includegraphics[scale=0.25]{doublePeaks_noCO.png} |
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\section{Conclusion} |
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\end{document} |
