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1 < \documentclass[a4paper,12pt]{article}
1 > \documentclass[journal = jpccck, manuscript = article]{achemso}
2 > \setkeys{acs}{usetitle = true}
3 > \usepackage{achemso}
4 > \usepackage{natbib}
5 > \usepackage{multirow}
6 > \usepackage{wrapfig}
7 > \usepackage{fixltx2e}
8 > %\mciteErrorOnUnknownfalse
9  
10 < \usepackage{setspace}
11 < \usepackage{float}
5 < \usepackage{cite}
6 < \usepackage[pdftex]{graphicx}
7 < \usepackage[font=small,labelfont=bf]{caption}
10 > \usepackage[version=3]{mhchem}  % this is a great package for formatting chemical reactions
11 > \usepackage{url}
12  
13 + \title{Molecular Dynamics simulations of the surface reconstructions
14 +  of Pt(557) and Au(557) under exposure to CO}
15 +
16 + \author{Joseph R. Michalka}
17 + \author{Patrick W. McIntyre}
18 + \author{J. Daniel Gezelter}
19 + \email{gezelter@nd.edu}
20 + \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
21 +  Department of Chemistry and Biochemistry\\ University of Notre
22 +  Dame\\ Notre Dame, Indiana 46556}
23 +
24 + \keywords{}
25 +
26 + \begin{document}
27 +
28 +
29   %%
30   %Introduction
31   %       Experimental observations
# Line 25 | Line 45
45   %%
46  
47  
48 + \begin{abstract}
49 +  The mechanism and dynamics of surface reconstructions of Pt(557) and
50 +  Au(557) exposed to various coverages of carbon monoxide (CO) were
51 +  investigated using molecular dynamics simulations.  Metal-CO
52 +  interactions were parameterized from experimental data and
53 +  plane-wave Density Functional Theory (DFT) calculations.  The large
54 +  difference in binding strengths of the Pt-CO and Au-CO interactions
55 +  was found to play a significant role in step-edge stability and
56 +  adatom diffusion constants.  Various mechanisms for CO-mediated step
57 +  wandering and step doubling were investigated on the Pt(557)
58 +  surface.  We find that the energetics of CO adsorbed to the surface
59 +  can explain the step-doubling reconstruction observed on Pt(557) and
60 +  the lack of such a reconstruction on the Au(557) surface.  However,
61 +  more complicated reconstructions into triangular clusters that have
62 +  been seen in recent experiments were not observed in these
63 +  simulations.
64 + \end{abstract}
65  
66 < \begin{document}
30 < %Title
31 < \title{Investigation of the Pt and Au 557 Surface Reconstructions under a CO Atmosphere}
32 < %Date
33 < \date{Dec 15,  2012}
34 < %authors
35 < \author{Joseph R.~Michalka, Patrick W. McIntyre, \& J.~Daniel Gezelter}
36 < % make the title
37 < \maketitle
66 > \newpage
67  
39 – \doublespacing
68  
41 –
42 –
69   \section{Introduction}
70   % Importance: catalytically active metals are important
71   %       Sub: Knowledge of how their surface structure affects their ability to catalytically facilitate certain reactions is growing, but is more reactionary than predictive
# Line 48 | Line 74
74   %       Sub: Also, easier to observe what is going on and provide reasons and explanations
75   %
76  
77 + Industrial catalysts usually consist of small particles that exhibit a
78 + high concentration of steps, kink sites, and vacancies at the edges of
79 + the facets.  These sites are thought to be the locations of catalytic
80 + activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now
81 + significant evidence that solid surfaces are often structurally,
82 + compositionally, and chemically modified by reactants under operating
83 + conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between
84 + surface oxidation states and catalytic activity for CO oxidation on
85 + Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002}
86 + Despite the well-documented role of these effects on reactivity, the
87 + ability to capture or predict them in atomistic models is somewhat
88 + limited.  While these effects are perhaps unsurprising on the highly
89 + disperse, multi-faceted nanoscale particles that characterize
90 + industrial catalysts, they are manifest even on ordered, well-defined
91 + surfaces. The Pt(557) surface, for example, exhibits substantial and
92 + reversible restructuring under exposure to moderate pressures of
93 + carbon monoxide.\cite{Tao:2010}
94  
95 < High-index surfaces of catalytically active metals are an important area of exploration because they are typically more reactive than an ideal surface of the same metal. The greater number of low-coordinated surface atoms is likely responsible for this increased reactivity \cite{}. Additionally, the activity and specificity of many metals towards certain chemical processes has been shown to strongly depend on the structure of the surface \cite{}. Prior work has also shown that reaction conditions: high pressures, temperatures, etc. are able to cause reconstructions of the surface, either through changing the displayed surface facets or by changing the number and types of high-index sites available for reactions \cite{doi:10.1126/science.1197461,doi:10.1021/nn3015322, doi:10.1021/jp302379x}. A greater understanding of these high-index surfaces and the restructuring processes they undergo is needed as a prerequisite for more intelligent catalyst design. While current experimental work has started exploring systems at \emph{in situ} conditions, for a long time such experiments were limited to ideal surfaces in high vacuum. New techniques, such as ambient pressure XPS (AP-XPS) \cite{}, high-pressure XPS (HP-XPS) \cite{}, high-pressure STM \cite{}, environmental transmission electron microscopy (E-TEM) \cite{} and many others, are giving a clearer picture of what processes are occurring on metal surfaces when exposed to \emph{in situ} conditions. But all of these techniques still have difficulties, especially in observing what is occurring on the surfaces at an atomic level. Theoretical models and simulations in combination with experiment have proven their worth in explaining the underlying reasons for some of these reconstructions \cite{}.
96 < \\
97 < By examining two different metal-CO systems the effect the metal and the metal-CO interaction plays can be elucidated. Our first system is composed of Platinum and CO and has been the subject of many experimental and theoretical studies primarily because of Platinum's strong reactivity toward CO oxidation. The focus has primarily been on absorption energies, preferred absorption sites, and catalytic activities. The second system we examined is composed of Gold and CO. The Gold-CO interaction is much weaker than the Platinum-CO interaction and it seems likely that this difference in attraction would lead to differences in any potential surface reconstructions.
98 < %It has also been a good test for new quantum methods because of the difficulty with modeling the preference CO has for the atop binding site \cite{doi:10.1021/jp002302t}.
99 < %Now that dynamic surface events are known to play a role in many catalytic systems, additional research is being done to more closely examine many systems. Recent work by Tao et al. \cite{doi:10.1126/science.1182122} shows that a high-index platinum surface will undergo surface reconstructions when exposed to a small amount of CO, $\sim$~1 torr. Unexpectedly,  the reconstruction was metastable and reverted upon removal of the CO. Work by McCarthy et al. \cite{doi:10.1021/jp302379x} examined temperature programmed desorption's of CO from various Platinum samples and saw that species which had large amounts of low-coordinated surface atoms, highly sputtered surfaces or small nano particles, developed a higher temperature desorption peak, suggesting that binding of CO to the Platinum surface is strongly dependent on local geometry.
95 > This work is an investigation into the mechanism and timescale for the
96 > Pt(557) \& Au(557) surface restructuring using molecular simulation.
97 > Since the dynamics of the process are of particular interest, we
98 > employ classical force fields that represent a compromise between
99 > chemical accuracy and the computational efficiency necessary to
100 > simulate the process of interest.  Since restructuring typically
101 > occurs as a result of specific interactions of the catalyst with
102 > adsorbates, in this work, two metal systems exposed to carbon monoxide
103 > were examined. The Pt(557) surface has already been shown to undergo a
104 > large scale reconstruction under certain conditions.\cite{Tao:2010}
105 > The Au(557) surface, because of weaker interactions with CO, is less
106 > likely to undergo this kind of reconstruction. However, Peters {\it et
107 >  al}.\cite{Peters:2000} and Piccolo {\it et al}.\cite{Piccolo:2004}
108 > have both observed CO-induced modification of reconstructions to the
109 > Au(111) surface. Peters {\it et al}. observed the Au(111)-($22 \times
110 > \sqrt{3}$) ``herringbone'' reconstruction relaxing slightly under CO
111 > adsorption. They argued that only a few Au atoms become adatoms,
112 > limiting the stress of this reconstruction, while allowing the rest to
113 > relax and approach the ideal (111) configuration.  Piccolo {\it et
114 >  al}. on the other hand, saw a more significant disruption of the
115 > Au(111)-($22 \times \sqrt{3}$) herringbone pattern as CO adsorbed on
116 > the surface. Both groups suggested that the preference CO shows for
117 > low-coordinated Au atoms was the primary driving force for the
118 > relaxation.  Although the Au(111) reconstruction was not the primary
119 > goal of our work, the classical models we have fit may be of future
120 > use in simulating this reconstruction.
121  
122 + %Platinum molecular dynamics
123 + %gold molecular dynamics
124  
125 + \section{Simulation Methods}
126 + The challenge in modeling any solid/gas interface is the development
127 + of a sufficiently general yet computationally tractable model of the
128 + chemical interactions between the surface atoms and adsorbates.  Since
129 + the interfaces involved are quite large (10$^3$ - 10$^4$ atoms), have
130 + many electrons, and respond slowly to perturbations, {\it ab initio}
131 + molecular dynamics
132 + (AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello
133 + methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum
134 + mechanical potential energy surfaces remain out of reach.
135 + Additionally, the ``bonds'' between metal atoms at a surface are
136 + typically not well represented in terms of classical pairwise
137 + interactions in the same way that bonds in a molecular material are,
138 + nor are they captured by simple non-directional interactions like the
139 + Coulomb potential.  For this work, we have used classical molecular
140 + dynamics with potential energy surfaces that are specifically tuned
141 + for transition metals.  In particular, we used the EAM potential for
142 + Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using
143 + a rigid three-site model developed by Straub and Karplus for studying
144 + photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and
145 + Pt-CO cross interactions were parameterized as part of this work.
146 +  
147 + \subsection{Metal-metal interactions}
148 + Many of the potentials used for modeling transition metals are based
149 + on a non-pairwise additive functional of the local electron
150 + density. The embedded atom method (EAM) is perhaps the best known of
151 + these
152 + methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98}
153 + but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and
154 + the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler
155 + parameter sets. The glue model of Ercolessi {\it et
156 +  al}.\cite{Ercolessi88} is among the fastest of these density
157 + functional approaches. In all of these models, atoms are treated as a
158 + positively charged core with a radially-decaying valence electron
159 + distribution. To calculate the energy for embedding the core at a
160 + particular location, the electron density due to the valence electrons
161 + at all of the other atomic sites is computed at atom $i$'s location,
162 + \begin{equation*}
163 + \bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
164 + \end{equation*}
165 + Here, $\rho_j(r_{ij})$ is the function that describes the distance
166 + dependence of the valence electron distribution of atom $j$. The
167 + contribution to the potential that comes from placing atom $i$ at that
168 + location is then
169 + \begin{equation*}
170 + V_i =  F[ \bar{\rho}_i ]  + \sum_{j \neq i} \phi_{ij}(r_{ij})
171 + \end{equation*}
172 + where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and
173 + $\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the
174 + repulsive overlap of the two positively charged cores.  
175  
176 + % The {\it modified} embedded atom method (MEAM) adds angular terms to
177 + % the electron density functions and an angular screening factor to the
178 + % pairwise interaction between two
179 + % atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
180 + % MEAM has become widely used to simulate systems in which angular
181 + % interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
182 + % metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
183 + % MEAM presents significant additional computational costs, however.
184  
185 + The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials
186 + have all been widely used by the materials simulation community for
187 + simulations of bulk and nanoparticle
188 + properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq,mishin99:_inter}
189 + melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
190 + fracture,\cite{Shastry:1996qg,Shastry:1998dx,mishin01:cu} crack
191 + propagation,\cite{BECQUART:1993rg,Rifkin1992} and alloying
192 + dynamics.\cite{Shibata:2002hh,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
193 + One of EAM's strengths is its sensitivity to small changes in
194 + structure. This is due to the inclusion of up to the third nearest
195 + neighbor interactions during fitting of the parameters.\cite{Voter95a}
196 + In comparison, the glue model of Ercolessi {\it et
197 +  al}.\cite{Ercolessi88} was only parameterized to include
198 + nearest-neighbor interactions, EAM is a suitable choice for systems
199 + where the bulk properties are of secondary importance to low-index
200 + surface structures. Additionally, the similarity of EAM's functional
201 + treatment of the embedding energy to standard density functional
202 + theory (DFT) makes fitting DFT-derived cross potentials with
203 + adsorbates somewhat easier.
204  
205 < \section{Simulation Methods}
206 < Our model systems are composed of nearly 4000 metal atoms cut along the 557 plane. This cut creates a stepped surface of 6x(111) surface plateaus separated by a single (100) atomic step height. The large number of low-coordination atoms along the step edges provide a suitable model for industrial catalysts which tend to have a prevalence of lower CN, i.e. more reactive, sites. Drawing from experimental conclusions, the reconstructions seen for the Pt 557 surface involve doubling of the step height and the formation of triangular motifs along the steps \cite{doi:10.1126/science.1182122}. To properly observe these changes, our system size need to be greater than the periodic phenomena we are examining. The large size and the long time scales needed precluded us from using expensive quantum approaches. Thus, a forcefield describing the Metal-Metal, CO-CO, and CO-Metal interactions was parameterized.
207 < %Metal
208 < \subsection{Metal}
209 < Recent metallic forcefields, inspired by density-functional theory, including EAM\cite{doi:10.1103/PhysRevB.29.6443, doi:10.1103/PhysRevB.33.7983} and QSC\cite{} have become very popular for modeling novel metallic systems.  What makes these forcefields more suitable for metals than their pair-wise predecessors is that they work with the total electron density of the system in a manner akin to DFT. The energy contributed by a single atom is a function of the total background electron density at the point where the atom is to be embedded. The density at any given point is well-approximated by a linear superposition of the electron density as contributed by all the other atoms in the system. This description of the embedding energy allows this method to more accurately treat surfaces, alloys, and other non-bulk systems. The function describing the energy as related to the density is parameterized for each element, rather than by solving the Kohn-Sham equations which is what allows this method to be used for large systems. The embedding energy is completely enclosed within the functional $F_i[\rho_{h,i}]$ which is dependent on the host density $\rho_{h}$ at atom $i$. The density at $i$ is the sum of the density as generated by the rest of the metal. The $\phi_{ij}$ term is a purely repulsive pair-pair interaction parameterized from effective charge repulsions.
210 < %Can I increase the \sum size, not sure how...
211 < \begin{equation}
212 < E_{tot} = \sum_i F_i[\rho_{h,i}] + \frac{1}{2}\sum_i\sum_{j(\ne i)} \phi_{ij}(R_{ij})
213 < \end{equation}
214 < \begin{equation}
215 < \rho_{h,i} = \sum_{j (\ne i)} \rho_j^a(R_{ij})
216 < \end{equation}
217 < The EAM functional forms are used to model the Au and Pt self-interactions in all of our simulations.
75 < %CO
76 < \subsection{CO}
77 < Our CO model was obtained from work done by Karplus and Straub\cite{}. In their description of the biological importance of CO they developed an accurate quadrupolar model of CO which we make use of in this work. It has been suggested that the strong electrostatic repulsion that arises from this linear quadrupole may play an important role in the restructuring of metal surfaces to which CO is bound\cite{}.
205 > \subsection{Carbon Monoxide model}
206 > Previous explanations for the surface rearrangements center on the
207 > large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} We
208 > used a model first proposed by Karplus and Straub to study the
209 > photodissociation of CO from myoglobin because it reproduces the
210 > quadrupole moment well.\cite{Straub} The Straub and Karplus model
211 > treats CO as a rigid three site molecule with a massless
212 > charge-carrying ``M'' site at the center of mass. The geometry and
213 > interaction parameters are reproduced in Table~\ref{tab:CO}. The
214 > effective dipole moment, calculated from the assigned charges, is
215 > still small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is
216 > close to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
217 > mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
218   %CO Table
219   \begin{table}[H]
220 < \caption{$\sigma$, $\epsilon$ and charges for CO self-interactions\cite{}. Distances are in \AA~, energies are in kcal/mol, and charges are in $e$.}
220 >  \caption{Positions, Lennard-Jones parameters ($\sigma$ and
221 >    $\epsilon$), and charges for CO-CO
222 >    interactions. Distances are in \AA, energies are
223 >    in kcal/mol, and charges are in atomic units.  The CO model
224 >    from Ref.\bibpunct{}{}{,}{n}{}{,}
225 >    \protect\cite{Straub} was used without modification.}
226   \centering
227 < \begin{tabular}{| c | ccc |}
227 > \begin{tabular}{| c | c | ccc |}
228   \hline
229 < \multicolumn{4}{|c|}{\textbf{Self-Interactions}}\\
229 > &  {\it z} & $\sigma$ & $\epsilon$ & q\\
230   \hline
231 < &  $\sigma$ & $\epsilon$ & q\\
231 > \textbf{C} & -0.6457 &  3.83 & 0.0262   &   -0.75 \\
232 > \textbf{O} &  0.4843 &  3.12 &  0.1591  &   -0.85 \\
233 > \textbf{M} & 0.0 & -  &  -  &    1.6 \\
234   \hline
88 – \textbf{C} &  0.0262  & 3.83   &   -0.75 \\
89 – \textbf{O} &   0.1591 &   3.12 &   -0.85 \\
90 – \textbf{M} & -  &  -  &    1.6 \\
91 – \hline
235   \end{tabular}
236 + \label{tab:CO}
237   \end{table}
94 – %Cross
95 – \subsection{Cross-Interactions}
96 – To finish the forcefield, the cross-interactions between the metals and the CO needed to be parameterized. Previous attempts at parameterization have used two different functional forms to model these interactions\cite{}. A LJ model was fit for the Metal-Carbon interaction and a Morse potential was parameterized for the Metal-Oxygen interaction. The parameter sets chosen, as shown in Table 2, did a suitable job at reproducing experimental adsorption energies as shown in Table 3, but more importantly, they were able to capture the binding site preference. The Pt-CO parameters show a slight preference for the atop binding site which matches the experimental observations.
238  
239 + \subsection{Cross-Interactions between the metals and carbon monoxide}
240  
241 + Since the adsorption of CO onto a Pt surface has been the focus
242 + of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
243 + and theoretical work
244 + \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
245 + there is a significant amount of data on adsorption energies for CO on
246 + clean metal surfaces. An earlier model by Korzeniewski {\it et
247 +  al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were
248 + modified to ensure that the Pt-CO interaction favored the atop binding
249 + position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}.
250 + The modified parameters yield binding energies that are slightly higher
251 + than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski
252 + {\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
253 + Lennard-Jones interaction to mimic strong, but short-ranged, partial
254 + binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The
255 + Pt-O interaction was modeled with a Morse potential with a large
256 + equilibrium distance, ($r_o$).  These choices ensure that the C is preferred
257 + over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak
258 + repulsion which favors the atop site.  The resulting potential-energy
259 + surface suitably recovers the calculated Pt-C separation length
260 + (1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding
261 + position.\cite{Deshlahra:2012, Hopster:1978}
262  
263 + %where did you actually get the functionals for citation?
264 + %scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think
265 + %same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there...
266 + The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and
267 + Morse potentials, respectively, to reproduce Au-CO binding energies.
268 + The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations.
269 + Adsorption energies were obtained from gas-surface DFT calculations with a
270 + periodic supercell plane-wave basis approach, as implemented in the
271 + Quantum ESPRESSO package.\cite{QE-2009} Electron cores were
272 + described with the projector augmented-wave (PAW)
273 + method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
274 + included to an energy cutoff of 20 Ry. Electronic energies are
275 + computed with the PBE implementation of the generalized gradient
276 + approximation (GGA) for gold, carbon, and oxygen that was constructed
277 + by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
278 + In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4
279 + Au x 2 Au surface planes and separated from vertical images by six
280 + layers of vacuum space. The surface atoms were all allowed to relax
281 + before CO was added to the system. Electronic relaxations were
282 + performed until the energy difference between subsequent steps
283 + was less than $10^{-8}$ Ry.   Nonspin-polarized supercell calculations
284 + were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
285 + zone.\cite{Monkhorst:1976} The relaxed gold slab was
286 + then used in numerous single point calculations with CO at various
287 + heights (and angles relative to the surface) to allow fitting of the
288 + empirical force field.
289  
290 < %\subsection{System}
291 < %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.
290 > %Hint at future work
291 > The parameters employed for the metal-CO cross-interactions in this work
292 > are shown in Table~\ref{tab:co_parameters} and the binding energies on the
293 > (111) surfaces are displayed in Table~\ref{tab:co_energies}.  Charge transfer
294 > and polarization are neglected in this model, although these effects could have
295 > an effect on binding energies and binding site preferences.
296  
104 –
297   %Table  of Parameters
298   %Pt Parameter Set 9
299   %Au Parameter Set 35
300   \begin{table}[H]
301 < \caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol}
301 >  \caption{Parameters for the metal-CO cross-interactions. Metal-C
302 >    interactions are modeled with Lennard-Jones potentials, while the
303 >    metal-O interactions were fit to broad Morse
304 >    potentials.  Distances are given in \AA~and energies in kcal/mol. }
305   \centering
306   \begin{tabular}{| c | cc | c | ccc |}
307   \hline
308 < \multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\
308 > &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
309   \hline
115 – &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\
116 – \hline
310   \textbf{Pt-C} & 1.3 & 15  & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\
311   \textbf{Au-C} & 1.9 & 6.5  & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\
312  
313   \hline
314   \end{tabular}
315 + \label{tab:co_parameters}
316   \end{table}
317  
318   %Table of energies
319   \begin{table}[H]
320 < \caption{Absorption energies in eV}
320 >  \caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials
321 >    described in this work.  All values are in eV.}
322   \centering
323   \begin{tabular}{| c | cc |}
324 < \hline
325 < & Calc. & Exp. \\
326 < \hline
327 < \textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen}-- -1.9~\cite{Yeo} \\
328 < \textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\
329 < \hline
324 >  \hline
325 >  & Calculated & Experimental \\
326 >  \hline
327 >  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.84} & -1.4 \bibpunct{}{}{,}{n}{}{,}
328 >  (Ref. \protect\cite{Kelemen:1979}) \\
329 > & &  -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline
330 >  \textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,}  (Ref. \protect\cite{TPDGold}) \\
331 >  \hline
332   \end{tabular}
333 + \label{tab:co_energies}
334   \end{table}
335  
336  
337 + \subsection{Validation of forcefield selections}
338 + By calculating minimum energies for commensurate systems of
339 + single and double layer Pt and Au systems with 0 and 50\% coverages
340 + (arranged in a c(2x4) pattern), our forcefield selections were able to be
341 + indirectly compared to results shown in the supporting information of Tao
342 + {\it et al.} \cite{Tao:2010}. Five layer thick systems, displaying a 557 facet
343 + were constructed, each composed of 480 metal atoms. Double layers systems
344 + were constructed from six layer thick systems where an entire layer was
345 + removed from both displayed facets to create a double step. By design, the
346 + double step system also contains 480 atoms, five layers thick, so energy
347 + comparisons between the arrangements can be made directly. The positions
348 + of the atoms were allowed to relax, along with the box sizes, before a
349 + minimum energy was calculated. Carbon monoxide, equivalent to 50\%
350 + coverage on one side of the metal system was added in a c(2x4) arrangement
351 + and again allowed to relax before a minimum energy was calculated.
352  
353 + Energies for the various systems are displayed in Table ~\ref{tab:steps}. Examining
354 + the Pt systems first, it is apparent that the double layer system is slightly less stable
355 + then the original single step. However, upon addition of carbon monoxide, the
356 + stability is reversed and the double layer system becomes more stable. This result
357 + is in agreement with DFT calculations in Tao {\it et al.}\cite{Tao:2010}, who also show
358 + that the addition of CO leads to a reversal in the most stable system. While our
359 + results agree qualitatively, quantitatively, they are approximately an order of magnitude
360 + different. Looking at additional stability per atom in kcal/mol, the DFT calculations suggest
361 + an increased stability of 0.1 kcal/mol per Pt atom, whereas we are seeing closer to a 0.4 kcal/mol
362 + increase in stability per Pt atom.
363  
364 + The gold systems show a much smaller energy difference between the single and double
365 + systems, likely arising from their lower energy per atom values. Additionally, the weaker
366 + binding of CO to Au is evidenced by the much smaller energy change between the two systems,
367 + when compared to the Pt results. This limited change helps explain our lack of any reconstruction
368 + on the Au systems.
369  
370  
371 < % Just results, leave discussion for discussion section
144 < \section{Results}
145 < \subsection{Diffusion}
146 < 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.
147 <
148 < %Table of Diffusion Constants
149 < %Add gold?M
371 > %Table of single step double step calculations
372   \begin{table}[H]
373 < \caption{Platinum diffusion constants parallel and perpendicular to the 557 step edge. As the coverage increases, the diffusion constants parallel and  perpendicular to the step edge both initially increase and then decrease slightly. There were two approaches of analysis. One looking at the surface atoms that had moved more than a prescribed amount over the run time and the other looking at all surface atoms. Units are \AA\textsuperscript{2}/ns}
373 > \caption{Minimized single point energies of unit cell crystals displaying (S)ingle or (D)double steps. Systems are periodic along and perpendicular to the step-edge axes with a large vacuum above the displayed 557 facet. The relative energies are calculated as $E_{relative} = E_{system} - E_{M-557-S} - N_{CO}\Delta E_{CO-M}$ , where $E_{CO-M}$  is -1.84 eV for Pt-CO and -0.39 eV for Pt-CO. The addition of CO in a 50\% c(2x4) coverage acts as a stabilizing presence and suggests a driving force for the observed reconstruction on the highest coverage Pt system. All energies are in kcal/mol.}
374   \centering
375 < \begin{tabular}{| c | ccc | ccc | c |}
375 > \begin{tabular}{| c | c | c | c | c | c |}
376   \hline
377 < \textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & \textbf{Time (ns)}\\
377 > \textbf{Step} & \textbf{N}\textsubscript{M} & \textbf{N\textsubscript{CO}} & \textbf{Relative Energy} & \textbf{$\Delta$E/M} & \textbf{$\Delta$E/CO} \\
378   \hline
379 < &\multicolumn{3}{c|}{\textbf{Mobile}}&\multicolumn{3}{c|}{\textbf{Surface Atoms}} & \\
379 > Pt(557)-S & 480 & 0 & 0 & 0 & - \\
380 > Pt(557)-D & 480 & 0 & 114.783 & 0.239 & -\\
381 > Pt(557)-S & 480 & 40 & -124.546 & -0.259 & -3.114\\
382 > Pt(557)-D & 480 & 44 & -34.953 & -0.073 & -0.794\\
383   \hline
159 – 50\% & 3.74 & 0.89 & 497 & 2.05 & 0.49 & 912 & 116 \\
160 – 50\% & 5.81 & 1.59 & 365 & 2.41 & 0.68 & 912 & 46   \\
161 – 33\% & 6.73 & 2.47 & 332 & 2.51 & 0.93 & 912 & 46   \\
162 – 25\% & 5.38 & 2.04 & 361 & 2.18 & 0.84 & 912 & 46  \\
163 – 5\% & 5.54 & 0.63 & 230 & 1.44 & 0.19 & 912 & 46  \\
164 – 0\% & 3.53 & 0.61 & 282 & 1.11 & 0.22 & 912 & 56  \\
384   \hline
385 < 50\%-r & 6.91 & 2.00 & 198 & 2.23 & 0.68  & 925 & 25\\
386 < 0\%-r  & 4.73 & 0.27 & 128 & 0.72 & 0.05 & 925 & 43\\
387 < \hline
385 > Au(557)-S & 480 & 0 & 0 & 0 & - \\
386 > Au(557)-D & 480 & 0 & 79.572 & 0.166 & - \\
387 > Au(557)-S & 480 & 40 & -157.199 & -0.327 & -3.930\\
388 > Au(557)-D & 480 & 44 & -123.297 & -0.257 & -2.802 \\
389 > \hline
390   \end{tabular}
391 + \label{tab:steps}
392   \end{table}
393  
394  
395 + \subsection{Pt(557) and Au(557) metal interfaces}
396 + Our Pt system is an orthorhombic periodic box of dimensions
397 + 54.482~x~50.046~x~120.88~\AA~while our Au system has
398 + dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs
399 + are 9 and 8 atoms deep respectively, corresponding to a slab
400 + thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
401 + The systems are arranged in a FCC crystal that have been cut
402 + along the (557) plane so that they are periodic in the {\it x} and
403 + {\it y} directions, and have been oriented to expose two aligned
404 + (557) cuts along the extended {\it z}-axis.  Simulations of the
405 + bare metal interfaces at temperatures ranging from 300~K to
406 + 1200~K were performed to confirm the relative
407 + stability of the surfaces without a CO overlayer.  
408  
409 < %Discussion
410 < \section{Discussion}
411 < 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.
409 > The different bulk melting temperatures predicted by EAM
410 > (1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for
411 > Pt\cite{Pt:melting}) suggest that any reconstructions should happen at
412 > different temperatures for the two metals.  The bare Au and Pt
413 > surfaces were initially run in the canonical (NVT) ensemble at 800~K
414 > and 1000~K respectively for 100 ps. The two surfaces were relatively
415 > stable at these temperatures when no CO was present, but experienced
416 > increased surface mobility on addition of CO. Each surface was then
417 > dosed with different concentrations of CO that was initially placed in
418 > the vacuum region.  Upon full adsorption, these concentrations
419 > correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher
420 > coverages resulted in the formation of a double layer of CO, which
421 > introduces artifacts that are not relevant to (557) reconstruction.
422 > Because of the difference in binding energies, nearly all of the CO
423 > was bound to the Pt surface, while the Au surfaces often had a
424 > significant CO population in the gas phase.  These systems were
425 > allowed to reach thermal equilibrium (over 5~ns) before being run in
426 > the microcanonical (NVE) ensemble for data collection. All of the
427 > systems examined had at least 40~ns in the data collection stage,
428 > although simulation times for some Pt of the systems exceeded 200~ns.
429 > Simulations were carried out using the open source molecular dynamics
430 > package, OpenMD.\cite{Ewald,OOPSE,openmd}
431  
432 < \subsection{Diffusion}
433 < 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?)
434 < \\
435 < \\
432 >
433 > % RESULTS
434 > %
435 > \section{Results}
436 > \subsection{Structural remodeling}
437 > The bare metal surfaces experienced minor roughening of the step-edge
438 > because of the elevated temperatures, but the (557) face was stable
439 > throughout the simulations. The surfaces of both systems, upon dosage
440 > of CO, began to undergo extensive remodeling that was not observed in
441 > the bare systems. Reconstructions of the Au systems were limited to
442 > breakup of the step-edges and some step wandering. The lower coverage
443 > Pt systems experienced similar step edge wandering but to a greater
444 > extent. The 50\% coverage Pt system was unique among our simulations
445 > in that it formed well-defined and stable double layers through step
446 > coalescence, similar to results reported by Tao {\it et
447 >  al}.\cite{Tao:2010}
448 >
449 > \subsubsection{Step wandering}
450 > The bare surfaces for both metals showed minimal step-wandering at
451 > their respective temperatures. As the CO coverage increased however,
452 > the mobility of the surface atoms, described through adatom diffusion
453 > and step-edge wandering, also increased.  Except for the 50\% Pt
454 > system where step coalescence occurred, the step-edges in the other
455 > simulations preferred to keep nearly the same distance between steps
456 > as in the original (557) lattice, $\sim$13\AA~for Pt and
457 > $\sim$14\AA~for Au.  Previous work by Williams {\it et
458 >  al}.\cite{Williams:1991, Williams:1994} highlights the repulsion
459 > that exists between step-edges even when no direct interactions are
460 > present in the system. This repulsion is caused by an entropic barrier
461 > that arises from the fact that steps cannot cross over one
462 > another. This entropic repulsion does not completely define the
463 > interactions between steps, however, so it is possible to observe step
464 > coalescence on some surfaces.\cite{Williams:1991} The presence and
465 > concentration of adsorbates, as shown in this work, can affect
466 > step-step interactions, potentially leading to a new surface structure
467 > as the thermodynamic equilibrium.
468 >
469 > \subsubsection{Double layers}
470 > Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the
471 > Pt(557) surface undergoes two separate reconstructions upon CO
472 > adsorption.  The first involves a doubling of the step height and
473 > plateau length.  Similar behavior has been seen on a number of
474 > surfaces at varying conditions, including Ni(977) and
475 > Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we
476 > examined, the Pt system showed a greater propensity for reconstruction
477 > because of the larger surface mobility and the greater extent of step
478 > wandering.  The amount of reconstruction was strongly correlated to
479 > the amount of CO adsorbed upon the surface.  This appears to be
480 > related to the effect that adsorbate coverage has on edge breakup and
481 > on the surface diffusion of metal adatoms. Only the 50\% Pt surface
482 > underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within
483 > the time scales studied here.  Over a longer time scale (150~ns) two
484 > more double layers formed on this surface. Although double layer
485 > formation did not occur in the other Pt systems, they exhibited more
486 > step-wandering and roughening compared to their Au counterparts. The
487 > 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
488 > various times along the simulation showing the evolution of a double
489 > layer step-edge.
490 >
491 > The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010}
492 > involved the formation of triangular clusters that stretched across
493 > the plateau between two step-edges. Neither of the simulated metal
494 > interfaces, within the 40~ns time scale or the extended time of 150~ns
495 > for the 50\% Pt system, experienced this reconstruction.
496 >
497   %Evolution of surface
498   \begin{figure}[H]
499 < \includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
500 < \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.}
499 > \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation}
500 > \caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a)
501 >  258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after
502 >  exposure. Disruption of the (557) step-edges occurs quickly.  The
503 >  doubling of the layers appears only after two adjacent step-edges
504 >  touch.  The circled spot in (b) nucleated the growth of the double
505 >  step observed in the later configurations.}
506 >  \label{fig:reconstruct}
507   \end{figure}
508  
509 + \subsection{Dynamics}
510 + Previous experimental work by Pearl and Sibener\cite{Pearl}, using
511 + STM, has been able to capture the coalescence of steps on Ni(977). The
512 + time scale of the image acquisition, $\sim$70~s/image, provides an
513 + upper bound for the time required for the doubling to occur. By
514 + utilizing Molecular Dynamics we are able to probe the dynamics of
515 + these reconstructions at elevated temperatures and in this section we
516 + provide data on the timescales for transport properties,
517 + e.g. diffusion and layer formation time.
518  
519  
520 + \subsubsection{Transport of surface metal atoms}
521 + %forcedSystems/stepSeparation
522  
523 + The wandering of a step-edge is a cooperative effect arising from the
524 + individual movements of the atoms making up the steps. An ideal metal
525 + surface displaying a low index facet, (111) or (100), is unlikely to
526 + experience much surface diffusion because of the large energetic
527 + barrier that must be overcome to lift an atom out of the surface. The
528 + presence of step-edges and other surface features on higher-index
529 + facets provides a lower energy source for mobile metal atoms.  Using
530 + our potential model, single-atom break-away from a step-edge on a
531 + clean surface still imposes an energetic penalty around
532 + $\sim$~45~kcal/mol, but this is certainly easier than lifting the same
533 + metal atom vertically out of the surface, \textgreater~60~kcal/mol.
534 + The penalty lowers significantly when CO is present in sufficient
535 + quantities on the surface. For certain distributions of CO, the
536 + energetic penalty can fall to as low as $\sim$~20~kcal/mol. The
537 + configurations that create these lower barriers are detailed in the
538 + discussion section below.
539 +
540 + Once an adatom exists on the surface, the barrier for diffusion is
541 + negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are
542 + then able to explore the terrace before rejoining either their
543 + original step-edge or becoming a part of a different edge. It is an
544 + energetically unfavorable process with a high barrier for an atom to
545 + traverse to a separate terrace although the presence of CO can lower
546 + the energy barrier required to lift or lower an adatom. By tracking
547 + the mobility of individual metal atoms on the Pt and Au surfaces we
548 + were able to determine the relative diffusion constants, as well as
549 + how varying coverages of CO affect the diffusion. Close observation of
550 + the mobile metal atoms showed that they were typically in equilibrium
551 + with the step-edges.  At times, their motion was concerted, and two or
552 + more adatoms would be observed moving together across the surfaces.
553 +
554 + A particle was considered ``mobile'' once it had traveled more than
555 + 2~\AA~ between saved configurations of the system (typically 10-100
556 + ps). A mobile atom would typically travel much greater distances than
557 + this, but the 2~\AA~cutoff was used to prevent swamping the diffusion
558 + data with the in-place vibrational movement of buried atoms. Diffusion
559 + on a surface is strongly affected by local structures and the presence
560 + of single and double layer step-edges causes the diffusion parallel to
561 + the step-edges to be larger than the diffusion perpendicular to these
562 + edges. Parallel and perpendicular diffusion constants are shown in
563 + Figure \ref{fig:diff}.  Diffusion parallel to the step-edge is higher
564 + than diffusion perpendicular to the edge because of the lower energy
565 + barrier associated with sliding along an edge compared to breaking
566 + away to form an isolated adatom.
567 +
568 + %Diffusion graph
569 + \begin{figure}[H]
570 + \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1}
571 + \caption{Diffusion constants for mobile surface atoms along directions
572 +  parallel ($\mathbf{D}_{\parallel}$) and perpendicular
573 +  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
574 +  surface coverage.  The two reported diffusion constants for the 50\%
575 +  Pt system correspond to a 20~ns period before the formation of the
576 +  double layer (upper points), and to the full 40~ns sampling period
577 +  (lower points).}
578 + \label{fig:diff}
579 + \end{figure}
580 +
581 + The weaker Au-CO interaction is evident in the weak CO-coverage
582 + dependance of Au diffusion. This weak interaction leads to lower
583 + observed coverages when compared to dosage amounts. This further
584 + limits the effect the CO can have on surface diffusion. The correlation
585 + between coverage and Pt diffusion rates shows a near linear relationship
586 + at the earliest times in the simulations. Following double layer formation,
587 + however, there is a precipitous drop in adatom diffusion. As the double
588 + layer forms, many atoms that had been tracked for mobility data have
589 + now been buried, resulting in a smaller reported diffusion constant. A
590 + secondary effect of higher coverages is CO-CO cross interactions that
591 + lower the effective mobility of the Pt adatoms that are bound to each CO.
592 + This effect would become evident only at higher coverages. A detailed
593 + account of Pt adatom energetics follows in the Discussion.
594 +
595 + \subsubsection{Dynamics of double layer formation}
596 + The increased diffusion on Pt at the higher CO coverages is the primary
597 + contributor to double layer formation. However, this is not a complete
598 + explanation -- the 33\%~Pt system has higher diffusion constants, but
599 + did not show any signs of edge doubling in 40~ns. On the 50\%~Pt
600 + system, one double layer formed within the first 40~ns of simulation time,
601 + while two more were formed as the system was allowed to run for an
602 + additional 110~ns (150~ns total). This suggests that this reconstruction
603 + is a rapid process and that the previously mentioned upper bound is a
604 + very large overestimate.\cite{Williams:1991,Pearl} In this system the first
605 + appearance of a double layer appears at 19~ns into the simulation.
606 + Within 12~ns of this nucleation event, nearly half of the step has formed
607 + the double layer and by 86~ns the complete layer has flattened out.
608 + From the appearance of the first nucleation event to the first observed
609 + double layer, the process took $\sim$20~ns. Another $\sim$40~ns was
610 + necessary for the layer to completely straighten. The other two layers in
611 + this simulation formed over periods of 22~ns and 42~ns respectively.
612 + A possible explanation for this rapid reconstruction is the elevated
613 + temperatures under which our systems were simulated. The process
614 + would almost certainly take longer at lower temperatures. Additionally,
615 + our measured times for completion of the doubling after the appearance
616 + of a nucleation site are likely affected by our periodic boxes. A longer
617 + step-edge will likely take longer to ``zipper''.
618 +
619 +
620 + %Discussion
621 + \section{Discussion}
622 + We have shown that a classical potential is able to model the initial
623 + reconstruction of the Pt(557) surface upon CO adsorption, and have
624 + reproduced the double layer structure observed by Tao {\it et
625 +  al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be
626 + rapid -- occurring within 100 ns of the initial exposure to CO.  Here
627 + we discuss the features of the classical potential that are
628 + contributing to the stability and speed of the Pt(557) reconstruction.
629 +
630 + \subsection{Diffusion}
631 + The perpendicular diffusion constant appears to be the most important
632 + indicator of double layer formation. As highlighted in Figure
633 + \ref{fig:reconstruct}, the formation of the double layer did not begin
634 + until a nucleation site appeared.  Williams {\it et
635 +  al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge
636 + repulsion arising from the inability of edge crossing.  This repulsion
637 + must be overcome to allow step coalescence.  A larger
638 + $\textbf{D}_\perp$ value implies more step-wandering and a larger
639 + chance for the stochastic meeting of two edges to create a nucleation
640 + point.  Diffusion parallel to the step-edge can help ``zipper'' up a
641 + nascent double layer. This helps explain the rapid time scale for
642 + double layer completion after the appearance of a nucleation site, while
643 + the initial appearance of the nucleation site was unpredictable.
644 +
645 + \subsection{Mechanism for restructuring}
646 + Since the Au surface showed no large scale restructuring in any of our
647 + simulations, our discussion will focus on the 50\% Pt-CO system which
648 + did exhibit doubling. A number of possible mechanisms exist to explain
649 + the role of adsorbed CO in restructuring the Pt surface. Quadrupolar
650 + repulsion between adjacent CO molecules adsorbed on the surface is one
651 + possibility.  However, the quadrupole-quadrupole interaction is
652 + short-ranged and is attractive for some orientations.  If the CO
653 + molecules are ``locked'' in a vertical orientation, through atop
654 + adsorption for example, this explanation would gain credence. Within
655 + the framework of our classical potential, the calculated energetic
656 + repulsion between two CO molecules located a distance of
657 + 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a
658 + vertical orientation, is 8.62 kcal/mol. Moving the CO to the second
659 + nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly
660 + 0. Allowing the CO to rotate away from a purely vertical orientation
661 + also lowers the repulsion. When the carbons are locked at a distance
662 + of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle
663 + between the 2 CO is $\sim$24\textsuperscript{o}.  The calculated
664 + barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
665 + repulsion between adjacent CO molecules bound to Pt could indeed
666 + increase the surface diffusion. However, the residence time of CO on
667 + Pt suggests that the CO molecules are extremely mobile, with diffusion
668 + constants 40 to 2500 times larger than surface Pt atoms. This mobility
669 + suggests that the CO molecules jump between different Pt atoms
670 + throughout the simulation.  However, they do stay bound to individual
671 + Pt atoms for long enough to modify the local energy landscape for the
672 + mobile adatoms.
673 +
674 + A different interpretation of the above mechanism which takes the
675 + large mobility of the CO into account, would be in the destabilization
676 + of Pt-Pt interactions due to bound CO.  Destabilizing Pt-Pt bonds at
677 + the edges could lead to increased step-edge breakup and diffusion. On
678 + the bare Pt(557) surface the barrier to completely detach an edge atom
679 + is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
680 + \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain
681 + configurations, cases (e), (g), and (h), the barrier can be lowered to
682 + $\sim$23~kcal/mol by the presence of bound CO molecules. In these
683 + instances, it becomes energetically favorable to roughen the edge by
684 + introducing a small separation of 0.5 to 1.0~\AA. This roughening
685 + becomes immediately obvious in simulations with significant CO
686 + populations. The roughening is present to a lesser extent on surfaces
687 + with lower CO coverage (and even on the bare surfaces), although in
688 + these cases it is likely due to random fluctuations that squeeze out
689 + step-edge atoms. Step-edge breakup by direct single-atom translations
690 + (as suggested by these energy curves) is probably a worst-case
691 + scenario.  Multistep mechanisms in which an adatom moves laterally on
692 + the surface after being ejected would be more energetically favorable.
693 + This would leave the adatom alongside the ledge, providing it with
694 + five nearest neighbors.  While fewer than the seven neighbors it had
695 + as part of the step-edge, it keeps more Pt neighbors than the three
696 + neighbors an isolated adatom has on the terrace. In this proposed
697 + mechanism, the CO quadrupolar repulsion still plays a role in the
698 + initial roughening of the step-edge, but not in any long-term bonds
699 + with individual Pt atoms.  Higher CO coverages create more
700 + opportunities for the crowded CO configurations shown in Figure
701 + \ref{fig:SketchGraphic}, and this is likely to cause an increased
702 + propensity for step-edge breakup.
703 +
704 + %Sketch graphic of different configurations
705 + \begin{figure}[H]
706 + \includegraphics[width=\linewidth]{COpaths}
707 + \caption{Configurations used to investigate the mechanism of step-edge
708 +  breakup on Pt(557). In each case, the central (starred) atom was
709 +  pulled directly across the surface away from the step edge.  The Pt
710 +  atoms on the upper terrace are colored dark grey, while those on the
711 +  lower terrace are in white.  In each of these configurations, some
712 +  of the atoms (highlighted in blue) had CO molecules bound in the
713 +  vertical atop position.  The energies of these configurations as a
714 +  function of central atom displacement are displayed in Figure
715 +  \ref{fig:SketchEnergies}.}
716 + \label{fig:SketchGraphic}
717 + \end{figure}
718 +
719 + %energy graph corresponding to sketch graphic
720 + \begin{figure}[H]
721 + \includegraphics[width=\linewidth]{Portrait_SeparationComparison}
722 + \caption{Energies for displacing a single edge atom perpendicular to
723 +  the step edge as a function of atomic displacement. Each of the
724 +  energy curves corresponds to one of the labeled configurations in
725 +  Figure \ref{fig:SketchGraphic}, and the energies are referenced to
726 +  the unperturbed step-edge.  Certain arrangements of bound CO
727 +  (notably configurations g and h) can lower the energetic barrier for
728 +  creating an adatom relative to the bare surface (configuration a).}
729 + \label{fig:SketchEnergies}
730 + \end{figure}
731 +
732 + While configurations of CO on the surface are able to increase
733 + diffusion and the likelihood of edge wandering, this does not provide
734 + a complete explanation for the formation of double layers. If adatoms
735 + were constrained to their original terraces then doubling could not
736 + occur.  A mechanism for vertical displacement of adatoms at the
737 + step-edge is required to explain the doubling.
738 +
739 + We have discovered one possible mechanism for a CO-mediated vertical
740 + displacement of Pt atoms at the step edge. Figure \ref{fig:lambda}
741 + shows four points along a reaction coordinate in which a CO-bound
742 + adatom along the step-edge ``burrows'' into the edge and displaces the
743 + original edge atom onto the higher terrace.  A number of events
744 + similar to this mechanism were observed during the simulations.  We
745 + predict an energetic barrier of 20~kcal/mol for this process (in which
746 + the displaced edge atom follows a curvilinear path into an adjacent
747 + 3-fold hollow site).  The barrier heights we obtain for this reaction
748 + coordinate are approximate because the exact path is unknown, but the
749 + calculated energy barriers would be easily accessible at operating
750 + conditions.  Additionally, this mechanism is exothermic, with a final
751 + energy 15~kcal/mol below the original $\lambda = 0$ configuration.
752 + When CO is not present and this reaction coordinate is followed, the
753 + process is endothermic by 3~kcal/mol.  The difference in the relative
754 + energies for the $\lambda=0$ and $\lambda=1$ case when CO is present
755 + provides strong support for CO-mediated Pt-Pt interactions giving rise
756 + to the doubling reconstruction.
757 +
758 + %lambda progression of Pt -> shoving its way into the step
759 + \begin{figure}[H]
760 + \includegraphics[width=\linewidth]{EPS_rxnCoord}
761 + \caption{Points along a possible reaction coordinate for CO-mediated
762 +  edge doubling. Here, a CO-bound adatom burrows into an established
763 +  step edge and displaces an edge atom onto the upper terrace along a
764 +  curvilinear path.  The approximate barrier for the process is
765 +  20~kcal/mol, and the complete process is exothermic by 15~kcal/mol
766 +  in the presence of CO, but is endothermic by 3~kcal/mol without CO.}
767 + \label{fig:lambda}
768 + \end{figure}
769 +
770 + The mechanism for doubling on the Pt(557) surface appears to require
771 + the cooperation of at least two distinct processes. For complete
772 + doubling of a layer to occur there must be a breakup of one
773 + terrace. These atoms must then ``disappear'' from that terrace, either
774 + by travelling to the terraces above or below their original levels.
775 + The presence of CO helps explain mechanisms for both of these
776 + situations. There must be sufficient breakage of the step-edge to
777 + increase the concentration of adatoms on the surface and these adatoms
778 + must then undergo the burrowing highlighted above (or a comparable
779 + mechanism) to create the double layer.  With sufficient time, these
780 + mechanisms working in concert lead to the formation of a double layer.
781 +
782 + \subsection{CO Removal and double layer stability}
783 + Once the double layers had formed on the 50\%~Pt system, they remained
784 + stable for the rest of the simulation time with minimal movement.
785 + Random fluctuations that involved small clusters or divots were
786 + observed, but these features typically healed within a few
787 + nanoseconds.  Within our simulations, the formation of the double
788 + layer appeared to be irreversible and a double layer was never
789 + observed to split back into two single layer step-edges while CO was
790 + present.
791 +
792 + To further gauge the effect CO has on this surface, additional
793 + simulations were run starting from a late configuration of the 50\%~Pt
794 + system that had already formed double layers. These simulations then
795 + had their CO molecules suddenly removed.  The double layer broke apart
796 + rapidly in these simulations, showing a well-defined edge-splitting
797 + after 100~ps. Configurations of this system are shown in Figure
798 + \ref{fig:breaking}. The coloring of the top and bottom layers helps to
799 + show how much mixing the edges experience as they split. These systems
800 + were only examined for 10~ns, and within that time despite the initial
801 + rapid splitting, the edges only moved another few \AA~apart. It is
802 + possible that with longer simulation times, the (557) surface recovery
803 + observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered.
804 +
805 + %breaking of the double layer upon removal of CO
806 + \begin{figure}[H]
807 + \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking}
808 + \caption{Behavior of an established (111) double step after removal of
809 +  the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the
810 +  removal of CO.  Nearly immediately after the CO is removed, the
811 +  step edge reforms in a (100) configuration, which is also the step
812 +  type seen on clean (557) surfaces. The step separation involves
813 +  significant mixing of the lower and upper atoms at the edge.}
814 + \label{fig:breaking}
815 + \end{figure}
816 +
817 +
818   %Peaks!
819 < \includegraphics[scale=0.25]{doublePeaks_noCO.png}
820 < \section{Conclusion}
819 > %\begin{figure}[H]
820 > %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
821 > %\caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
822 > %of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with
823 > %aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
824 > %\label{fig:peaks}
825 > %\end{figure}
826  
827  
828 + %Don't think I need this
829 + %clean surface...
830 + %\begin{figure}[H]
831 + %\includegraphics[width=\linewidth]{557_300K_cleanPDF}
832 + %\caption{}
833  
834 + %\end{figure}
835 + %\label{fig:clean}
836  
837  
838 + \section{Conclusion}
839 + The strength and directionality of the Pt-CO binding interaction, as
840 + well as the large quadrupolar repulsion between atop-bound CO
841 + molecules, help to explain the observed increase in surface mobility
842 + of Pt(557) and the resultant reconstruction into a double-layer
843 + configuration at the highest simulated CO-coverages.  The weaker Au-CO
844 + interaction results in significantly lower adataom diffusion
845 + constants, less step-wandering, and a lack of the double layer
846 + reconstruction on the Au(557) surface.
847  
848 + An in-depth examination of the energetics shows the important role CO
849 + plays in increasing step-breakup and in facilitating edge traversal
850 + which are both necessary for double layer formation.
851  
852 + %Things I am not ready to remove yet
853  
854 + %Table of Diffusion Constants
855 + %Add gold?M
856 + % \begin{table}[H]
857 + %   \caption{}
858 + %   \centering
859 + % \begin{tabular}{| c | cc | cc | }
860 + %   \hline
861 + %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
862 + %   \hline
863 + %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
864 + %   \hline
865 + %   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
866 + %   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
867 + %   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
868 + %   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
869 + %   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
870 + %   \hline
871 + % \end{tabular}
872 + % \end{table}
873  
874 + \begin{acknowledgement}
875 +  We gratefully acknowledge conversations with Dr. William
876 +  F. Schneider and Dr. Feng Tao.  Support for this project was
877 +  provided by the National Science Foundation under grant CHE-0848243
878 +  and by the Center for Sustainable Energy at Notre Dame
879 +  (cSEND). Computational time was provided by the Center for Research
880 +  Computing (CRC) at the University of Notre Dame.
881 + \end{acknowledgement}
882 + \newpage
883 + \bibstyle{achemso}
884 + \bibliography{COonPtAu}
885 + %\end{doublespace}
886  
887 + \begin{tocentry}
888 + \begin{wrapfigure}{l}{0.5\textwidth}
889 + \begin{center}
890 + \includegraphics[width=\linewidth]{TOC_doubleLayer}
891 + \end{center}
892 + \end{wrapfigure}
893 + A reconstructed Pt(557) surface after 86~ns exposure to a half a
894 + monolayer of CO.  The double layer that forms is a result of
895 + CO-mediated step-edge wandering as well as a burrowing mechanism that
896 + helps lift edge atoms onto an upper terrace.
897 + \end{tocentry}
898  
899 < \end{document}
899 > \end{document}

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