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1   \documentclass[journal = jpccck, manuscript = article]{achemso}
2   \setkeys{acs}{usetitle = true}
3   \usepackage{achemso}
4 – \usepackage{caption}
5 – \usepackage{float}
6 – \usepackage{geometry}
4   \usepackage{natbib}
8 – \usepackage{setspace}
9 – \usepackage{xkeyval}
10 – %%%%%%%%%%%%%%%%%%%%%%%
11 – \usepackage{amsmath}
12 – \usepackage{amssymb}
13 – \usepackage{times}
14 – \usepackage{mathptm}
15 – \usepackage{setspace}
16 – \usepackage{endfloat}
17 – \usepackage{caption}
18 – \usepackage{tabularx}
19 – \usepackage{longtable}
20 – \usepackage{graphicx}
5   \usepackage{multirow}
6 < \usepackage{multicol}
6 > \usepackage{wrapfig}
7 > \usepackage{fixltx2e}
8 > %\mciteErrorOnUnknownfalse
9  
10   \usepackage[version=3]{mhchem}  % this is a great package for formatting chemical reactions
25 – % \usepackage[square, comma, sort&compress]{natbib}
11   \usepackage{url}
27 – \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
28 – \evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
29 – 9.0in \textwidth 6.5in \brokenpenalty=10000
12  
31 – % double space list of tables and figures
32 – %\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}}
33 – \setlength{\abovecaptionskip}{20 pt}
34 – \setlength{\belowcaptionskip}{30 pt}
35 – % \bibpunct{}{}{,}{s}{}{;}
36 –
37 – %\citestyle{nature}
38 – % \bibliographystyle{achemso}
39 –
13   \title{Molecular Dynamics simulations of the surface reconstructions
14    of Pt(557) and Au(557) under exposure to CO}
15  
# Line 73 | Line 46 | We examine surface reconstructions of Pt and Au(557) u
46  
47  
48   \begin{abstract}
49 < We examine surface reconstructions of Pt and Au(557) under
50 < various CO coverages using molecular dynamics in order to
51 < explore possible mechanisms for any observed reconstructions
52 < and their dynamics. The metal-CO interactions were parameterized
53 < as part of this work so that an efficient large-scale treatment of
54 < this system could be undertaken. The large difference in binding
55 < strengths of the metal-CO interactions was found to play a significant
56 < role with regards to step-edge stability and adatom diffusion. A
57 < small correlation between coverage and the diffusion constant
58 < was also determined. The energetics of CO adsorbed to the surface
59 < is sufficient to explain the reconstructions observed on the Pt
60 < systems and the lack  of reconstruction of the Au systems.
61 <
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 117 | Line 92 | This work is an investigation into the mechanism and t
92   reversible restructuring under exposure to moderate pressures of
93   carbon monoxide.\cite{Tao:2010}
94  
95 < This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557)
96 < surface restructuring using molecular simulations.  Since the dynamics
97 < of the process are of particular interest, we employ classical force
98 < fields that represent a compromise between chemical accuracy and the
99 < computational efficiency necessary to simulate the process of interest.
100 < Since restructuring typically occurs as a result of specific interactions of the
101 < catalyst with adsorbates, in this work, two metal systems exposed
102 < to carbon monoxide were examined. The Pt(557) surface has already been shown
103 < to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010}
104 < The Au(557) surface, because of a weaker interaction with CO, is less
105 < likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000}
106 < and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced
107 < reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the
108 < 22 x $\sqrt{3}$ cell. They argued that only a few Au atoms
109 < become adatoms, limiting the stress of this reconstruction, while
110 < allowing the rest to relax and approach the ideal (111)
111 < configuration. They did not see the usual herringbone pattern on Au(111) being greatly
112 < affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a
113 < disruption of the herringbone pattern as CO was adsorbed to the
114 < surface. Both groups suggested that the preference CO shows for
115 < low-coordinated Au atoms was the primary driving force for the reconstruction.
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  
142 –
143 –
122   %Platinum molecular dynamics
123   %gold molecular dynamics
124  
125   \section{Simulation Methods}
126 < The challenge in modeling any solid/gas interface 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$^4$ 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 161 | Line 139 | Au-Au and Pt-Pt interactions.\cite{EAM} The CO was mod
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{EAM} The CO was modeled 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 174 | 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 treated 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 207 | Line 185 | properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007
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} One of EAM's strengths
193 < is its sensitivity to small changes in structure. This arises
194 < because interactions
195 < up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a}
196 < Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88}
197 < which is only parameterized up to the nearest-neighbor
198 < interactions, EAM is a suitable choice for systems where
199 < 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 adsorbates somewhat easier.
203 < \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  
227 –
228 –
229 –
205   \subsection{Carbon Monoxide model}
206 < Previous explanations for the surface rearrangements center on
207 < the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010}  
208 < We used a model first proposed by Karplus and Straub to study
209 < the photodissociation of CO from myoglobin because it reproduces
210 < the quadrupole moment well.\cite{Straub} The Straub and
211 < Karplus model treats CO as a rigid three site molecule with a massless M
212 < site at the molecular center of mass. The geometry and interaction
213 < parameters are reproduced in Table~\ref{tab:CO}. 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 in 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
# Line 291 | Line 268 | periodic supercell plane-wave basis approach, as imple
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 were
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
# Line 315 | Line 292 | an effect on  binding energies and binding site prefer
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.
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 potentials. While the
303 <    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 347 | Line 324 | an effect on  binding energies and binding site prefer
324    \hline
325    & Calculated & Experimental \\
326    \hline
327 <  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,}
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}) \\
# Line 356 | Line 333 | an effect on  binding energies and binding site prefer
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 + %Table of single step double step calculations
377 + \begin{table}[H]
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 | c | c | c | c | c |}
385 + \hline
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 + 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 + \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
# Line 370 | Line 415 | The different bulk melting temperatures predicted by E
415   1200~K were performed to confirm the relative
416   stability of the surfaces without a CO overlayer.  
417  
418 < The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting}
419 < and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at
420 < different temperatures for the two metals.  The bare Au and Pt surfaces were
421 < initially run in the canonical (NVT) ensemble at 800~K and 1000~K
422 < respectively for 100 ps. The two surfaces were relatively stable at these
423 < temperatures when no CO was present, but experienced increased surface
424 < mobility on addition of CO. Each surface was then dosed with different concentrations of CO
425 < that was initially placed in the vacuum region.  Upon full adsorption,
426 < these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
427 < coverage. Higher coverages resulted in the formation of a double layer of CO,
428 < which introduces artifacts that are not relevant to (557) reconstruction.
429 < Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
430 < the Au surfaces often had a significant CO population in the gas
431 < phase.  These systems were allowed to reach thermal equilibrium (over
432 < 5~ns) before being run in the microcanonical (NVE) ensemble for
433 < data collection. All of the systems examined had at least 40~ns in the
434 < data collection stage, although simulation times for some Pt of the
435 < systems exceeded 200~ns.  Simulations were carried out using the open
436 < source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}
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  
394 –
395 –
442   % RESULTS
443   %
444   \section{Results}
445   \subsection{Structural remodeling}
446 < The bare metal surfaces experienced minor roughening of the
447 < step-edge because of the elevated temperatures, but the (557)
448 < face was stable throughout the simulations. The surface of both
449 < systems, upon dosage of CO, began to undergo extensive remodeling
450 < that was not observed in the bare systems. Reconstructions of
451 < the Au systems were limited to breakup of the step-edges and
452 < some step wandering. The lower coverage Pt systems experienced
453 < similar restructuring but to a greater extent. The 50\% coverage
454 < Pt system was unique among our simulations in that it formed
455 < well-defined and stable double layers through step coalescence,
456 < similar to results reported by Tao {\it et al}.\cite{Tao:2010}
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  
412 –
458   \subsubsection{Step wandering}
459 < The 0\% coverage surfaces for both metals showed minimal
460 < step-wandering at their respective temperatures. As the CO
461 < coverage increased however, the mobility of the surface atoms,
462 < described through adatom diffusion and step-edge wandering,
463 < also increased.  Except for the 50\% Pt system where step
464 < coalescence occurred, the step-edges in the other simulations
465 < preferred to keep nearly the same distance between steps as in
466 < the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au.
467 < Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994}
468 < highlights the repulsion that exists between step-edges even
469 < when no direct interactions are present in the system. This
470 < repulsion is caused by an entropic barrier that arises from
471 < the fact that steps cannot cross over one another. This entropic
472 < repulsion does not completely define the interactions between
473 < steps, however, so it is possible to observe step coalescence
474 < on some surfaces.\cite{Williams:1991} The presence and
475 < concentration of adsorbates, as shown in this work, can
476 < affect step-step interactions, potentially leading to a new
432 < surface structure as the thermodynamic equilibrium.
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 Pt(557) surface
480 < undergoes two separate reconstructions upon CO adsorption.
481 < The first involves a doubling of the step height and plateau length.
482 < Similar behavior has been seen on a number of surfaces
483 < at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl}
484 < Of the two systems we examined, the Pt system showed a greater
485 < propensity for reconstruction  
486 < because of the larger surface mobility and the greater extent of step wandering.
487 < The amount of reconstruction was strongly correlated to the amount of CO
488 < adsorbed upon the surface.  This appears to be related to the
489 < effect that adsorbate coverage has on edge breakup and on the
490 < surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the
491 < doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here.
492 < Over a longer time scale (150~ns) two more double layers formed
493 < on this surface. Although double layer formation did not occur
494 < in the other Pt systems, they exhibited more step-wandering and
495 < 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 layer step-edge.
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
501 < Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched
502 < across the plateau between two step-edges. Neither metal, within
503 < the 40~ns time scale or the extended simulation time of 150~ns for
504 < the 50\% Pt system, experienced this reconstruction.
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[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
509 < \caption{The Pt(557) / 50\% CO system at a sequence of times after
510 <  initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and
511 <  (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly.  The
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.}
# Line 471 | Line 516 | Previous experimental work by Pearl and Sibener\cite{P
516   \end{figure}
517  
518   \subsection{Dynamics}
519 < Previous experimental work by Pearl and Sibener\cite{Pearl},
520 < using STM, has been able to capture the coalescence of steps
521 < on Ni(977). The time scale of the image acquisition, $\sim$70~s/image,
522 < provides an upper bound for the time required for the doubling
523 < to occur. By utilizing Molecular Dynamics we are able to probe
524 < the dynamics of these reconstructions at elevated temperatures
525 < and in this section we provide data on the timescales for transport
526 < properties, e.g. diffusion and layer formation time.
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
486 – The wandering of a step-edge is a cooperative effect
487 – arising from the individual movements of the atoms making up the steps. An ideal metal surface
488 – displaying a low index facet, (111) or (100), is unlikely to experience
489 – much surface diffusion because of the large energetic barrier that must
490 – be overcome to lift an atom out of the surface. The presence of step-edges and other surface features
491 – on higher-index facets provides a lower energy source for mobile metal atoms.
492 – Single-atom break-away from a step-edge on a clean surface still imposes an
493 – energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting
494 – the same metal atom vertically out of the surface,  \textgreater~60 kcal/mol.
495 – The penalty lowers significantly when CO is present in sufficient quantities
496 – on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as
497 – $\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for
498 – diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then
499 – able to explore the terrace before rejoining either their original step-edge or
500 – becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom
501 – to traverse to a separate terrace although the presence of CO can lower the
502 – energy barrier required to lift or lower an adatom. By tracking the mobility of individual
503 – metal atoms on the Pt and Au surfaces we were able to determine the relative
504 – diffusion constants, as well as how varying coverages of CO affect the diffusion. Close
505 – observation of the mobile metal atoms showed that they were typically in
506 – equilibrium with the step-edges.
507 – At times, their motion was concerted and two or more adatoms would be
508 – observed moving together across the surfaces.
531  
532 < A particle was considered ``mobile'' once it had traveled more than 2~\AA~
533 < between saved configurations of the system (typically 10-100 ps). A mobile atom
534 < would typically travel much greater distances than this, but the 2~\AA~cutoff
535 < was used to prevent swamping the diffusion data with the in-place vibrational
536 < movement of buried atoms. Diffusion on a surface is strongly affected by
537 < local structures and in this work, the presence of single and double layer
538 < step-edges causes the diffusion parallel to the step-edges to be larger than
539 < the diffusion perpendicular to these edges. Parallel and perpendicular
540 < diffusion constants are shown in Figure \ref{fig:diff}.
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[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf}
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.  Diffusion parallel to the step-edge is higher
584 <  than that perpendicular to the edge because of the lower energy
585 <  barrier associated with traversing along the edge as compared to
586 <  completely breaking away. The two reported diffusion constants for
530 <  the 50\% Pt system arise from different sample sets. The lower values
531 <  correspond to the same 40~ns amount that all of the other systems were
532 <  examined at, while the larger values correspond to a 20~ns period }
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}
589  
# Line 541 | Line 595 | now been buried resulting in a smaller reported diffus
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
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  
550 –
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
# Line 575 | Line 628 | We have shown that a classical potential model is able
628  
629   %Discussion
630   \section{Discussion}
631 < We have shown that a classical potential model is able to model the
632 < initial reconstruction of the Pt(557) surface upon CO adsorption as
633 < shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were
634 < able to observe features of the dynamic processes necessary for
635 < this reconstruction. Here we discuss the features of the model that
636 < give rise to the observed dynamical properties of the (557) reconstruction.
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
641 < appears to be the most important indicator of double layer
642 < formation. As highlighted in Figure \ref{fig:reconstruct}, the
643 < formation of the double layer did not begin until a nucleation
644 < site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994},
645 < the inability for edges to cross leads to an effective edge-edge repulsion that
646 < must be overcome to allow step coalescence.
647 < A greater $\textbf{D}_\perp$ implies more step-wandering
648 < and a larger chance for the stochastic meeting of two edges
649 < to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double
650 < layer. This helps explain why the time scale for formation after
651 < the appearance of a nucleation site was rapid, while the initial
652 < appearance of the nucleation site was unpredictable.
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
656 < our simulations, our discussion will focus on the 50\% Pt-CO system
657 < which did exhibit doubling featured in Figure \ref{fig:reconstruct}. A
658 < number of possible mechanisms exist to explain the role of adsorbed
659 < CO in restructuring the Pt surface. Quadrupolar repulsion between
660 < adjacent CO molecules adsorbed on the surface is one possibility.  
661 < However, the quadrupole-quadrupole interaction is short-ranged and
662 < is attractive for some orientations.  If the CO molecules are ``locked'' in
663 < a specific orientation relative to each other, through atop adsorption for
664 < example, this explanation would gain credence. The energetic repulsion
665 < between two CO molecules located a distance of 2.77~\AA~apart
666 < (nearest-neighbor distance of Pt) and both in a vertical orientation,
667 < is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance
668 < of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away
669 < from a purely vertical orientation also lowers the repulsion. When the
670 < carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is
671 < reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}.
672 < The barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
673 < repulsion between adjacent CO molecules bound to Pt could increase the surface
674 < diffusion. However, the residence time of CO on Pt suggests that these
675 < molecules are extremely mobile, with diffusion constants 40 to 2500 times
676 < larger than surface Pt atoms. This mobility suggests that the CO are more
677 < likely to shift their positions without dragging the Pt along with them.
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, taking into account the large
684 < mobility of the CO, looks at how instantaneous and short-lived configurations of
685 < CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge
686 < breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach
687 < an edge atom is $\sim$~43~kcal/mol, as is shown in configuration (a) in Figures
688 < \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases
689 < (e), (g), and (h), the barrier can be lowered to $\sim$~23~kcal/mole. In these instances,
690 < it becomes quite energetically favorable to roughen the edge by introducing a small
691 < separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in
692 < simulations with significant CO populations, although it is present to a lesser extent
693 < on lower coverage surfaces and even on the bare surfaces. In these cases it is likely
694 < due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism
695 < of step-edge breakup suggested by these energy curves is one the most difficult
696 < processes, a complete break-away from the step-edge in one unbroken movement.
697 < Easier multistep mechanisms likely exist where an adatom moves laterally on the surface
698 < after being ejected so it is sitting on the edge. This provides the atom with 5 nearest
699 < neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher
700 < than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO
701 < quadrupolar repulsion is still playing a primary role, but for its importance in roughening
702 < the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not
703 < born out by their mobility data. The requirement for a large density of CO on the surface
704 < for some of the more favorable suggested mechanisms in Figure \ref{fig:SketchGraphic}
705 < correspond well with the increased mobility seen on higher coverage surfaces.
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=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf}
716 < \caption{The dark grey atoms refer to the upper ledge, while the white atoms are
717 < the lower terrace. The blue highlighted atoms had a CO in a vertical atop position
718 < upon them. These are a sampling of the configurations examined to gain a more
719 < complete understanding of the effects CO has on surface diffusion and edge breakup.
720 < Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.}
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]{stepSeparationComparison.pdf}
731 < \caption{The energy curves directly correspond to the labeled model
732 < surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative
733 < to their initial configuration so the energy of a and h do not have the
734 < same zero value. As is seen, certain arrangements of CO can lower
735 < the energetic barrier that must be overcome to create an adatom.
736 < However, it is the highest coverages where these higher-energy
737 < configurations of CO will be more likely. }
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 diffusion,
742 < this does not immediately provide an explanation for the formation of double
743 < layers. If adatoms were constrained to their terrace then doubling would be
744 < much less likely to occur. Nucleation sites could still potentially form, but there
745 < would not be enough atoms to finish the doubling. Real materials, where the
746 < step lengths can be taken as infinite, local doubling would be possible, but in
679 < our simulations with our periodic treatment of the system, this is not possible.
680 < Thus, there must be a mechanism that explains how adatoms are able to move
681 < amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate
682 < where an adatom along the step-edge with an adsorbed CO ``burrows'' into the
683 < edge displacing an atom onto the higher terrace. This mechanism was chosen
684 < because of similar events that were observed during the simulations. The barrier
685 < heights we obtained are only approximations because we constrained the movement
686 < of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s
687 < are the more interesting results from this investigation. When CO is not present and
688 < this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown
689 < in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol.
690 < While the barrier height is comparable to the non-CO case, that is a nearly a 20~kcal/mol
691 < difference in energies and moves the process from slightly unfavorable to energetically favorable.
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]{lambdaProgression_atopCO_withLambda.png}
770 < \caption{A model system of the Pt(557) surface was used as the framework
771 < for exploring energy barriers along a reaction coordinate. Various numbers,
772 < placements, and rotations of CO were examined as they affect Pt movement.
773 < The coordinate displayed in this Figure was a representative run.  relative to the energy of the system at 0\%, there
774 < is a slight decrease upon insertion of the Pt atom into the step-edge along
775 < with the resultant lifting of the other Pt atom when CO is present at certain positions.}
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 this surface appears to be a convolution of at least
780 < these two described processes. For complete doubling of a layer to occur there must
781 < be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from
782 < that terrace they must either rise up on the ledge above them or drop to the ledge below
783 < them. The presence of CO helps with both of these situations. There must be sufficient
784 < breakage of the step-edge to increase the concentration of adatoms on the surface.
785 < These adatoms must then undergo the burrowing highlighted above or some comparable
786 < mechanism to traverse the step-edge. Over time, these mechanisms working in concert
787 < led to the formation of a double layer.
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 a double layer had formed on the 50\%~Pt system it
793 < remained for the rest of the simulation time with minimal
794 < movement. There were configurations that showed small
795 < wells or peaks forming, but typically within a few nanoseconds
796 < the feature would smooth away. Within our simulation time,
797 < the formation of the double layer was irreversible and a double
798 < layer was never observed to split back into two single layer
799 < step-edges while CO was present. To further gauge the effect
724 < CO had on this system, additional simulations were run starting
725 < from a late configuration of the 50\%~Pt system that had formed
726 < double layers. These simulations then had their CO removed.
727 < The double layer breaks rapidly in these simulations, already
728 < showing a well-defined splitting after 100~ps. Configurations of
729 < this system are shown in Figure \ref{fig:breaking}. The coloring
730 < of the top and bottom layers helps to exhibit how much mixing
731 < the edges experience as they split. These systems were only
732 < examined briefly, 10~ns, and within that time despite the initial
733 < rapid splitting, the edges only moved another few \AA~apart.
734 < It is possible with longer simulation times that the
735 < (557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010}
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  
738 –
814   %breaking of the double layer upon removal of CO
815   \begin{figure}[H]
816 < \includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png}
817 < \caption{(A)  0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO
818 < helped maintain the stability of the double layer and upon removal the two layers break
819 < and begin separating. The separation is not a simple pulling apart however, rather
820 < there is a mixing of the lower and upper atoms at the edge.}
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  
750 –
751 –
827   %Peaks!
828   %\begin{figure}[H]
829   %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
# Line 762 | Line 837 | It is possible with longer simulation times that the
837   %Don't think I need this
838   %clean surface...
839   %\begin{figure}[H]
840 < %\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
840 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF}
841   %\caption{}
842  
843   %\end{figure}
# Line 770 | Line 845 | In this work we have shown the reconstruction of the P
845  
846  
847   \section{Conclusion}
848 < In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in less than a $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems.
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
# Line 795 | Line 881 | Support for this project was provided by the National
881   % \end{table}
882  
883   \begin{acknowledgement}
884 < Support for this project was provided by the National Science
885 < Foundation under grant CHE-0848243 and by the Center for Sustainable
886 < Energy at Notre Dame (cSEND). Computational time was provided by the
887 < Center for Research Computing (CRC) at the University of Notre Dame.
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}
892 > \bibstyle{achemso}
893 > \bibliography{COonPtAu}
894   %\end{doublespace}
895  
896   \begin{tocentry}
897 < %\includegraphics[height=3.5cm]{timelapse}
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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