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Revision 3870 by jmichalk, Fri Mar 8 22:06:22 2013 UTC

# Line 1 | Line 1
1   \documentclass[11pt]{article}
2   \usepackage{amsmath}
3   \usepackage{amssymb}
4 + \usepackage{times}
5 + \usepackage{mathptm}
6   \usepackage{setspace}
7   \usepackage{endfloat}
8   \usepackage{caption}
# Line 10 | Line 12
12   %\usepackage{booktabs}
13   %\usepackage{bibentry}
14   %\usepackage{mathrsfs}
13 – %\usepackage[ref]{overcite}
15   \usepackage[square, comma, sort&compress]{natbib}
16   \usepackage{url}
17   \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
# Line 18 | Line 19
19   9.0in \textwidth 6.5in \brokenpenalty=10000
20  
21   % double space list of tables and figures
22 < \AtBeginDelayedFloats{\renewcommand{\baselinestretch}{1.66}}
22 > %\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}}
23   \setlength{\abovecaptionskip}{20 pt}
24   \setlength{\belowcaptionskip}{30 pt}
25  
26 < %\renewcommand\citemid{\ } % no comma in optional reference note
26 < \bibpunct{[}{]}{,}{n}{}{;}
26 > \bibpunct{}{}{,}{s}{}{;}
27   \bibliographystyle{achemso}
28  
29   \begin{document}
# Line 48 | Line 48
48   %%
49  
50   %Title
51 < \title{Investigation of the Pt and Au 557 Surface Reconstructions
52 <  under a CO Atmosphere}
53 < \author{Joseph R. Michalka, Patrick W. MacIntyre and J. Daniel
51 > \title{Molecular Dynamics simulations of the surface reconstructions
52 >  of Pt(557) and Au(557) under exposure to CO}
53 >
54 > \author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel
55   Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\
56   Department of Chemistry and Biochemistry,\\
57   University of Notre Dame\\
58   Notre Dame, Indiana 46556}
59 +
60   %Date
61 < \date{Dec 15,  2012}
61 > \date{Mar 5, 2013}
62 >
63   %authors
64  
65   % make the title
# Line 65 | Line 68 | Notre Dame, Indiana 46556}
68   \begin{doublespace}
69  
70   \begin{abstract}
71 + We examine surface reconstructions of Pt and Au(557) under
72 + various CO coverages using molecular dynamics in order to
73 + explore possible mechanisms for any observed reconstructions
74 + and their dynamics. The metal-CO interactions were parameterized
75 + as part of this work so that an efficient large-scale treatment of
76 + this system could be undertaken. The large difference in binding
77 + strengths of the metal-CO interactions was found to play a significant
78 + role with regards to step-edge stability and adatom diffusion. A
79 + small correlation between coverage and the diffusion constant
80 + was also determined. The energetics of CO adsorbed to the surface
81 + is sufficient to explain the reconstructions observed on the Pt
82 + systems and the lack  of reconstruction of the Au systems.
83  
84   \end{abstract}
85  
# Line 79 | Line 94 | Industrial catalysts usually consist of small particle
94   %       Sub: Also, easier to observe what is going on and provide reasons and explanations
95   %
96  
97 < Industrial catalysts usually consist of small particles exposing
98 < different atomic terminations that exhibit a high concentration of
99 < step, kink sites, and vacancies at the edges of the facets.  These
85 < sites are thought to be the locations of catalytic
97 > Industrial catalysts usually consist of small particles that exhibit a
98 > high concentration of steps, kink sites, and vacancies at the edges of
99 > the facets.  These sites are thought to be the locations of catalytic
100   activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now
101 < significant evidence to demonstrate that solid surfaces are often
102 < structurally, compositionally, and chemically {\it modified} by
103 < reactants under operating conditions.\cite{Tao2008,Tao:2010,Tao2011}
104 < The coupling between surface oxidation state and catalytic activity
105 < for CO oxidation on Pt, for instance, is widely
106 < documented.\cite{Ertl08,Hendriksen:2002} Despite the well-documented
107 < role of these effects on reactivity, the ability to capture or predict
108 < them in atomistic models is currently somewhat limited.  While these
109 < effects are perhaps unsurprising on the highly disperse, multi-faceted
110 < nanoscale particles that characterize industrial catalysts, they are
111 < manifest even on ordered, well-defined surfaces. The Pt(557) surface,
112 < for example, exhibits substantial and reversible restructuring under
113 < exposure to moderate pressures of carbon monoxide.\cite{Tao:2010}
101 > significant evidence that solid surfaces are often structurally,
102 > compositionally, and chemically modified by reactants under operating
103 > conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between
104 > surface oxidation states and catalytic activity for CO oxidation on
105 > Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002}
106 > Despite the well-documented role of these effects on reactivity, the
107 > ability to capture or predict them in atomistic models is somewhat
108 > limited.  While these effects are perhaps unsurprising on the highly
109 > disperse, multi-faceted nanoscale particles that characterize
110 > industrial catalysts, they are manifest even on ordered, well-defined
111 > surfaces. The Pt(557) surface, for example, exhibits substantial and
112 > reversible restructuring under exposure to moderate pressures of
113 > carbon monoxide.\cite{Tao:2010}
114  
115 < This work is part of an ongoing effort to understand the causes,
116 < mechanisms and timescales for surface restructuring using molecular
117 < simulation methods.  Since the dynamics of the process is of
118 < particular interest, we utilize classical molecular dynamic methods
119 < with force fields that represent a compromise between chemical
120 < accuracy and the computational efficiency necessary to observe the
121 < process of interest.
115 > This work is an attempt to understand the mechanism and timescale for
116 > surface restructuring by using molecular simulations.  Since the dynamics
117 > of the process are of particular interest, we employ classical force
118 > fields that represent a compromise between chemical accuracy and the
119 > computational efficiency necessary to simulate the process of interest.
120 > Since restructuring typically occurs as a result of specific interactions of the
121 > catalyst with adsorbates, in this work, two metal systems exposed
122 > to carbon monoxide were examined. The Pt(557) surface has already been shown
123 > to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010}
124 > The Au(557) surface, because of a weaker interaction with CO, is seen as less
125 > likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000}
126 > and Piccolo et al.\cite{Piccolo:2004} have both observed CO induced
127 > reconstruction of a Au(111) surface. Peters et al. saw a relaxing of the
128 > 22 x $\sqrt{3}$ cell. They argued that a very small number of Au atoms
129 > would become adatoms, limiting the stress of this reconstruction while
130 > allowing the rest of the row to relax and approach the ideal (111)
131 > configuration. They did not see the ``herringbone'' pattern being greatly
132 > affected by this relaxation. Piccolo et al. on the other hand, did see a
133 > disruption of the ``herringbone'' pattern as CO was adsorbed to the
134 > surface. Both groups suggested that the preference CO shows for
135 > low-coordinated Au particles was the primary driving force for these reconstructions.
136  
137 < Since restructuring occurs as a result of specific interactions of the catalyst
138 < with adsorbates, two metals systems exposed to the same adsorbate, CO,
111 < were examined in this work. The Pt(557) surface has already been shown to
112 < reconstruct under certain conditions. The Au(557) surface, because of gold's
113 < weaker interaction with CO, is less likely to undergo such a large reconstruction.
137 >
138 >
139   %Platinum molecular dynamics
140   %gold molecular dynamics
141  
117 –
118 –
119 –
120 –
121 –
142   \section{Simulation Methods}
143 < The challenge in modeling any solid/gas interface problem is the
143 > The challenge in modeling any solid/gas interface is the
144   development of a sufficiently general yet computationally tractable
145   model of the chemical interactions between the surface atoms and
146   adsorbates.  Since the interfaces involved are quite large (10$^3$ -
# Line 133 | Line 153 | Coulomb potential.  For this work, we have been using
153   typically not well represented in terms of classical pairwise
154   interactions in the same way that bonds in a molecular material are,
155   nor are they captured by simple non-directional interactions like the
156 < Coulomb potential.  For this work, we have been using classical
157 < molecular dynamics with potential energy surfaces that are
158 < specifically tuned for transition metals.  In particular, we use the
159 < EAM potential for Au-Au and Pt-Pt interactions, while modeling the CO
160 < using a model developed by Straub and Karplus for studying
161 < photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and Pt-CO
162 < cross interactions were parameterized as part of this work.
156 > Coulomb potential.  For this work, we have used classical molecular
157 > dynamics with potential energy surfaces that are specifically tuned
158 > for transition metals.  In particular, we used the EAM potential for
159 > Au-Au and Pt-Pt interactions\cite{EAM}. The CO was modeled using a rigid
160 > three-site model developed by Straub and Karplus for studying
161 > photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and
162 > Pt-CO cross interactions were parameterized as part of this work.
163    
164   \subsection{Metal-metal interactions}
165 < Many of the potentials used for classical simulation of transition
166 < metals are based on a non-pairwise additive functional of the local
167 < electron density. The embedded atom method (EAM) is perhaps the best
168 < known of these
165 > Many of the potentials used for modeling transition metals are based
166 > on a non-pairwise additive functional of the local electron
167 > density. The embedded atom method (EAM) is perhaps the best known of
168 > these
169   methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98}
170   but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and
171   the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler
172 < parameter sets. The glue model of Ercolessi {\it et al.} is among the
172 > parameter sets. The glue model of Ercolessi et al. is among the
173   fastest of these density functional approaches.\cite{Ercolessi88} In
174   all of these models, atoms are conceptualized as a positively charged
175   core with a radially-decaying valence electron distribution. To
176   calculate the energy for embedding the core at a particular location,
177   the electron density due to the valence electrons at all of the other
178 < atomic sites is computed at atom $i$'s location,
178 > atomic sites is computed at atom $i$'s location,
179   \begin{equation*}
180   \bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
181   \end{equation*}
# Line 167 | Line 187 | $\phi_{ij}(r_{ij})$ is an pairwise term that is meant
187   V_i =  F[ \bar{\rho}_i ]  + \sum_{j \neq i} \phi_{ij}(r_{ij})
188   \end{equation*}
189   where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and
190 < $\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the
191 < overlap of the two positively charged cores.  
190 > $\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the
191 > repulsive overlap of the two positively charged cores.  
192  
193 < The {\it modified} embedded atom method (MEAM) adds angular terms to
194 < the electron density functions and an angular screening factor to the
195 < pairwise interaction between two
196 < atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
197 < MEAM has become widely used to simulate systems in which angular
198 < interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
199 < metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
200 < MEAM presents significant additional computational costs, however.
193 > % The {\it modified} embedded atom method (MEAM) adds angular terms to
194 > % the electron density functions and an angular screening factor to the
195 > % pairwise interaction between two
196 > % atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
197 > % MEAM has become widely used to simulate systems in which angular
198 > % interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
199 > % metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
200 > % MEAM presents significant additional computational costs, however.
201  
202 < The EAM, Finnis-Sinclair, MEAM, and the Quantum Sutton-Chen potentials
202 > The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials
203   have all been widely used by the materials simulation community for
204   simulations of bulk and nanoparticle
205   properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq}
206   melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
207   fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack
208   propagation,\cite{BECQUART:1993rg} and alloying
209 < dynamics.\cite{Shibata:2002hh} All of these potentials have their
210 < strengths and weaknesses.  One of the strengths common to all of the
211 < methods is the relatively large library of metals for which these
212 < potentials have been
213 < parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
209 > dynamics.\cite{Shibata:2002hh} One of EAM's strengths
210 > is its sensitivity to small changes in structure. This arises
211 > from the original parameterization, where the interactions
212 > up to the third nearest-neighbor were taken into account.\cite{Voter95a}
213 > Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88}
214 > which only parameterized up to the nearest-neighbor
215 > interactions, EAM is a suitable choice for systems where
216 > the bulk properties are of secondary importance to low-index
217 > surface structures. Additionally, the similarity of EAMs functional
218 > treatment of the embedding energy to standard density functional
219 > theory (DFT) approaches gives EAM, and conclusions derived, a firm theoretical footing.
220 > \cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  
221  
222 < \subsection{CO}
223 < Since one explanation for the strong surface CO repulsion on metals is
224 < the large linear quadrupole moment of carbon monoxide, the model
225 < chosen for this molecule exhibits this property in an efficient
226 < manner.  We used a model first proposed by Karplus and Straub to study
227 < the photodissociation of CO from myoglobin.\cite{Straub} The Straub and
228 < Karplus model is a rigid three site model which places a massless M
229 < site at the center of mass along the CO bond.  The geometry used along
230 < with the interaction parameters are reproduced in Table 1. The effective
222 >
223 >
224 >
225 > \subsection{Carbon Monoxide model}
226 > Previous explanations for the surface rearrangements center on
227 > the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010}  
228 > We used a model first proposed by Karplus and Straub to study
229 > the photodissociation of CO from myoglobin because it reproduces
230 > the quadrupole moment well.\cite{Straub} The Straub and
231 > Karplus model, treats CO as a rigid three site molecule with a massless M
232 > site at the molecular center of mass. The geometry and interaction
233 > parameters are reproduced in Table~\ref{tab:CO}. The effective
234   dipole moment, calculated from the assigned charges, is still
235   small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
236   to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
237   mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
238   %CO Table
239   \begin{table}[H]
240 < \caption{Positions, $\sigma$, $\epsilon$ and charges for CO geometry and self-interactions\cite{Straub}. Distances are in \AA~, energies are in kcal/mol, and charges are in $e$.}
240 >  \caption{Positions, Lennard-Jones parameters ($\sigma$ and
241 >    $\epsilon$), and charges for the CO-CO
242 >    interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are
243 >    in kcal/mol, and charges are in atomic units.}
244   \centering
245   \begin{tabular}{| c | c | ccc |}
246   \hline
214 – \multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\
215 – \hline
247   &  {\it z} & $\sigma$ & $\epsilon$ & q\\
248   \hline
249 < \textbf{C} & -0.6457 &  0.0262  & 3.83   &   -0.75 \\
250 < \textbf{O} &  0.4843 &   0.1591 &   3.12 &   -0.85 \\
249 > \textbf{C} & -0.6457 &  3.83 & 0.0262   &   -0.75 \\
250 > \textbf{O} &  0.4843 &  3.12 &  0.1591  &   -0.85 \\
251   \textbf{M} & 0.0 & -  &  -  &    1.6 \\
252   \hline
253   \end{tabular}
254 + \label{tab:CO}
255   \end{table}
256  
257 < \subsection{Cross-Interactions}
257 > \subsection{Cross-Interactions between the metals and carbon monoxide}
258  
259 < One hurdle that must be overcome in classical molecular simulations
260 < is the proper parameterization of the potential interactions present
261 < in the system. Since the adsorption of CO onto a platinum surface has been
262 < the focus of many experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
263 < and theoretical studies \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
264 < there is a large amount of data in the literature to fit too. We started with parameters
265 < reported by Korzeniewski et al. \cite{Pons:1986} and then
266 < modified them to ensure that the Pt-CO interaction favored
267 < an atop binding position for the CO upon the Pt surface. This
268 < constraint led to the binding energies being on the higher side
269 < of reported values. Following the method laid out by Korzeniewski,
270 < the Pt-C interaction was fit to a strong Lennard-Jones 12-6
271 < interaction to mimic binding, while the Pt-O interaction
272 < was parameterized to a Morse potential with a large $r_o$
273 < to contribute a weak repulsion. The resultant potential-energy
274 < surface suitably recovers the calculated Pt-C bond length ( 1.6\AA)\cite{Beurden:2002ys} and affinity
275 < for the atop binding position.\cite{Deshlahra:2012, Hopster:1978}
259 > Since the adsorption of CO onto a Pt surface has been the focus
260 > of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
261 > and theoretical work
262 > \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
263 > there is a significant amount of data on adsorption energies for CO on
264 > clean metal surfaces. An earlier model by Korzeniewski {\it et
265 >  al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were
266 > modified to ensure that the Pt-CO interaction favored the atop binding
267 > position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}.
268 > The modified parameters yield binding energies that are slightly higher
269 > than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski
270 > et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
271 > Lennard-Jones interaction to mimic strong, but short-ranged partial
272 > binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The
273 > Pt-O interaction was modeled with a Morse potential with a large
274 > equilibrium distance, ($r_o$).  These choices ensure that the C is preferred
275 > over O as the surface-binding atom. In most cases, the Pt-O parameterization contributes a weak
276 > repulsion which favors the atop site.  The resulting potential-energy
277 > surface suitably recovers the calculated Pt-C separation length
278 > (1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding
279 > position.\cite{Deshlahra:2012, Hopster:1978}
280  
281   %where did you actually get the functionals for citation?
282   %scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think
283   %same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there...
284 < The Au-C and Au-O interaction parameters were also fit to a Lennard-Jones
285 < and Morse potential respectively, to reproduce Au-CO binding energies.
286 < These energies were obtained from quantum calculations carried out using
287 < the PBE GGA exchange-correlation functionals\cite{Perdew_GGA} for gold, carbon, and oxygen
288 < constructed by Rappe, Rabe, Kaxiras, and Joannopoulos. \cite{RRKJ_PP}.
289 < All calculations were run using the {\sc Quantum ESPRESSO} package. \cite{QE-2009}  
290 < First, a four layer slab of gold comprised of 32 atoms displaying a (111) surface was
291 < converged using a 4X4X4 grid of Monkhorst-Pack \emph{k}-points.\cite{Monkhorst:1976}
292 < The kinetic energy of the wavefunctions were truncated at 20 Ry while the
293 < cutoff for the charge density and potential was set at 80 Ry. This relaxed
294 < gold slab was then used in numerous single point calculations  with CO at various heights
295 < to create a potential energy surface for the Au-CO interaction.
284 > The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and
285 > Morse potentials, respectively, to reproduce Au-CO binding energies.
286 > The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations.
287 > Adsorption energies were obtained from gas-surface DFT calculations with a
288 > periodic supercell plane-wave basis approach, as implemented in the
289 > {\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were
290 > described with the projector augmented-wave (PAW)
291 > method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
292 > included to an energy cutoff of 20 Ry. Electronic energies are
293 > computed with the PBE implementation of the generalized gradient
294 > approximation (GGA) for gold, carbon, and oxygen that was constructed
295 > by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
296 > In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4
297 > Au x 2 Au surface planes and separated from vertical images by six
298 > layers of vacuum space. The surface atoms were all allowed to relax
299 > before CO was added to the system. Electronic relaxations were
300 > performed until the energy difference between subsequent steps
301 > was less than $10^{-8}$ Ry.   Nonspin-polarized supercell calculations
302 > were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
303 > zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was
304 > then used in numerous single point calculations with CO at various
305 > heights (and angles relative to the surface) to allow fitting of the
306 > empirical force field.
307  
308   %Hint at future work
309 < The fit parameter sets employed in this work are shown in Table 2 and their
310 < reproduction of the binding energies are displayed in Table 3. Currently,
311 < charge transfer is not being treated in this system, however, that is a goal
312 < for future work as the effect has been seen to affect binding energies and
313 < binding site preferences. \cite{Deshlahra:2012}
309 > The parameters employed for the metal-CO cross-interactions in this work
310 > are shown in Table~\ref{tab:co_parameters} and the binding energies on the
311 > (111) surfaces are displayed in Table~\ref{tab:co_energies}.  Charge transfer
312 > and polarization are neglected in this model, although these effects are likely to
313 > affect binding energies and binding site preferences, and will be addressed in
314 > a future work.\cite{Deshlahra:2012,StreitzMintmire:1994}
315  
268 –
269 –
270 –
271 – \subsection{Construction and Equilibration of 557 Metal interfaces}
272 –
273 – Our model systems are composed of approximately 4000 metal atoms
274 – cut along the 557 plane so that they are periodic in the {\it x} and {\it y}
275 – directions exposing the 557 plane in the {\it z} direction. Runs at various
276 – temperatures ranging from 300~K to 1200~K were started with the intent
277 – of viewing relative stability of the surface when CO was not present in the
278 – system.  Owing to the different melting points (1337~K for Au and 2045~K for Pt),
279 – the bare crystal systems were initially run in the Canonical ensemble at
280 – 800~K and 1000~K respectively for 100 ps. Various amounts of CO were
281 – placed in the vacuum region, which upon full adsorption to the surface
282 – corresponded to 5\%, 25\%, 33\%, and 50\% coverages. These systems
283 – were again allowed to reach thermal equilibrium before being run in the
284 – microcanonical ensemble. All of the systems examined in this work were
285 – run for at least 40 ns. A subset that were undergoing interesting effects
286 – have been allowed to continue running with one system approaching 200 ns.
287 – All simulations were run using the open source molecular dynamics package, OpenMD. \cite{Ewald, OOPSE}
288 –
289 –
290 –
291 –
292 –
293 –
294 – %\subsection{System}
295 – %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.
296 –
297 –
316   %Table  of Parameters
317   %Pt Parameter Set 9
318   %Au Parameter Set 35
319   \begin{table}[H]
320 < \caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol}
320 >  \caption{Best fit parameters for metal-CO cross-interactions. Metal-C
321 >    interactions are modeled with Lennard-Jones potentials. While the
322 >    metal-O interactions were fit to Morse
323 >    potentials.  Distances are given in \AA~and energies in kcal/mol. }
324   \centering
325   \begin{tabular}{| c | cc | c | ccc |}
326   \hline
327 < \multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\
327 > &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
328   \hline
308 – &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\
309 – \hline
329   \textbf{Pt-C} & 1.3 & 15  & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\
330   \textbf{Au-C} & 1.9 & 6.5  & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\
331  
332   \hline
333   \end{tabular}
334 + \label{tab:co_parameters}
335   \end{table}
336  
337   %Table of energies
338   \begin{table}[H]
339 < \caption{Adsorption energies in eV}
339 >  \caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials
340 >    described in this work.  All values are in eV.}
341   \centering
342   \begin{tabular}{| c | cc |}
343 < \hline
344 < & Calc. & Exp. \\
345 < \hline
346 < \textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\
347 < \textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\
348 < \hline
343 >  \hline
344 >  & Calculated & Experimental \\
345 >  \hline
346 >  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,}
347 >  (Ref. \protect\cite{Kelemen:1979}) \\
348 > & &  -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline
349 >  \textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,}  (Ref. \protect\cite{TPD_Gold}) \\
350 >  \hline
351   \end{tabular}
352 + \label{tab:co_energies}
353   \end{table}
354  
355 + \subsection{Pt(557) and Au(557) metal interfaces}
356 + Our Pt system has dimensions of 18~x~24~x~9 in a box of size
357 + 54.482~x~50.046~x~120.88~\AA while our Au system has
358 + dimensions of 18~x~24~x~8 in a box of size 57.4~x~51.9285~x~100~\AA.
359 + The systems are arranged in a FCC crystal that have been cut
360 + along the (557) plane so that they are periodic in the {\it x} and
361 + {\it y} directions, and have been oriented to expose two aligned
362 + (557) cuts along the extended {\it z}-axis.  Simulations of the
363 + bare metal interfaces at temperatures ranging from 300~K to
364 + 1200~K were performed to observe the relative
365 + stability of the surfaces without a CO overlayer.  
366  
367 + The different bulk melting temperatures (1337~K for Au
368 + and 2045~K for Pt) suggest that any possible reconstruction should happen at
369 + different temperatures for the two metals.  The bare Au and Pt surfaces were
370 + initially run in the canonical (NVT) ensemble at 800~K and 1000~K
371 + respectively for 100 ps. The two surfaces were relatively stable at these
372 + temperatures when no CO was present, but experienced increased surface
373 + mobility on addition of CO. Each surface was then dosed with different concentrations of CO
374 + that was initially placed in the vacuum region.  Upon full adsorption,
375 + these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
376 + coverage. Higher coverages resulted in CO double layer formation, which introduces artifacts that are not relevant to (557) reconstruction.
377 + Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
378 + the Au surfaces often had a significant CO population in the gas
379 + phase.  These systems were allowed to reach thermal equilibrium (over
380 + 5 ns) before being run in the microcanonical (NVE) ensemble for
381 + data collection. All of the systems examined had at least 40 ns in the
382 + data collection stage, although simulation times for some of the
383 + systems exceeded 200~ns.  Simulations were run using the open
384 + source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}
385  
386 + % Just results, leave discussion for discussion section
387 + % structure
388 + %       Pt: step wandering, double layers, no triangular motifs
389 + %       Au: step wandering, no double layers
390 + % dynamics
391 + %       diffusion
392 + %       time scale, formation, breakage
393 + \section{Results}
394 + \subsection{Structural remodeling}
395 + Tao et al. have shown experimentally that the Pt(557) surface
396 + undergoes two separate reconstructions upon CO
397 + adsorption.\cite{Tao:2010} The first involves a doubling of
398 + the step height and plateau length. Similar behavior has been
399 + seen to occur on numerous surfaces at varying conditions: Ni(977), Si(111).
400 + \cite{Williams:1994,Williams:1991,Pearl} Of the two systems
401 + we examined, the Pt system showed a larger amount of
402 + reconstruction when compared to the Au system. The amount
403 + of reconstruction is correlated to the amount of CO
404 + adsorbed upon the surface.  This appears to be related to the
405 + effect that adsorbate coverage has on edge breakup and on the surface
406 + diffusion of metal adatoms. While both systems displayed step-edge
407 + wandering, only the Pt surface underwent the doubling seen by
408 + Tao et al. within the time scales studied here.  
409 + Only the 50\% coverage Pt system exhibited
410 + a complete doubling in the time scales we
411 + were able to monitor. Over longer periods (150~ns) two more double layers formed on this interface.
412 + Although double layer formation did not occur in the other Pt systems, they show
413 + more lateral movement of the step-edges
414 + compared to their Au counterparts. The 50\% Pt system is highlighted
415 + in Figure \ref{fig:reconstruct} at various times along the simulation
416 + showing the evolution of a step-edge.
417  
418 + The second reconstruction on the Pt(557) surface observed by
419 + Tao involved the formation of triangular clusters that stretched
420 + across the plateau between two step-edges. Neither system, within
421 + the 40~ns time scale, experienced this reconstruction.
422  
423 + \subsection{Dynamics}
424 + Previous atomistic simulations of stepped surfaces were largely
425 + concerned with the energetics and structures at different conditions
426 + \cite{Williams:1991,Williams:1994}. Consequently, the most common
427 + technique has been Monte Carlo. Monte Carlo gives an efficient
428 + sampling of the equilibrium thermodynamic landscape at the expense
429 + of ignoring the dynamics of the system. Previous work by Pearl and
430 + Sibener\cite{Pearl}, using STM, has been able to show the coalescing
431 + of steps on Ni(977). The time scale of the image acquisition,
432 + $\sim$70 s/image provides an upper bound for the time required for
433 + the doubling to occur. In this section we give data on dynamic and
434 + transport properties, e.g. diffusion, layer formation time, etc.
435  
336 – % Just results, leave discussion for discussion section
337 – \section{Results}
338 – \subsection{Diffusion}
339 – While an ideal metallic surface is unlikely to experience much surface diffusion, high-index surfaces have large numbers of low-coordinated atoms which have a much easier time overcoming the energetic barriers limiting diffusion, leading to easier surface reconstructions. Surface movement was divided between the parallel ($\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.
436  
437 < %Table of Diffusion Constants
438 < %Add gold?M
439 < \begin{table}[H]
440 < \caption{Platinum and gold diffusion constants parallel and perpendicular to the 557 step edge. As the coverage increases, the diffusion constants parallel and  perpendicular to the step edge both initially increase and then decrease slightly. Units are \AA\textsuperscript{2}/ns}
441 < \centering
442 < \begin{tabular}{| c | cc | cc | c |}
443 < \hline
444 < \textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  & \textbf{Time (ns)}\\
445 < \hline
446 < &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} & \\
447 < \hline
448 < 50\% & 4.32 $\pm$ 0.02 & 1.185 $\pm$ 0.008 & 1.72 $\pm$ 0.02 & 0.455 $\pm$ 0.006 & 40 \\
449 < 33\% & 5.18 $\pm$ 0.03 & 1.999 $\pm$ 0.005 & 1.95 $\pm$ 0.02 & 0.337 $\pm$ 0.004 & 40   \\
450 < 25\% & 5.01 $\pm$ 0.02 & 1.574 $\pm$ 0.004 & 1.26 $\pm$ 0.03 & 0.377 $\pm$ 0.006 & 40  \\
451 < 5\%   & 3.61 $\pm$ 0.02 & 0.355 $\pm$ 0.002 & 1.84 $\pm$ 0.03 & 0.169 $\pm$ 0.004 & 40  \\
452 < 0\%   & 3.27 $\pm$ 0.02 & 0.147 $\pm$ 0.004 & 1.50 $\pm$ 0.02 & 0.194 $\pm$ 0.002  & 40  \\
453 < \hline
454 < \end{tabular}
455 < \end{table}
437 > \subsubsection{Transport of surface metal atoms}
438 > %forcedSystems/stepSeparation
439 > The movement or wandering of a step-edge is a cooperative effect
440 > arising from the individual movements, primarily through surface
441 > 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
443 > much surface diffusion because of the large energetic barrier that must
444 > be overcome to lift an atom out of the surface. The presence of step-edges
445 > on higher-index surfaces provide a source for mobile metal atoms.
446 > Breaking away from the step-edge on a clean surface still imposes an
447 > energetic penalty around $\sim$~40 kcal/mol, but is much less than lifting
448 > the same metal atom vertically out of the surface,  \textgreater~60 kcal/mol.
449 > The penalty lowers significantly when CO is present in sufficient quantities
450 > on the surface. For certain distributions of CO, the penalty can be as low as
451 > $\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for
452 > diffusion is negligible ( \textless~4 kcal/mol) and these adatoms are well
453 > able to explore the terrace before rejoining either the original step-edge or becoming a part
454 > of a different edge. Atoms traversing separate terraces is a more difficult
455 > process, but can be overcome through a joining and lifting stage which is
456 > examined in the discussion section. By tracking the mobility of individual
457 > metal atoms on the Pt and Au surfaces we were able to determine the relative
458 > diffusion constants, as well as how varying coverages of CO affect the diffusion. Close
459 > observation of the mobile metal atoms showed that they were typically in
460 > equilibrium with the step-edges, dynamically breaking apart and rejoining the edges.
461 > At times, their motion was concerted and two or more adatoms would be
462 > observed moving together across the surfaces. The primary challenge in
463 > quantifying the overall surface mobility was in defining ``mobile" vs. ``static" atoms.
464  
465 + A particle was considered mobile once it had traveled more than 2~\AA~
466 + between saved configurations of the system (typically 10-100 ps). An atom that was
467 + truly mobile would typically travel much greater distances than this, but the 2~\AA~ cutoff
468 + was to prevent swamping the diffusion data with the in-place vibrational
469 + movement of buried atoms. Diffusion on  a surface is strongly affected by
470 + local structures and in this work, the presence of single and double layer
471 + step-edges causes the diffusion parallel to the step-edges to be different
472 + from the diffusion perpendicular to these edges. Parallel and perpendicular
473 + 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$40 ns was necessary for the layer to completely straighten. The other two layers in this simulation form over a period of 22 ns and 42 ns respectively. Comparing this to the upper bounds of the image scan, it is likely that aspects of this reconstruction occur very quickly. A possible explanation for this rapid reconstruction is the elevated temperatures our systems were run at. It is likely that the process would take longer at lower temperatures and is an area of exploration for future work.
477  
478 + %Evolution of surface
479 + \begin{figure}[H]
480 + \includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
481 + \caption{The Pt(557) / 50\% CO system at a sequence of times after
482 +  initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and
483 +  (d) 86.1 ns. Disruption of the (557) step-edges occurs quickly.  The
484 +  doubling of the layers appears only after two adjacent step-edges
485 +  touch.  The circled spot in (b) nucleated the growth of the double
486 +  step observed in the later configurations.}
487 +  \label{fig:reconstruct}
488 + \end{figure}
489 +
490 + \begin{figure}[H]
491 + \includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf}
492 + \caption{Diffusion constants for mobile surface atoms along directions
493 +  parallel ($\mathbf{D}_{\parallel}$) and perpendicular
494 +  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
495 +  surface coverage.  Diffusion parallel to the step-edge is higher
496 +  than that perpendicular to the edge because of the lower energy
497 +  barrier associated with traversing along the edge as compared to
498 +  completely breaking away. Additionally, the observed
499 +  maximum and subsequent decrease for the Pt system suggests that the
500 +  CO self-interactions are playing a significant role with regards to
501 +  movement of the Pt atoms around and across the surface. }
502 + \label{fig:diff}
503 + \end{figure}
504 +
505 +
506 +
507 +
508   %Discussion
509   \section{Discussion}
510 < 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.
510 > In this paper we have shown that we were able to accurately model the initial reconstruction of the
511 > Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we
512 > were able to observe the dynamic processes necessary for this reconstruction.
513  
514 + \subsection{Mechanism for restructuring}
515 + Since the Au surface showed no large scale restructuring throughout
516 + our simulation time our discussion will focus on the 50\% Pt-CO system
517 + which did undergo the doubling featured in Figure \ref{fig:reconstruct}.
518 + Comparing the results from this simulation to those reported previously by
519 + Tao et al.\cite{Tao:2010} the similarities in the Pt-CO system are quite
520 + strong. As shown in Figure \ref{fig:reconstruct}, the simulated Pt
521 + system exposed to a large dosage of CO will restructure by doubling the terrace
522 + 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.
523 + Looking at individual configurations of the system, the adatoms either
524 + break away from the step-edge and stay on the lower terrace or they lift
525 + up onto the higher terrace. Once ``free'', they will diffuse on the terrace
526 + until reaching another step-edge or rejoining their original edge.  
527 + This combination of growth and decay of the step-edges is in a state of
528 + dynamic equilibrium. However, once two previously separated edges
529 + meet as shown in Figure 1.B, this meeting point tends to act as a focus
530 + 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.
534 +
535 + A number of possible mechanisms exist to explain the role of adsorbed
536 + CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent
537 + CO molecules adsorbed on the surface is one likely possibility.  However,
538 + the quadrupole-quadrupole interaction is short-ranged and is attractive for
539 + some orientations.  If the CO molecules are ``locked'' in a specific orientation
540 + relative to each other, through atop adsorption for example, this explanation
541 + gains some weight.  The energetic repulsion between two CO located a
542 + distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in
543 + a  vertical orientation is 8.62 kcal/mol. Moving the CO apart to the second
544 + nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to
545 + nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation
546 + 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.
547 + As mentioned above, the energy barrier for surface diffusion
548 + of a Pt adatom is only 4 kcal/mol. So this repulsion between CO can help
549 + increase the surface diffusion. However, the residence time of CO on Pt was
550 + examined and while the majority of the CO is on or near the surface throughout
551 + the run, it is extremely mobile. This mobility suggests that the CO are more
552 + likely to shift their positions without necessarily dragging the Pt along with them.
553 +
554 + Another possible and more likely mechanism for the restructuring is in the
555 + destabilization of strong Pt-Pt interactions by CO adsorbed on surface
556 + Pt atoms.  This would then have the effect of increasing surface mobility
557 + of these atoms.  To test this hypothesis, numerous configurations of
558 + CO in varying quantities were arranged on the higher and lower plateaus
559 + around a step on a otherwise clean Pt(557) surface. One representative
560 + configuration is displayed in Figure \ref{fig:lambda}. Single or concerted movement
561 + of Pt atoms was then examined to determine possible barriers. Because
562 + the movement was forced along a pre-defined reaction coordinate that may differ
563 + from the true minimum of this path, only the beginning and ending energies
564 + are displayed in Table \ref{tab:energies}. These values suggest that the presence of CO at suitable
565 + locations can lead to lowered barriers for Pt breaking apart from the step-edge.
566 + Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the
567 + burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral
568 + in terms of energetics.
569 +
570 + %lambda progression of Pt -> shoving its way into the step
571 + \begin{figure}[H]
572 + \includegraphics[width=\linewidth]{lambdaProgression_atopCO.png}
573 + \caption{A model system of the Pt(557) surface was used as the framework
574 + for exploring energy barriers along a reaction coordinate. Various numbers,
575 + placements, and rotations of CO were examined as they affect Pt movement.
576 + 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
578 + is a slight decrease upon insertion of the Pt atom into the step-edge along
579 + with the resultant lifting of the other Pt atom when CO is present at certain positions.}
580 + \label{fig:lambda}
581 + \end{figure}
582 +
583 +
584 +
585   \subsection{Diffusion}
586 < 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?)
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   \\
598 < \\
599 < %Evolution of surface
598 >
599 >
600 > %breaking of the double layer upon removal of CO
601   \begin{figure}[H]
602 < \includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
603 < \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.}
602 > \includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png}
603 > %:
604 > \caption{(A)  0 ps, (B) 100 ps, (C) 1 ns, after the removal of CO. The presence of the CO
605 > helped maintain the stability of the double layer and upon removal the two layers break
606 > and begin separating. The separation is not a simple pulling apart however, rather
607 > there is a mixing of the lower and upper atoms at the edge.}
608 > \label{fig:breaking}
609   \end{figure}
610  
611  
612  
613  
614   %Peaks!
615 < \includegraphics[scale=0.25]{doublePeaks_noCO.png}
615 > \begin{figure}[H]
616 > \includegraphics[width=\linewidth]{doublePeaks_noCO.png}
617 > \caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
618 > of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with
619 > aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
620 > \label{fig:peaks}
621 > \end{figure}
622 >
623 >
624 > %Don't think I need this
625 > %clean surface...
626 > %\begin{figure}[H]
627 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
628 > %\caption{}
629 >
630 > %\end{figure}
631 > %\label{fig:clean}
632 >
633 >
634   \section{Conclusion}
635 + In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in less than a $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems.
636  
637 + %Things I am not ready to remove yet
638  
639 + %Table of Diffusion Constants
640 + %Add gold?M
641 + % \begin{table}[H]
642 + %   \caption{}
643 + %   \centering
644 + % \begin{tabular}{| c | cc | cc | }
645 + %   \hline
646 + %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
647 + %   \hline
648 + %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
649 + %   \hline
650 + %   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
651 + %   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
652 + %   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
653 + %   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
654 + %   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
655 + %   \hline
656 + % \end{tabular}
657 + % \end{table}
658 +
659   \section{Acknowledgments}
660   Support for this project was provided by the National Science
661   Foundation under grant CHE-0848243 and by the Center for Sustainable

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