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# Line 1 | Line 1
1 < \documentclass[11pt]{article}
2 < \usepackage{amsmath}
3 < \usepackage{amssymb}
4 < \usepackage{setspace}
5 < \usepackage{endfloat}
6 < \usepackage{caption}
7 < %\usepackage{tabularx}
8 < \usepackage{graphicx}
1 > \documentclass[journal = jpccck, manuscript = article]{achemso}
2 > \setkeys{acs}{usetitle = true}
3 > \usepackage{achemso}
4 > \usepackage{natbib}
5   \usepackage{multirow}
6 < %\usepackage{booktabs}
7 < %\usepackage{bibentry}
8 < %\usepackage{mathrsfs}
9 < %\usepackage[ref]{overcite}
14 < \usepackage[square, comma, sort&compress]{natbib}
6 > \usepackage{wrapfig}
7 > %\mciteErrorOnUnknownfalse
8 >
9 > \usepackage[version=3]{mhchem}  % this is a great package for formatting chemical reactions
10   \usepackage{url}
16 – \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
17 – \evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
18 – 9.0in \textwidth 6.5in \brokenpenalty=10000
11  
12 < % double space list of tables and figures
13 < \AtBeginDelayedFloats{\renewcommand{\baselinestretch}{1.66}}
22 < \setlength{\abovecaptionskip}{20 pt}
23 < \setlength{\belowcaptionskip}{30 pt}
12 > \title{Molecular Dynamics simulations of the surface reconstructions
13 >  of Pt(557) and Au(557) under exposure to CO}
14  
15 < %\renewcommand\citemid{\ } % no comma in optional reference note
16 < \bibpunct{[}{]}{,}{n}{}{;}
17 < \bibliographystyle{achemso}
15 > \author{Joseph R. Michalka}
16 > \author{Patrick W. McIntyre}
17 > \author{J. Daniel Gezelter}
18 > \email{gezelter@nd.edu}
19 > \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
20 >  Department of Chemistry and Biochemistry\\ University of Notre
21 >  Dame\\ Notre Dame, Indiana 46556}
22  
23 + \keywords{}
24 +
25   \begin{document}
26  
27 <
27 >
28   %%
29   %Introduction
30   %       Experimental observations
# Line 47 | Line 43
43   %Summary
44   %%
45  
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
54 – Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\
55 – Department of Chemistry and Biochemistry,\\
56 – University of Notre Dame\\
57 – Notre Dame, Indiana 46556}
58 – %Date
59 – \date{Dec 15,  2012}
60 – %authors
46  
62 – % make the title
63 – \maketitle
64 –
65 – \begin{doublespace}
66 –
47   \begin{abstract}
48 <
48 >  The mechanism and dynamics of surface reconstructions of Pt(557) and
49 >  Au(557) exposed to various coverages of carbon monoxide (CO) were
50 >  investigated using molecular dynamics simulations.  Metal-CO
51 >  interactions were parameterized from experimental data and
52 >  plane-wave Density Functional Theory (DFT) calculations.  The large
53 >  difference in binding strengths of the Pt-CO and Au-CO interactions
54 >  was found to play a significant role in step-edge stability and
55 >  adatom diffusion constants.  Various mechanisms for CO-mediated step
56 >  wandering and step doubling were investigated on the Pt(557)
57 >  surface.  We find that the energetics of CO adsorbed to the surface
58 >  can explain the step-doubling reconstruction observed on Pt(557) and
59 >  the lack of such a reconstruction on the Au(557) surface.  However,
60 >  more complicated reconstructions into triangular clusters that have
61 >  been seen in recent experiments were not observed in these
62 >  simulations.
63   \end{abstract}
64  
65   \newpage
# Line 79 | Line 73 | Industrial catalysts usually consist of small particle
73   %       Sub: Also, easier to observe what is going on and provide reasons and explanations
74   %
75  
76 < Industrial catalysts usually consist of small particles exposing
77 < different atomic terminations that exhibit a high concentration of
78 < step, kink sites, and vacancies at the edges of the facets.  These
85 < sites are thought to be the locations of catalytic
76 > Industrial catalysts usually consist of small particles that exhibit a
77 > high concentration of steps, kink sites, and vacancies at the edges of
78 > the facets.  These sites are thought to be the locations of catalytic
79   activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now
80 < significant evidence to demonstrate that solid surfaces are often
81 < structurally, compositionally, and chemically {\it modified} by
82 < reactants under operating conditions.\cite{Tao2008,Tao:2010,Tao2011}
83 < The coupling between surface oxidation state and catalytic activity
84 < for CO oxidation on Pt, for instance, is widely
85 < documented.\cite{Ertl08,Hendriksen:2002} Despite the well-documented
86 < role of these effects on reactivity, the ability to capture or predict
87 < them in atomistic models is currently somewhat limited.  While these
88 < effects are perhaps unsurprising on the highly disperse, multi-faceted
89 < nanoscale particles that characterize industrial catalysts, they are
90 < manifest even on ordered, well-defined surfaces. The Pt(557) surface,
91 < for example, exhibits substantial and reversible restructuring under
92 < exposure to moderate pressures of carbon monoxide.\cite{Tao:2010}
80 > significant evidence that solid surfaces are often structurally,
81 > compositionally, and chemically modified by reactants under operating
82 > conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between
83 > surface oxidation states and catalytic activity for CO oxidation on
84 > Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002}
85 > Despite the well-documented role of these effects on reactivity, the
86 > ability to capture or predict them in atomistic models is somewhat
87 > limited.  While these effects are perhaps unsurprising on the highly
88 > disperse, multi-faceted nanoscale particles that characterize
89 > industrial catalysts, they are manifest even on ordered, well-defined
90 > surfaces. The Pt(557) surface, for example, exhibits substantial and
91 > reversible restructuring under exposure to moderate pressures of
92 > carbon monoxide.\cite{Tao:2010}
93  
94 < This work is part of an ongoing effort to understand the causes,
95 < mechanisms and timescales for surface restructuring using molecular
96 < simulation methods.  Since the dynamics of the process is of
97 < particular interest, we utilize classical molecular dynamic methods
98 < with force fields that represent a compromise between chemical
99 < accuracy and the computational efficiency necessary to observe the
100 < process of interest.
94 > This work is an investigation into the mechanism and timescale for the
95 > Pt(557) \& Au(557) surface restructuring using molecular simulation.
96 > Since the dynamics of the process are of particular interest, we
97 > employ classical force fields that represent a compromise between
98 > chemical accuracy and the computational efficiency necessary to
99 > simulate the process of interest.  Since restructuring typically
100 > occurs as a result of specific interactions of the catalyst with
101 > adsorbates, in this work, two metal systems exposed to carbon monoxide
102 > were examined. The Pt(557) surface has already been shown to undergo a
103 > large scale reconstruction under certain conditions.\cite{Tao:2010}
104 > The Au(557) surface, because of weaker interactions with CO, is less
105 > likely to undergo this kind of reconstruction. However, Peters {\it et
106 >  al}.\cite{Peters:2000} and Piccolo {\it et al}.\cite{Piccolo:2004}
107 > have both observed CO-induced modification of reconstructions to the
108 > Au(111) surface. Peters {\it et al}. observed the Au(111)-($22 \times
109 > \sqrt{3}$) ``herringbone'' reconstruction relaxing slightly under CO
110 > adsorption. They argued that only a few Au atoms become adatoms,
111 > limiting the stress of this reconstruction, while allowing the rest to
112 > relax and approach the ideal (111) configuration.  Piccolo {\it et
113 >  al}. on the other hand, saw a more significant disruption of the
114 > Au(111)-($22 \times \sqrt{3}$) herringbone pattern as CO adsorbed on
115 > the surface. Both groups suggested that the preference CO shows for
116 > low-coordinated Au atoms was the primary driving force for the
117 > relaxation.  Although the Au(111) reconstruction was not the primary
118 > goal of our work, the classical models we have fit may be of future
119 > use in simulating this reconstruction.
120  
109 – Since restructuring occurs as a result of specific interactions of the catalyst
110 – 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.
121   %Platinum molecular dynamics
122   %gold molecular dynamics
123  
117 –
118 –
119 –
120 –
121 –
124   \section{Simulation Methods}
125 < The challenge in modeling any solid/gas interface problem is the
126 < development of a sufficiently general yet computationally tractable
127 < model of the chemical interactions between the surface atoms and
128 < adsorbates.  Since the interfaces involved are quite large (10$^3$ -
129 < 10$^6$ atoms) and respond slowly to perturbations, {\it ab initio}
125 > The challenge in modeling any solid/gas interface is the development
126 > of a sufficiently general yet computationally tractable model of the
127 > chemical interactions between the surface atoms and adsorbates.  Since
128 > the interfaces involved are quite large (10$^3$ - 10$^4$ atoms), have
129 > many electrons, and respond slowly to perturbations, {\it ab initio}
130   molecular dynamics
131   (AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello
132   methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum
# Line 133 | Line 135 | Coulomb potential.  For this work, we have been using
135   typically not well represented in terms of classical pairwise
136   interactions in the same way that bonds in a molecular material are,
137   nor are they captured by simple non-directional interactions like the
138 < Coulomb potential.  For this work, we have been using classical
139 < molecular dynamics with potential energy surfaces that are
140 < specifically tuned for transition metals.  In particular, we use the
141 < EAM potential for Au-Au and Pt-Pt interactions, while modeling the CO
142 < using a model developed by Straub and Karplus for studying
143 < photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and Pt-CO
144 < cross interactions were parameterized as part of this work.
138 > Coulomb potential.  For this work, we have used classical molecular
139 > dynamics with potential energy surfaces that are specifically tuned
140 > for transition metals.  In particular, we used the EAM potential for
141 > Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using
142 > a rigid three-site model developed by Straub and Karplus for studying
143 > photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and
144 > Pt-CO cross interactions were parameterized as part of this work.
145    
146   \subsection{Metal-metal interactions}
147 < Many of the potentials used for classical simulation of transition
148 < metals are based on a non-pairwise additive functional of the local
149 < electron density. The embedded atom method (EAM) is perhaps the best
150 < known of these
147 > Many of the potentials used for modeling transition metals are based
148 > on a non-pairwise additive functional of the local electron
149 > density. The embedded atom method (EAM) is perhaps the best known of
150 > these
151   methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98}
152   but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and
153   the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler
154 < parameter sets. The glue model of Ercolessi {\it et al.} is among the
155 < fastest of these density functional approaches.\cite{Ercolessi88} In
156 < all of these models, atoms are conceptualized as a positively charged
157 < core with a radially-decaying valence electron distribution. To
158 < calculate the energy for embedding the core at a particular location,
159 < the electron density due to the valence electrons at all of the other
160 < atomic sites is computed at atom $i$'s location,
154 > parameter sets. The glue model of Ercolessi {\it et
155 >  al}.\cite{Ercolessi88} is among the fastest of these density
156 > functional approaches. In all of these models, atoms are treated as a
157 > positively charged core with a radially-decaying valence electron
158 > distribution. To calculate the energy for embedding the core at a
159 > particular location, the electron density due to the valence electrons
160 > at all of the other atomic sites is computed at atom $i$'s location,
161   \begin{equation*}
162   \bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
163   \end{equation*}
# Line 167 | Line 169 | $\phi_{ij}(r_{ij})$ is an pairwise term that is meant
169   V_i =  F[ \bar{\rho}_i ]  + \sum_{j \neq i} \phi_{ij}(r_{ij})
170   \end{equation*}
171   where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and
172 < $\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the
173 < overlap of the two positively charged cores.  
172 > $\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the
173 > repulsive overlap of the two positively charged cores.  
174  
175 < The {\it modified} embedded atom method (MEAM) adds angular terms to
176 < the electron density functions and an angular screening factor to the
177 < pairwise interaction between two
178 < atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
179 < MEAM has become widely used to simulate systems in which angular
180 < interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
181 < metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
182 < MEAM presents significant additional computational costs, however.
175 > % The {\it modified} embedded atom method (MEAM) adds angular terms to
176 > % the electron density functions and an angular screening factor to the
177 > % pairwise interaction between two
178 > % atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
179 > % MEAM has become widely used to simulate systems in which angular
180 > % interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
181 > % metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
182 > % MEAM presents significant additional computational costs, however.
183  
184 < The EAM, Finnis-Sinclair, MEAM, and the Quantum Sutton-Chen potentials
184 > The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials
185   have all been widely used by the materials simulation community for
186   simulations of bulk and nanoparticle
187 < properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq}
187 > properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq,mishin99:_inter}
188   melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
189 < fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack
190 < propagation,\cite{BECQUART:1993rg} and alloying
191 < dynamics.\cite{Shibata:2002hh} All of these potentials have their
192 < strengths and weaknesses.  One of the strengths common to all of the
193 < methods is the relatively large library of metals for which these
194 < potentials have been
195 < parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
189 > fracture,\cite{Shastry:1996qg,Shastry:1998dx,mishin01:cu} crack
190 > propagation,\cite{BECQUART:1993rg,Rifkin1992} and alloying
191 > dynamics.\cite{Shibata:2002hh,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
192 > One of EAM's strengths is its sensitivity to small changes in
193 > structure. This is due to the inclusion of up to the third nearest
194 > neighbor interactions during fitting of the parameters.\cite{Voter95a}
195 > In comparison, the glue model of Ercolessi {\it et
196 >  al}.\cite{Ercolessi88} was only parameterized to include
197 > nearest-neighbor interactions, EAM is a suitable choice for systems
198 > where the bulk properties are of secondary importance to low-index
199 > surface structures. Additionally, the similarity of EAM's functional
200 > treatment of the embedding energy to standard density functional
201 > theory (DFT) makes fitting DFT-derived cross potentials with
202 > adsorbates somewhat easier.
203  
204 < \subsection{CO}
205 < Since one explanation for the strong surface CO repulsion on metals is
206 < the large linear quadrupole moment of carbon monoxide, the model
207 < chosen for this molecule exhibits this property in an efficient
208 < manner.  We used a model first proposed by Karplus and Straub to study
209 < the photodissociation of CO from myoglobin.\cite{Straub} The Straub and
210 < Karplus model is a rigid three site model which places a massless M
211 < site at the center of mass along the CO bond.  The geometry used along
212 < with the interaction parameters are reproduced in Table 1. The effective
213 < dipole moment, calculated from the assigned charges, is still
214 < small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
215 < to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
204 > \subsection{Carbon Monoxide model}
205 > Previous explanations for the surface rearrangements center on the
206 > large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} We
207 > used a model first proposed by Karplus and Straub to study the
208 > photodissociation of CO from myoglobin because it reproduces the
209 > quadrupole moment well.\cite{Straub} The Straub and Karplus model
210 > treats CO as a rigid three site molecule with a massless
211 > charge-carrying ``M'' site at the center of mass. The geometry and
212 > interaction parameters are reproduced in Table~\ref{tab:CO}. The
213 > effective dipole moment, calculated from the assigned charges, is
214 > still small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is
215 > close to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
216   mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
217   %CO Table
218   \begin{table}[H]
219 < \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 $e$.}
219 >  \caption{Positions, Lennard-Jones parameters ($\sigma$ and
220 >    $\epsilon$), and charges for CO-CO
221 >    interactions. Distances are in \AA, energies are
222 >    in kcal/mol, and charges are in atomic units.  The CO model
223 >    from Ref.\bibpunct{}{}{,}{n}{}{,}
224 >    \protect\cite{Straub} was used without modification.}
225   \centering
226   \begin{tabular}{| c | c | ccc |}
227   \hline
228 < \multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\
228 > &  {\it z} & $\sigma$ & $\epsilon$ & q\\
229   \hline
230 < &  r & $\sigma$ & $\epsilon$ & q\\
230 > \textbf{C} & -0.6457 &  3.83 & 0.0262   &   -0.75 \\
231 > \textbf{O} &  0.4843 &  3.12 &  0.1591  &   -0.85 \\
232 > \textbf{M} & 0.0 & -  &  -  &    1.6 \\
233   \hline
218 – \textbf{C} & 0.0 &  0.0262  & 3.83   &   -0.75 \\
219 – \textbf{O} &  1.13 &   0.1591 &   3.12 &   -0.85 \\
220 – \textbf{M} & 0.6457 & -  &  -  &    1.6 \\
221 – \hline
234   \end{tabular}
235 + \label{tab:CO}
236   \end{table}
237  
238 < \subsection{Cross-Interactions}
238 > \subsection{Cross-Interactions between the metals and carbon monoxide}
239  
240 < One hurdle that must be overcome in classical molecular simulations
241 < is the proper parameterization of the potential interactions present
242 < in the system. Since the adsorption of CO onto a platinum surface has been
243 < the focus of many experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
244 < and theoretical studies \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
245 < there is a large amount of data in the literature to fit too. We started with parameters
246 < reported by Korzeniewski et al. \cite{Pons:1986} and then
247 < modified them to ensure that the Pt-CO interaction favored
248 < an atop binding position for the CO upon the Pt surface. This
249 < constraint led to the binding energies being on the higher side
250 < of reported values. Following the method laid out by Korzeniewski,
251 < the Pt-C interaction was fit to a strong Lennard-Jones 12-6
252 < interaction to mimic binding, while the Pt-O interaction
253 < was parameterized to a Morse potential with a large $r_o$
254 < to contribute a weak repulsion. The resultant potential-energy
255 < surface suitably recovers the calculated Pt-C bond length ( 1.6\AA)\cite{Beurden:2002ys} and affinity
256 < for the atop binding position.\cite{Deshlahra:2012, Hopster:1978}
240 > Since the adsorption of CO onto a Pt surface has been the focus
241 > of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
242 > and theoretical work
243 > \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
244 > there is a significant amount of data on adsorption energies for CO on
245 > clean metal surfaces. An earlier model by Korzeniewski {\it et
246 >  al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were
247 > modified to ensure that the Pt-CO interaction favored the atop binding
248 > position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}.
249 > The modified parameters yield binding energies that are slightly higher
250 > than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski
251 > {\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
252 > Lennard-Jones interaction to mimic strong, but short-ranged, partial
253 > binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The
254 > Pt-O interaction was modeled with a Morse potential with a large
255 > equilibrium distance, ($r_o$).  These choices ensure that the C is preferred
256 > over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak
257 > repulsion which favors the atop site.  The resulting potential-energy
258 > surface suitably recovers the calculated Pt-C separation length
259 > (1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding
260 > position.\cite{Deshlahra:2012, Hopster:1978}
261  
262   %where did you actually get the functionals for citation?
263   %scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think
264   %same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there...
265 < The Au-C and Au-O interaction parameters were also fit to a Lennard-Jones
266 < and Morse potential respectively, to reproduce Au-CO binding energies.
267 < These energies were obtained from quantum calculations carried out using
268 < the PBE GGA exchange-correlation functionals\cite{Perdew_GGA} for gold, carbon, and oxygen
269 < constructed by Rappe, Rabe, Kaxiras, and Joannopoulos. \cite{RRKJ_PP}.
270 < All calculations were run using the {\sc Quantum ESPRESSO} package. \cite{QE-2009}  
271 < First, a four layer slab of gold comprised of 32 atoms displaying a (111) surface was
272 < converged using a 4X4X4 grid of Monkhorst-Pack \emph{k}-points.\cite{Monkhorst:1976}
273 < The kinetic energy of the wavefunctions were truncated at 20 Ry while the
274 < cutoff for the charge density and potential was set at 80 Ry. This relaxed
275 < gold slab was then used in numerous single point calculations  with CO at various heights
276 < to create a potential energy surface for the Au-CO interaction.
265 > The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and
266 > Morse potentials, respectively, to reproduce Au-CO binding energies.
267 > The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations.
268 > Adsorption energies were obtained from gas-surface DFT calculations with a
269 > periodic supercell plane-wave basis approach, as implemented in the
270 > Quantum ESPRESSO package.\cite{QE-2009} Electron cores were
271 > described with the projector augmented-wave (PAW)
272 > method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
273 > included to an energy cutoff of 20 Ry. Electronic energies are
274 > computed with the PBE implementation of the generalized gradient
275 > approximation (GGA) for gold, carbon, and oxygen that was constructed
276 > by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
277 > In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4
278 > Au x 2 Au surface planes and separated from vertical images by six
279 > layers of vacuum space. The surface atoms were all allowed to relax
280 > before CO was added to the system. Electronic relaxations were
281 > performed until the energy difference between subsequent steps
282 > was less than $10^{-8}$ Ry.   Nonspin-polarized supercell calculations
283 > were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
284 > zone.\cite{Monkhorst:1976} The relaxed gold slab was
285 > then used in numerous single point calculations with CO at various
286 > heights (and angles relative to the surface) to allow fitting of the
287 > empirical force field.
288  
289   %Hint at future work
290 < The fit parameter sets employed in this work are shown in Table 2 and their
291 < reproduction of the binding energies are displayed in Table 3. Currently,
292 < charge transfer is not being treated in this system, however, that is a goal
293 < for future work as the effect has been seen to affect binding energies and
294 < binding site preferences. \cite{Deshlahra:2012}
290 > The parameters employed for the metal-CO cross-interactions in this work
291 > are shown in Table~\ref{tab:co_parameters} and the binding energies on the
292 > (111) surfaces are displayed in Table~\ref{tab:co_energies}.  Charge transfer
293 > and polarization are neglected in this model, although these effects could have
294 > an effect on binding energies and binding site preferences.
295  
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 –
296   %Table  of Parameters
297   %Pt Parameter Set 9
298   %Au Parameter Set 35
299   \begin{table}[H]
300 < \caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol}
300 >  \caption{Parameters for the metal-CO cross-interactions. Metal-C
301 >    interactions are modeled with Lennard-Jones potentials, while the
302 >    metal-O interactions were fit to broad Morse
303 >    potentials.  Distances are given in \AA~and energies in kcal/mol. }
304   \centering
305   \begin{tabular}{| c | cc | c | ccc |}
306   \hline
307 < \multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\
307 > &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
308   \hline
308 – &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\
309 – \hline
309   \textbf{Pt-C} & 1.3 & 15  & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\
310   \textbf{Au-C} & 1.9 & 6.5  & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\
311  
312   \hline
313   \end{tabular}
314 + \label{tab:co_parameters}
315   \end{table}
316  
317   %Table of energies
318   \begin{table}[H]
319 < \caption{Adsorption energies in eV}
319 >  \caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials
320 >    described in this work.  All values are in eV.}
321   \centering
322   \begin{tabular}{| c | cc |}
323 < \hline
324 < & Calc. & Exp. \\
325 < \hline
326 < \textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\
327 < \textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\
328 < \hline
323 >  \hline
324 >  & Calculated & Experimental \\
325 >  \hline
326 >  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,}
327 >  (Ref. \protect\cite{Kelemen:1979}) \\
328 > & &  -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline
329 >  \textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,}  (Ref. \protect\cite{TPDGold}) \\
330 >  \hline
331   \end{tabular}
332 + \label{tab:co_energies}
333   \end{table}
334  
335 + \subsection{Pt(557) and Au(557) metal interfaces}
336 + Our Pt system is an orthorhombic periodic box of dimensions
337 + 54.482~x~50.046~x~120.88~\AA~while our Au system has
338 + dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs
339 + are 9 and 8 atoms deep respectively, corresponding to a slab
340 + thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
341 + The systems are arranged in a FCC crystal that have been cut
342 + along the (557) plane so that they are periodic in the {\it x} and
343 + {\it y} directions, and have been oriented to expose two aligned
344 + (557) cuts along the extended {\it z}-axis.  Simulations of the
345 + bare metal interfaces at temperatures ranging from 300~K to
346 + 1200~K were performed to confirm the relative
347 + stability of the surfaces without a CO overlayer.  
348  
349 <
350 <
351 <
352 <
353 < % Just results, leave discussion for discussion section
354 < \section{Results}
355 < \subsection{Diffusion}
356 < While an ideal metallic surface is unlikely to experience much surface diffusion, high-index surfaces have large numbers of low-coordinated atoms which have a much easier time overcoming the energetic barriers limiting diffusion, leading to easier surface reconstructions. Surface movement was divided between the parallel ($\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.
357 <
358 < %Table of Diffusion Constants
359 < %Add gold?M
360 < \begin{table}[H]
361 < \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}
362 < \centering
363 < \begin{tabular}{| c | ccc | ccc | c |}
364 < \hline
365 < \textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & \textbf{Time (ns)}\\
366 < \hline
367 < &\multicolumn{3}{c|}{\textbf{Mobile}}&\multicolumn{3}{c|}{\textbf{Surface Atoms}} & \\
368 < \hline
369 < 50\% & 3.74 & 0.89 & 497 & 2.05 & 0.49 & 912 & 116 \\
370 < 50\% & 5.81 & 1.59 & 365 & 2.41 & 0.68 & 912 & 46   \\
354 < 33\% & 6.73 & 2.47 & 332 & 2.51 & 0.93 & 912 & 46   \\
355 < 25\% & 5.38 & 2.04 & 361 & 2.18 & 0.84 & 912 & 46  \\
356 < 5\% & 5.54 & 0.63 & 230 & 1.44 & 0.19 & 912 & 46  \\
357 < 0\% & 3.53 & 0.61 & 282 & 1.11 & 0.22 & 912 & 56  \\
358 < \hline
359 < 50\%-r & 6.91 & 2.00 & 198 & 2.23 & 0.68  & 925 & 25\\
360 < 0\%-r  & 4.73 & 0.27 & 128 & 0.72 & 0.05 & 925 & 43\\
361 < \hline
362 < \end{tabular}
363 < \end{table}
349 > The different bulk melting temperatures predicted by EAM
350 > (1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for
351 > Pt\cite{Pt:melting}) suggest that any reconstructions should happen at
352 > different temperatures for the two metals.  The bare Au and Pt
353 > surfaces were initially run in the canonical (NVT) ensemble at 800~K
354 > and 1000~K respectively for 100 ps. The two surfaces were relatively
355 > stable at these temperatures when no CO was present, but experienced
356 > increased surface mobility on addition of CO. Each surface was then
357 > dosed with different concentrations of CO that was initially placed in
358 > the vacuum region.  Upon full adsorption, these concentrations
359 > correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher
360 > coverages resulted in the formation of a double layer of CO, which
361 > introduces artifacts that are not relevant to (557) reconstruction.
362 > Because of the difference in binding energies, nearly all of the CO
363 > was bound to the Pt surface, while the Au surfaces often had a
364 > significant CO population in the gas phase.  These systems were
365 > allowed to reach thermal equilibrium (over 5~ns) before being run in
366 > the microcanonical (NVE) ensemble for data collection. All of the
367 > systems examined had at least 40~ns in the data collection stage,
368 > although simulation times for some Pt of the systems exceeded 200~ns.
369 > Simulations were carried out using the open source molecular dynamics
370 > package, OpenMD.\cite{Ewald,OOPSE,openmd}
371  
372  
373 + % RESULTS
374 + %
375 + \section{Results}
376 + \subsection{Structural remodeling}
377 + The bare metal surfaces experienced minor roughening of the step-edge
378 + because of the elevated temperatures, but the (557) face was stable
379 + throughout the simulations. The surfaces of both systems, upon dosage
380 + of CO, began to undergo extensive remodeling that was not observed in
381 + the bare systems. Reconstructions of the Au systems were limited to
382 + breakup of the step-edges and some step wandering. The lower coverage
383 + Pt systems experienced similar step edge wandering but to a greater
384 + extent. The 50\% coverage Pt system was unique among our simulations
385 + in that it formed well-defined and stable double layers through step
386 + coalescence, similar to results reported by Tao {\it et
387 +  al}.\cite{Tao:2010}
388  
389 + \subsubsection{Step wandering}
390 + The bare surfaces for both metals showed minimal step-wandering at
391 + their respective temperatures. As the CO coverage increased however,
392 + the mobility of the surface atoms, described through adatom diffusion
393 + and step-edge wandering, also increased.  Except for the 50\% Pt
394 + system where step coalescence occurred, the step-edges in the other
395 + simulations preferred to keep nearly the same distance between steps
396 + as in the original (557) lattice, $\sim$13\AA~for Pt and
397 + $\sim$14\AA~for Au.  Previous work by Williams {\it et
398 +  al}.\cite{Williams:1991, Williams:1994} highlights the repulsion
399 + that exists between step-edges even when no direct interactions are
400 + present in the system. This repulsion is caused by an entropic barrier
401 + that arises from the fact that steps cannot cross over one
402 + another. This entropic repulsion does not completely define the
403 + interactions between steps, however, so it is possible to observe step
404 + coalescence on some surfaces.\cite{Williams:1991} The presence and
405 + concentration of adsorbates, as shown in this work, can affect
406 + step-step interactions, potentially leading to a new surface structure
407 + as the thermodynamic equilibrium.
408 +
409 + \subsubsection{Double layers}
410 + Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the
411 + Pt(557) surface undergoes two separate reconstructions upon CO
412 + adsorption.  The first involves a doubling of the step height and
413 + plateau length.  Similar behavior has been seen on a number of
414 + surfaces at varying conditions, including Ni(977) and
415 + Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we
416 + examined, the Pt system showed a greater propensity for reconstruction
417 + because of the larger surface mobility and the greater extent of step
418 + wandering.  The amount of reconstruction was strongly correlated to
419 + the amount of CO adsorbed upon the surface.  This appears to be
420 + related to the effect that adsorbate coverage has on edge breakup and
421 + on the surface diffusion of metal adatoms. Only the 50\% Pt surface
422 + underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within
423 + the time scales studied here.  Over a longer time scale (150~ns) two
424 + more double layers formed on this surface. Although double layer
425 + formation did not occur in the other Pt systems, they exhibited more
426 + step-wandering and roughening compared to their Au counterparts. The
427 + 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
428 + various times along the simulation showing the evolution of a double
429 + layer step-edge.
430 +
431 + The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010}
432 + involved the formation of triangular clusters that stretched across
433 + the plateau between two step-edges. Neither of the simulated metal
434 + interfaces, within the 40~ns time scale or the extended time of 150~ns
435 + for the 50\% Pt system, experienced this reconstruction.
436 +
437 + %Evolution of surface
438 + \begin{figure}[H]
439 + \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation}
440 + \caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a)
441 +  258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after
442 +  exposure. Disruption of the (557) step-edges occurs quickly.  The
443 +  doubling of the layers appears only after two adjacent step-edges
444 +  touch.  The circled spot in (b) nucleated the growth of the double
445 +  step observed in the later configurations.}
446 +  \label{fig:reconstruct}
447 + \end{figure}
448 +
449 + \subsection{Dynamics}
450 + Previous experimental work by Pearl and Sibener\cite{Pearl}, using
451 + STM, has been able to capture the coalescence of steps on Ni(977). The
452 + time scale of the image acquisition, $\sim$70~s/image, provides an
453 + upper bound for the time required for the doubling to occur. By
454 + utilizing Molecular Dynamics we are able to probe the dynamics of
455 + these reconstructions at elevated temperatures and in this section we
456 + provide data on the timescales for transport properties,
457 + e.g. diffusion and layer formation time.
458 +
459 +
460 + \subsubsection{Transport of surface metal atoms}
461 + %forcedSystems/stepSeparation
462 +
463 + The wandering of a step-edge is a cooperative effect arising from the
464 + individual movements of the atoms making up the steps. An ideal metal
465 + surface displaying a low index facet, (111) or (100), is unlikely to
466 + experience much surface diffusion because of the large energetic
467 + barrier that must be overcome to lift an atom out of the surface. The
468 + presence of step-edges and other surface features on higher-index
469 + facets provides a lower energy source for mobile metal atoms.  Using
470 + our potential model, single-atom break-away from a step-edge on a
471 + clean surface still imposes an energetic penalty around
472 + $\sim$~45~kcal/mol, but this is certainly easier than lifting the same
473 + metal atom vertically out of the surface, \textgreater~60~kcal/mol.
474 + The penalty lowers significantly when CO is present in sufficient
475 + quantities on the surface. For certain distributions of CO, the
476 + energetic penalty can fall to as low as $\sim$~20~kcal/mol. The
477 + configurations that create these lower barriers are detailed in the
478 + discussion section below.
479 +
480 + Once an adatom exists on the surface, the barrier for diffusion is
481 + negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are
482 + then able to explore the terrace before rejoining either their
483 + original step-edge or becoming a part of a different edge. It is an
484 + energetically unfavorable process with a high barrier for an atom to
485 + traverse to a separate terrace although the presence of CO can lower
486 + the energy barrier required to lift or lower an adatom. By tracking
487 + the mobility of individual metal atoms on the Pt and Au surfaces we
488 + were able to determine the relative diffusion constants, as well as
489 + how varying coverages of CO affect the diffusion. Close observation of
490 + the mobile metal atoms showed that they were typically in equilibrium
491 + with the step-edges.  At times, their motion was concerted, and two or
492 + more adatoms would be observed moving together across the surfaces.
493 +
494 + A particle was considered ``mobile'' once it had traveled more than
495 + 2~\AA~ between saved configurations of the system (typically 10-100
496 + ps). A mobile atom would typically travel much greater distances than
497 + this, but the 2~\AA~cutoff was used to prevent swamping the diffusion
498 + data with the in-place vibrational movement of buried atoms. Diffusion
499 + on a surface is strongly affected by local structures and the presence
500 + of single and double layer step-edges causes the diffusion parallel to
501 + the step-edges to be larger than the diffusion perpendicular to these
502 + edges. Parallel and perpendicular diffusion constants are shown in
503 + Figure \ref{fig:diff}.  Diffusion parallel to the step-edge is higher
504 + than diffusion perpendicular to the edge because of the lower energy
505 + barrier associated with sliding along an edge compared to breaking
506 + away to form an isolated adatom.
507 +
508 + %Diffusion graph
509 + \begin{figure}[H]
510 + \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1}
511 + \caption{Diffusion constants for mobile surface atoms along directions
512 +  parallel ($\mathbf{D}_{\parallel}$) and perpendicular
513 +  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
514 +  surface coverage.  The two reported diffusion constants for the 50\%
515 +  Pt system correspond to a 20~ns period before the formation of the
516 +  double layer (upper points), and to the full 40~ns sampling period
517 +  (lower points).}
518 + \label{fig:diff}
519 + \end{figure}
520 +
521 + The weaker Au-CO interaction is evident in the weak CO-coverage
522 + dependance of Au diffusion. This weak interaction leads to lower
523 + observed coverages when compared to dosage amounts. This further
524 + limits the effect the CO can have on surface diffusion. The correlation
525 + between coverage and Pt diffusion rates shows a near linear relationship
526 + at the earliest times in the simulations. Following double layer formation,
527 + however, there is a precipitous drop in adatom diffusion. As the double
528 + layer forms, many atoms that had been tracked for mobility data have
529 + now been buried, resulting in a smaller reported diffusion constant. A
530 + secondary effect of higher coverages is CO-CO cross interactions that
531 + lower the effective mobility of the Pt adatoms that are bound to each CO.
532 + This effect would become evident only at higher coverages. A detailed
533 + account of Pt adatom energetics follows in the Discussion.
534 +
535 + \subsubsection{Dynamics of double layer formation}
536 + The increased diffusion on Pt at the higher CO coverages is the primary
537 + contributor to double layer formation. However, this is not a complete
538 + explanation -- the 33\%~Pt system has higher diffusion constants, but
539 + did not show any signs of edge doubling in 40~ns. On the 50\%~Pt
540 + system, one double layer formed within the first 40~ns of simulation time,
541 + while two more were formed as the system was allowed to run for an
542 + additional 110~ns (150~ns total). This suggests that this reconstruction
543 + is a rapid process and that the previously mentioned upper bound is a
544 + very large overestimate.\cite{Williams:1991,Pearl} In this system the first
545 + appearance of a double layer appears at 19~ns into the simulation.
546 + Within 12~ns of this nucleation event, nearly half of the step has formed
547 + the double layer and by 86~ns the complete layer has flattened out.
548 + From the appearance of the first nucleation event to the first observed
549 + double layer, the process took $\sim$20~ns. Another $\sim$40~ns was
550 + necessary for the layer to completely straighten. The other two layers in
551 + this simulation formed over periods of 22~ns and 42~ns respectively.
552 + A possible explanation for this rapid reconstruction is the elevated
553 + temperatures under which our systems were simulated. The process
554 + would almost certainly take longer at lower temperatures. Additionally,
555 + our measured times for completion of the doubling after the appearance
556 + of a nucleation site are likely affected by our periodic boxes. A longer
557 + step-edge will likely take longer to ``zipper''.
558 +
559 +
560   %Discussion
561   \section{Discussion}
562 < 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.
562 > We have shown that a classical potential is able to model the initial
563 > reconstruction of the Pt(557) surface upon CO adsorption, and have
564 > reproduced the double layer structure observed by Tao {\it et
565 >  al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be
566 > rapid -- occurring within 100 ns of the initial exposure to CO.  Here
567 > we discuss the features of the classical potential that are
568 > contributing to the stability and speed of the Pt(557) reconstruction.
569  
570   \subsection{Diffusion}
571 < 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?)
572 < \\
573 < \\
574 < %Evolution of surface
575 < \begin{figure}[H]
576 < \includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
577 < \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.}
571 > The perpendicular diffusion constant appears to be the most important
572 > indicator of double layer formation. As highlighted in Figure
573 > \ref{fig:reconstruct}, the formation of the double layer did not begin
574 > until a nucleation site appeared.  Williams {\it et
575 >  al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge
576 > repulsion arising from the inability of edge crossing.  This repulsion
577 > must be overcome to allow step coalescence.  A larger
578 > $\textbf{D}_\perp$ value implies more step-wandering and a larger
579 > chance for the stochastic meeting of two edges to create a nucleation
580 > point.  Diffusion parallel to the step-edge can help ``zipper'' up a
581 > nascent double layer. This helps explain the rapid time scale for
582 > double layer completion after the appearance of a nucleation site, while
583 > the initial appearance of the nucleation site was unpredictable.
584 >
585 > \subsection{Mechanism for restructuring}
586 > Since the Au surface showed no large scale restructuring in any of our
587 > simulations, our discussion will focus on the 50\% Pt-CO system which
588 > did exhibit doubling. A number of possible mechanisms exist to explain
589 > the role of adsorbed CO in restructuring the Pt surface. Quadrupolar
590 > repulsion between adjacent CO molecules adsorbed on the surface is one
591 > possibility.  However, the quadrupole-quadrupole interaction is
592 > short-ranged and is attractive for some orientations.  If the CO
593 > molecules are ``locked'' in a vertical orientation, through atop
594 > adsorption for example, this explanation would gain credence. Within
595 > the framework of our classical potential, the calculated energetic
596 > repulsion between two CO molecules located a distance of
597 > 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a
598 > vertical orientation, is 8.62 kcal/mol. Moving the CO to the second
599 > nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly
600 > 0. Allowing the CO to rotate away from a purely vertical orientation
601 > also lowers the repulsion. When the carbons are locked at a distance
602 > of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle
603 > between the 2 CO is $\sim$24\textsuperscript{o}.  The calculated
604 > barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
605 > repulsion between adjacent CO molecules bound to Pt could indeed
606 > increase the surface diffusion. However, the residence time of CO on
607 > Pt suggests that the CO molecules are extremely mobile, with diffusion
608 > constants 40 to 2500 times larger than surface Pt atoms. This mobility
609 > suggests that the CO molecules jump between different Pt atoms
610 > throughout the simulation.  However, they do stay bound to individual
611 > Pt atoms for long enough to modify the local energy landscape for the
612 > mobile adatoms.
613 >
614 > A different interpretation of the above mechanism which takes the
615 > large mobility of the CO into account, would be in the destabilization
616 > of Pt-Pt interactions due to bound CO.  Destabilizing Pt-Pt bonds at
617 > the edges could lead to increased step-edge breakup and diffusion. On
618 > the bare Pt(557) surface the barrier to completely detach an edge atom
619 > is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
620 > \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain
621 > configurations, cases (e), (g), and (h), the barrier can be lowered to
622 > $\sim$23~kcal/mol by the presence of bound CO molecules. In these
623 > instances, it becomes energetically favorable to roughen the edge by
624 > introducing a small separation of 0.5 to 1.0~\AA. This roughening
625 > becomes immediately obvious in simulations with significant CO
626 > populations. The roughening is present to a lesser extent on surfaces
627 > with lower CO coverage (and even on the bare surfaces), although in
628 > these cases it is likely due to random fluctuations that squeeze out
629 > step-edge atoms. Step-edge breakup by direct single-atom translations
630 > (as suggested by these energy curves) is probably a worst-case
631 > scenario.  Multistep mechanisms in which an adatom moves laterally on
632 > the surface after being ejected would be more energetically favorable.
633 > This would leave the adatom alongside the ledge, providing it with
634 > five nearest neighbors.  While fewer than the seven neighbors it had
635 > as part of the step-edge, it keeps more Pt neighbors than the three
636 > neighbors an isolated adatom has on the terrace. In this proposed
637 > mechanism, the CO quadrupolar repulsion still plays a role in the
638 > initial roughening of the step-edge, but not in any long-term bonds
639 > with individual Pt atoms.  Higher CO coverages create more
640 > opportunities for the crowded CO configurations shown in Figure
641 > \ref{fig:SketchGraphic}, and this is likely to cause an increased
642 > propensity for step-edge breakup.
643 >
644 > %Sketch graphic of different configurations
645 > \begin{figure}[H]
646 > \includegraphics[width=\linewidth]{COpaths}
647 > \caption{Configurations used to investigate the mechanism of step-edge
648 >  breakup on Pt(557). In each case, the central (starred) atom was
649 >  pulled directly across the surface away from the step edge.  The Pt
650 >  atoms on the upper terrace are colored dark grey, while those on the
651 >  lower terrace are in white.  In each of these configurations, some
652 >  of the atoms (highlighted in blue) had CO molecules bound in the
653 >  vertical atop position.  The energies of these configurations as a
654 >  function of central atom displacement are displayed in Figure
655 >  \ref{fig:SketchEnergies}.}
656 > \label{fig:SketchGraphic}
657   \end{figure}
658  
659 + %energy graph corresponding to sketch graphic
660 + \begin{figure}[H]
661 + \includegraphics[width=\linewidth]{Portrait_SeparationComparison}
662 + \caption{Energies for displacing a single edge atom perpendicular to
663 +  the step edge as a function of atomic displacement. Each of the
664 +  energy curves corresponds to one of the labeled configurations in
665 +  Figure \ref{fig:SketchGraphic}, and the energies are referenced to
666 +  the unperturbed step-edge.  Certain arrangements of bound CO
667 +  (notably configurations g and h) can lower the energetic barrier for
668 +  creating an adatom relative to the bare surface (configuration a).}
669 + \label{fig:SketchEnergies}
670 + \end{figure}
671  
672 + While configurations of CO on the surface are able to increase
673 + diffusion and the likelihood of edge wandering, this does not provide
674 + a complete explanation for the formation of double layers. If adatoms
675 + were constrained to their original terraces then doubling could not
676 + occur.  A mechanism for vertical displacement of adatoms at the
677 + step-edge is required to explain the doubling.
678  
679 + We have discovered one possible mechanism for a CO-mediated vertical
680 + displacement of Pt atoms at the step edge. Figure \ref{fig:lambda}
681 + shows four points along a reaction coordinate in which a CO-bound
682 + adatom along the step-edge ``burrows'' into the edge and displaces the
683 + original edge atom onto the higher terrace.  A number of events
684 + similar to this mechanism were observed during the simulations.  We
685 + predict an energetic barrier of 20~kcal/mol for this process (in which
686 + the displaced edge atom follows a curvilinear path into an adjacent
687 + 3-fold hollow site).  The barrier heights we obtain for this reaction
688 + coordinate are approximate because the exact path is unknown, but the
689 + calculated energy barriers would be easily accessible at operating
690 + conditions.  Additionally, this mechanism is exothermic, with a final
691 + energy 15~kcal/mol below the original $\lambda = 0$ configuration.
692 + When CO is not present and this reaction coordinate is followed, the
693 + process is endothermic by 3~kcal/mol.  The difference in the relative
694 + energies for the $\lambda=0$ and $\lambda=1$ case when CO is present
695 + provides strong support for CO-mediated Pt-Pt interactions giving rise
696 + to the doubling reconstruction.
697  
698 + %lambda progression of Pt -> shoving its way into the step
699 + \begin{figure}[H]
700 + \includegraphics[width=\linewidth]{EPS_rxnCoord}
701 + \caption{Points along a possible reaction coordinate for CO-mediated
702 +  edge doubling. Here, a CO-bound adatom burrows into an established
703 +  step edge and displaces an edge atom onto the upper terrace along a
704 +  curvilinear path.  The approximate barrier for the process is
705 +  20~kcal/mol, and the complete process is exothermic by 15~kcal/mol
706 +  in the presence of CO, but is endothermic by 3~kcal/mol without CO.}
707 + \label{fig:lambda}
708 + \end{figure}
709 +
710 + The mechanism for doubling on the Pt(557) surface appears to require
711 + the cooperation of at least two distinct processes. For complete
712 + doubling of a layer to occur there must be a breakup of one
713 + terrace. These atoms must then ``disappear'' from that terrace, either
714 + by travelling to the terraces above or below their original levels.
715 + The presence of CO helps explain mechanisms for both of these
716 + situations. There must be sufficient breakage of the step-edge to
717 + increase the concentration of adatoms on the surface and these adatoms
718 + must then undergo the burrowing highlighted above (or a comparable
719 + mechanism) to create the double layer.  With sufficient time, these
720 + mechanisms working in concert lead to the formation of a double layer.
721 +
722 + \subsection{CO Removal and double layer stability}
723 + Once the double layers had formed on the 50\%~Pt system, they remained
724 + stable for the rest of the simulation time with minimal movement.
725 + Random fluctuations that involved small clusters or divots were
726 + observed, but these features typically healed within a few
727 + nanoseconds.  Within our simulations, the formation of the double
728 + layer appeared to be irreversible and a double layer was never
729 + observed to split back into two single layer step-edges while CO was
730 + present.
731 +
732 + To further gauge the effect CO has on this surface, additional
733 + simulations were run starting from a late configuration of the 50\%~Pt
734 + system that had already formed double layers. These simulations then
735 + had their CO molecules suddenly removed.  The double layer broke apart
736 + rapidly in these simulations, showing a well-defined edge-splitting
737 + after 100~ps. Configurations of this system are shown in Figure
738 + \ref{fig:breaking}. The coloring of the top and bottom layers helps to
739 + show how much mixing the edges experience as they split. These systems
740 + were only examined for 10~ns, and within that time despite the initial
741 + rapid splitting, the edges only moved another few \AA~apart. It is
742 + possible that with longer simulation times, the (557) surface recovery
743 + observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered.
744 +
745 + %breaking of the double layer upon removal of CO
746 + \begin{figure}[H]
747 + \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking}
748 + \caption{Behavior of an established (111) double step after removal of
749 +  the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the
750 +  removal of CO.  Nearly immediately after the CO is removed, the
751 +  step edge reforms in a (100) configuration, which is also the step
752 +  type seen on clean (557) surfaces. The step separation involves
753 +  significant mixing of the lower and upper atoms at the edge.}
754 + \label{fig:breaking}
755 + \end{figure}
756 +
757 +
758   %Peaks!
759 < \includegraphics[scale=0.25]{doublePeaks_noCO.png}
759 > %\begin{figure}[H]
760 > %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
761 > %\caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
762 > %of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with
763 > %aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
764 > %\label{fig:peaks}
765 > %\end{figure}
766 >
767 >
768 > %Don't think I need this
769 > %clean surface...
770 > %\begin{figure}[H]
771 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF}
772 > %\caption{}
773 >
774 > %\end{figure}
775 > %\label{fig:clean}
776 >
777 >
778   \section{Conclusion}
779 + The strength and directionality of the Pt-CO binding interaction, as
780 + well as the large quadrupolar repulsion between atop-bound CO
781 + molecules, help to explain the observed increase in surface mobility
782 + of Pt(557) and the resultant reconstruction into a double-layer
783 + configuration at the highest simulated CO-coverages.  The weaker Au-CO
784 + interaction results in significantly lower adataom diffusion
785 + constants, less step-wandering, and a lack of the double layer
786 + reconstruction on the Au(557) surface.
787  
788 + An in-depth examination of the energetics shows the important role CO
789 + plays in increasing step-breakup and in facilitating edge traversal
790 + which are both necessary for double layer formation.
791  
792 < \section{Acknowledgments}
390 < Support for this project was provided by the National Science
391 < Foundation under grant CHE-0848243 and by the Center for Sustainable
392 < Energy at Notre Dame (cSEND). Computational time was provided by the
393 < Center for Research Computing (CRC) at the University of Notre Dame.
792 > %Things I am not ready to remove yet
793  
794 + %Table of Diffusion Constants
795 + %Add gold?M
796 + % \begin{table}[H]
797 + %   \caption{}
798 + %   \centering
799 + % \begin{tabular}{| c | cc | cc | }
800 + %   \hline
801 + %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
802 + %   \hline
803 + %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
804 + %   \hline
805 + %   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
806 + %   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
807 + %   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
808 + %   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
809 + %   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
810 + %   \hline
811 + % \end{tabular}
812 + % \end{table}
813 +
814 + \begin{acknowledgement}
815 +  We gratefully acknowledge conversations with Dr. William
816 +  F. Schneider and Dr. Feng Tao.  Support for this project was
817 +  provided by the National Science Foundation under grant CHE-0848243
818 +  and by the Center for Sustainable Energy at Notre Dame
819 +  (cSEND). Computational time was provided by the Center for Research
820 +  Computing (CRC) at the University of Notre Dame.
821 + \end{acknowledgement}
822   \newpage
823 < \bibliography{firstTryBibliography}
824 < \end{doublespace}
823 > \bibstyle{achemso}
824 > \bibliography{COonPtAu}
825 > %\end{doublespace}
826 >
827 > \begin{tocentry}
828 > \begin{wrapfigure}{l}{0.5\textwidth}
829 > \begin{center}
830 > \includegraphics[width=\linewidth]{TOC_doubleLayer}
831 > \end{center}
832 > \end{wrapfigure}
833 > A reconstructed Pt(557) surface after 86~ns exposure to a half a
834 > monolayer of CO.  The double layer that forms is a result of
835 > CO-mediated step-edge wandering as well as a burrowing mechanism that
836 > helps lift edge atoms onto an upper terrace.
837 > \end{tocentry}
838 >
839   \end{document}

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