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1 < \documentclass[11pt]{article}
2 < \usepackage{amsmath}
3 < \usepackage{amssymb}
4 < \usepackage{times}
5 < \usepackage{mathptm}
6 < \usepackage{setspace}
7 < \usepackage{float}
8 < \usepackage{caption}
9 <
10 < %\usepackage{tabularx}
11 < \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}
10 < \usepackage[square, comma, sort&compress]{natbib}
6 > \usepackage{wrapfig}
7 > \usepackage{fixltx2e}
8 > %\mciteErrorOnUnknownfalse
9 >
10 > \usepackage[version=3]{mhchem}  % this is a great package for formatting chemical reactions
11   \usepackage{url}
19 – \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
20 – \evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
21 – 9.0in \textwidth 6.5in \brokenpenalty=10000
12  
13 < % double space list of tables and figures
14 < %\AtBeginDelayedFloats{\renewcommand{\baselinestretch}{1.66}}
25 < \setlength{\abovecaptionskip}{20 pt}
26 < \setlength{\belowcaptionskip}{30 pt}
13 > \title{Molecular Dynamics simulations of the surface reconstructions
14 >  of Pt(557) and Au(557) under exposure to CO}
15  
16 < %\renewcommand\citemid{\ } % no comma in optional reference note
17 < \bibpunct{[}{]}{,}{n}{}{;}
18 < \bibliographystyle{achemso}
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 <
28 >
29   %%
30   %Introduction
31   %       Experimental observations
# Line 50 | Line 44
44   %Summary
45   %%
46  
53 – %Title
54 – \title{Molecular Dynamics simulations of the surface reconstructions
55 –  of Pt(557) and Au(557) under exposure to CO}
47  
57 – \author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel
58 – Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\
59 – Department of Chemistry and Biochemistry,\\
60 – University of Notre Dame\\
61 – Notre Dame, Indiana 46556}
62 –
63 – %Date
64 – \date{Dec 15, 2012}
65 –
66 – %authors
67 –
68 – % make the title
69 – \maketitle
70 –
71 – \begin{doublespace}
72 –
48   \begin{abstract}
49 <
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   \newpage
# Line 85 | Line 74 | Industrial catalysts usually consist of small particle
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 exposing
78 < different atomic terminations that exhibit a high concentration of
79 < step, kink sites, and vacancies at the edges of the facets.  These
91 < sites are thought to be the locations of catalytic
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 to demonstrate that solid surfaces are often
82 < structurally, compositionally, and chemically {\it modified} by
83 < reactants under operating conditions.\cite{Tao2008,Tao:2010,Tao2011}
84 < The coupling between surface oxidation state and catalytic activity
85 < for CO oxidation on Pt, for instance, is widely
86 < documented.\cite{Ertl08,Hendriksen:2002} Despite the well-documented
87 < role of these effects on reactivity, the ability to capture or predict
88 < them in atomistic models is currently somewhat limited.  While these
89 < effects are perhaps unsurprising on the highly disperse, multi-faceted
90 < nanoscale particles that characterize industrial catalysts, they are
91 < manifest even on ordered, well-defined surfaces. The Pt(557) surface,
92 < for example, exhibits substantial and reversible restructuring under
93 < exposure to moderate pressures of carbon monoxide.\cite{Tao:2010}
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 < This work is part of an ongoing effort to understand the causes,
96 < mechanisms and timescales for surface restructuring using molecular
97 < simulation methods.  Since the dynamics of the process is of
98 < particular interest, we utilize classical molecular dynamic methods
99 < with force fields that represent a compromise between chemical
100 < accuracy and the computational efficiency necessary to observe the
101 < process of interest.
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  
115 – Since restructuring occurs as a result of specific interactions of the catalyst
116 – with adsorbates, two metals systems exposed to the same adsorbate, CO,
117 – were examined in this work. The Pt(557) surface has already been shown to
118 – reconstruct under certain conditions. The Au(557) surface, because of gold's
119 – weaker interaction with CO, is less likely to undergo such a large reconstruction.
122   %Platinum molecular dynamics
123   %gold molecular dynamics
124  
123 –
124 –
125   \section{Simulation Methods}
126 < The challenge in modeling any solid/gas interface problem is the
127 < development of a sufficiently general yet computationally tractable
128 < model of the chemical interactions between the surface atoms and
129 < adsorbates.  Since the interfaces involved are quite large (10$^3$ -
130 < 10$^6$ atoms) and respond slowly to perturbations, {\it ab initio}
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
# Line 136 | Line 136 | Coulomb potential.  For this work, we have been using
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 been using classical
140 < molecular dynamics with potential energy surfaces that are
141 < specifically tuned for transition metals.  In particular, we use the
142 < EAM potential for Au-Au and Pt-Pt interactions, while modeling the CO
143 < using a model developed by Straub and Karplus for studying
144 < photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and Pt-CO
145 < cross interactions were parameterized as part of this work.
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 classical simulation of transition
149 < metals are based on a non-pairwise additive functional of the local
150 < electron density. The embedded atom method (EAM) is perhaps the best
151 < known of these
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 al.} is among the
156 < fastest of these density functional approaches.\cite{Ercolessi88} In
157 < all of these models, atoms are conceptualized as a positively charged
158 < core with a radially-decaying valence electron distribution. To
159 < calculate the energy for embedding the core at a particular location,
160 < the electron density due to the valence electrons at all of the other
161 < atomic sites is computed at atom $i$'s location,
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*}
# Line 170 | Line 170 | $\phi_{ij}(r_{ij})$ is an pairwise term that is meant
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 an pairwise term that is meant to represent the
174 < overlap of the two positively charged cores.  
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.
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, MEAM, and the Quantum Sutton-Chen potentials
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}
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} crack
191 < propagation,\cite{BECQUART:1993rg} and alloying
192 < dynamics.\cite{Shibata:2002hh} All of these potentials have their
193 < strengths and weaknesses.  One of the strengths common to all of the
194 < methods is the relatively large library of metals for which these
195 < potentials have been
196 < parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
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 < \subsection{CO}
206 < Since one explanation for the strong surface CO repulsion on metals is
207 < the large linear quadrupole moment of carbon monoxide, the model
208 < chosen for this molecule exhibits this property in an efficient
209 < manner.  We used a model first proposed by Karplus and Straub to study
210 < the photodissociation of CO from myoglobin.\cite{Straub} The Straub and
211 < Karplus model is a rigid three site model which places a massless M
212 < site at the center of mass along the CO bond.  The geometry used along
213 < with the interaction parameters are reproduced in Table 1. The effective
214 < dipole moment, calculated from the assigned charges, is still
215 < small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
216 < to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
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{Positions, $\sigma$, $\epsilon$ and charges for CO geometry
221 < and self-interactions\cite{Straub}. Distances are in \AA~, energies are
222 < 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 | c | ccc |}
228   \hline
219 – \multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\
220 – \hline
229   &  {\it z} & $\sigma$ & $\epsilon$ & q\\
230   \hline
231 < \textbf{C} & -0.6457 &  0.0262  & 3.83   &   -0.75 \\
232 < \textbf{O} &  0.4843 &   0.1591 &   3.12 &   -0.85 \\
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
235   \end{tabular}
236 + \label{tab:CO}
237   \end{table}
238  
239 < \subsection{Cross-Interactions}
239 > \subsection{Cross-Interactions between the metals and carbon monoxide}
240  
241 < One hurdle that must be overcome in classical molecular simulations
242 < is the proper parameterization of the potential interactions present
243 < in the system. Since the adsorption of CO onto a platinum surface has been
244 < the focus of many experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
245 < and theoretical studies \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
246 < there is a large amount of data in the literature to fit too. We started with parameters
247 < reported by Korzeniewski et al. \cite{Pons:1986} and then
248 < modified them to ensure that the Pt-CO interaction favored
249 < an atop binding position for the CO upon the Pt surface. This
250 < constraint led to the binding energies being on the higher side
251 < of reported values. Following the method laid out by Korzeniewski,
252 < the Pt-C interaction was fit to a strong Lennard-Jones 12-6
253 < interaction to mimic binding, while the Pt-O interaction
254 < was parameterized to a Morse potential with a large $r_o$
255 < to contribute a weak repulsion. The resultant potential-energy
256 < surface suitably recovers the calculated Pt-C bond length ( 1.6\AA)\cite{Beurden:2002ys} and affinity
257 < for the atop binding position.\cite{Deshlahra:2012, Hopster:1978}
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 fit using Lennard-Jones and
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 <
269 < The fits were refined against gas-surface calculations using DFT with
270 < a periodic supercell plane-wave basis approach, as implemented in the
271 < {\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are
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 < Ionic relaxations were performed until the energy difference between
266 < subsequent steps was less than 0.0001 eV.  In testing the CO-Au
267 < interaction, Au(111) supercells were constructed of four layers of 4
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 < Supercell calculations were performed nonspin-polarized, and energies
282 < were converged to within 0.03 meV per Au atom with a 4 x 4 x 4
283 < Monkhorst-Pack\cite{Monkhorst:1976,PhysRevB.13.5188} {\bf k}-point
284 < sampling of the first Brillouin zone.  The relaxed gold slab was then
285 < used in numerous single point calculations with CO at various heights
286 < (and angles relative to the surface) to allow fitting of the empirical
287 < force field.
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   %Hint at future work
291 < The fit parameter sets employed in this work are shown in Table 2 and their
292 < reproduction of the binding energies are displayed in Table 3. Currently,
293 < charge transfer is not being treated in this system, however, that is a goal
294 < for future work as the effect has been seen to affect binding energies and
295 < binding site preferences. \cite{Deshlahra:2012}
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  
285 –
286 –
287 –
288 – \subsection{Construction and Equilibration of 557 Metal interfaces}
289 –
290 – Our model systems are composed of approximately 4000 metal atoms
291 – cut along the 557 plane so that they are periodic in the {\it x} and {\it y}
292 – directions exposing the 557 plane in the {\it z} direction. Runs at various
293 – temperatures ranging from 300~K to 1200~K were started with the intent
294 – of viewing relative stability of the surface when CO was not present in the
295 – system.  Owing to the different melting points (1337~K for Au and 2045~K for Pt),
296 – the bare crystal systems were initially run in the Canonical ensemble at
297 – 800~K and 1000~K respectively for 100 ps. Various amounts of CO were
298 – placed in the vacuum region, which upon full adsorption to the surface
299 – corresponded to 5\%, 25\%, 33\%, and 50\% coverages. Because of the
300 – high temperature and the difference in binding energies, the platinum systems
301 – very rarely had CO that was not adsorbed to the surface whereas the gold systems
302 – often had a substantial minority of CO away from the surface.
303 – These systems were again allowed to reach thermal equilibrium before being run in the
304 – microcanonical ensemble. All of the systems examined in this work were
305 – run for at least 40 ns. A subset that were undergoing interesting effects
306 – have been allowed to continue running with one system approaching 200 ns.
307 – All simulations were run using the open source molecular dynamics package, OpenMD. \cite{Ewald, OOPSE}
308 –
309 –
310 –
311 –
312 –
313 –
314 – %\subsection{System}
315 – %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.
316 –
317 –
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
328 – &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\
329 – \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{Adsorption 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:1979}-- -1.9~\cite{Yeo} \\
328 < \textbf{Au-CO} & -0.39 & -0.40~\cite{TPD_Gold} \\
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{Forcefield validation}
338 + The CO-metal cross interactions were compared directly to DFT results
339 + found in the supporting information of Tao {\it et al.}
340 + \cite{Tao:2010} These calculations are estimates of the stabilization
341 + energy provided to double-layer reconstructions of the perfect 557
342 + surface by an overlayer of CO molecules in a $c (2 \times 4)$ pattern.
343 + To make the comparison, metal slabs that were five atoms thick and
344 + which displayed a 557 facet were constructed.  Double-layer
345 + (reconstructed) systems were created using six atomic layers where
346 + enough of a layer was removed from both exposed 557 facets to create
347 + the double step.  In all cases, the metal slabs contained 480 atoms
348 + and were minimized using steepest descent under the EAM force
349 + field. Both the bare metal slabs and slabs with 50\% carbon monoxide
350 + coverage (arranged in the $c (2 \times 4)$ pattern) were used.  The
351 + systems are periodic along and perpendicular to the step-edge axes
352 + with a large vacuum above the displayed 557 facet.
353  
354 + Energies using our force field for the various systems are displayed
355 + in Table ~\ref{tab:steps}.  The relative energies are calculated as
356 + $E_{relative} = E_{system} - E_{M-557-S} - N_{CO} E_{CO-M}$,
357 + where $E_{CO-M}$ is -1.84 eV for CO-Pt and -0.39 eV for CO-Au. For
358 + platinum, the bare double layer is slightly less stable then the
359 + original single (557) step. However, addition of carbon monoxide
360 + stabilizes the reconstructed double layer relative to the perfect 557.
361 + This result is in qualitative agreement with DFT calculations in Tao
362 + {\it et al.}\cite{Tao:2010}, who also showed that the addition of CO
363 + leads to a reversal in stability.
364  
365 + The DFT calculations suggest an increased stability of 0.08 kcal/mol
366 + (0.7128 eV) per Pt atom for going from the single to double step
367 + structure in the presence of carbon monoxide.
368  
369 + The gold systems show much smaller energy differences between the
370 + single and double layers. The weaker binding of CO to Au is evidenced
371 + by the much smaller change in relative energy between the structures
372 + when carbon monoxide is present.  Additionally, as CO-Au binding is
373 + much weaker than CO-Pt, it would be unlikely that CO would approach
374 + the 50\% coverage levels operating temperatures for the gold surfaces.
375  
376 < % Just results, leave discussion for discussion section
357 < \section{Results}
358 < \subsection{Diffusion}
359 < An ideal metal surface displaying a low-energy facet, a (111) face for
360 < instance, is unlikely to experience much surface diffusion because of
361 < the large energy barrier associated with atoms 'lifting' from the top
362 < layer to then be able to explore the surface. Rougher surfaces, those
363 < that already contain numerous adatoms, step edges, and kinks, should
364 < have concomitantly higher surface diffusion rates. Tao et al. showed
365 < that the platinum 557 surface undergoes two separate reconstructions
366 < upon CO adsorption. \cite{Tao:2010} The first reconstruction involves a
367 < doubling of the step edge height which is accomplished by a doubling
368 < of the plateau length. The second reconstruction led to the formation of
369 < triangular motifs stretching across the lengthened plateaus.
370 <
371 < As shown in Figure 2, over a period of approximately 100 ns, the surface
372 < has reconstructed from a 557 surface by doubling the step height and
373 < step length. Focusing on only the platinum, or gold, atoms that were
374 < deemed mobile on the surface, an analysis of the surface diffusion was
375 < performed. A particle was considered mobile once it had traveled more
376 < than 2~\AA between snapshots. This immediately eliminates all of the
377 < bulk metal and greatly limits the number of surface atoms examined.
378 < Since diffusion on a surface is strongly affected by overcoming energy
379 < barriers, the diffusion parallel to the step edge axis was determined
380 < separately from the diffusion perpendicular to the step edge. The results
381 < at various coverages on both platinum and gold are shown in Table 4.
382 <
383 < %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 has been running continuously. The lowered diffusion constant at longer run times will be examined in-depth in the discussion section.
384 <
385 < \begin{figure}[H]
386 < \includegraphics[scale=0.6]{DiffusionComparison_error.png}
387 < \caption{Diffusion parallel to the step edge will always be higher than that perpendicular to the edge because of the lower energy barrier associated with going from approximately 7 nearest neighbors to 5, as compared to the 3 of an adatom. Additionally, the observed maximum and subsequent decrease for the Pt system suggests that the CO self-interactions are playing a significant role with regards to movement of the platinum atoms around and more importantly across the surface. }
388 < \end{figure}
389 <
390 < %Table of Diffusion Constants
391 < %Add gold?M
376 > %Table of single step double step calculations
377   \begin{table}[H]
378 < \caption{Platinum and gold diffusion constants parallel and perpendicular to the 557 step edge. As the coverage increases, the diffusion constants parallel and  perpendicular to the step edge both initially increase and then decrease slightly. Units are \AA\textsuperscript{2}/ns}
378 >  \caption{Minimized single point energies of (S)ingle and (D)ouble
379 >    steps.  The addition of CO in a 50\% $c(2 \times 4)$ coverage acts as a
380 >    stabilizing presence and suggests a driving force for the observed
381 >    reconstruction on the highest coverage Pt system. All energies are
382 >    in kcal/mol.}
383   \centering
384 < \begin{tabular}{| c | cc | cc | c |}
384 > \begin{tabular}{| c | c | c | c | c | c |}
385   \hline
386 < \textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  & \textbf{Time (ns)}\\
386 > \textbf{Step} & \textbf{N}\textsubscript{M} & \textbf{N\textsubscript{CO}} & \textbf{Relative Energy} & \textbf{$\Delta$E/M} & \textbf{$\Delta$E/CO} \\
387   \hline
388 < &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} & \\
388 > Pt(557)-S & 480 & 0 & 0 & 0 & - \\
389 > Pt(557)-D & 480 & 0 & 114.783 & 0.239 & -\\
390 > Pt(557)-S & 480 & 40 & -124.546 & -0.259 & -3.114\\
391 > Pt(557)-D & 480 & 44 & -34.953 & -0.073 & -0.794\\
392   \hline
393 < 50\% & 4.32 $\pm$ 0.02 & 1.185 $\pm$ 0.008 & 1.72 $\pm$ 0.02 & 0.455 $\pm$ 0.006 & 40 \\
394 < 33\% & 5.18 $\pm$ 0.03 & 1.999 $\pm$ 0.005 & 1.95 $\pm$ 0.02 & 0.337 $\pm$ 0.004 & 40   \\
395 < 25\% & 5.01 $\pm$ 0.02 & 1.574 $\pm$ 0.004 & 1.26 $\pm$ 0.03 & 0.377 $\pm$ 0.006 & 40  \\
396 < 5\%   & 3.61 $\pm$ 0.02 & 0.355 $\pm$ 0.002 & 1.84 $\pm$ 0.03 & 0.169 $\pm$ 0.004 & 40  \\
397 < 0\%   & 3.27 $\pm$ 0.02 & 0.147 $\pm$ 0.004 & 1.50 $\pm$ 0.02 & 0.194 $\pm$ 0.002  & 40  \\
398 < \hline
393 > \hline
394 > Au(557)-S & 480 & 0 & 0 & 0 & - \\
395 > Au(557)-D & 480 & 0 & 79.572 & 0.166 & - \\
396 > Au(557)-S & 480 & 40 & -157.199 & -0.327 & -3.930\\
397 > Au(557)-D & 480 & 44 & -123.297 & -0.257 & -2.802 \\
398 > \hline
399   \end{tabular}
400 + \label{tab:steps}
401   \end{table}
402  
403  
404 + \subsection{Pt(557) and Au(557) metal interfaces}
405 + Our Pt system is an orthorhombic periodic box of dimensions
406 + 54.482~x~50.046~x~120.88~\AA~while our Au system has
407 + dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs
408 + are 9 and 8 atoms deep respectively, corresponding to a slab
409 + thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
410 + The systems are arranged in a FCC crystal that have been cut
411 + along the (557) plane so that they are periodic in the {\it x} and
412 + {\it y} directions, and have been oriented to expose two aligned
413 + (557) cuts along the extended {\it z}-axis.  Simulations of the
414 + bare metal interfaces at temperatures ranging from 300~K to
415 + 1200~K were performed to confirm the relative
416 + stability of the surfaces without a CO overlayer.  
417  
418 < %Discussion
419 < \section{Discussion}
420 < 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.
418 > The different bulk melting temperatures predicted by EAM
419 > (1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for
420 > Pt\cite{Pt:melting}) suggest that any reconstructions should happen at
421 > different temperatures for the two metals.  The bare Au and Pt
422 > surfaces were initially run in the canonical (NVT) ensemble at 800~K
423 > and 1000~K respectively for 100 ps. The two surfaces were relatively
424 > stable at these temperatures when no CO was present, but experienced
425 > increased surface mobility on addition of CO. Each surface was then
426 > dosed with different concentrations of CO that was initially placed in
427 > the vacuum region.  Upon full adsorption, these concentrations
428 > correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher
429 > coverages resulted in the formation of a double layer of CO, which
430 > introduces artifacts that are not relevant to (557) reconstruction.
431 > Because of the difference in binding energies, nearly all of the CO
432 > was bound to the Pt surface, while the Au surfaces often had a
433 > significant CO population in the gas phase.  These systems were
434 > allowed to reach thermal equilibrium (over 5~ns) before being run in
435 > the microcanonical (NVE) ensemble for data collection. All of the
436 > systems examined had at least 40~ns in the data collection stage,
437 > although simulation times for some Pt of the systems exceeded 200~ns.
438 > Simulations were carried out using the open source molecular dynamics
439 > package, OpenMD.\cite{Ewald,OOPSE,openmd}
440  
441 < \subsection{Diffusion}
442 < 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?)
443 < \\
444 < \\
441 >
442 > % RESULTS
443 > %
444 > \section{Results}
445 > \subsection{Structural remodeling}
446 > The bare metal surfaces experienced minor roughening of the step-edge
447 > because of the elevated temperatures, but the (557) face was stable
448 > throughout the simulations. The surfaces of both systems, upon dosage
449 > of CO, began to undergo extensive remodeling that was not observed in
450 > the bare systems. Reconstructions of the Au systems were limited to
451 > breakup of the step-edges and some step wandering. The lower coverage
452 > Pt systems experienced similar step edge wandering but to a greater
453 > extent. The 50\% coverage Pt system was unique among our simulations
454 > in that it formed well-defined and stable double layers through step
455 > coalescence, similar to results reported by Tao {\it et
456 >  al}.\cite{Tao:2010}
457 >
458 > \subsubsection{Step wandering}
459 > The bare surfaces for both metals showed minimal step-wandering at
460 > their respective temperatures. As the CO coverage increased however,
461 > the mobility of the surface atoms, described through adatom diffusion
462 > and step-edge wandering, also increased.  Except for the 50\% Pt
463 > system where step coalescence occurred, the step-edges in the other
464 > simulations preferred to keep nearly the same distance between steps
465 > as in the original (557) lattice, $\sim$13\AA~for Pt and
466 > $\sim$14\AA~for Au.  Previous work by Williams {\it et
467 >  al}.\cite{Williams:1991, Williams:1994} highlights the repulsion
468 > that exists between step-edges even when no direct interactions are
469 > present in the system. This repulsion is caused by an entropic barrier
470 > that arises from the fact that steps cannot cross over one
471 > another. This entropic repulsion does not completely define the
472 > interactions between steps, however, so it is possible to observe step
473 > coalescence on some surfaces.\cite{Williams:1991} The presence and
474 > concentration of adsorbates, as shown in this work, can affect
475 > step-step interactions, potentially leading to a new surface structure
476 > as the thermodynamic equilibrium.
477 >
478 > \subsubsection{Double layers}
479 > Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the
480 > Pt(557) surface undergoes two separate reconstructions upon CO
481 > adsorption.  The first involves a doubling of the step height and
482 > plateau length.  Similar behavior has been seen on a number of
483 > surfaces at varying conditions, including Ni(977) and
484 > Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we
485 > examined, the Pt system showed a greater propensity for reconstruction
486 > because of the larger surface mobility and the greater extent of step
487 > wandering.  The amount of reconstruction was strongly correlated to
488 > the amount of CO adsorbed upon the surface.  This appears to be
489 > related to the effect that adsorbate coverage has on edge breakup and
490 > on the surface diffusion of metal adatoms. Only the 50\% Pt surface
491 > underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within
492 > the time scales studied here.  Over a longer time scale (150~ns) two
493 > more double layers formed on this surface. Although double layer
494 > formation did not occur in the other Pt systems, they exhibited more
495 > step-wandering and roughening compared to their Au counterparts. The
496 > 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
497 > various times along the simulation showing the evolution of a double
498 > layer step-edge.
499 >
500 > The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010}
501 > involved the formation of triangular clusters that stretched across
502 > the plateau between two step-edges. Neither of the simulated metal
503 > interfaces, within the 40~ns time scale or the extended time of 150~ns
504 > for the 50\% Pt system, experienced this reconstruction.
505 >
506   %Evolution of surface
507   \begin{figure}[H]
508 < \includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
509 < \caption{Four snapshots of the $\frac{1}{2}$ monolayer system at various times a) 258 ps b) 19 ns c) 31.2 ns and 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.}
508 > \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation}
509 > \caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a)
510 >  258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after
511 >  exposure. Disruption of the (557) step-edges occurs quickly.  The
512 >  doubling of the layers appears only after two adjacent step-edges
513 >  touch.  The circled spot in (b) nucleated the growth of the double
514 >  step observed in the later configurations.}
515 >  \label{fig:reconstruct}
516   \end{figure}
517  
518 + \subsection{Dynamics}
519 + Previous experimental work by Pearl and Sibener\cite{Pearl}, using
520 + STM, has been able to capture the coalescence of steps on Ni(977). The
521 + time scale of the image acquisition, $\sim$70~s/image, provides an
522 + upper bound for the time required for the doubling to occur. By
523 + utilizing Molecular Dynamics we are able to probe the dynamics of
524 + these reconstructions at elevated temperatures and in this section we
525 + provide data on the timescales for transport properties,
526 + e.g. diffusion and layer formation time.
527  
528  
529 + \subsubsection{Transport of surface metal atoms}
530 + %forcedSystems/stepSeparation
531  
532 < %Peaks!
532 > The wandering of a step-edge is a cooperative effect arising from the
533 > individual movements of the atoms making up the steps. An ideal metal
534 > surface displaying a low index facet, (111) or (100), is unlikely to
535 > experience much surface diffusion because of the large energetic
536 > barrier that must be overcome to lift an atom out of the surface. The
537 > presence of step-edges and other surface features on higher-index
538 > facets provides a lower energy source for mobile metal atoms.  Using
539 > our potential model, single-atom break-away from a step-edge on a
540 > clean surface still imposes an energetic penalty around
541 > $\sim$~45~kcal/mol, but this is certainly easier than lifting the same
542 > metal atom vertically out of the surface, \textgreater~60~kcal/mol.
543 > The penalty lowers significantly when CO is present in sufficient
544 > quantities on the surface. For certain distributions of CO, the
545 > energetic penalty can fall to as low as $\sim$~20~kcal/mol. The
546 > configurations that create these lower barriers are detailed in the
547 > discussion section below.
548 >
549 > Once an adatom exists on the surface, the barrier for diffusion is
550 > negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are
551 > then able to explore the terrace before rejoining either their
552 > original step-edge or becoming a part of a different edge. It is an
553 > energetically unfavorable process with a high barrier for an atom to
554 > traverse to a separate terrace although the presence of CO can lower
555 > the energy barrier required to lift or lower an adatom. By tracking
556 > the mobility of individual metal atoms on the Pt and Au surfaces we
557 > were able to determine the relative diffusion constants, as well as
558 > how varying coverages of CO affect the diffusion. Close observation of
559 > the mobile metal atoms showed that they were typically in equilibrium
560 > with the step-edges.  At times, their motion was concerted, and two or
561 > more adatoms would be observed moving together across the surfaces.
562 >
563 > A particle was considered ``mobile'' once it had traveled more than
564 > 2~\AA~ between saved configurations of the system (typically 10-100
565 > ps). A mobile atom would typically travel much greater distances than
566 > this, but the 2~\AA~cutoff was used to prevent swamping the diffusion
567 > data with the in-place vibrational movement of buried atoms. Diffusion
568 > on a surface is strongly affected by local structures and the presence
569 > of single and double layer step-edges causes the diffusion parallel to
570 > the step-edges to be larger than the diffusion perpendicular to these
571 > edges. Parallel and perpendicular diffusion constants are shown in
572 > Figure \ref{fig:diff}.  Diffusion parallel to the step-edge is higher
573 > than diffusion perpendicular to the edge because of the lower energy
574 > barrier associated with sliding along an edge compared to breaking
575 > away to form an isolated adatom.
576 >
577 > %Diffusion graph
578   \begin{figure}[H]
579 < \includegraphics[scale=0.25]{doublePeaks_noCO.png}
580 < \caption{}
579 > \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1}
580 > \caption{Diffusion constants for mobile surface atoms along directions
581 >  parallel ($\mathbf{D}_{\parallel}$) and perpendicular
582 >  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
583 >  surface coverage.  The two reported diffusion constants for the 50\%
584 >  Pt system correspond to a 20~ns period before the formation of the
585 >  double layer (upper points), and to the full 40~ns sampling period
586 >  (lower points).}
587 > \label{fig:diff}
588   \end{figure}
434 – \section{Conclusion}
589  
590 + The weaker Au-CO interaction is evident in the weak CO-coverage
591 + dependance of Au diffusion. This weak interaction leads to lower
592 + observed coverages when compared to dosage amounts. This further
593 + limits the effect the CO can have on surface diffusion. The correlation
594 + between coverage and Pt diffusion rates shows a near linear relationship
595 + at the earliest times in the simulations. Following double layer formation,
596 + however, there is a precipitous drop in adatom diffusion. As the double
597 + layer forms, many atoms that had been tracked for mobility data have
598 + now been buried, resulting in a smaller reported diffusion constant. A
599 + secondary effect of higher coverages is CO-CO cross interactions that
600 + lower the effective mobility of the Pt adatoms that are bound to each CO.
601 + This effect would become evident only at higher coverages. A detailed
602 + account of Pt adatom energetics follows in the Discussion.
603 +
604 + \subsubsection{Dynamics of double layer formation}
605 + The increased diffusion on Pt at the higher CO coverages is the primary
606 + contributor to double layer formation. However, this is not a complete
607 + explanation -- the 33\%~Pt system has higher diffusion constants, but
608 + did not show any signs of edge doubling in 40~ns. On the 50\%~Pt
609 + system, one double layer formed within the first 40~ns of simulation time,
610 + while two more were formed as the system was allowed to run for an
611 + additional 110~ns (150~ns total). This suggests that this reconstruction
612 + is a rapid process and that the previously mentioned upper bound is a
613 + very large overestimate.\cite{Williams:1991,Pearl} In this system the first
614 + appearance of a double layer appears at 19~ns into the simulation.
615 + Within 12~ns of this nucleation event, nearly half of the step has formed
616 + the double layer and by 86~ns the complete layer has flattened out.
617 + From the appearance of the first nucleation event to the first observed
618 + double layer, the process took $\sim$20~ns. Another $\sim$40~ns was
619 + necessary for the layer to completely straighten. The other two layers in
620 + this simulation formed over periods of 22~ns and 42~ns respectively.
621 + A possible explanation for this rapid reconstruction is the elevated
622 + temperatures under which our systems were simulated. The process
623 + would almost certainly take longer at lower temperatures. Additionally,
624 + our measured times for completion of the doubling after the appearance
625 + of a nucleation site are likely affected by our periodic boxes. A longer
626 + step-edge will likely take longer to ``zipper''.
627  
437 – \section{Acknowledgments}
438 – Support for this project was provided by the National Science
439 – Foundation under grant CHE-0848243 and by the Center for Sustainable
440 – Energy at Notre Dame (cSEND). Computational time was provided by the
441 – Center for Research Computing (CRC) at the University of Notre Dame.
628  
629 + %Discussion
630 + \section{Discussion}
631 + We have shown that a classical potential is able to model the initial
632 + reconstruction of the Pt(557) surface upon CO adsorption, and have
633 + reproduced the double layer structure observed by Tao {\it et
634 +  al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be
635 + rapid -- occurring within 100 ns of the initial exposure to CO.  Here
636 + we discuss the features of the classical potential that are
637 + contributing to the stability and speed of the Pt(557) reconstruction.
638 +
639 + \subsection{Diffusion}
640 + The perpendicular diffusion constant appears to be the most important
641 + indicator of double layer formation. As highlighted in Figure
642 + \ref{fig:reconstruct}, the formation of the double layer did not begin
643 + until a nucleation site appeared.  Williams {\it et
644 +  al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge
645 + repulsion arising from the inability of edge crossing.  This repulsion
646 + must be overcome to allow step coalescence.  A larger
647 + $\textbf{D}_\perp$ value implies more step-wandering and a larger
648 + chance for the stochastic meeting of two edges to create a nucleation
649 + point.  Diffusion parallel to the step-edge can help ``zipper'' up a
650 + nascent double layer. This helps explain the rapid time scale for
651 + double layer completion after the appearance of a nucleation site, while
652 + the initial appearance of the nucleation site was unpredictable.
653 +
654 + \subsection{Mechanism for restructuring}
655 + Since the Au surface showed no large scale restructuring in any of our
656 + simulations, our discussion will focus on the 50\% Pt-CO system which
657 + did exhibit doubling. A number of possible mechanisms exist to explain
658 + the role of adsorbed CO in restructuring the Pt surface. Quadrupolar
659 + repulsion between adjacent CO molecules adsorbed on the surface is one
660 + possibility.  However, the quadrupole-quadrupole interaction is
661 + short-ranged and is attractive for some orientations.  If the CO
662 + molecules are ``locked'' in a vertical orientation, through atop
663 + adsorption for example, this explanation would gain credence. Within
664 + the framework of our classical potential, the calculated energetic
665 + repulsion between two CO molecules located a distance of
666 + 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a
667 + vertical orientation, is 8.62 kcal/mol. Moving the CO to the second
668 + nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly
669 + 0. Allowing the CO to rotate away from a purely vertical orientation
670 + also lowers the repulsion. When the carbons are locked at a distance
671 + of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle
672 + between the 2 CO is $\sim$24\textsuperscript{o}.  The calculated
673 + barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
674 + repulsion between adjacent CO molecules bound to Pt could indeed
675 + increase the surface diffusion. However, the residence time of CO on
676 + Pt suggests that the CO molecules are extremely mobile, with diffusion
677 + constants 40 to 2500 times larger than surface Pt atoms. This mobility
678 + suggests that the CO molecules jump between different Pt atoms
679 + throughout the simulation.  However, they do stay bound to individual
680 + Pt atoms for long enough to modify the local energy landscape for the
681 + mobile adatoms.
682 +
683 + A different interpretation of the above mechanism which takes the
684 + large mobility of the CO into account, would be in the destabilization
685 + of Pt-Pt interactions due to bound CO.  Destabilizing Pt-Pt bonds at
686 + the edges could lead to increased step-edge breakup and diffusion. On
687 + the bare Pt(557) surface the barrier to completely detach an edge atom
688 + is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
689 + \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain
690 + configurations, cases (e), (g), and (h), the barrier can be lowered to
691 + $\sim$23~kcal/mol by the presence of bound CO molecules. In these
692 + instances, it becomes energetically favorable to roughen the edge by
693 + introducing a small separation of 0.5 to 1.0~\AA. This roughening
694 + becomes immediately obvious in simulations with significant CO
695 + populations. The roughening is present to a lesser extent on surfaces
696 + with lower CO coverage (and even on the bare surfaces), although in
697 + these cases it is likely due to random fluctuations that squeeze out
698 + step-edge atoms. Step-edge breakup by direct single-atom translations
699 + (as suggested by these energy curves) is probably a worst-case
700 + scenario.  Multistep mechanisms in which an adatom moves laterally on
701 + the surface after being ejected would be more energetically favorable.
702 + This would leave the adatom alongside the ledge, providing it with
703 + five nearest neighbors.  While fewer than the seven neighbors it had
704 + as part of the step-edge, it keeps more Pt neighbors than the three
705 + neighbors an isolated adatom has on the terrace. In this proposed
706 + mechanism, the CO quadrupolar repulsion still plays a role in the
707 + initial roughening of the step-edge, but not in any long-term bonds
708 + with individual Pt atoms.  Higher CO coverages create more
709 + opportunities for the crowded CO configurations shown in Figure
710 + \ref{fig:SketchGraphic}, and this is likely to cause an increased
711 + propensity for step-edge breakup.
712 +
713 + %Sketch graphic of different configurations
714 + \begin{figure}[H]
715 + \includegraphics[width=\linewidth]{COpaths}
716 + \caption{Configurations used to investigate the mechanism of step-edge
717 +  breakup on Pt(557). In each case, the central (starred) atom was
718 +  pulled directly across the surface away from the step edge.  The Pt
719 +  atoms on the upper terrace are colored dark grey, while those on the
720 +  lower terrace are in white.  In each of these configurations, some
721 +  of the atoms (highlighted in blue) had CO molecules bound in the
722 +  vertical atop position.  The energies of these configurations as a
723 +  function of central atom displacement are displayed in Figure
724 +  \ref{fig:SketchEnergies}.}
725 + \label{fig:SketchGraphic}
726 + \end{figure}
727 +
728 + %energy graph corresponding to sketch graphic
729 + \begin{figure}[H]
730 + \includegraphics[width=\linewidth]{Portrait_SeparationComparison}
731 + \caption{Energies for displacing a single edge atom perpendicular to
732 +  the step edge as a function of atomic displacement. Each of the
733 +  energy curves corresponds to one of the labeled configurations in
734 +  Figure \ref{fig:SketchGraphic}, and the energies are referenced to
735 +  the unperturbed step-edge.  Certain arrangements of bound CO
736 +  (notably configurations g and h) can lower the energetic barrier for
737 +  creating an adatom relative to the bare surface (configuration a).}
738 + \label{fig:SketchEnergies}
739 + \end{figure}
740 +
741 + While configurations of CO on the surface are able to increase
742 + diffusion and the likelihood of edge wandering, this does not provide
743 + a complete explanation for the formation of double layers. If adatoms
744 + were constrained to their original terraces then doubling could not
745 + occur.  A mechanism for vertical displacement of adatoms at the
746 + step-edge is required to explain the doubling.
747 +
748 + We have discovered one possible mechanism for a CO-mediated vertical
749 + displacement of Pt atoms at the step edge. Figure \ref{fig:lambda}
750 + shows four points along a reaction coordinate in which a CO-bound
751 + adatom along the step-edge ``burrows'' into the edge and displaces the
752 + original edge atom onto the higher terrace.  A number of events
753 + similar to this mechanism were observed during the simulations.  We
754 + predict an energetic barrier of 20~kcal/mol for this process (in which
755 + the displaced edge atom follows a curvilinear path into an adjacent
756 + 3-fold hollow site).  The barrier heights we obtain for this reaction
757 + coordinate are approximate because the exact path is unknown, but the
758 + calculated energy barriers would be easily accessible at operating
759 + conditions.  Additionally, this mechanism is exothermic, with a final
760 + energy 15~kcal/mol below the original $\lambda = 0$ configuration.
761 + When CO is not present and this reaction coordinate is followed, the
762 + process is endothermic by 3~kcal/mol.  The difference in the relative
763 + energies for the $\lambda=0$ and $\lambda=1$ case when CO is present
764 + provides strong support for CO-mediated Pt-Pt interactions giving rise
765 + to the doubling reconstruction.
766 +
767 + %lambda progression of Pt -> shoving its way into the step
768 + \begin{figure}[H]
769 + \includegraphics[width=\linewidth]{EPS_rxnCoord}
770 + \caption{Points along a possible reaction coordinate for CO-mediated
771 +  edge doubling. Here, a CO-bound adatom burrows into an established
772 +  step edge and displaces an edge atom onto the upper terrace along a
773 +  curvilinear path.  The approximate barrier for the process is
774 +  20~kcal/mol, and the complete process is exothermic by 15~kcal/mol
775 +  in the presence of CO, but is endothermic by 3~kcal/mol without CO.}
776 + \label{fig:lambda}
777 + \end{figure}
778 +
779 + The mechanism for doubling on the Pt(557) surface appears to require
780 + the cooperation of at least two distinct processes. For complete
781 + doubling of a layer to occur there must be a breakup of one
782 + terrace. These atoms must then ``disappear'' from that terrace, either
783 + by travelling to the terraces above or below their original levels.
784 + The presence of CO helps explain mechanisms for both of these
785 + situations. There must be sufficient breakage of the step-edge to
786 + increase the concentration of adatoms on the surface and these adatoms
787 + must then undergo the burrowing highlighted above (or a comparable
788 + mechanism) to create the double layer.  With sufficient time, these
789 + mechanisms working in concert lead to the formation of a double layer.
790 +
791 + \subsection{CO Removal and double layer stability}
792 + Once the double layers had formed on the 50\%~Pt system, they remained
793 + stable for the rest of the simulation time with minimal movement.
794 + Random fluctuations that involved small clusters or divots were
795 + observed, but these features typically healed within a few
796 + nanoseconds.  Within our simulations, the formation of the double
797 + layer appeared to be irreversible and a double layer was never
798 + observed to split back into two single layer step-edges while CO was
799 + present.
800 +
801 + To further gauge the effect CO has on this surface, additional
802 + simulations were run starting from a late configuration of the 50\%~Pt
803 + system that had already formed double layers. These simulations then
804 + had their CO molecules suddenly removed.  The double layer broke apart
805 + rapidly in these simulations, showing a well-defined edge-splitting
806 + after 100~ps. Configurations of this system are shown in Figure
807 + \ref{fig:breaking}. The coloring of the top and bottom layers helps to
808 + show how much mixing the edges experience as they split. These systems
809 + were only examined for 10~ns, and within that time despite the initial
810 + rapid splitting, the edges only moved another few \AA~apart. It is
811 + possible that with longer simulation times, the (557) surface recovery
812 + observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered.
813 +
814 + %breaking of the double layer upon removal of CO
815 + \begin{figure}[H]
816 + \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking}
817 + \caption{Behavior of an established (111) double step after removal of
818 +  the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the
819 +  removal of CO.  Nearly immediately after the CO is removed, the
820 +  step edge reforms in a (100) configuration, which is also the step
821 +  type seen on clean (557) surfaces. The step separation involves
822 +  significant mixing of the lower and upper atoms at the edge.}
823 + \label{fig:breaking}
824 + \end{figure}
825 +
826 +
827 + %Peaks!
828 + %\begin{figure}[H]
829 + %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
830 + %\caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
831 + %of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with
832 + %aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
833 + %\label{fig:peaks}
834 + %\end{figure}
835 +
836 +
837 + %Don't think I need this
838 + %clean surface...
839 + %\begin{figure}[H]
840 + %\includegraphics[width=\linewidth]{557_300K_cleanPDF}
841 + %\caption{}
842 +
843 + %\end{figure}
844 + %\label{fig:clean}
845 +
846 +
847 + \section{Conclusion}
848 + The strength and directionality of the Pt-CO binding interaction, as
849 + well as the large quadrupolar repulsion between atop-bound CO
850 + molecules, help to explain the observed increase in surface mobility
851 + of Pt(557) and the resultant reconstruction into a double-layer
852 + configuration at the highest simulated CO-coverages.  The weaker Au-CO
853 + interaction results in significantly lower adataom diffusion
854 + constants, less step-wandering, and a lack of the double layer
855 + reconstruction on the Au(557) surface.
856 +
857 + An in-depth examination of the energetics shows the important role CO
858 + plays in increasing step-breakup and in facilitating edge traversal
859 + which are both necessary for double layer formation.
860 +
861 + %Things I am not ready to remove yet
862 +
863 + %Table of Diffusion Constants
864 + %Add gold?M
865 + % \begin{table}[H]
866 + %   \caption{}
867 + %   \centering
868 + % \begin{tabular}{| c | cc | cc | }
869 + %   \hline
870 + %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
871 + %   \hline
872 + %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
873 + %   \hline
874 + %   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
875 + %   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
876 + %   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
877 + %   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
878 + %   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
879 + %   \hline
880 + % \end{tabular}
881 + % \end{table}
882 +
883 + \begin{acknowledgement}
884 +  We gratefully acknowledge conversations with Dr. William
885 +  F. Schneider and Dr. Feng Tao.  Support for this project was
886 +  provided by the National Science Foundation under grant CHE-0848243
887 +  and by the Center for Sustainable Energy at Notre Dame
888 +  (cSEND). Computational time was provided by the Center for Research
889 +  Computing (CRC) at the University of Notre Dame.
890 + \end{acknowledgement}
891   \newpage
892 < \bibliography{firstTryBibliography}
893 < \end{doublespace}
892 > \bibstyle{achemso}
893 > \bibliography{COonPtAu}
894 > %\end{doublespace}
895 >
896 > \begin{tocentry}
897 > \begin{wrapfigure}{l}{0.5\textwidth}
898 > \begin{center}
899 > \includegraphics[width=\linewidth]{TOC_doubleLayer}
900 > \end{center}
901 > \end{wrapfigure}
902 > A reconstructed Pt(557) surface after 86~ns exposure to a half a
903 > monolayer of CO.  The double layer that forms is a result of
904 > CO-mediated step-edge wandering as well as a burrowing mechanism that
905 > helps lift edge atoms onto an upper terrace.
906 > \end{tocentry}
907 >
908   \end{document}

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