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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{endfloat}
8 < \usepackage{caption}
9 < %\usepackage{tabularx}
10 < \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[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}
17 – \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
18 – \evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
19 – 9.0in \textwidth 6.5in \brokenpenalty=10000
12  
13 < % double space list of tables and figures
14 < %\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}}
23 < \setlength{\abovecaptionskip}{20 pt}
24 < \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 < \bibpunct{}{}{,}{s}{}{;}
17 < \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 47 | Line 44
44   %Summary
45   %%
46  
50 – %Title
51 – \title{Molecular Dynamics simulations of the surface reconstructions
52 –  of Pt(557) and Au(557) under exposure to CO}
47  
54 – \author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel
55 – Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\
56 – Department of Chemistry and Biochemistry,\\
57 – University of Notre Dame\\
58 – Notre Dame, Indiana 46556}
59 –
60 – %Date
61 – \date{Dec 15, 2012}
62 –
63 – %authors
64 –
65 – % make the title
66 – \maketitle
67 –
68 – \begin{doublespace}
69 –
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 100 | Line 92 | This work an effort to understand the mechanism and ti
92   reversible restructuring under exposure to moderate pressures of
93   carbon monoxide.\cite{Tao:2010}
94  
95 < This work an effort to understand the mechanism and timescale for
96 < surface restructuring using molecular simulations.  Since the dynamics
97 < of the process is of particular interest, we utilize classical force
98 < fields that represent a compromise between chemical accuracy and the
99 < computational efficiency necessary to observe the 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  
109 – Since restructuring occurs as a result of specific interactions of the
110 – catalyst with adsorbates, two metal systems exposed to carbon monoxide
111 – were examined in this work. The Pt(557) surface has already been shown
112 – to reconstruct under certain conditions. The Au(557) surface, because
113 – of a weaker interaction with CO, is less likely to undergo this kind
114 – of reconstruction.  MORE HERE ON PT AND AU PREVIOUS WORK.
115 –
122   %Platinum molecular dynamics
123   %gold molecular dynamics
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 133 | Line 139 | Au-Au and Pt-Pt interactions, while modeling the CO us
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, while modeling the CO using a rigid
143 < three-site model developed by Straub and Karplus for studying
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    
# Line 146 | Line 152 | parameter sets. The glue model of Ercolessi {\it et al
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 164 | 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
# Line 176 | Line 182 | The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen
182   % metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
183   % MEAM presents significant additional computational costs, however.
184  
185 < The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen 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{Carbon Monoxide model}
206 < Since previous explanations for the surface rearrangements center on
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
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, Lennard-Jones parameters ($\sigma$ and
221 <    $\epsilon$), and charges for the CO-CO
222 <    interactions borrowed from Ref. \bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA~, energies are
223 <    in kcal/mol, and charges are in atomic units.}
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
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 between the metals and carbon monoxide}
240  
241 < Since the adsorption of CO onto a platinum surface has been the focus
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. Parameters reported by Korzeniewski {\it et
247 <  al.}\cite{Pons:1986} were a starting point for our fits, which were
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). This resulting binding energies are on the higher
250 < side of the experimentally-reported values. 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
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 parameterized to a Morse potential with a large
256 < range parameter ($r_o$).  In most cases, this contributes a weak
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
# Line 245 | Line 263 | The Au-C and Au-O cross-interactions were fit using Le
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 DFT calculations with a
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 < {\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are
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
261 < subsequent steps was less than $10^{-8}$ Ry.  In testing the CO-Au
262 < 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 with a 4 x 4 x
282 < 4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
283 < zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was
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 parameters employed in this work are shown in Table 2 and the
292 < binding energies on the 111 surfaces are displayed in Table 3.  To
293 < speed up the computations, charge transfer and polarization are not
294 < being treated in this model, although these effects are likely to
295 < affect binding energies and binding site
278 < 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  
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-CO cross-interactions.   Metal-C
302 <    interactions are modeled with Lennard-Jones potential, while the
303 <    (mostly-repulsive) metal-O interactions were fit to Morse
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 |}
# Line 295 | Line 312 | preferences.\cite{Deshlahra:2012}
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 for CO on M(111) using the potentials
321 <    described in this work.  All values are 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
# Line 309 | Line 327 | preferences.\cite{Deshlahra:2012}
327    \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -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{TPD_Gold}) \\
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  
317 – \subsection{Pt(557) and Au(557) metal interfaces}
336  
337 < Our model systems are composed of 3888 Pt atoms and 3384 Au atoms in a
338 < FCC crystal that have been cut along the 557 plane so that they are
339 < periodic in the {\it x} and {\it y} directions, and have been rotated
340 < to expose two parallel 557 cuts along the positive and negative {\it
341 <  z}-axis.  Simulations of the bare metal interfaces at temperatures
342 < ranging from 300~K to 1200~K were done to observe the relative
337 > \subsection{Validation of forcefield selections}
338 > By calculating minimum energies for commensurate systems of
339 > single and double layer Pt and Au systems with 0 and 50\% coverages
340 > (arranged in a c(2x4) pattern), our forcefield selections were able to be
341 > indirectly compared to results shown in the supporting information of Tao
342 > {\it et al.} \cite{Tao:2010}. Five layer thick systems, displaying a 557 facet
343 > were constructed, each composed of 480 metal atoms. Double layers systems
344 > were constructed from six layer thick systems where an entire layer was
345 > removed from both displayed facets to create a double step. By design, the
346 > double step system also contains 480 atoms, five layers thick, so energy
347 > comparisons between the arrangements can be made directly. The positions
348 > of the atoms were allowed to relax, along with the box sizes, before a
349 > minimum energy was calculated. Carbon monoxide, equivalent to 50\%
350 > coverage on one side of the metal system was added in a c(2x4) arrangement
351 > and again allowed to relax before a minimum energy was calculated.
352 >
353 > Energies for the various systems are displayed in Table ~\ref{tab:steps}. Examining
354 > the Pt systems first, it is apparent that the double layer system is slightly less stable
355 > then the original single step. However, upon addition of carbon monoxide, the
356 > stability is reversed and the double layer system becomes more stable. This result
357 > is in agreement with DFT calculations in Tao {\it et al.}\cite{Tao:2010}, who also show
358 > that the addition of CO leads to a reversal in the most stable system. While our
359 > results agree qualitatively, quantitatively, they are approximately an order of magnitude
360 > different. Looking at additional stability per atom in kcal/mol, the DFT calculations suggest
361 > an increased stability of 0.1 kcal/mol per Pt atom, whereas we are seeing closer to a 0.4 kcal/mol
362 > increase in stability per Pt atom.
363 >
364 > The gold systems show a much smaller energy difference between the single and double
365 > systems, likely arising from their lower energy per atom values. Additionally, the weaker
366 > binding of CO to Au is evidenced by the much smaller energy change between the two systems,
367 > when compared to the Pt results. This limited change helps explain our lack of any reconstruction
368 > on the Au systems.
369 >
370 >
371 > %Table of single step double step calculations
372 > \begin{table}[H]
373 > \caption{Minimized single point energies of unit cell crystals displaying (S)ingle or (D)double steps. Systems are periodic along and perpendicular to the step-edge axes with a large vacuum above the displayed 557 facet. The addition of CO in a 50\% c(2x4) coverage acts as a stabilizing presence and suggests a driving force for the observed reconstruction on the highest coverage Pt system. All energies are in kcal/mol.}
374 > \centering
375 > \begin{tabular}{| c | c | c | c | c | c | c |}
376 > \hline
377 > \textbf{Step} & \textbf{N}\textsubscript{M} & \textbf{N\textsubscript{CO}} & \textbf{Unit-Cell Energy} & \textbf{Energy per M} & \textbf{Energy per CO} & \textbf{Difference per M} \\
378 > \hline
379 > Pt(557)-S & 480 & 0 & -61142.624 & -127.381 & - & 0 \\
380 > Pt(557)-D & 480 & 0 & -61027.841 & -127.141 & - & 0.240 \\
381 > \hline
382 > Pt(557)-S & 480 & 40 & -62960.289 & -131.167 & -45.442 & 0 \\
383 > Pt(557)-D & 480 & 44 & -63040.007 & -131.333 & -45.731 & -0.166\\
384 > \hline
385 > \hline
386 > Au(557)-S & 480 & 0 & -41879.286 & -87.249 & - &0 \\
387 > Au(557)-D & 480 & 0 & -41799.714 & -87.084 & - & 0.165 \\
388 > \hline
389 > Au(557)-S & 480 & 40 & -42423.899 & -88.381 & -13.615 & 0 \\
390 > Au(557)-D & 480 & 44 & -42428.738 & -88.393 & -14.296 & -0.012 \\
391 > \hline
392 > \end{tabular}
393 > \label{tab:steps}
394 > \end{table}
395 >
396 >
397 > \subsection{Pt(557) and Au(557) metal interfaces}
398 > Our Pt system is an orthorhombic periodic box of dimensions
399 > 54.482~x~50.046~x~120.88~\AA~while our Au system has
400 > dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs
401 > are 9 and 8 atoms deep respectively, corresponding to a slab
402 > thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
403 > The systems are arranged in a FCC crystal that have been cut
404 > along the (557) plane so that they are periodic in the {\it x} and
405 > {\it y} directions, and have been oriented to expose two aligned
406 > (557) cuts along the extended {\it z}-axis.  Simulations of the
407 > bare metal interfaces at temperatures ranging from 300~K to
408 > 1200~K were performed to confirm the relative
409   stability of the surfaces without a CO overlayer.  
410  
411 < The different bulk (and surface) melting temperatures (1337~K for Au
412 < and 2045~K for Pt) suggest that the reconstruction may happen at
413 < different temperatures for the two metals.  To copy experimental
414 < conditions for the CO-exposed surfaces, the bare surfaces were
415 < initially run in the canonical (NVT) ensemble at 800~K and 1000~K
416 < respectively for 100 ps.  Each surface was exposed to a range of CO
417 < that was initially placed in the vacuum region.  Upon full adsorption,
418 < these amounts correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
419 < coverage.  Because of the difference in binding energies, the platinum
420 < systems very rarely had CO that was not bound to the surface, while
421 < the gold surfaces often had a significant CO population in the gas
422 < phase.  These systems were allowed to reach thermal equilibrium (over
423 < 5 ns) before being shifted to the microcanonical (NVE) ensemble for
424 < data collection. All of the systems examined had at least 40 ns in the
425 < data collection stage, although simulation times for some of the
426 < systems exceeded 200ns.  All simulations were run using the open
427 < source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,OpenMD}
411 > The different bulk melting temperatures predicted by EAM
412 > (1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for
413 > Pt\cite{Pt:melting}) suggest that any reconstructions should happen at
414 > different temperatures for the two metals.  The bare Au and Pt
415 > surfaces were initially run in the canonical (NVT) ensemble at 800~K
416 > and 1000~K respectively for 100 ps. The two surfaces were relatively
417 > stable at these temperatures when no CO was present, but experienced
418 > increased surface mobility on addition of CO. Each surface was then
419 > dosed with different concentrations of CO that was initially placed in
420 > the vacuum region.  Upon full adsorption, these concentrations
421 > correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher
422 > coverages resulted in the formation of a double layer of CO, which
423 > introduces artifacts that are not relevant to (557) reconstruction.
424 > Because of the difference in binding energies, nearly all of the CO
425 > was bound to the Pt surface, while the Au surfaces often had a
426 > significant CO population in the gas phase.  These systems were
427 > allowed to reach thermal equilibrium (over 5~ns) before being run in
428 > the microcanonical (NVE) ensemble for data collection. All of the
429 > systems examined had at least 40~ns in the data collection stage,
430 > although simulation times for some Pt of the systems exceeded 200~ns.
431 > Simulations were carried out using the open source molecular dynamics
432 > package, OpenMD.\cite{Ewald,OOPSE,openmd}
433  
434 < % Just results, leave discussion for discussion section
435 < % structure
436 < %       Pt: step wandering, double layers, no triangular motifs
348 < %       Au: step wandering, no double layers
349 < % dynamics
350 < %       diffusion
351 < %       time scale, formation, breakage
434 >
435 > % RESULTS
436 > %
437   \section{Results}
438   \subsection{Structural remodeling}
439 < Tao {\it et al.} showed experimentally that the Pt(557) surface undergoes
440 < two separate reconstructions upon CO adsorption.\cite{Tao:2010} The first
441 < reconstruction involves a doubling of the step height and plateau length. Similar
442 < behavior has been seen to occur on numerous surfaces at varying conditions.\cite{}
443 < Of the two systems we examined, the Platinum system showed the most surface
444 < reconstruction. Additionally, the amount of reconstruction appears to be
445 < dependent on the amount of CO adsorbed upon the surface. This result is likely
446 < related to the effect that coverage has on surface diffusion. While both systems
447 < displayed step edge wandering, only the Pt surface underwent doubling within
448 < the time scales we were modeling. Specifically only the 50 \% coverage Pt system
449 < was observed to undergo doubling in the time scales we were able to monitor.
365 < Although, the other Platinum systems tended to show more cumulative lateral movement of
366 < the step edges when compared to the Gold systems. The 50 \% Pt system is highlighted
367 < in figure \ref{fig:reconstruct} at various times along the simulation showing
368 < the evolution of the system.
439 > The bare metal surfaces experienced minor roughening of the step-edge
440 > because of the elevated temperatures, but the (557) face was stable
441 > throughout the simulations. The surfaces of both systems, upon dosage
442 > of CO, began to undergo extensive remodeling that was not observed in
443 > the bare systems. Reconstructions of the Au systems were limited to
444 > breakup of the step-edges and some step wandering. The lower coverage
445 > Pt systems experienced similar step edge wandering but to a greater
446 > extent. The 50\% coverage Pt system was unique among our simulations
447 > in that it formed well-defined and stable double layers through step
448 > coalescence, similar to results reported by Tao {\it et
449 >  al}.\cite{Tao:2010}
450  
451 < The second reconstruction on the Pt(557) surface observed by Tao involved the
452 < formation of triangular clusters that stretched across the plateau between two step edges.
453 < Neither system, within our simulated time scales, experiences this reconstruction. A constructed
454 < system in which the triangular motifs were constructed on the surface will be explored in future
455 < work and is shown in the supporting information.
451 > \subsubsection{Step wandering}
452 > The bare surfaces for both metals showed minimal step-wandering at
453 > their respective temperatures. As the CO coverage increased however,
454 > the mobility of the surface atoms, described through adatom diffusion
455 > and step-edge wandering, also increased.  Except for the 50\% Pt
456 > system where step coalescence occurred, the step-edges in the other
457 > simulations preferred to keep nearly the same distance between steps
458 > as in the original (557) lattice, $\sim$13\AA~for Pt and
459 > $\sim$14\AA~for Au.  Previous work by Williams {\it et
460 >  al}.\cite{Williams:1991, Williams:1994} highlights the repulsion
461 > that exists between step-edges even when no direct interactions are
462 > present in the system. This repulsion is caused by an entropic barrier
463 > that arises from the fact that steps cannot cross over one
464 > another. This entropic repulsion does not completely define the
465 > interactions between steps, however, so it is possible to observe step
466 > coalescence on some surfaces.\cite{Williams:1991} The presence and
467 > concentration of adsorbates, as shown in this work, can affect
468 > step-step interactions, potentially leading to a new surface structure
469 > as the thermodynamic equilibrium.
470  
471 < \subsection{Dynamics}
472 < While atomistic simulations of stepped surfaces have been performed before \cite{}, they tend to be
473 < performed using Monte Carlo techniques\cite{}. This allows them to efficiently sample the thermodynamic
474 < landscape but at the expense of ignoring the dynamics of the system. Previous work, using STM (?)\cite{},
475 < has been able to visualize the coalescing of steps of (system). The time scale of the image acquisition
476 < provides an upper bounds for the time required for the doubling to actually occur. While statistical treatments
477 < of step edges are adept at analyzing such systems, it is important to remember that the edges are made
478 < up of individual atoms and thus can be examined in numerous ways.
471 > \subsubsection{Double layers}
472 > Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the
473 > Pt(557) surface undergoes two separate reconstructions upon CO
474 > adsorption.  The first involves a doubling of the step height and
475 > plateau length.  Similar behavior has been seen on a number of
476 > surfaces at varying conditions, including Ni(977) and
477 > Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we
478 > examined, the Pt system showed a greater propensity for reconstruction
479 > because of the larger surface mobility and the greater extent of step
480 > wandering.  The amount of reconstruction was strongly correlated to
481 > the amount of CO adsorbed upon the surface.  This appears to be
482 > related to the effect that adsorbate coverage has on edge breakup and
483 > on the surface diffusion of metal adatoms. Only the 50\% Pt surface
484 > underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within
485 > the time scales studied here.  Over a longer time scale (150~ns) two
486 > more double layers formed on this surface. Although double layer
487 > formation did not occur in the other Pt systems, they exhibited more
488 > step-wandering and roughening compared to their Au counterparts. The
489 > 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
490 > various times along the simulation showing the evolution of a double
491 > layer step-edge.
492  
493 + The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010}
494 + involved the formation of triangular clusters that stretched across
495 + the plateau between two step-edges. Neither of the simulated metal
496 + interfaces, within the 40~ns time scale or the extended time of 150~ns
497 + for the 50\% Pt system, experienced this reconstruction.
498 +
499 + %Evolution of surface
500 + \begin{figure}[H]
501 + \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation}
502 + \caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a)
503 +  258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after
504 +  exposure. Disruption of the (557) step-edges occurs quickly.  The
505 +  doubling of the layers appears only after two adjacent step-edges
506 +  touch.  The circled spot in (b) nucleated the growth of the double
507 +  step observed in the later configurations.}
508 +  \label{fig:reconstruct}
509 + \end{figure}
510 +
511 + \subsection{Dynamics}
512 + Previous experimental work by Pearl and Sibener\cite{Pearl}, using
513 + STM, has been able to capture the coalescence of steps on Ni(977). The
514 + time scale of the image acquisition, $\sim$70~s/image, provides an
515 + upper bound for the time required for the doubling to occur. By
516 + utilizing Molecular Dynamics we are able to probe the dynamics of
517 + these reconstructions at elevated temperatures and in this section we
518 + provide data on the timescales for transport properties,
519 + e.g. diffusion and layer formation time.
520 +
521 +
522   \subsubsection{Transport of surface metal atoms}
523 < The movement of a step edge is a cooperative effect arising from the individual movements of the atoms
387 < making up the step. An ideal metal surface displaying a low index facet (111, 100, 110) is unlikely to
388 < experience much surface diffusion because of the large energetic barrier to lift an atom out of the surface.
389 < For our surfaces, the presence of step edges provide a source for mobile metal atoms. Breaking away
390 < from the step edge is still an energetic penalty around (value) but is much less than lifting the same metal
391 < atom out from the surface and the penalty lowers even further when CO is present in sufficient quantities
392 < on the surface. Once an adatom exists on the surface, its barrier for diffusion is negligible ( < 4 kcal/mole)
393 < and is well able to explore its terrace because both steps act as barriers constraining the area in which
394 < diffusion is allowed. By tracking the mobility of individual metal atoms on the surface we were able to determine
395 < the relative diffusion rates and how varying coverages of CO affected the diffusion constants. Close
396 < observation of the mobile metal atoms showed that they were typically in equilibrium with the
397 < step edges, constantly breaking apart and rejoining. Additionally, at times their motion was concerted and
398 < two or more atoms would be observed moving together across the surfaces. The primary challenge in quantifying
399 < the overall surface mobility is in defining ``mobile" vs. ``static" atoms.
523 > %forcedSystems/stepSeparation
524  
525 < A particle was considered mobile once it had traveled more than 2~\AA~ between saved configurations
526 < of the system (10-100 ps). An atom that was truly mobile would typically travel much greater than this, but
527 < the 2~\AA~ cutoff was to prevent the in place vibrational movement of atoms from being included in the analysis.
528 < Since diffusion on  a surface is strongly affected by local structures, in this case the presence of single and double
529 < layer step edges, the diffusion parallel to the step edges was determined separately from the diffusion perpendicular
530 < to these edges. The parallel and perpendicular diffusion constants are shown in figure \ref{fig:diff}.
525 > The wandering of a step-edge is a cooperative effect arising from the
526 > individual movements of the atoms making up the steps. An ideal metal
527 > surface displaying a low index facet, (111) or (100), is unlikely to
528 > experience much surface diffusion because of the large energetic
529 > barrier that must be overcome to lift an atom out of the surface. The
530 > presence of step-edges and other surface features on higher-index
531 > facets provides a lower energy source for mobile metal atoms.  Using
532 > our potential model, single-atom break-away from a step-edge on a
533 > clean surface still imposes an energetic penalty around
534 > $\sim$~45~kcal/mol, but this is certainly easier than lifting the same
535 > metal atom vertically out of the surface, \textgreater~60~kcal/mol.
536 > The penalty lowers significantly when CO is present in sufficient
537 > quantities on the surface. For certain distributions of CO, the
538 > energetic penalty can fall to as low as $\sim$~20~kcal/mol. The
539 > configurations that create these lower barriers are detailed in the
540 > discussion section below.
541  
542 < \subsubsection{Double layer formation}
543 < The increased amounts of diffusion on Pt at the higher CO coverages appears to play a role in the
544 < formation of double layers. Seeing as how that was the only system within our observed simulation time
545 < that showed the formation. As mentioned earlier, previous experimental work has given some insight into
546 < the upper bounds of the time required for enough atoms to move around to allow two steps to coalesce\cite{}.
547 < As seen in figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into
548 < the simulation. Within 10 ns, nearly half of the step has formed the double layer and by 86 ns, the complete
549 < layer has formed. From the appearance of the first node to the complete doubling of the layers, only ~65 ns
550 < have elapsed. The other two layers in this simulation form over a period of ---- and ---- ns respectively.
542 > Once an adatom exists on the surface, the barrier for diffusion is
543 > negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are
544 > then able to explore the terrace before rejoining either their
545 > original step-edge or becoming a part of a different edge. It is an
546 > energetically unfavorable process with a high barrier for an atom to
547 > traverse to a separate terrace although the presence of CO can lower
548 > the energy barrier required to lift or lower an adatom. By tracking
549 > the mobility of individual metal atoms on the Pt and Au surfaces we
550 > were able to determine the relative diffusion constants, as well as
551 > how varying coverages of CO affect the diffusion. Close observation of
552 > the mobile metal atoms showed that they were typically in equilibrium
553 > with the step-edges.  At times, their motion was concerted, and two or
554 > more adatoms would be observed moving together across the surfaces.
555  
556 + A particle was considered ``mobile'' once it had traveled more than
557 + 2~\AA~ between saved configurations of the system (typically 10-100
558 + ps). A mobile atom would typically travel much greater distances than
559 + this, but the 2~\AA~cutoff was used to prevent swamping the diffusion
560 + data with the in-place vibrational movement of buried atoms. Diffusion
561 + on a surface is strongly affected by local structures and the presence
562 + of single and double layer step-edges causes the diffusion parallel to
563 + the step-edges to be larger than the diffusion perpendicular to these
564 + edges. Parallel and perpendicular diffusion constants are shown in
565 + Figure \ref{fig:diff}.  Diffusion parallel to the step-edge is higher
566 + than diffusion perpendicular to the edge because of the lower energy
567 + barrier associated with sliding along an edge compared to breaking
568 + away to form an isolated adatom.
569 +
570 + %Diffusion graph
571   \begin{figure}[H]
572 < \includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf}
572 > \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1}
573   \caption{Diffusion constants for mobile surface atoms along directions
574    parallel ($\mathbf{D}_{\parallel}$) and perpendicular
575 <  ($\mathbf{D}_{\perp}$) to the 557 step edges as a function of CO
576 <  surface coverage.  Diffusion parallel to the step edge is higher
577 <  than that perpendicular to the edge because of the lower energy
578 <  barrier associated with going from approximately 7 nearest neighbors
579 <  to 5, as compared to the 3 of an adatom. Additionally, the observed
427 <  maximum and subsequent decrease for the Pt system suggests that the
428 <  CO self-interactions are playing a significant role with regards to
429 <  movement of the platinum atoms around and more importantly across
430 <  the surface. }
575 >  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
576 >  surface coverage.  The two reported diffusion constants for the 50\%
577 >  Pt system correspond to a 20~ns period before the formation of the
578 >  double layer (upper points), and to the full 40~ns sampling period
579 >  (lower points).}
580   \label{fig:diff}
581 + \end{figure}
582 +
583 + The weaker Au-CO interaction is evident in the weak CO-coverage
584 + dependance of Au diffusion. This weak interaction leads to lower
585 + observed coverages when compared to dosage amounts. This further
586 + limits the effect the CO can have on surface diffusion. The correlation
587 + between coverage and Pt diffusion rates shows a near linear relationship
588 + at the earliest times in the simulations. Following double layer formation,
589 + however, there is a precipitous drop in adatom diffusion. As the double
590 + layer forms, many atoms that had been tracked for mobility data have
591 + now been buried, resulting in a smaller reported diffusion constant. A
592 + secondary effect of higher coverages is CO-CO cross interactions that
593 + lower the effective mobility of the Pt adatoms that are bound to each CO.
594 + This effect would become evident only at higher coverages. A detailed
595 + account of Pt adatom energetics follows in the Discussion.
596 +
597 + \subsubsection{Dynamics of double layer formation}
598 + The increased diffusion on Pt at the higher CO coverages is the primary
599 + contributor to double layer formation. However, this is not a complete
600 + explanation -- the 33\%~Pt system has higher diffusion constants, but
601 + did not show any signs of edge doubling in 40~ns. On the 50\%~Pt
602 + system, one double layer formed within the first 40~ns of simulation time,
603 + while two more were formed as the system was allowed to run for an
604 + additional 110~ns (150~ns total). This suggests that this reconstruction
605 + is a rapid process and that the previously mentioned upper bound is a
606 + very large overestimate.\cite{Williams:1991,Pearl} In this system the first
607 + appearance of a double layer appears at 19~ns into the simulation.
608 + Within 12~ns of this nucleation event, nearly half of the step has formed
609 + the double layer and by 86~ns the complete layer has flattened out.
610 + From the appearance of the first nucleation event to the first observed
611 + double layer, the process took $\sim$20~ns. Another $\sim$40~ns was
612 + necessary for the layer to completely straighten. The other two layers in
613 + this simulation formed over periods of 22~ns and 42~ns respectively.
614 + A possible explanation for this rapid reconstruction is the elevated
615 + temperatures under which our systems were simulated. The process
616 + would almost certainly take longer at lower temperatures. Additionally,
617 + our measured times for completion of the doubling after the appearance
618 + of a nucleation site are likely affected by our periodic boxes. A longer
619 + step-edge will likely take longer to ``zipper''.
620 +
621 +
622 + %Discussion
623 + \section{Discussion}
624 + We have shown that a classical potential is able to model the initial
625 + reconstruction of the Pt(557) surface upon CO adsorption, and have
626 + reproduced the double layer structure observed by Tao {\it et
627 +  al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be
628 + rapid -- occurring within 100 ns of the initial exposure to CO.  Here
629 + we discuss the features of the classical potential that are
630 + contributing to the stability and speed of the Pt(557) reconstruction.
631 +
632 + \subsection{Diffusion}
633 + The perpendicular diffusion constant appears to be the most important
634 + indicator of double layer formation. As highlighted in Figure
635 + \ref{fig:reconstruct}, the formation of the double layer did not begin
636 + until a nucleation site appeared.  Williams {\it et
637 +  al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge
638 + repulsion arising from the inability of edge crossing.  This repulsion
639 + must be overcome to allow step coalescence.  A larger
640 + $\textbf{D}_\perp$ value implies more step-wandering and a larger
641 + chance for the stochastic meeting of two edges to create a nucleation
642 + point.  Diffusion parallel to the step-edge can help ``zipper'' up a
643 + nascent double layer. This helps explain the rapid time scale for
644 + double layer completion after the appearance of a nucleation site, while
645 + the initial appearance of the nucleation site was unpredictable.
646 +
647 + \subsection{Mechanism for restructuring}
648 + Since the Au surface showed no large scale restructuring in any of our
649 + simulations, our discussion will focus on the 50\% Pt-CO system which
650 + did exhibit doubling. A number of possible mechanisms exist to explain
651 + the role of adsorbed CO in restructuring the Pt surface. Quadrupolar
652 + repulsion between adjacent CO molecules adsorbed on the surface is one
653 + possibility.  However, the quadrupole-quadrupole interaction is
654 + short-ranged and is attractive for some orientations.  If the CO
655 + molecules are ``locked'' in a vertical orientation, through atop
656 + adsorption for example, this explanation would gain credence. Within
657 + the framework of our classical potential, the calculated energetic
658 + repulsion between two CO molecules located a distance of
659 + 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a
660 + vertical orientation, is 8.62 kcal/mol. Moving the CO to the second
661 + nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly
662 + 0. Allowing the CO to rotate away from a purely vertical orientation
663 + also lowers the repulsion. When the carbons are locked at a distance
664 + of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle
665 + between the 2 CO is $\sim$24\textsuperscript{o}.  The calculated
666 + barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
667 + repulsion between adjacent CO molecules bound to Pt could indeed
668 + increase the surface diffusion. However, the residence time of CO on
669 + Pt suggests that the CO molecules are extremely mobile, with diffusion
670 + constants 40 to 2500 times larger than surface Pt atoms. This mobility
671 + suggests that the CO molecules jump between different Pt atoms
672 + throughout the simulation.  However, they do stay bound to individual
673 + Pt atoms for long enough to modify the local energy landscape for the
674 + mobile adatoms.
675 +
676 + A different interpretation of the above mechanism which takes the
677 + large mobility of the CO into account, would be in the destabilization
678 + of Pt-Pt interactions due to bound CO.  Destabilizing Pt-Pt bonds at
679 + the edges could lead to increased step-edge breakup and diffusion. On
680 + the bare Pt(557) surface the barrier to completely detach an edge atom
681 + is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
682 + \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain
683 + configurations, cases (e), (g), and (h), the barrier can be lowered to
684 + $\sim$23~kcal/mol by the presence of bound CO molecules. In these
685 + instances, it becomes energetically favorable to roughen the edge by
686 + introducing a small separation of 0.5 to 1.0~\AA. This roughening
687 + becomes immediately obvious in simulations with significant CO
688 + populations. The roughening is present to a lesser extent on surfaces
689 + with lower CO coverage (and even on the bare surfaces), although in
690 + these cases it is likely due to random fluctuations that squeeze out
691 + step-edge atoms. Step-edge breakup by direct single-atom translations
692 + (as suggested by these energy curves) is probably a worst-case
693 + scenario.  Multistep mechanisms in which an adatom moves laterally on
694 + the surface after being ejected would be more energetically favorable.
695 + This would leave the adatom alongside the ledge, providing it with
696 + five nearest neighbors.  While fewer than the seven neighbors it had
697 + as part of the step-edge, it keeps more Pt neighbors than the three
698 + neighbors an isolated adatom has on the terrace. In this proposed
699 + mechanism, the CO quadrupolar repulsion still plays a role in the
700 + initial roughening of the step-edge, but not in any long-term bonds
701 + with individual Pt atoms.  Higher CO coverages create more
702 + opportunities for the crowded CO configurations shown in Figure
703 + \ref{fig:SketchGraphic}, and this is likely to cause an increased
704 + propensity for step-edge breakup.
705 +
706 + %Sketch graphic of different configurations
707 + \begin{figure}[H]
708 + \includegraphics[width=\linewidth]{COpaths}
709 + \caption{Configurations used to investigate the mechanism of step-edge
710 +  breakup on Pt(557). In each case, the central (starred) atom was
711 +  pulled directly across the surface away from the step edge.  The Pt
712 +  atoms on the upper terrace are colored dark grey, while those on the
713 +  lower terrace are in white.  In each of these configurations, some
714 +  of the atoms (highlighted in blue) had CO molecules bound in the
715 +  vertical atop position.  The energies of these configurations as a
716 +  function of central atom displacement are displayed in Figure
717 +  \ref{fig:SketchEnergies}.}
718 + \label{fig:SketchGraphic}
719   \end{figure}
720  
721 + %energy graph corresponding to sketch graphic
722 + \begin{figure}[H]
723 + \includegraphics[width=\linewidth]{Portrait_SeparationComparison}
724 + \caption{Energies for displacing a single edge atom perpendicular to
725 +  the step edge as a function of atomic displacement. Each of the
726 +  energy curves corresponds to one of the labeled configurations in
727 +  Figure \ref{fig:SketchGraphic}, and the energies are referenced to
728 +  the unperturbed step-edge.  Certain arrangements of bound CO
729 +  (notably configurations g and h) can lower the energetic barrier for
730 +  creating an adatom relative to the bare surface (configuration a).}
731 + \label{fig:SketchEnergies}
732 + \end{figure}
733 +
734 + While configurations of CO on the surface are able to increase
735 + diffusion and the likelihood of edge wandering, this does not provide
736 + a complete explanation for the formation of double layers. If adatoms
737 + were constrained to their original terraces then doubling could not
738 + occur.  A mechanism for vertical displacement of adatoms at the
739 + step-edge is required to explain the doubling.
740 +
741 + We have discovered one possible mechanism for a CO-mediated vertical
742 + displacement of Pt atoms at the step edge. Figure \ref{fig:lambda}
743 + shows four points along a reaction coordinate in which a CO-bound
744 + adatom along the step-edge ``burrows'' into the edge and displaces the
745 + original edge atom onto the higher terrace.  A number of events
746 + similar to this mechanism were observed during the simulations.  We
747 + predict an energetic barrier of 20~kcal/mol for this process (in which
748 + the displaced edge atom follows a curvilinear path into an adjacent
749 + 3-fold hollow site).  The barrier heights we obtain for this reaction
750 + coordinate are approximate because the exact path is unknown, but the
751 + calculated energy barriers would be easily accessible at operating
752 + conditions.  Additionally, this mechanism is exothermic, with a final
753 + energy 15~kcal/mol below the original $\lambda = 0$ configuration.
754 + When CO is not present and this reaction coordinate is followed, the
755 + process is endothermic by 3~kcal/mol.  The difference in the relative
756 + energies for the $\lambda=0$ and $\lambda=1$ case when CO is present
757 + provides strong support for CO-mediated Pt-Pt interactions giving rise
758 + to the doubling reconstruction.
759 +
760 + %lambda progression of Pt -> shoving its way into the step
761 + \begin{figure}[H]
762 + \includegraphics[width=\linewidth]{EPS_rxnCoord}
763 + \caption{Points along a possible reaction coordinate for CO-mediated
764 +  edge doubling. Here, a CO-bound adatom burrows into an established
765 +  step edge and displaces an edge atom onto the upper terrace along a
766 +  curvilinear path.  The approximate barrier for the process is
767 +  20~kcal/mol, and the complete process is exothermic by 15~kcal/mol
768 +  in the presence of CO, but is endothermic by 3~kcal/mol without CO.}
769 + \label{fig:lambda}
770 + \end{figure}
771 +
772 + The mechanism for doubling on the Pt(557) surface appears to require
773 + the cooperation of at least two distinct processes. For complete
774 + doubling of a layer to occur there must be a breakup of one
775 + terrace. These atoms must then ``disappear'' from that terrace, either
776 + by travelling to the terraces above or below their original levels.
777 + The presence of CO helps explain mechanisms for both of these
778 + situations. There must be sufficient breakage of the step-edge to
779 + increase the concentration of adatoms on the surface and these adatoms
780 + must then undergo the burrowing highlighted above (or a comparable
781 + mechanism) to create the double layer.  With sufficient time, these
782 + mechanisms working in concert lead to the formation of a double layer.
783 +
784 + \subsection{CO Removal and double layer stability}
785 + Once the double layers had formed on the 50\%~Pt system, they remained
786 + stable for the rest of the simulation time with minimal movement.
787 + Random fluctuations that involved small clusters or divots were
788 + observed, but these features typically healed within a few
789 + nanoseconds.  Within our simulations, the formation of the double
790 + layer appeared to be irreversible and a double layer was never
791 + observed to split back into two single layer step-edges while CO was
792 + present.
793 +
794 + To further gauge the effect CO has on this surface, additional
795 + simulations were run starting from a late configuration of the 50\%~Pt
796 + system that had already formed double layers. These simulations then
797 + had their CO molecules suddenly removed.  The double layer broke apart
798 + rapidly in these simulations, showing a well-defined edge-splitting
799 + after 100~ps. Configurations of this system are shown in Figure
800 + \ref{fig:breaking}. The coloring of the top and bottom layers helps to
801 + show how much mixing the edges experience as they split. These systems
802 + were only examined for 10~ns, and within that time despite the initial
803 + rapid splitting, the edges only moved another few \AA~apart. It is
804 + possible that with longer simulation times, the (557) surface recovery
805 + observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered.
806 +
807 + %breaking of the double layer upon removal of CO
808 + \begin{figure}[H]
809 + \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking}
810 + \caption{Behavior of an established (111) double step after removal of
811 +  the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the
812 +  removal of CO.  Nearly immediately after the CO is removed, the
813 +  step edge reforms in a (100) configuration, which is also the step
814 +  type seen on clean (557) surfaces. The step separation involves
815 +  significant mixing of the lower and upper atoms at the edge.}
816 + \label{fig:breaking}
817 + \end{figure}
818 +
819 +
820 + %Peaks!
821 + %\begin{figure}[H]
822 + %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
823 + %\caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
824 + %of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with
825 + %aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
826 + %\label{fig:peaks}
827 + %\end{figure}
828 +
829 +
830 + %Don't think I need this
831 + %clean surface...
832 + %\begin{figure}[H]
833 + %\includegraphics[width=\linewidth]{557_300K_cleanPDF}
834 + %\caption{}
835 +
836 + %\end{figure}
837 + %\label{fig:clean}
838 +
839 +
840 + \section{Conclusion}
841 + The strength and directionality of the Pt-CO binding interaction, as
842 + well as the large quadrupolar repulsion between atop-bound CO
843 + molecules, help to explain the observed increase in surface mobility
844 + of Pt(557) and the resultant reconstruction into a double-layer
845 + configuration at the highest simulated CO-coverages.  The weaker Au-CO
846 + interaction results in significantly lower adataom diffusion
847 + constants, less step-wandering, and a lack of the double layer
848 + reconstruction on the Au(557) surface.
849 +
850 + An in-depth examination of the energetics shows the important role CO
851 + plays in increasing step-breakup and in facilitating edge traversal
852 + which are both necessary for double layer formation.
853 +
854 + %Things I am not ready to remove yet
855 +
856   %Table of Diffusion Constants
857   %Add gold?M
858   % \begin{table}[H]
# Line 451 | Line 873 | have elapsed. The other two layers in this simulation
873   % \end{tabular}
874   % \end{table}
875  
876 < %Discussion
877 < \section{Discussion}
876 > \begin{acknowledgement}
877 >  We gratefully acknowledge conversations with Dr. William
878 >  F. Schneider and Dr. Feng Tao.  Support for this project was
879 >  provided by the National Science Foundation under grant CHE-0848243
880 >  and by the Center for Sustainable Energy at Notre Dame
881 >  (cSEND). Computational time was provided by the Center for Research
882 >  Computing (CRC) at the University of Notre Dame.
883 > \end{acknowledgement}
884 > \newpage
885 > \bibstyle{achemso}
886 > \bibliography{COonPtAu}
887 > %\end{doublespace}
888  
889 < Mechanism for restructuring
889 > \begin{tocentry}
890 > \begin{wrapfigure}{l}{0.5\textwidth}
891 > \begin{center}
892 > \includegraphics[width=\linewidth]{TOC_doubleLayer}
893 > \end{center}
894 > \end{wrapfigure}
895 > A reconstructed Pt(557) surface after 86~ns exposure to a half a
896 > monolayer of CO.  The double layer that forms is a result of
897 > CO-mediated step-edge wandering as well as a burrowing mechanism that
898 > helps lift edge atoms onto an upper terrace.
899 > \end{tocentry}
900  
459 – There are a number of possible mechanisms to explain the role of
460 – adsorbed CO in restructuring the Pt surface. Quadrupolar repulsion
461 – between adjacent CO molecules adsorbed on the surface is one
462 – possibility.  However, the quadrupole-quadrupole interaction is
463 – short-ranged and is attractive for some orientations.  If the CO
464 – molecules are locked in a specific orientation relative to each other,
465 – this explanation gains some weight.  
466 –
467 – Another possible mechanism for the restructuring is in the
468 – destabilization of strong Pt-Pt interactions by CO adsorbed on surface
469 – Pt atoms.  This could have the effect of increasing surface mobility
470 – of these atoms.  
471 –
472 – Comparing the results from simulation to those reported previously by
473 – Tao et al. the similarities in the platinum and CO system are quite
474 – strong. As shown in figure, the simulated platinum system under a CO
475 – atmosphere will restructure slightly by doubling the terrace
476 – heights. The restructuring appears to occur slowly, one to two
477 – platinum atoms at a time. Looking at individual snapshots, these
478 – adatoms tend to either rise on top of the plateau or break away from
479 – the step edge and then diffuse perpendicularly to the step direction
480 – until reaching another step edge. This combination of growth and decay
481 – of the step edges appears to be in somewhat of a state of dynamic
482 – equilibrium. However, once two previously separated edges meet as
483 – shown in figure 1.B, this point tends to act as a focus or growth
484 – point for the rest of the edge to meet up, akin to that of a
485 – zipper. From the handful of cases where a double layer was formed
486 – during the simulation, measuring from the initial appearance of a
487 – growth point, the double layer tends to be fully formed within
488 – $\sim$~35 ns.
489 –
490 – \subsection{Diffusion}
491 – 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?)
492 – \\
493 – \\
494 – %Evolution of surface
495 – \begin{figure}[H]
496 – \includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
497 – \caption{The Pt(557) / 50\% CO system at a sequence of times after
498 –  initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and
499 –  (d) 86.1 ns. Disruption of the 557 step edges occurs quickly.  The
500 –  doubling of the layers appears only after two adjacent step edges
501 –  touch.  The circled spot in (b) nucleated the growth of the double
502 –  step observed in the later configurations.}
503 –  \label{fig:reconstruct}
504 – \end{figure}
505 –
506 –
507 – %Peaks!
508 – \begin{figure}[H]
509 – \includegraphics[width=\linewidth]{doublePeaks_noCO.png}
510 – \caption{}
511 – \end{figure}
512 – \begin{figure}[H]
513 – \includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
514 – \caption{}
515 – \end{figure}
516 – \section{Conclusion}
517 –
518 –
519 – \section{Acknowledgments}
520 – Support for this project was provided by the National Science
521 – Foundation under grant CHE-0848243 and by the Center for Sustainable
522 – Energy at Notre Dame (cSEND). Computational time was provided by the
523 – Center for Research Computing (CRC) at the University of Notre Dame.
524 –
525 – \newpage
526 – \bibliography{firstTryBibliography}
527 – \end{doublespace}
901   \end{document}

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