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\begin{document} |
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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} |
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\author{Patrick W. McIntyre} |
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\author{J. Daniel Gezelter} |
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\email{gezelter@nd.edu} |
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\affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\ |
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Department of Chemistry and Biochemistry\\ University of Notre |
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Dame\\ Notre Dame, Indiana 46556} |
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\keywords{} |
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\begin{document} |
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%% |
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%Introduction |
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% Experimental observations |
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%Summary |
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%% |
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%Title |
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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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|
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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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|
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%Date |
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\date{Mar 5, 2013} |
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%authors |
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|
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% make the title |
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\maketitle |
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\begin{doublespace} |
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\begin{abstract} |
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We examine surface reconstructions of Pt and Au(557) under |
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various CO coverages using molecular dynamics in order to |
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reversible restructuring under exposure to moderate pressures of |
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carbon monoxide.\cite{Tao:2010} |
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|
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This work is an attempt to understand the mechanism and timescale for |
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surface restructuring by using molecular simulations. Since the dynamics |
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This work is an investigation into the mechanism and timescale for |
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surface restructuring using molecular simulations. Since the dynamics |
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of the process are of particular interest, we employ classical force |
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fields that represent a compromise between chemical accuracy and the |
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computational efficiency necessary to simulate the process of interest. |
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to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010} |
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The Au(557) surface, because of a weaker interaction with CO, is seen as less |
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likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000} |
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and Piccolo et al.\cite{Piccolo:2004} have both observed CO induced |
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reconstruction of a Au(111) surface. Peters et al. saw a relaxing of the |
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22 x $\sqrt{3}$ cell. They argued that a very small number of Au atoms |
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would become adatoms, limiting the stress of this reconstruction while |
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allowing the rest of the row to relax and approach the ideal (111) |
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configuration. They did not see the ``herringbone'' pattern being greatly |
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affected by this relaxation. Piccolo et al. on the other hand, did see a |
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disruption of the ``herringbone'' pattern as CO was adsorbed to the |
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and Piccolo et al.\cite{Piccolo:2004} have both observed CO-induced |
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reconstruction of a Au(111) surface. Peters et al. saw a relaxation to the |
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22 x $\sqrt{3}$ cell. They argued that only a few Au atoms |
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become adatoms, limiting the stress of this reconstruction while |
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allowing the rest to relax and approach the ideal (111) |
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configuration. They did not see the usual herringbone pattern being greatly |
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affected by this relaxation. Piccolo et al. on the other hand, did see a |
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disruption of the herringbone pattern as CO was adsorbed to the |
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surface. Both groups suggested that the preference CO shows for |
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low-coordinated Au particles was the primary driving force for these reconstructions. |
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low-coordinated Au atoms was the primary driving force for the reconstruction. |
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|
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dynamics.\cite{Shibata:2002hh} One of EAM's strengths |
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is its sensitivity to small changes in structure. This arises |
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from the original parameterization, where the interactions |
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up to the third nearest-neighbor were taken into account.\cite{Voter95a} |
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up to the third nearest neighbor were taken into account.\cite{Voter95a} |
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Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88} |
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which only parameterized up to the nearest-neighbor |
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which is only parameterized up to the nearest-neighbor |
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interactions, EAM is a suitable choice for systems where |
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the bulk properties are of secondary importance to low-index |
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surface structures. Additionally, the similarity of EAMs functional |
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treatment of the embedding energy to standard density functional |
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theory (DFT) approaches gives EAM, and conclusions derived, a firm theoretical footing. |
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theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier. |
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\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
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We used a model first proposed by Karplus and Straub to study |
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the photodissociation of CO from myoglobin because it reproduces |
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the quadrupole moment well.\cite{Straub} The Straub and |
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Karplus model, treats CO as a rigid three site molecule with a massless M |
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Karplus model treats CO as a rigid three site molecule with a massless M |
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site at the molecular center of mass. The geometry and interaction |
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parameters are reproduced in Table~\ref{tab:CO}. The effective |
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dipole moment, calculated from the assigned charges, is still |
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performed until the energy difference between subsequent steps |
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was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
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were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
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zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was |
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zone.\cite{Monkhorst:1976} The relaxed gold slab was |
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then used in numerous single point calculations with CO at various |
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heights (and angles relative to the surface) to allow fitting of the |
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empirical force field. |
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(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
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and polarization are neglected in this model, although these effects are likely to |
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affect binding energies and binding site preferences, and will be addressed in |
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a future work.\cite{Deshlahra:2012,StreitzMintmire:1994} |
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future work. |
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|
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%Table of Parameters |
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%Pt Parameter Set 9 |
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\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
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(Ref. \protect\cite{Kelemen:1979}) \\ |
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& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
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\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPD_Gold}) \\ |
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\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPDGold}) \\ |
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\hline |
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\end{tabular} |
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\label{tab:co_energies} |
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\end{table} |
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|
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\subsection{Pt(557) and Au(557) metal interfaces} |
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Our Pt system has dimensions of 18~x~24~x~9 in a box of size |
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54.482~x~50.046~x~120.88~\AA while our Au system has |
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dimensions of 18~x~24~x~8 in a box of size 57.4~x~51.9285~x~100~\AA. |
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Our Pt system is an orthorhombic periodic box of dimensions |
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54.482~x~50.046~x~120.88~\AA~while our Au system has |
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dimensions of 57.4~x~51.9285~x~100~\AA. |
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The systems are arranged in a FCC crystal that have been cut |
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along the (557) plane so that they are periodic in the {\it x} and |
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{\it y} directions, and have been oriented to expose two aligned |
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(557) cuts along the extended {\it z}-axis. Simulations of the |
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bare metal interfaces at temperatures ranging from 300~K to |
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1200~K were performed to observe the relative |
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1200~K were performed to confirm the relative |
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stability of the surfaces without a CO overlayer. |
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The different bulk melting temperatures (1337~K for Au |
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and 2045~K for Pt) suggest that any possible reconstruction should happen at |
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The different bulk melting temperatures (1345~$\pm$~10~K for Au\cite{Au:melting} |
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and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
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different temperatures for the two metals. The bare Au and Pt surfaces were |
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initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
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respectively for 100 ps. The two surfaces were relatively stable at these |
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mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
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that was initially placed in the vacuum region. Upon full adsorption, |
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these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
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coverage. Higher coverages resulted in CO double layer formation, which introduces artifacts that are not relevant to (557) reconstruction. |
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coverage. Higher coverages resulted in the formation of a double layer of CO, |
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which introduces artifacts that are not relevant to (557) reconstruction. |
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Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
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the Au surfaces often had a significant CO population in the gas |
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phase. These systems were allowed to reach thermal equilibrium (over |
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5 ns) before being run in the microcanonical (NVE) ensemble for |
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data collection. All of the systems examined had at least 40 ns in the |
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data collection stage, although simulation times for some of the |
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systems exceeded 200~ns. Simulations were run using the open |
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5~ns) before being run in the microcanonical (NVE) ensemble for |
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data collection. All of the systems examined had at least 40~ns in the |
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data collection stage, although simulation times for some Pt of the |
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systems exceeded 200~ns. Simulations were carried out using the open |
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source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} |
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|
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% Just results, leave discussion for discussion section |
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% structure |
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% Pt: step wandering, double layers, no triangular motifs |
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% Au: step wandering, no double layers |
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% dynamics |
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% diffusion |
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% time scale, formation, breakage |
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|
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|
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% RESULTS |
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% |
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\section{Results} |
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\subsection{Structural remodeling} |
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Tao et al. have shown experimentally that the Pt(557) surface |
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undergoes two separate reconstructions upon CO |
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adsorption.\cite{Tao:2010} The first involves a doubling of |
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the step height and plateau length. Similar behavior has been |
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seen to occur on numerous surfaces at varying conditions: Ni(977), Si(111). |
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\cite{Williams:1994,Williams:1991,Pearl} Of the two systems |
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we examined, the Pt system showed a larger amount of |
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reconstruction when compared to the Au system. The amount |
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of reconstruction is correlated to the amount of CO |
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The surfaces of both systems, upon dosage of CO, began |
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to undergo extensive remodeling that was not observed in the bare |
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systems. The bare metal surfaces |
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experienced minor roughening of the step-edge because |
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of the elevated temperatures, but the |
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(557) lattice was well-maintained throughout the simulation |
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time. The Au systems were limited to greater amounts of |
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roughening, i.e. breakup of the step-edge, and some step |
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wandering. The lower coverage Pt systems experienced |
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similar restructuring but to a greater extent when |
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compared to the Au systems. The 50\% coverage |
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Pt system was unique among our simulations in that it |
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formed numerous double layers through step coalescence, |
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similar to results reported by Tao et al.\cite{Tao:2010} |
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|
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|
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\subsubsection{Step wandering} |
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The 0\% coverage surfaces for both metals showed minimal |
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movement at their respective run temperatures. As the CO |
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coverage increased however, the mobility of the surface, |
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described through adatom diffusion and step-edge wandering, |
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also increased. Except for the 50\% Pt system, the step-edges |
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did not coalesce in any of the other simulations, instead |
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preferring to keep nearly the same distance between steps |
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as in the original (557) lattice, $\sim$13\AA for Pt and $\sim$14\AA for Au. |
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Previous work by Williams et al.\cite{Williams:1991, Williams:1994} |
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highlights the repulsion that exists between step-edges even |
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when no direct interactions are present in the system. This |
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repulsion arises because step-edge crossing is not allowed |
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which constrains the entropy. This entropic repulsion does |
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not completely define the interactions between steps, which |
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is why some surfaces will undergo step coalescence, where |
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additional attractive interactions can overcome the repulsion.\cite{Williams:1991} |
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The presence and concentration of adsorbates, as shown in |
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this work, can affect these step interactions, potentially leading |
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to a new surface structure as the thermodynamic minimum. |
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|
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\subsubsection{Double layers} |
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Tao et al.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
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undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} |
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The first involves a doubling of the step height and plateau length. |
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Similar behavior has been seen on numerous surfaces |
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at varying conditions: Ni(977), Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
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Of the two systems we examined, the Pt system showed a greater |
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propensity for reconstruction when compared to the Au system |
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because of the larger surface mobility and extent of step wandering. |
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The amount of reconstruction is strongly correlated to the amount of CO |
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adsorbed upon the surface. This appears to be related to the |
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effect that adsorbate coverage has on edge breakup and on the surface |
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diffusion of metal adatoms. While both systems displayed step-edge |
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wandering, only the Pt surface underwent the doubling seen by |
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Tao et al. within the time scales studied here. |
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Only the 50\% coverage Pt system exhibited |
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a complete doubling in the time scales we |
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were able to monitor. Over longer periods (150~ns) two more double layers formed on this interface. |
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Although double layer formation did not occur in the other Pt systems, they show |
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more lateral movement of the step-edges |
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compared to their Au counterparts. The 50\% Pt system is highlighted |
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in Figure \ref{fig:reconstruct} at various times along the simulation |
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showing the evolution of a step-edge. |
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effect that adsorbate coverage has on edge breakup and on the |
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surface diffusion of metal adatoms. While both systems displayed |
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step-edge wandering, only the 50\% Pt surface underwent the |
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doubling seen by Tao et al.\cite{Tao:2010} within the time scales studied here. |
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Over longer periods, (150~ns) two more double layers formed |
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on this interface. Although double layer formation did not occur |
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in the other Pt systems, they show more step-wandering and |
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general roughening compared to their Au counterparts. The |
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50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
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various times along the simulation showing the evolution of a double layer step-edge. |
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|
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The second reconstruction on the Pt(557) surface observed by |
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Tao involved the formation of triangular clusters that stretched |
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across the plateau between two step-edges. Neither system, within |
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the 40~ns time scale, experienced this reconstruction. |
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the 40~ns time scale or the extended simulation time of 150~ns for |
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the 50\% Pt system, experienced this reconstruction. |
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|
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%Evolution of surface |
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\begin{figure}[H] |
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\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
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\caption{The Pt(557) / 50\% CO system at a sequence of times after |
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initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
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(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
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doubling of the layers appears only after two adjacent step-edges |
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touch. The circled spot in (b) nucleated the growth of the double |
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step observed in the later configurations.} |
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\label{fig:reconstruct} |
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\end{figure} |
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|
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\subsection{Dynamics} |
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Previous atomistic simulations of stepped surfaces were largely |
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concerned with the energetics and structures at different conditions |
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Previous atomistic simulations of stepped surfaces dealt largely |
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with the energetics and structures at different conditions |
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\cite{Williams:1991,Williams:1994}. Consequently, the most common |
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technique has been Monte Carlo. Monte Carlo gives an efficient |
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technique utilized to date has been Monte Carlo sampling. Monte Carlo approaches give an efficient |
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sampling of the equilibrium thermodynamic landscape at the expense |
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of ignoring the dynamics of the system. Previous work by Pearl and |
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Sibener\cite{Pearl}, using STM, has been able to show the coalescing |
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of ignoring the dynamics of the system. Previous experimental work by Pearl and |
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Sibener\cite{Pearl}, using STM, has been able to capture the coalescing |
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of steps on Ni(977). The time scale of the image acquisition, |
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$\sim$70 s/image provides an upper bound for the time required for |
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the doubling to occur. In this section we give data on dynamic and |
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$\sim$70~s/image provides an upper bound for the time required for |
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the doubling to occur. By utilizing Molecular Dynamics we were able to probe the dynamics of these reconstructions and in this section we give data on dynamic and |
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transport properties, e.g. diffusion, layer formation time, etc. |
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|
| 489 |
|
|
| 490 |
|
\subsubsection{Transport of surface metal atoms} |
| 491 |
|
%forcedSystems/stepSeparation |
| 492 |
|
The movement or wandering of a step-edge is a cooperative effect |
| 493 |
< |
arising from the individual movements, primarily through surface |
| 494 |
< |
diffusion, of the atoms making up the steps An ideal metal surface |
| 442 |
< |
displaying a low index facet, (111) or (100) is unlikely to experience |
| 493 |
> |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
| 494 |
> |
displaying a low index facet, (111) or (100), is unlikely to experience |
| 495 |
|
much surface diffusion because of the large energetic barrier that must |
| 496 |
< |
be overcome to lift an atom out of the surface. The presence of step-edges |
| 497 |
< |
on higher-index surfaces provide a source for mobile metal atoms. |
| 496 |
> |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
| 497 |
> |
on higher-index facets provides a lower energy source for mobile metal atoms. |
| 498 |
|
Breaking away from the step-edge on a clean surface still imposes an |
| 499 |
< |
energetic penalty around $\sim$~40 kcal/mol, but is much less than lifting |
| 499 |
> |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
| 500 |
|
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 501 |
|
The penalty lowers significantly when CO is present in sufficient quantities |
| 502 |
< |
on the surface. For certain distributions of CO, the penalty can be as low as |
| 502 |
> |
on the surface. For certain distributions of CO, see Figures \ref{fig:sketchGraphic} and \ref{fig:sketchEnergies}, the penalty can fall to as low as |
| 503 |
|
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 504 |
< |
diffusion is negligible ( \textless~4 kcal/mol) and these adatoms are well |
| 505 |
< |
able to explore the terrace before rejoining either the original step-edge or becoming a part |
| 506 |
< |
of a different edge. Atoms traversing separate terraces is a more difficult |
| 507 |
< |
process, but can be overcome through a joining and lifting stage which is |
| 508 |
< |
examined in the discussion section. By tracking the mobility of individual |
| 504 |
> |
diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are then |
| 505 |
> |
able to explore the terrace before rejoining either their original step-edge or |
| 506 |
> |
becoming a part of a different edge. It is a difficult process for an atom |
| 507 |
> |
to traverse to a separate terrace although the presence of CO can lower the |
| 508 |
> |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
| 509 |
|
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 510 |
|
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 511 |
|
observation of the mobile metal atoms showed that they were typically in |
| 512 |
|
equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. |
| 513 |
|
At times, their motion was concerted and two or more adatoms would be |
| 514 |
< |
observed moving together across the surfaces. The primary challenge in |
| 463 |
< |
quantifying the overall surface mobility was in defining ``mobile" vs. ``static" atoms. |
| 514 |
> |
observed moving together across the surfaces. |
| 515 |
|
|
| 516 |
< |
A particle was considered mobile once it had traveled more than 2~\AA~ |
| 516 |
> |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 517 |
|
between saved configurations of the system (typically 10-100 ps). An atom that was |
| 518 |
< |
truly mobile would typically travel much greater distances than this, but the 2~\AA~ cutoff |
| 519 |
< |
was to prevent swamping the diffusion data with the in-place vibrational |
| 520 |
< |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 518 |
> |
truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 519 |
> |
was used to prevent swamping the diffusion data with the in-place vibrational |
| 520 |
> |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 521 |
|
local structures and in this work, the presence of single and double layer |
| 522 |
< |
step-edges causes the diffusion parallel to the step-edges to be different |
| 523 |
< |
from the diffusion perpendicular to these edges. Parallel and perpendicular |
| 524 |
< |
diffusion constants are shown in Figure \ref{fig:diff}. |
| 474 |
< |
|
| 475 |
< |
\subsubsection{Double layer formation dynamics} |
| 476 |
< |
The increased amounts of diffusion on Pt at the higher CO coverages plays a primary role in the formation of the double layers observed on Pt. However, this is not a complete explanation as seen by the 33\% Pt system which has higher diffusion constants but did not show any signs of undergoing the doubling. This difference will be explored more fully in the discussion. On the 50\% Pt system, three separate layers were formed over the extended run time of this system. Previous experimental work has given some insight into the upper bounds of the time required for step coalescing.\cite{Williams:1991,Pearl} In this system, as seen in Figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into the simulation. Within 12 ns, nearly half of the step has formed the double layer and by 86 ns, the complete layer has been smoothed. The double layer could be considered ``complete" by 37 ns but is a bit rough or wavy. From the appearance of the first node to the first observed double layer, ignoring roughening, the process took $\sim$20 ns. Another $\sim$40 ns was necessary for the layer to completely straighten. The other two layers in this simulation form over a period of 22 ns and 42 ns respectively. Comparing this to the upper bounds of the image scan, it is likely that aspects of this reconstruction occur very quickly. A possible explanation for this rapid reconstruction is the elevated temperatures our systems were run at. It is likely that the process would take longer at lower temperatures and is an area of exploration for future work. |
| 477 |
< |
|
| 478 |
< |
%Evolution of surface |
| 479 |
< |
\begin{figure}[H] |
| 480 |
< |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 481 |
< |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 482 |
< |
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
| 483 |
< |
(d) 86.1 ns. Disruption of the (557) step-edges occurs quickly. The |
| 484 |
< |
doubling of the layers appears only after two adjacent step-edges |
| 485 |
< |
touch. The circled spot in (b) nucleated the growth of the double |
| 486 |
< |
step observed in the later configurations.} |
| 487 |
< |
\label{fig:reconstruct} |
| 488 |
< |
\end{figure} |
| 522 |
> |
step-edges causes the diffusion parallel to the step-edges to be larger than |
| 523 |
> |
the diffusion perpendicular to these edges. Parallel and perpendicular |
| 524 |
> |
diffusion constants are shown in Figure \ref{fig:diff}. |
| 525 |
|
|
| 526 |
+ |
%Diffusion graph |
| 527 |
|
\begin{figure}[H] |
| 528 |
< |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
| 528 |
> |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf} |
| 529 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
| 530 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 531 |
|
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 532 |
|
surface coverage. Diffusion parallel to the step-edge is higher |
| 533 |
|
than that perpendicular to the edge because of the lower energy |
| 534 |
|
barrier associated with traversing along the edge as compared to |
| 535 |
< |
completely breaking away. Additionally, the observed |
| 536 |
< |
maximum and subsequent decrease for the Pt system suggests that the |
| 537 |
< |
CO self-interactions are playing a significant role with regards to |
| 538 |
< |
movement of the Pt atoms around and across the surface. } |
| 535 |
> |
completely breaking away. The two reported diffusion constants for |
| 536 |
> |
the 50\% Pt system arise from different sample sets. The lower values |
| 537 |
> |
correspond to the same 40~ns amount that all of the other systems were |
| 538 |
> |
examined at, while the larger values correspond to a 20~ns period } |
| 539 |
|
\label{fig:diff} |
| 540 |
|
\end{figure} |
| 541 |
|
|
| 542 |
+ |
The lack of a definite trend in the Au diffusion data in Figure \ref{fig:diff} is likely due |
| 543 |
+ |
to the weaker bonding between Au and CO. This leads to a lower observed |
| 544 |
+ |
coverage ({\it x}-axis) when compared to dosage amount, which |
| 545 |
+ |
then further limits the effect the CO can have on surface diffusion. The correlation |
| 546 |
+ |
between coverage and Pt diffusion rates conversely shows a |
| 547 |
+ |
definite trend marred by the highest coverage surface. Two |
| 548 |
+ |
explanations arise for this drop. First, upon a visual inspection of |
| 549 |
+ |
the system, after a double layer has been formed, it maintains its |
| 550 |
+ |
stability strongly and is no longer a good source for adatoms and so |
| 551 |
+ |
atoms that had been tracked for mobility data have now been buried. By |
| 552 |
+ |
performing the same diffusion calculation but on a shorter run time |
| 553 |
+ |
(20~ns), only including data before the formation of the double layer, we obtain |
| 554 |
+ |
the larger values for both $\mathbf{D}_{\parallel}$ and $\mathbf{D}_{\perp}$ at the 50\% coverage. |
| 555 |
+ |
This places the parallel diffusion constant more closely in line with the |
| 556 |
+ |
expected trend, while the perpendicular diffusion constant does not |
| 557 |
+ |
drop as far. A secondary explanation arising from our analysis of the |
| 558 |
+ |
mechanism of double layer formation focuses on the effect that CO on the |
| 559 |
+ |
surface has with respect to overcoming surface diffusion of Pt. If the |
| 560 |
+ |
coverage is too sparse, the Pt engages in minimal interactions and |
| 561 |
+ |
thus minimal diffusion. As coverage increases, there are more favorable |
| 562 |
+ |
arrangements of CO on the surface allowing the formation of a path, |
| 563 |
+ |
a minimum energy trajectory, for the adatom to explore the surface. |
| 564 |
+ |
As the CO is constantly moving on the surface, this path is constantly |
| 565 |
+ |
changing. If the coverage becomes too great, the paths could |
| 566 |
+ |
potentially be clogged leading to a decrease in diffusion despite |
| 567 |
+ |
their being more adatoms and step-wandering. |
| 568 |
|
|
| 569 |
|
|
| 570 |
|
|
| 571 |
+ |
\subsubsection{Dynamics of double layer formation} |
| 572 |
+ |
The increased diffusion on Pt at the higher |
| 573 |
+ |
CO coverages plays a primary role in double layer formation. However, this is not |
| 574 |
+ |
a complete explanation -- the 33\%~Pt system |
| 575 |
+ |
has higher diffusion constants but did not show |
| 576 |
+ |
any signs of edge doubling in the observed run time. On the |
| 577 |
+ |
50\%~Pt system, one layer formed within the first 40~ns of simulation time, while two more were formed as the system was run for an additional |
| 578 |
+ |
110~ns (150~ns total). Previous experimental |
| 579 |
+ |
work gives insight into the upper bounds of the |
| 580 |
+ |
time required for step coalescence.\cite{Williams:1991,Pearl} |
| 581 |
+ |
In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 582 |
+ |
appearance of a double layer, appears at 19~ns |
| 583 |
+ |
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
| 584 |
+ |
formed the double layer and by 86~ns, the complete layer |
| 585 |
+ |
has been flattened out. The double layer could be considered |
| 586 |
+ |
``complete" by 37~ns but remains a bit rough. From the |
| 587 |
+ |
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
| 588 |
+ |
$\sim$40~ns was necessary for the layer to completely straighten. |
| 589 |
+ |
The other two layers in this simulation formed over periods of |
| 590 |
+ |
22~ns and 42~ns respectively. Comparing this to the upper |
| 591 |
+ |
bounds of the image scan, it is likely that most aspects of this |
| 592 |
+ |
reconstruction occur very rapidly. A possible explanation |
| 593 |
+ |
for this rapid reconstruction is the elevated temperatures |
| 594 |
+ |
under which our systems were simulated. It is probable that the process would |
| 595 |
+ |
take longer at lower temperatures. |
| 596 |
+ |
|
| 597 |
+ |
|
| 598 |
+ |
|
| 599 |
+ |
|
| 600 |
+ |
|
| 601 |
+ |
|
| 602 |
+ |
%Sketch graphic of different configurations |
| 603 |
+ |
\begin{figure}[H] |
| 604 |
+ |
\includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf} |
| 605 |
+ |
\caption{The dark grey atoms refer to the upper ledge, while the white atoms are |
| 606 |
+ |
the lower terrace. The blue highlighted atoms had a CO in a vertical atop position |
| 607 |
+ |
upon them. These are a sampling of the configurations examined to gain a more |
| 608 |
+ |
complete understanding of the effects CO has on surface diffusion and edge breakup. |
| 609 |
+ |
Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.} |
| 610 |
+ |
\label{fig:SketchGraphic} |
| 611 |
+ |
\end{figure} |
| 612 |
+ |
|
| 613 |
+ |
%energy graph corresponding to sketch graphic |
| 614 |
+ |
\begin{figure}[H] |
| 615 |
+ |
\includegraphics[width=\linewidth]{stepSeparationComparison.pdf} |
| 616 |
+ |
\caption{The energy curves directly correspond to the labeled model |
| 617 |
+ |
surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative |
| 618 |
+ |
to their initial configuration so the energy of a and h do not have the |
| 619 |
+ |
same zero value. As is seen, certain arrangements of CO can lower |
| 620 |
+ |
the energetic barrier that must be overcome to create an adatom. |
| 621 |
+ |
However, it is the highest coverages where these higher-energy |
| 622 |
+ |
configurations of CO will be more likely. } |
| 623 |
+ |
\label{fig:SketchEnergies} |
| 624 |
+ |
\end{figure} |
| 625 |
+ |
|
| 626 |
|
%Discussion |
| 627 |
|
\section{Discussion} |
| 628 |
< |
In this paper we have shown that we were able to accurately model the initial reconstruction of the |
| 628 |
> |
We have shown that the classical potential models are able to model the initial reconstruction of the |
| 629 |
|
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 630 |
< |
were able to observe the dynamic processes necessary for this reconstruction. |
| 630 |
> |
were able to observe features of the dynamic processes necessary for this reconstruction. |
| 631 |
|
|
| 632 |
+ |
\subsection{Diffusion} |
| 633 |
+ |
As shown in Figure \ref{fig:diff}, for the Pt systems, there |
| 634 |
+ |
is a strong trend toward higher diffusion constants as |
| 635 |
+ |
surface coverage of CO increases. The drop for the 50\% |
| 636 |
+ |
case being explained as double layer formation already |
| 637 |
+ |
beginning to occur in the analyzed 40~ns, which lowered |
| 638 |
+ |
the calculated diffusion rates. Between the parallel and |
| 639 |
+ |
perpendicular rates, the perpendicular diffusion constant |
| 640 |
+ |
appears to be the most important indicator of double layer |
| 641 |
+ |
formation. As highlighted in Figure \ref{fig:reconstruct}, the |
| 642 |
+ |
formation of the double layer did not begin until a nucleation |
| 643 |
+ |
site appeared. And as mentioned by Williams et al.\cite{Williams:1991, Williams:1994}, |
| 644 |
+ |
the inability for edges to cross leads to an effective repulsion. |
| 645 |
+ |
This repulsion must be overcome to allow step coalescence. |
| 646 |
+ |
A greater $\textbf{D}_\perp$ implies more step-wandering |
| 647 |
+ |
and a larger chance for the stochastic meeting of two edges |
| 648 |
+ |
to form the nucleation point. Upon that appearance, parallel |
| 649 |
+ |
diffusion along the step-edge can help ``zipper'' up the double |
| 650 |
+ |
layer. This helps explain why the time scale for formation after |
| 651 |
+ |
the appearance of a nucleation site was rapid, while the initial |
| 652 |
+ |
appearance of said site was unpredictable. |
| 653 |
+ |
|
| 654 |
|
\subsection{Mechanism for restructuring} |
| 655 |
< |
Since the Au surface showed no large scale restructuring throughout |
| 656 |
< |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 657 |
< |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 658 |
< |
Comparing the results from this simulation to those reported previously by |
| 659 |
< |
Tao et al.\cite{Tao:2010} the similarities in the Pt-CO system are quite |
| 660 |
< |
strong. As shown in Figure \ref{fig:reconstruct}, the simulated Pt |
| 661 |
< |
system exposed to a large dosage of CO will restructure by doubling the terrace |
| 662 |
< |
widths and step heights. The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a time and as such is a fairly stochastic event. |
| 663 |
< |
Looking at individual configurations of the system, the adatoms either |
| 664 |
< |
break away from the step-edge and stay on the lower terrace or they lift |
| 665 |
< |
up onto the higher terrace. Once ``free'', they will diffuse on the terrace |
| 666 |
< |
until reaching another step-edge or rejoining their original edge. |
| 667 |
< |
This combination of growth and decay of the step-edges is in a state of |
| 668 |
< |
dynamic equilibrium. However, once two previously separated edges |
| 669 |
< |
meet as shown in Figure 1.B, this meeting point tends to act as a focus |
| 670 |
< |
or growth point for the rest of the edge to meet up, akin to that of a zipper. |
| 531 |
< |
From the handful of cases where a double layer was formed during the |
| 532 |
< |
simulation, measuring from the initial appearance of a growth point, the |
| 533 |
< |
double layer tends to be fully formed within $\sim$35 ns. |
| 655 |
> |
Since the Au surface showed no large scale restructuring throughout |
| 656 |
> |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 657 |
> |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 658 |
> |
Similarities of our results to those reported previously by Tao et al.\cite{Tao:2010} |
| 659 |
> |
are quite strong. The simulated Pt system exposed to a large dosage |
| 660 |
> |
of CO readily restructures by doubling the terrace widths and step heights. |
| 661 |
> |
The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a |
| 662 |
> |
time, but is rapid on experimental timescales. The adatoms either break |
| 663 |
> |
away from the step-edge and stay on the lower terrace or they lift up onto |
| 664 |
> |
a higher terrace. Once ``free'', they diffuse on the terrace until reaching |
| 665 |
> |
another step-edge or rejoining their original edge. This combination of |
| 666 |
> |
growth and decay of the step-edges is in a state of dynamic equilibrium. |
| 667 |
> |
However, once two previously separated edges meet as shown in Figure 1.B, |
| 668 |
> |
this nucleates the rest of the edge to meet up, forming a double layer. |
| 669 |
> |
From simulations which exhibit a double layer, the time delay from the |
| 670 |
> |
initial appearance of a nucleation point to a fully formed double layer is $\sim$35~ns. |
| 671 |
|
|
| 672 |
|
A number of possible mechanisms exist to explain the role of adsorbed |
| 673 |
|
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 674 |
< |
CO molecules adsorbed on the surface is one likely possibility. However, |
| 674 |
> |
CO molecules adsorbed on the surface is one possibility. However, |
| 675 |
|
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 676 |
|
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 677 |
|
relative to each other, through atop adsorption for example, this explanation |
| 678 |
< |
gains some weight. The energetic repulsion between two CO located a |
| 679 |
< |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in |
| 680 |
< |
a vertical orientation is 8.62 kcal/mol. Moving the CO apart to the second |
| 678 |
> |
gains some credence. The energetic repulsion between two CO located a |
| 679 |
> |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in |
| 680 |
> |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 681 |
|
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 682 |
< |
nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation |
| 683 |
< |
also quickly drops the repulsion, a minimum of 6.2 kcal/mol is reached at $\sim$24 degrees between the 2 CO when the carbons are locked at a distance of 2.77 \AA apart. |
| 684 |
< |
As mentioned above, the energy barrier for surface diffusion |
| 685 |
< |
of a Pt adatom is only 4 kcal/mol. So this repulsion between CO can help |
| 686 |
< |
increase the surface diffusion. However, the residence time of CO on Pt was |
| 687 |
< |
examined and while the majority of the CO is on or near the surface throughout |
| 688 |
< |
the run, it is extremely mobile. This mobility suggests that the CO are more |
| 689 |
< |
likely to shift their positions without necessarily dragging the Pt along with them. |
| 682 |
> |
nearly 0 kcal/mol. Allowing the CO to rotate away from a purely vertical orientation |
| 683 |
> |
also lowers the repulsion. A minimum of 6.2 kcal/mol is reached at when the |
| 684 |
> |
angle between the 2 CO is $\sim$24\textsuperscript{o}, when the carbons are |
| 685 |
> |
locked at a distance of 2.77 \AA apart. As mentioned above, the energy barrier |
| 686 |
> |
for surface diffusion of a Pt adatom is only 4 kcal/mol. So this repulsion between |
| 687 |
> |
neighboring CO molecules can increase the surface diffusion. However, the |
| 688 |
> |
residence time of CO on Pt was examined and while the majority of the CO is |
| 689 |
> |
on or near the surface throughout the run, the molecules are extremely mobile, |
| 690 |
> |
with diffusion constants 40 to 2500 times larger, depending on coverage. This |
| 691 |
> |
mobility suggests that the CO are more likely to shift their positions without |
| 692 |
> |
necessarily the Pt along with them. |
| 693 |
|
|
| 694 |
|
Another possible and more likely mechanism for the restructuring is in the |
| 695 |
|
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 696 |
< |
Pt atoms. This would then have the effect of increasing surface mobility |
| 557 |
< |
of these atoms. To test this hypothesis, numerous configurations of |
| 696 |
> |
Pt atoms. To test this hypothesis, numerous configurations of |
| 697 |
|
CO in varying quantities were arranged on the higher and lower plateaus |
| 698 |
< |
around a step on a otherwise clean Pt(557) surface. One representative |
| 699 |
< |
configuration is displayed in Figure \ref{fig:lambda}. Single or concerted movement |
| 700 |
< |
of Pt atoms was then examined to determine possible barriers. Because |
| 701 |
< |
the movement was forced along a pre-defined reaction coordinate that may differ |
| 702 |
< |
from the true minimum of this path, only the beginning and ending energies |
| 703 |
< |
are displayed in Table \ref{tab:energies}. These values suggest that the presence of CO at suitable |
| 704 |
< |
locations can lead to lowered barriers for Pt breaking apart from the step-edge. |
| 705 |
< |
Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the |
| 706 |
< |
burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral |
| 707 |
< |
in terms of energetics. |
| 698 |
> |
around a step on a otherwise clean Pt(557) surface. A few sample |
| 699 |
> |
configurations are displayed in Figure \ref{fig:lambdaTable}, with |
| 700 |
> |
energies at various positions along the path displayed in Table |
| 701 |
> |
\ref{tab:rxcoord}. Certain configurations of CO, cases B and D for |
| 702 |
> |
example, can have quite strong energetic reasons for breaking |
| 703 |
> |
away from the step-edge. Although the packing of these configurations |
| 704 |
> |
is unlikely until CO coverage has reached a high enough value. |
| 705 |
> |
These examples are showing the most difficult cases, immediate |
| 706 |
> |
adatom formation through breakage away from the step-edge, which |
| 707 |
> |
is why their energies at large distances are relatively high. There are |
| 708 |
> |
mechanistic paths where an edge atom could get shifted to onto the |
| 709 |
> |
step-edge to form a small peak before fully breaking away. And again, |
| 710 |
> |
once the adatom is formed, the barrier for diffusion on the surface is |
| 711 |
> |
negligible. These sample configurations help explain CO's effect on |
| 712 |
> |
general surface mobility and step wandering, but they are lacking in |
| 713 |
> |
providing a mechanism for the formation of double layers. One possible |
| 714 |
> |
mechanism is elucidated in Figure \ref{fig:lambda}, where a burrowing |
| 715 |
> |
and lifting process of an adatom and step-edge atom respectively is |
| 716 |
> |
examined. The system, without CO present, is nearly energetically |
| 717 |
> |
neutral, whereas with CO present there is a $\sim$ 15 kcal/mol drop |
| 718 |
> |
in the energy of the system. |
| 719 |
|
|
| 720 |
|
%lambda progression of Pt -> shoving its way into the step |
| 721 |
|
\begin{figure}[H] |
| 722 |
< |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO.png} |
| 722 |
> |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
| 723 |
|
\caption{A model system of the Pt(557) surface was used as the framework |
| 724 |
|
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 725 |
|
placements, and rotations of CO were examined as they affect Pt movement. |
| 726 |
< |
The coordinate displayed in this Figure was a representative run. As shown |
| 577 |
< |
in Table \ref{tab:rxcoord}, relative to the energy of the system at 0\%, there |
| 726 |
> |
The coordinate displayed in this Figure was a representative run. relative to the energy of the system at 0\%, there |
| 727 |
|
is a slight decrease upon insertion of the Pt atom into the step-edge along |
| 728 |
|
with the resultant lifting of the other Pt atom when CO is present at certain positions.} |
| 729 |
|
\label{fig:lambda} |
| 731 |
|
|
| 732 |
|
|
| 733 |
|
|
| 585 |
– |
\subsection{Diffusion} |
| 586 |
– |
As shown in the results section, the diffusion parallel to the step-edge tends to be |
| 587 |
– |
much larger than that perpendicular to the step-edge, likely because of the dynamic |
| 588 |
– |
equilibrium that is established between the step-edge and adatom interface. The coverage |
| 589 |
– |
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}. |
| 590 |
– |
The |
| 591 |
– |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
| 592 |
– |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
| 593 |
– |
appears, parallel diffusion, along the now slightly angled step-edge, will allow for |
| 594 |
– |
a faster formation of the double layer than if the entire process were dependent on |
| 595 |
– |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
| 596 |
– |
more likely a growth point is to be formed. |
| 597 |
– |
\\ |
| 734 |
|
|
| 735 |
|
|
| 736 |
|
%breaking of the double layer upon removal of CO |
| 737 |
|
\begin{figure}[H] |
| 738 |
|
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 739 |
< |
%: |
| 604 |
< |
\caption{(A) 0 ps, (B) 100 ps, (C) 1 ns, after the removal of CO. The presence of the CO |
| 739 |
> |
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
| 740 |
|
helped maintain the stability of the double layer and upon removal the two layers break |
| 741 |
|
and begin separating. The separation is not a simple pulling apart however, rather |
| 742 |
|
there is a mixing of the lower and upper atoms at the edge.} |
| 747 |
|
|
| 748 |
|
|
| 749 |
|
%Peaks! |
| 750 |
< |
\begin{figure}[H] |
| 751 |
< |
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 752 |
< |
\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 753 |
< |
of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 754 |
< |
aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 755 |
< |
\label{fig:peaks} |
| 756 |
< |
\end{figure} |
| 750 |
> |
%\begin{figure}[H] |
| 751 |
> |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 752 |
> |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 753 |
> |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 754 |
> |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 755 |
> |
%\label{fig:peaks} |
| 756 |
> |
%\end{figure} |
| 757 |
|
|
| 758 |
|
|
| 759 |
|
%Don't think I need this |
| 791 |
|
% \end{tabular} |
| 792 |
|
% \end{table} |
| 793 |
|
|
| 794 |
< |
\section{Acknowledgments} |
| 794 |
> |
\begin{acknowledgement} |
| 795 |
|
Support for this project was provided by the National Science |
| 796 |
|
Foundation under grant CHE-0848243 and by the Center for Sustainable |
| 797 |
|
Energy at Notre Dame (cSEND). Computational time was provided by the |
| 798 |
|
Center for Research Computing (CRC) at the University of Notre Dame. |
| 799 |
< |
|
| 799 |
> |
\end{acknowledgement} |
| 800 |
|
\newpage |
| 801 |
|
\bibliography{firstTryBibliography} |
| 802 |
< |
\end{doublespace} |
| 802 |
> |
%\end{doublespace} |
| 803 |
> |
|
| 804 |
> |
\begin{tocentry} |
| 805 |
> |
%\includegraphics[height=3.5cm]{timelapse} |
| 806 |
> |
\end{tocentry} |
| 807 |
> |
|
| 808 |
|
\end{document} |
