--- trunk/COonPt/firstTry.tex 2013/03/19 18:08:24 3881 +++ trunk/COonPt/firstTry.tex 2013/03/19 21:43:34 3884 @@ -20,7 +20,8 @@ \usepackage{graphicx} \usepackage{multirow} \usepackage{multicol} -\usepackage{epstopdf} +\mciteErrorOnUnknownfalse +%\usepackage{epstopdf} \usepackage[version=3]{mhchem} % this is a great package for formatting chemical reactions % \usepackage[square, comma, sort&compress]{natbib} @@ -74,30 +75,18 @@ We examine surface reconstructions of Pt and Au(557) u \begin{abstract} -We examine surface reconstructions of Pt and Au(557) under -various CO coverages using molecular dynamics in order to -explore possible mechanisms for any observed reconstructions -and their dynamics. The metal-CO interactions were parameterized -as part of this work so that an efficient large-scale treatment of -this system could be undertaken. The large difference in binding -strengths of the metal-CO interactions was found to play a significant -role with regards to step-edge stability and adatom diffusion. A -small correlation between coverage and the diffusion constant -was also determined. The energetics of CO adsorbed to the surface -is sufficient to explain the reconstructions observed on the Pt -systems and the lack of reconstruction of the Au systems. - - -The mechanism and dynamics of surface reconstructions of Pt(557) -and Au(557) exposed to various coverages of carbon monoxide (CO) -were investigated using molecular dynamics simulations. Metal-CO -interactions were parameterized from experimental data and plane-wave -Density Functional Theory (DFT) calculations. The large difference in -binding strengths of the Pt-CO and Au-CO interactions was found to play -a significant role in step-edge stability and adatom diffusion constants. -The energetics of CO adsorbed to the surface is sufficient to explain the -step-doubling reconstruction observed on Pt(557) and the lack of such -a reconstruction on the Au(557) surface. + The mechanism and dynamics of surface reconstructions of Pt(557) and + Au(557) exposed to various coverages of carbon monoxide (CO) were + investigated using molecular dynamics simulations. Metal-CO + interactions were parameterized from experimental data and + plane-wave Density Functional Theory (DFT) calculations. The large + difference in binding strengths of the Pt-CO and Au-CO interactions + was found to play a significant role in step-edge stability and + adatom diffusion constants. Various mechanisms for CO-mediated step + wandering and step doubling were investigated on the Pt(557) + surface. We find that the energetics of CO adsorbed to the surface + can explain the step-doubling reconstruction observed on Pt(557) and + the lack of such a reconstruction on the Au(557) surface. \end{abstract} \newpage @@ -400,7 +389,7 @@ source molecular dynamics package, OpenMD.\cite{Ewald, data collection. All of the systems examined had at least 40~ns in the data collection stage, although simulation times for some Pt of the systems exceeded 200~ns. Simulations were carried out using the open -source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} +source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,openmd} @@ -472,7 +461,7 @@ the 50\% Pt system, experienced this reconstruction. %Evolution of surface \begin{figure}[H] -\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation.pdf} +\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation} \caption{The Pt(557) / 50\% CO system at a sequence of times after initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The @@ -531,7 +520,7 @@ diffusion constants are shown in Figure \ref{fig:diff} %Diffusion graph \begin{figure}[H] -\includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1.pdf} +\includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1} \caption{Diffusion constants for mobile surface atoms along directions parallel ($\mathbf{D}_{\parallel}$) and perpendicular ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO @@ -587,180 +576,200 @@ We have shown that a classical potential model is able %Discussion \section{Discussion} -We have shown that a classical potential model is able to model the -initial reconstruction of the Pt(557) surface upon CO adsorption as -shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were -able to observe features of the dynamic processes necessary for -this reconstruction. Here we discuss the features of the model that -give rise to the observed dynamical properties of the (557) reconstruction. +We have shown that a classical potential is able to model the initial +reconstruction of the Pt(557) surface upon CO adsorption, and have +reproduced the double layer structure observed by Tao {\it et + al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be +rapid -- occurring within 100 ns of the initial exposure to CO. Here +we discuss the features of the classical potential that are +contributing to the stability and speed of the Pt(557) reconstruction. \subsection{Diffusion} -The perpendicular diffusion constant -appears to be the most important indicator of double layer -formation. As highlighted in Figure \ref{fig:reconstruct}, the -formation of the double layer did not begin until a nucleation -site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994}, -the inability for edges to cross leads to an effective edge-edge repulsion that -must be overcome to allow step coalescence. -A greater $\textbf{D}_\perp$ implies more step-wandering -and a larger chance for the stochastic meeting of two edges -to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double -layer. This helps explain why the time scale for formation after -the appearance of a nucleation site was rapid, while the initial -appearance of the nucleation site was unpredictable. +The perpendicular diffusion constant appears to be the most important +indicator of double layer formation. As highlighted in Figure +\ref{fig:reconstruct}, the formation of the double layer did not begin +until a nucleation site appeared. Williams {\it et + al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge +repulsion arising from the inability of edge crossing. This repulsion +must be overcome to allow step coalescence. A larger +$\textbf{D}_\perp$ value implies more step-wandering and a larger +chance for the stochastic meeting of two edges to create a nucleation +point. Diffusion parallel to the step-edge can help ``zipper'' up a +nascent double layer. This helps explain the rapid time scale for +double layer completion after the appearance of a nucleation site, while +the initial appearance of the nucleation site was unpredictable. \subsection{Mechanism for restructuring} -Since the Au surface showed no large scale restructuring in any of -our simulations, our discussion will focus on the 50\% Pt-CO system -which did exhibit doubling. A -number of possible mechanisms exist to explain the role of adsorbed -CO in restructuring the Pt surface. Quadrupolar repulsion between -adjacent CO molecules adsorbed on the surface is one possibility. -However, the quadrupole-quadrupole interaction is short-ranged and -is attractive for some orientations. If the CO molecules are ``locked'' in -a specific orientation relative to each other, through atop adsorption for -example, this explanation would gain credence. The calculated energetic repulsion -between two CO molecules located a distance of 2.77~\AA~apart -(nearest-neighbor distance of Pt) and both in a vertical orientation, -is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance -of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away -from a purely vertical orientation also lowers the repulsion. When the -carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is -reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}. -The calculated barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so -repulsion between adjacent CO molecules bound to Pt could increase the surface -diffusion. However, the residence time of CO on Pt suggests that these -molecules are extremely mobile, with diffusion constants 40 to 2500 times -larger than surface Pt atoms. This mobility suggests that the CO molecules jump -between different Pt atoms throughout the simulation, but will stay bound for -significant periods of time. +Since the Au surface showed no large scale restructuring in any of our +simulations, our discussion will focus on the 50\% Pt-CO system which +did exhibit doubling. A number of possible mechanisms exist to explain +the role of adsorbed CO in restructuring the Pt surface. Quadrupolar +repulsion between adjacent CO molecules adsorbed on the surface is one +possibility. However, the quadrupole-quadrupole interaction is +short-ranged and is attractive for some orientations. If the CO +molecules are ``locked'' in a vertical orientation, through atop +adsorption for example, this explanation would gain credence. The +calculated energetic repulsion between two CO molecules located a +distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both +in a vertical orientation, is 8.62 kcal/mol. Moving the CO to the +second nearest-neighbor distance of 4.8~\AA~drops the repulsion to +nearly 0. Allowing the CO to rotate away from a purely vertical +orientation also lowers the repulsion. When the carbons are locked at +a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the +angle between the 2 CO is $\sim$24\textsuperscript{o}. The calculated +barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so +repulsion between adjacent CO molecules bound to Pt could increase the +surface diffusion. However, the residence time of CO on Pt suggests +that the CO molecules are extremely mobile, with diffusion constants 40 +to 2500 times larger than surface Pt atoms. This mobility suggests +that the CO molecules jump between different Pt atoms throughout the +simulation, but can stay bound for significant periods of time. -A different interpretation of the above mechanism, taking into account the large -mobility of the CO, looks at how instantaneous and short-lived configurations of -CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge -breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach -an edge atom is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures -\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases -(e), (g), and (h), the barrier can be lowered to $\sim$23~kcal/mole. In these instances, -it becomes quite energetically favorable to roughen the edge by introducing a small -separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in -simulations with significant CO populations. The roughening is present to a lesser extent -on lower coverage surfaces and even on the bare surfaces, although in these cases it is likely -due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism -of step-edge breakup suggested by these energy curves is one of the most difficult -processes, a complete break-away from the step-edge in one unbroken movement. -Easier multistep mechanisms likely exist where an adatom moves laterally on the surface -after being ejected so it ends up alongside the ledge. This provides the atom with 5 nearest -neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher -than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO -quadrupolar repulsion is still playing a primary role, but for its importance in roughening -the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not -born out by their mobility data. The requirement for a large density of CO on the surface -for some of the more favorable suggested configurations in Figure \ref{fig:SketchGraphic} -correspond well with the increased mobility seen on higher coverage surfaces. +A different interpretation of the above mechanism which takes the +large mobility of the CO into account, would be in the destabilization +of Pt-Pt interactions due to bound CO. Destabilizing Pt-Pt bonds at +the edges could lead to increased step-edge breakup and diffusion. On +the bare Pt(557) surface the barrier to completely detach an edge atom +is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures +\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain +configurations, cases (e), (g), and (h), the barrier can be lowered to +$\sim$23~kcal/mol by the presence of bound CO molecules. In these +instances, it becomes energetically favorable to roughen the edge by +introducing a small separation of 0.5 to 1.0~\AA. This roughening +becomes immediately obvious in simulations with significant CO +populations. The roughening is present to a lesser extent on surfaces +with lower CO coverage (and even on the bare surfaces), although in +these cases it is likely due to random fluctuations that squeeze out +step-edge atoms. Step-edge breakup by continuous single-atom +translations (as suggested by these energy curves) is probably a +worst-case scenario. Multistep mechanisms in which an adatom moves +laterally on the surface after being ejected would be more +energetically favorable. This would leave the adatom alongside the +ledge, providing it with 5 nearest neighbors. While fewer than the 7 +neighbors it had as part of the step-edge, it keeps more Pt neighbors +than the 3 an isolated adatom would have on the terrace. In this +proposed mechanism, the CO quadrupolar repulsion still plays a role in +the initial roughening of the step-edge, but not in any long-term +bonds with individual Pt atoms. Higher CO coverages create more +opportunities for the crowded CO configurations shown in Figure +\ref{fig:SketchGraphic}, and this is likely to cause an increased +propensity for step-edge breakup. %Sketch graphic of different configurations \begin{figure}[H] -\includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf} -\caption{The dark grey atoms refer to the upper ledge, while the white atoms are -the lower terrace. The blue highlighted atoms had a CO in a vertical atop position -upon them. These are a sampling of the configurations examined to gain a more -complete understanding of the effects CO has on surface diffusion and edge breakup. -Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.} +\includegraphics[width=\linewidth]{COpaths} +\caption{Configurations used to investigate the mechanism of step-edge + breakup on Pt(557). In each case, the central (starred) atom is + pulled directly across the surface away from the step edge. The Pt + atoms on the upper terrace are colored dark grey, while those on the + lower terrace are in white. In each of these configurations, some + number of the atoms (highlighted in blue) had a CO molecule bound in + a vertical atop position. The energies of these configurations as a + function of central atom displacement are displayed in Figure + \ref{fig:SketchEnergies}.} \label{fig:SketchGraphic} \end{figure} %energy graph corresponding to sketch graphic \begin{figure}[H] -\includegraphics[width=\linewidth]{Portrait_SeparationComparison.pdf} -\caption{The energy curves directly correspond to the labeled model -surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative -to their initial configuration so the energy of a and h do not have the -same zero value. As is seen, certain arrangements of CO can lower -the energetic barrier that must be overcome to create an adatom. -However, it is the highest coverages where these higher-energy -configurations of CO will be more likely. } +\includegraphics[width=\linewidth]{Portrait_SeparationComparison} +\caption{Energies for displacing a single edge atom perpendicular to + the step edge as a function of atomic displacement. Each of the + energy curves corresponds to one of the labeled configurations in + Figure \ref{fig:SketchGraphic}, and are referenced to the + unperturbed step-edge. Certain arrangements of bound CO (notably + configurations g and h) can lower the energetic barrier for creating + an adatom relative to the bare surface (configuration a).} \label{fig:SketchEnergies} \end{figure} -While configurations of CO on the surface are able to increase diffusion, -this does not immediately provide an explanation for the formation of double -layers. If adatoms were constrained to their terrace then doubling would be -much less likely to occur. Nucleation sites could still potentially form, but there -would not be enough atoms to finish the doubling. For a non-simulated metal surface, where the -step lengths can be assumed to be infinite relative to atomic sizes, local doubling would be possible, but in -our simulations with our periodic treatment of the system, the system is not large enough to experience this effect. -Thus, there must be a mechanism that explains how adatoms are able to move -amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate -where an adatom along the step-edge with an adsorbed CO ``burrows'' into the -edge displacing an atom onto the higher terrace. This mechanism was chosen -because of similar events that were observed during the simulations. The barrier -heights we obtained are only approximations because we constrained the movement -of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s -are provide a strong energetic support for this modeled lifting mechanism. When CO is not present and -this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown -in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol. -While the barrier height is comparable for both cases, there is nearly a 20~kcal/mol -difference in energies and makes the process energetically favorable. +While configurations of CO on the surface are able to increase +diffusion and the likelihood of edge wandering, this does not provide +a complete explanation for the formation of double layers. If adatoms +were constrained to their original terraces then doubling could not +occur. A mechanism for vertical displacement of adatoms at the +step-edge is required to explain the doubling. +We have discovered one possible mechanism for a CO-mediated vertical +displacement of Pt atoms at the step edge. Figure \ref{fig:lambda} +shows four points along a reaction coordinate in which a CO-bound +adatom along the step-edge ``burrows'' into the edge and displaces the +original edge atom onto the higher terrace. A number of events similar +to this mechanism were observed during the simulations. We predict an +energetic barrier of 20~kcal/mol for this process (in which the +displaced edge atom follows a curvilinear path into an adjacent 3-fold +hollow site). The barrier heights we obtain for this reaction +coordinate are approximate because the exact path is unknown, but the +calculated energy barriers would be easily accessible at operating +conditions. Additionally, this mechanism is exothermic, with a final +energy 15~kcal/mol below the original $\lambda = 0$ configuration. +When CO is not present and this reaction coordinate is followed, the +process is endothermic by 3~kcal/mol. The difference in the relative +energies for the $\lambda=0$ and $\lambda=1$ case when CO is present +provides strong support for CO-mediated Pt-Pt interactions giving rise +to the doubling reconstruction. + %lambda progression of Pt -> shoving its way into the step \begin{figure}[H] -\includegraphics[width=\linewidth]{EPS_rxnCoord.pdf} -\caption{ Various points along a reaction coordinate are displayed in the figure. -The mechanism of edge traversal is examined in the presence of CO. The approximate -barrier for the displayed process is 20~kcal/mol. However, the $\Delta E$ of this process -is -15~kcal/mol making it an energetically favorable process.} +\includegraphics[width=\linewidth]{EPS_rxnCoord} +\caption{Points along a possible reaction coordinate for CO-mediated + edge doubling. Here, a CO-bound adatom burrows into an established + step edge and displaces an edge atom onto the upper terrace along a + curvilinear path. The approximate barrier for the process is + 20~kcal/mol, and the complete process is exothermic by 15~kcal/mol + in the presence of CO, but is endothermic by 3~kcal/mol without.} \label{fig:lambda} \end{figure} -The mechanism for doubling on this surface appears to require the cooperation of at least -these two described processes. For complete doubling of a layer to occur there must -be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from -that terrace they must either rise up on the ledge above them or drop to the ledge below -them. The presence of CO helps with the energetics of both of these situations. There must be sufficient -breakage of the step-edge to increase the concentration of adatoms on the surface and -these adatoms must then undergo the burrowing highlighted above or some comparable -mechanism to traverse the step-edge. Over time, these mechanisms working in concert -lead to the formation of a double layer. +The mechanism for doubling on the Pt(557) surface appears to require +the cooperation of at least two distinct processes. For complete +doubling of a layer to occur there must be a breakup of one +terrace. These atoms must then ``disappear'' from that terrace, either +by travelling to the terraces above of below their original levels. +The presence of CO helps explain mechanisms for both of these +situations. There must be sufficient breakage of the step-edge to +increase the concentration of adatoms on the surface and these adatoms +must then undergo the burrowing highlighted above (or a comparable +mechanism) to create the double layer. With sufficient time, these +mechanisms working in concert lead to the formation of a double layer. \subsection{CO Removal and double layer stability} -Once a double layer had formed on the 50\%~Pt system it -remained for the rest of the simulation time with minimal -movement. There were configurations that showed small -wells or peaks forming, but typically within a few nanoseconds -the feature would smooth away. Within our simulation time, -the formation of the double layer was irreversible and a double -layer was never observed to split back into two single layer -step-edges while CO was present. To further gauge the effect -CO had on this system, additional simulations were run starting -from a late configuration of the 50\%~Pt system that had formed -double layers. These simulations then had their CO removed. -The double layer breaks rapidly in these simulations, already -showing a well-defined splitting after 100~ps. Configurations of -this system are shown in Figure \ref{fig:breaking}. The coloring -of the top and bottom layers helps to exhibit how much mixing -the edges experience as they split. These systems were only -examined briefly, 10~ns, and within that time despite the initial -rapid splitting, the edges only moved another few \AA~apart. -It is possible with longer simulation times that the -(557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010} +Once a double layer had formed on the 50\%~Pt system, it remained for +the rest of the simulation time with minimal movement. Random +fluctuations that involved small clusters or divots were observed, but +these features typically healed within a few nanoseconds. Within our +simulations, the formation of the double layer appeared to be +irreversible and a double layer was never observed to split back into +two single layer step-edges while CO was present. +To further gauge the effect CO has on this surface, additional +simulations were run starting from a late configuration of the 50\%~Pt +system that had already formed double layers. These simulations then +had their CO forcibly removed. The double layer broke apart rapidly +in these simulations, showing a well-defined edge-splitting after +100~ps. Configurations of this system are shown in Figure +\ref{fig:breaking}. The coloring of the top and bottom layers helps to +exhibit how much mixing the edges experience as they split. These +systems were only examined for 10~ns, and within that time despite the +initial rapid splitting, the edges only moved another few +\AA~apart. It is possible that with longer simulation times, the (557) +surface recovery observed by Tao {\it et al}.\cite{Tao:2010} could +also be recovered. - %breaking of the double layer upon removal of CO \begin{figure}[H] -\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking.pdf} -\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO -helped maintain the stability of the double layer and its microfaceting of the double layer -into a (111) configuration. This microfacet immediately reverts to the original (100) step -edge which is a hallmark of the (557) surface. The separation is not a simple sliding apart, rather -there is a mixing of the lower and upper atoms at the edge.} +\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking} +\caption{Dynamics of an established (111) double step after removal of + the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the removal + of CO. The presence of the CO helped maintain the stability of the + double step. Nearly immediately after the CO is removed, the step + edge reforms in a (100) configuration, which is also the step type + seen on clean (557) surfaces. The step separation involves + significant mixing of the lower and upper atoms at the edge.} \label{fig:breaking} \end{figure} - - %Peaks! %\begin{figure}[H] %\includegraphics[width=\linewidth]{doublePeaks_noCO.png} @@ -774,7 +783,7 @@ there is a mixing of the lower and upper atoms at the %Don't think I need this %clean surface... %\begin{figure}[H] -%\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} +%\includegraphics[width=\linewidth]{557_300K_cleanPDF} %\caption{} %\end{figure} @@ -782,18 +791,19 @@ The strength of the Pt-CO binding interaction as well \section{Conclusion} -The strength of the Pt-CO binding interaction as well as the large -quadrupolar repulsion between CO molecules are sufficient to -explain the observed increase in surface mobility and the resultant -reconstructions at the highest simulated coverage. The weaker -Au-CO interaction results in lower diffusion constants, less step-wandering, -and a lack of the double layer reconstruction. An in-depth examination -of the energetics shows the important role CO plays in increasing -step-breakup and in facilitating edge traversal which are both -necessary for double layer formation. +The strength and directionality of the Pt-CO binding interaction, as +well as the large quadrupolar repulsion between atop-bound CO +molecules, help to explain the observed increase in surface mobility +of Pt(557) and the resultant reconstruction into a double-layer +configuration at the highest simulated CO-coverages. The weaker Au-CO +interaction results in significantly lower adataom diffusion +constants, less step-wandering, and a lack of the double layer +reconstruction on the Au(557) surface. +An in-depth examination of the energetics shows the important role CO +plays in increasing step-breakup and in facilitating edge traversal +which are both necessary for double layer formation. - %Things I am not ready to remove yet %Table of Diffusion Constants @@ -817,10 +827,12 @@ Support for this project was provided by the National % \end{table} \begin{acknowledgement} -Support for this project was provided by the National Science -Foundation under grant CHE-0848243 and by the Center for Sustainable -Energy at Notre Dame (cSEND). Computational time was provided by the -Center for Research Computing (CRC) at the University of Notre Dame. + We gratefully acknowledge conversations with Dr. William + F. Schneider and Dr. Feng Tao. Support for this project was + provided by the National Science Foundation under grant CHE-0848243 + and by the Center for Sustainable Energy at Notre Dame + (cSEND). Computational time was provided by the Center for Research + Computing (CRC) at the University of Notre Dame. \end{acknowledgement} \newpage \bibliography{firstTryBibliography} @@ -828,6 +840,7 @@ Center for Research Computing (CRC) at the University \begin{tocentry} %\includegraphics[height=3.5cm]{timelapse} +\includegraphics[height=3.5cm]{TOC_doubleLayer.pdf} \end{tocentry} \end{document}