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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}{*}{-1.81} & -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-Pt cross interactions were compared directly to DFT results
339 + found in the supporting information of Tao {\it et al.}
340 + \cite{Tao:2010}, while the CO-Au results are interpreted on their own.
341 + These calculations are estimates of the stabilization
342 + energy provided to double-layer reconstructions of the perfect (557)
343 + surface by an overlayer of CO molecules in a $c (2 \times 4)$ pattern.
344 + To make the comparison, metal slabs of both Pt and Au that were five atoms thick and
345 + which displayed a (557) facet were constructed.  Double-layer
346 + (reconstructed) systems were created using six atomic layers where
347 + enough of a layer was removed from both exposed (557) facets to create
348 + the double step.  In all cases, the metal slabs contained 480 atoms
349 + and were minimized using steepest descent under the EAM force
350 + field. Both the bare metal slabs and slabs with 50\% carbon monoxide
351 + coverage (arranged in the $c (2 \times 4)$ pattern) were used.  The
352 + systems are periodic along and perpendicular to the step-edge axes
353 + with a large vacuum above the displayed (557) facet.
354 +
355 + Energies calculated using our force field for the various systems are
356 + displayed in Table ~\ref{tab:steps}.  The relative energies are calculated
357 + as $E_{relative} = E_{system} - E_{M-557-S} - N_{CO}*E_{M-CO}$,
358 + where $E_{M-CO}$ is -1.8 eV for CO-Pt and -0.39 eV for CO-Au. Our
359 + calculated CO-Pt minimum is actually at -1.83 eV at a distance of 1.53~\AA,
360 + which was obtained from single-atom liftoffs from a Pt(111) surface. The
361 + arrangement of CO on the single and double steps however, leads to a
362 + slight displacement from the minimum. For a 1 ps run at 3 K, the single
363 + step Pt-CO average bond length was 1.60~\AA, and for the double step,
364 + the bond length was 1.58~\AA. This slight increase is likely due to small
365 + electrostatic interactions among the CO and the non-ideality of the surface.
366 +
367 + For platinum, the bare double layer is less stable then the original single
368 + (557) step by about 0.25 kcal/mole per Pt atom. However, addition of carbon
369 + monoxide to the double step system provides a greater amount of stabilization
370 + when compared to single step system with CO on the order of 230 kcal/mole
371 + for this system size. The absolute difference is minimal, but this result is in
372 + qualitative agreement with DFT calculations in Tao {\it et al.}\cite{Tao:2010},
373 + who also showed that the addition of CO leads to a reversal in stability.
374 +
375 + The gold systems show a smaller energy difference between the clean
376 + single and double layers when compared to platinum. Upon addition of
377 + CO however, the single step surface becomes much more stable. These
378 + results, while helpful, need to be tempered by the weaker binding energy
379 + of CO to Au. From our simulations we see that at the elevated temperatures
380 + we are running at, it is difficult for the gold systems to maintain > than 25\%
381 + coverage, despite their being enough CO in the system.
382 +
383 + %Table of single step double step calculations
384 + \begin{table}[H]
385 +  \caption{Minimized single point energies of (S)ingle and (D)ouble
386 +    steps.  The addition of CO in a 50\% $c(2 \times 4)$ coverage acts as a
387 +    stabilizing presence and suggests a driving force for the observed
388 +    reconstruction on the highest coverage Pt system. All energies are
389 +    in kcal/mol.}
390 + \centering
391 + \begin{tabular}{| c | c | c | c | c | c |}
392 + \hline
393 + \textbf{Step} & \textbf{N}\textsubscript{M} & \textbf{N\textsubscript{CO}} & \textbf{Relative Energy} & \textbf{$\Delta$E/M} & \textbf{$\Delta$E/CO} \\
394 + \hline
395 + Pt(557)-S & 480 & 0 & 0 & 0 & - \\
396 + Pt(557)-D & 480 & 0 & 119.788 & 0.2495 & -\\
397 + Pt(557)-S & 480 & 40 & -109.734 & -0.2286 & -2.743\\
398 + Pt(557)-D & 480 & 48 & -110.039 & -0.2292 & -2.292\\
399 + \hline
400 + \hline
401 + Au(557)-S & 480 & 0 & 0 & 0 & - \\
402 + Au(557)-D & 480 & 0 & 83.853 & 0.1747 & - \\
403 + Au(557)-S & 480 & 40 & -253.604 & -0.5283 & -6.340\\
404 + Au(557)-D & 480 & 48 & -156.150 & -0.3253 & -3.253 \\
405 + \hline
406 + \end{tabular}
407 + \label{tab:steps}
408 + \end{table}
409 +
410 +
411   \subsection{Pt(557) and Au(557) metal interfaces}
412   Our Pt system is an orthorhombic periodic box of dimensions
413   54.482~x~50.046~x~120.88~\AA~while our Au system has
# Line 370 | Line 422 | The different bulk melting temperatures predicted by E
422   1200~K were performed to confirm the relative
423   stability of the surfaces without a CO overlayer.  
424  
425 < The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting}
426 < and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at
427 < different temperatures for the two metals.  The bare Au and Pt surfaces were
428 < initially run in the canonical (NVT) ensemble at 800~K and 1000~K
429 < respectively for 100 ps. The two surfaces were relatively stable at these
430 < temperatures when no CO was present, but experienced increased surface
431 < mobility on addition of CO. Each surface was then dosed with different concentrations of CO
432 < that was initially placed in the vacuum region.  Upon full adsorption,
433 < these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
434 < coverage. Higher coverages resulted in the formation of a double layer of CO,
435 < which introduces artifacts that are not relevant to (557) reconstruction.
436 < Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
437 < the Au surfaces often had a significant CO population in the gas
438 < phase.  These systems were allowed to reach thermal equilibrium (over
439 < 5~ns) before being run in the microcanonical (NVE) ensemble for
440 < data collection. All of the systems examined had at least 40~ns in the
441 < data collection stage, although simulation times for some Pt of the
442 < systems exceeded 200~ns.  Simulations were carried out using the open
443 < source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}
425 > The different bulk melting temperatures predicted by EAM
426 > (1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for
427 > Pt\cite{Pt:melting}) suggest that any reconstructions should happen at
428 > different temperatures for the two metals.  The bare Au and Pt
429 > surfaces were initially run in the canonical (NVT) ensemble at 800~K
430 > and 1000~K respectively for 100 ps. The two surfaces were relatively
431 > stable at these temperatures when no CO was present, but experienced
432 > increased surface mobility on addition of CO. Each surface was then
433 > dosed with different concentrations of CO that was initially placed in
434 > the vacuum region.  Upon full adsorption, these concentrations
435 > correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher
436 > coverages resulted in the formation of a double layer of CO, which
437 > introduces artifacts that are not relevant to (557) reconstruction.
438 > Because of the difference in binding energies, nearly all of the CO
439 > was bound to the Pt surface, while the Au surfaces often had a
440 > significant CO population in the gas phase.  These systems were
441 > allowed to reach thermal equilibrium (over 5~ns) before being run in
442 > the microcanonical (NVE) ensemble for data collection. All of the
443 > systems examined had at least 40~ns in the data collection stage,
444 > although simulation times for some Pt of the systems exceeded 200~ns.
445 > Simulations were carried out using the open source molecular dynamics
446 > package, OpenMD.\cite{Ewald,OOPSE,openmd}
447  
448  
394 –
395 –
449   % RESULTS
450   %
451   \section{Results}
452   \subsection{Structural remodeling}
453 < The bare metal surfaces experienced minor roughening of the
454 < step-edge because of the elevated temperatures, but the (557)
455 < face was stable throughout the simulations. The surface of both
456 < systems, upon dosage of CO, began to undergo extensive remodeling
457 < that was not observed in the bare systems. Reconstructions of
458 < the Au systems were limited to breakup of the step-edges and
459 < some step wandering. The lower coverage Pt systems experienced
460 < similar restructuring but to a greater extent. The 50\% coverage
461 < Pt system was unique among our simulations in that it formed
462 < well-defined and stable double layers through step coalescence,
463 < similar to results reported by Tao {\it et al}.\cite{Tao:2010}
453 > The bare metal surfaces experienced minor roughening of the step-edge
454 > because of the elevated temperatures, but the (557) face was stable
455 > throughout the simulations. The surfaces of both systems, upon dosage
456 > of CO, began to undergo extensive remodeling that was not observed in
457 > the bare systems. Reconstructions of the Au systems were limited to
458 > breakup of the step-edges and some step wandering. The lower coverage
459 > Pt systems experienced similar step edge wandering but to a greater
460 > extent. The 50\% coverage Pt system was unique among our simulations
461 > in that it formed well-defined and stable double layers through step
462 > coalescence, similar to results reported by Tao {\it et
463 >  al}.\cite{Tao:2010}
464  
412 –
465   \subsubsection{Step wandering}
466 < The 0\% coverage surfaces for both metals showed minimal
467 < step-wandering at their respective temperatures. As the CO
468 < coverage increased however, the mobility of the surface atoms,
469 < described through adatom diffusion and step-edge wandering,
470 < also increased.  Except for the 50\% Pt system where step
471 < coalescence occurred, the step-edges in the other simulations
472 < preferred to keep nearly the same distance between steps as in
473 < the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au.
474 < Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994}
475 < highlights the repulsion that exists between step-edges even
476 < when no direct interactions are present in the system. This
477 < repulsion is caused by an entropic barrier that arises from
478 < the fact that steps cannot cross over one another. This entropic
479 < repulsion does not completely define the interactions between
480 < steps, however, so it is possible to observe step coalescence
481 < on some surfaces.\cite{Williams:1991} The presence and
482 < concentration of adsorbates, as shown in this work, can
483 < affect step-step interactions, potentially leading to a new
432 < surface structure as the thermodynamic equilibrium.
466 > The bare surfaces for both metals showed minimal step-wandering at
467 > their respective temperatures. As the CO coverage increased however,
468 > the mobility of the surface atoms, described through adatom diffusion
469 > and step-edge wandering, also increased.  Except for the 50\% Pt
470 > system where step coalescence occurred, the step-edges in the other
471 > simulations preferred to keep nearly the same distance between steps
472 > as in the original (557) lattice, $\sim$13\AA~for Pt and
473 > $\sim$14\AA~for Au.  Previous work by Williams {\it et
474 >  al}.\cite{Williams:1991, Williams:1994} highlights the repulsion
475 > that exists between step-edges even when no direct interactions are
476 > present in the system. This repulsion is caused by an entropic barrier
477 > that arises from the fact that steps cannot cross over one
478 > another. This entropic repulsion does not completely define the
479 > interactions between steps, however, so it is possible to observe step
480 > coalescence on some surfaces.\cite{Williams:1991} The presence and
481 > concentration of adsorbates, as shown in this work, can affect
482 > step-step interactions, potentially leading to a new surface structure
483 > as the thermodynamic equilibrium.
484  
485   \subsubsection{Double layers}
486 < Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface
487 < undergoes two separate reconstructions upon CO adsorption.
488 < The first involves a doubling of the step height and plateau length.
489 < Similar behavior has been seen on a number of surfaces
490 < at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl}
491 < Of the two systems we examined, the Pt system showed a greater
492 < propensity for reconstruction  
493 < because of the larger surface mobility and the greater extent of step wandering.
494 < The amount of reconstruction was strongly correlated to the amount of CO
495 < adsorbed upon the surface.  This appears to be related to the
496 < effect that adsorbate coverage has on edge breakup and on the
497 < surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the
498 < doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here.
499 < Over a longer time scale (150~ns) two more double layers formed
500 < on this surface. Although double layer formation did not occur
501 < in the other Pt systems, they exhibited more step-wandering and
502 < roughening compared to their Au counterparts. The
503 < 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
504 < various times along the simulation showing the evolution of a double layer step-edge.
486 > Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the
487 > Pt(557) surface undergoes two separate reconstructions upon CO
488 > adsorption.  The first involves a doubling of the step height and
489 > plateau length.  Similar behavior has been seen on a number of
490 > surfaces at varying conditions, including Ni(977) and
491 > Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we
492 > examined, the Pt system showed a greater propensity for reconstruction
493 > because of the larger surface mobility and the greater extent of step
494 > wandering.  The amount of reconstruction was strongly correlated to
495 > the amount of CO adsorbed upon the surface.  This appears to be
496 > related to the effect that adsorbate coverage has on edge breakup and
497 > on the surface diffusion of metal adatoms. Only the 50\% Pt surface
498 > underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within
499 > the time scales studied here.  Over a longer time scale (150~ns) two
500 > more double layers formed on this surface. Although double layer
501 > formation did not occur in the other Pt systems, they exhibited more
502 > step-wandering and roughening compared to their Au counterparts. The
503 > 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
504 > various times along the simulation showing the evolution of a double
505 > layer step-edge.
506  
507 < The second reconstruction observed by
508 < Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched
509 < across the plateau between two step-edges. Neither metal, within
510 < the 40~ns time scale or the extended simulation time of 150~ns for
511 < the 50\% Pt system, experienced this reconstruction.
507 > The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010}
508 > involved the formation of triangular clusters that stretched across
509 > the plateau between two step-edges. Neither of the simulated metal
510 > interfaces, within the 40~ns time scale or the extended time of 150~ns
511 > for the 50\% Pt system, experienced this reconstruction.
512  
513   %Evolution of surface
514   \begin{figure}[H]
515 < \includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
516 < \caption{The Pt(557) / 50\% CO system at a sequence of times after
517 <  initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and
518 <  (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly.  The
515 > \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation}
516 > \caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a)
517 >  258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after
518 >  exposure. Disruption of the (557) step-edges occurs quickly.  The
519    doubling of the layers appears only after two adjacent step-edges
520    touch.  The circled spot in (b) nucleated the growth of the double
521    step observed in the later configurations.}
# Line 471 | Line 523 | Previous experimental work by Pearl and Sibener\cite{P
523   \end{figure}
524  
525   \subsection{Dynamics}
526 < Previous experimental work by Pearl and Sibener\cite{Pearl},
527 < using STM, has been able to capture the coalescence of steps
528 < on Ni(977). The time scale of the image acquisition, $\sim$70~s/image,
529 < provides an upper bound for the time required for the doubling
530 < to occur. By utilizing Molecular Dynamics we are able to probe
531 < the dynamics of these reconstructions at elevated temperatures
532 < and in this section we provide data on the timescales for transport
533 < properties, e.g. diffusion and layer formation time.
526 > Previous experimental work by Pearl and Sibener\cite{Pearl}, using
527 > STM, has been able to capture the coalescence of steps on Ni(977). The
528 > time scale of the image acquisition, $\sim$70~s/image, provides an
529 > upper bound for the time required for the doubling to occur. By
530 > utilizing Molecular Dynamics we are able to probe the dynamics of
531 > these reconstructions at elevated temperatures and in this section we
532 > provide data on the timescales for transport properties,
533 > e.g. diffusion and layer formation time.
534  
535  
536   \subsubsection{Transport of surface metal atoms}
537   %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.
538  
539 < A particle was considered ``mobile'' once it had traveled more than 2~\AA~
540 < between saved configurations of the system (typically 10-100 ps). A mobile atom
541 < would typically travel much greater distances than this, but the 2~\AA~cutoff
542 < was used to prevent swamping the diffusion data with the in-place vibrational
543 < movement of buried atoms. Diffusion on a surface is strongly affected by
544 < local structures and in this work, the presence of single and double layer
545 < step-edges causes the diffusion parallel to the step-edges to be larger than
546 < the diffusion perpendicular to these edges. Parallel and perpendicular
547 < diffusion constants are shown in Figure \ref{fig:diff}.
539 > The wandering of a step-edge is a cooperative effect arising from the
540 > individual movements of the atoms making up the steps. An ideal metal
541 > surface displaying a low index facet, (111) or (100), is unlikely to
542 > experience much surface diffusion because of the large energetic
543 > barrier that must be overcome to lift an atom out of the surface. The
544 > presence of step-edges and other surface features on higher-index
545 > facets provides a lower energy source for mobile metal atoms.  Using
546 > our potential model, single-atom break-away from a step-edge on a
547 > clean surface still imposes an energetic penalty around
548 > $\sim$~45~kcal/mol, but this is certainly easier than lifting the same
549 > metal atom vertically out of the surface, \textgreater~60~kcal/mol.
550 > The penalty lowers significantly when CO is present in sufficient
551 > quantities on the surface. For certain distributions of CO, the
552 > energetic penalty can fall to as low as $\sim$~20~kcal/mol. The
553 > configurations that create these lower barriers are detailed in the
554 > discussion section below.
555  
556 + Once an adatom exists on the surface, the barrier for diffusion is
557 + negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are
558 + then able to explore the terrace before rejoining either their
559 + original step-edge or becoming a part of a different edge. It is an
560 + energetically unfavorable process with a high barrier for an atom to
561 + traverse to a separate terrace although the presence of CO can lower
562 + the energy barrier required to lift or lower an adatom. By tracking
563 + the mobility of individual metal atoms on the Pt and Au surfaces we
564 + were able to determine the relative diffusion constants, as well as
565 + how varying coverages of CO affect the diffusion. Close observation of
566 + the mobile metal atoms showed that they were typically in equilibrium
567 + with the step-edges.  At times, their motion was concerted, and two or
568 + more adatoms would be observed moving together across the surfaces.
569 +
570 + A particle was considered ``mobile'' once it had traveled more than
571 + 2~\AA~ between saved configurations of the system (typically 10-100
572 + ps). A mobile atom would typically travel much greater distances than
573 + this, but the 2~\AA~cutoff was used to prevent swamping the diffusion
574 + data with the in-place vibrational movement of buried atoms. Diffusion
575 + on a surface is strongly affected by local structures and the presence
576 + of single and double layer step-edges causes the diffusion parallel to
577 + the step-edges to be larger than the diffusion perpendicular to these
578 + edges. Parallel and perpendicular diffusion constants are shown in
579 + Figure \ref{fig:diff}.  Diffusion parallel to the step-edge is higher
580 + than diffusion perpendicular to the edge because of the lower energy
581 + barrier associated with sliding along an edge compared to breaking
582 + away to form an isolated adatom.
583 +
584   %Diffusion graph
585   \begin{figure}[H]
586 < \includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf}
586 > \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1}
587   \caption{Diffusion constants for mobile surface atoms along directions
588    parallel ($\mathbf{D}_{\parallel}$) and perpendicular
589    ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
590 <  surface coverage.  Diffusion parallel to the step-edge is higher
591 <  than that perpendicular to the edge because of the lower energy
592 <  barrier associated with traversing along the edge as compared to
593 <  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 }
590 >  surface coverage.  The two reported diffusion constants for the 50\%
591 >  Pt system correspond to a 20~ns period before the formation of the
592 >  double layer (upper points), and to the full 40~ns sampling period
593 >  (lower points).}
594   \label{fig:diff}
595   \end{figure}
596  
# Line 541 | Line 602 | now been buried resulting in a smaller reported diffus
602   at the earliest times in the simulations. Following double layer formation,
603   however, there is a precipitous drop in adatom diffusion. As the double
604   layer forms, many atoms that had been tracked for mobility data have
605 < now been buried resulting in a smaller reported diffusion constant. A
605 > now been buried, resulting in a smaller reported diffusion constant. A
606   secondary effect of higher coverages is CO-CO cross interactions that
607   lower the effective mobility of the Pt adatoms that are bound to each CO.
608   This effect would become evident only at higher coverages. A detailed
609   account of Pt adatom energetics follows in the Discussion.
610  
550 –
611   \subsubsection{Dynamics of double layer formation}
612   The increased diffusion on Pt at the higher CO coverages is the primary
613   contributor to double layer formation. However, this is not a complete
# Line 575 | Line 635 | We have shown that a classical potential model is able
635  
636   %Discussion
637   \section{Discussion}
638 < We have shown that a classical potential model is able to model the
639 < initial reconstruction of the Pt(557) surface upon CO adsorption as
640 < shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were
641 < able to observe features of the dynamic processes necessary for
642 < this reconstruction. Here we discuss the features of the model that
643 < give rise to the observed dynamical properties of the (557) reconstruction.
638 > We have shown that a classical potential is able to model the initial
639 > reconstruction of the Pt(557) surface upon CO adsorption, and have
640 > reproduced the double layer structure observed by Tao {\it et
641 >  al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be
642 > rapid -- occurring within 100 ns of the initial exposure to CO.  Here
643 > we discuss the features of the classical potential that are
644 > contributing to the stability and speed of the Pt(557) reconstruction.
645  
646   \subsection{Diffusion}
647 < The perpendicular diffusion constant
648 < appears to be the most important indicator of double layer
649 < formation. As highlighted in Figure \ref{fig:reconstruct}, the
650 < formation of the double layer did not begin until a nucleation
651 < site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994},
652 < the inability for edges to cross leads to an effective edge-edge repulsion that
653 < must be overcome to allow step coalescence.
654 < A greater $\textbf{D}_\perp$ implies more step-wandering
655 < and a larger chance for the stochastic meeting of two edges
656 < to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double
657 < layer. This helps explain why the time scale for formation after
658 < the appearance of a nucleation site was rapid, while the initial
659 < appearance of the nucleation site was unpredictable.
647 > The perpendicular diffusion constant appears to be the most important
648 > indicator of double layer formation. As highlighted in Figure
649 > \ref{fig:reconstruct}, the formation of the double layer did not begin
650 > until a nucleation site appeared.  Williams {\it et
651 >  al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge
652 > repulsion arising from the inability of edge crossing.  This repulsion
653 > must be overcome to allow step coalescence.  A larger
654 > $\textbf{D}_\perp$ value implies more step-wandering and a larger
655 > chance for the stochastic meeting of two edges to create a nucleation
656 > point.  Diffusion parallel to the step-edge can help ``zipper'' up a
657 > nascent double layer. This helps explain the rapid time scale for
658 > double layer completion after the appearance of a nucleation site, while
659 > the initial appearance of the nucleation site was unpredictable.
660  
661   \subsection{Mechanism for restructuring}
662 < Since the Au surface showed no large scale restructuring in any of
663 < our simulations, our discussion will focus on the 50\% Pt-CO system
664 < which did exhibit doubling featured in Figure \ref{fig:reconstruct}. A
665 < number of possible mechanisms exist to explain the role of adsorbed
666 < CO in restructuring the Pt surface. Quadrupolar repulsion between
667 < adjacent CO molecules adsorbed on the surface is one possibility.  
668 < However, the quadrupole-quadrupole interaction is short-ranged and
669 < is attractive for some orientations.  If the CO molecules are ``locked'' in
670 < a specific orientation relative to each other, through atop adsorption for
671 < example, this explanation would gain credence. The energetic repulsion
672 < between two CO molecules located a distance of 2.77~\AA~apart
673 < (nearest-neighbor distance of Pt) and both in a vertical orientation,
674 < is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance
675 < of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away
676 < from a purely vertical orientation also lowers the repulsion. When the
677 < carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is
678 < reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}.
679 < The barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
680 < repulsion between adjacent CO molecules bound to Pt could increase the surface
681 < diffusion. However, the residence time of CO on Pt suggests that these
682 < molecules are extremely mobile, with diffusion constants 40 to 2500 times
683 < larger than surface Pt atoms. This mobility suggests that the CO are more
684 < likely to shift their positions without dragging the Pt along with them.
662 > Since the Au surface showed no large scale restructuring in any of our
663 > simulations, our discussion will focus on the 50\% Pt-CO system which
664 > did exhibit doubling. A number of possible mechanisms exist to explain
665 > the role of adsorbed CO in restructuring the Pt surface. Quadrupolar
666 > repulsion between adjacent CO molecules adsorbed on the surface is one
667 > possibility.  However, the quadrupole-quadrupole interaction is
668 > short-ranged and is attractive for some orientations.  If the CO
669 > molecules are ``locked'' in a vertical orientation, through atop
670 > adsorption for example, this explanation would gain credence. Within
671 > the framework of our classical potential, the calculated energetic
672 > repulsion between two CO molecules located a distance of
673 > 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a
674 > vertical orientation, is 8.62 kcal/mol. Moving the CO to the second
675 > nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly
676 > 0. Allowing the CO to rotate away from a purely vertical orientation
677 > also lowers the repulsion. When the carbons are locked at a distance
678 > of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle
679 > between the 2 CO is $\sim$24\textsuperscript{o}.  The calculated
680 > barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
681 > repulsion between adjacent CO molecules bound to Pt could indeed
682 > increase the surface diffusion. However, the residence time of CO on
683 > Pt suggests that the CO molecules are extremely mobile, with diffusion
684 > constants 40 to 2500 times larger than surface Pt atoms. This mobility
685 > suggests that the CO molecules jump between different Pt atoms
686 > throughout the simulation.  However, they do stay bound to individual
687 > Pt atoms for long enough to modify the local energy landscape for the
688 > mobile adatoms.
689  
690 < A different interpretation of the above mechanism, taking into account the large
691 < mobility of the CO, looks at how instantaneous and short-lived configurations of
692 < CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge
693 < breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach
694 < an edge atom is $\sim$~43~kcal/mol, as is shown in configuration (a) in Figures
695 < \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases
696 < (e), (g), and (h), the barrier can be lowered to $\sim$~23~kcal/mole. In these instances,
697 < it becomes quite energetically favorable to roughen the edge by introducing a small
698 < separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in
699 < simulations with significant CO populations, although it is present to a lesser extent
700 < on lower coverage surfaces and even on the bare surfaces. In these cases it is likely
701 < due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism
702 < of step-edge breakup suggested by these energy curves is one the most difficult
703 < processes, a complete break-away from the step-edge in one unbroken movement.
704 < Easier multistep mechanisms likely exist where an adatom moves laterally on the surface
705 < after being ejected so it is sitting on the edge. This provides the atom with 5 nearest
706 < neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher
707 < than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO
708 < quadrupolar repulsion is still playing a primary role, but for its importance in roughening
709 < the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not
710 < born out by their mobility data. The requirement for a large density of CO on the surface
711 < for some of the more favorable suggested mechanisms in Figure \ref{fig:SketchGraphic}
712 < correspond well with the increased mobility seen on higher coverage surfaces.
690 > A different interpretation of the above mechanism which takes the
691 > large mobility of the CO into account, would be in the destabilization
692 > of Pt-Pt interactions due to bound CO.  Destabilizing Pt-Pt bonds at
693 > the edges could lead to increased step-edge breakup and diffusion. On
694 > the bare Pt(557) surface the barrier to completely detach an edge atom
695 > is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
696 > \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain
697 > configurations, cases (e), (g), and (h), the barrier can be lowered to
698 > $\sim$23~kcal/mol by the presence of bound CO molecules. In these
699 > instances, it becomes energetically favorable to roughen the edge by
700 > introducing a small separation of 0.5 to 1.0~\AA. This roughening
701 > becomes immediately obvious in simulations with significant CO
702 > populations. The roughening is present to a lesser extent on surfaces
703 > with lower CO coverage (and even on the bare surfaces), although in
704 > these cases it is likely due to random fluctuations that squeeze out
705 > step-edge atoms. Step-edge breakup by direct single-atom translations
706 > (as suggested by these energy curves) is probably a worst-case
707 > scenario.  Multistep mechanisms in which an adatom moves laterally on
708 > the surface after being ejected would be more energetically favorable.
709 > This would leave the adatom alongside the ledge, providing it with
710 > five nearest neighbors.  While fewer than the seven neighbors it had
711 > as part of the step-edge, it keeps more Pt neighbors than the three
712 > neighbors an isolated adatom has on the terrace. In this proposed
713 > mechanism, the CO quadrupolar repulsion still plays a role in the
714 > initial roughening of the step-edge, but not in any long-term bonds
715 > with individual Pt atoms.  Higher CO coverages create more
716 > opportunities for the crowded CO configurations shown in Figure
717 > \ref{fig:SketchGraphic}, and this is likely to cause an increased
718 > propensity for step-edge breakup.
719  
720   %Sketch graphic of different configurations
721   \begin{figure}[H]
722 < \includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf}
723 < \caption{The dark grey atoms refer to the upper ledge, while the white atoms are
724 < the lower terrace. The blue highlighted atoms had a CO in a vertical atop position
725 < upon them. These are a sampling of the configurations examined to gain a more
726 < complete understanding of the effects CO has on surface diffusion and edge breakup.
727 < Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.}
722 > \includegraphics[width=\linewidth]{COpaths}
723 > \caption{Configurations used to investigate the mechanism of step-edge
724 >  breakup on Pt(557). In each case, the central (starred) atom was
725 >  pulled directly across the surface away from the step edge.  The Pt
726 >  atoms on the upper terrace are colored dark grey, while those on the
727 >  lower terrace are in white.  In each of these configurations, some
728 >  of the atoms (highlighted in blue) had CO molecules bound in the
729 >  vertical atop position.  The energies of these configurations as a
730 >  function of central atom displacement are displayed in Figure
731 >  \ref{fig:SketchEnergies}.}
732   \label{fig:SketchGraphic}
733   \end{figure}
734  
735   %energy graph corresponding to sketch graphic
736   \begin{figure}[H]
737 < \includegraphics[width=\linewidth]{stepSeparationComparison.pdf}
738 < \caption{The energy curves directly correspond to the labeled model
739 < surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative
740 < to their initial configuration so the energy of a and h do not have the
741 < same zero value. As is seen, certain arrangements of CO can lower
742 < the energetic barrier that must be overcome to create an adatom.
743 < However, it is the highest coverages where these higher-energy
744 < configurations of CO will be more likely. }
737 > \includegraphics[width=\linewidth]{Portrait_SeparationComparison}
738 > \caption{Energies for displacing a single edge atom perpendicular to
739 >  the step edge as a function of atomic displacement. Each of the
740 >  energy curves corresponds to one of the labeled configurations in
741 >  Figure \ref{fig:SketchGraphic}, and the energies are referenced to
742 >  the unperturbed step-edge.  Certain arrangements of bound CO
743 >  (notably configurations g and h) can lower the energetic barrier for
744 >  creating an adatom relative to the bare surface (configuration a).}
745   \label{fig:SketchEnergies}
746   \end{figure}
747  
748 < While configurations of CO on the surface are able to increase diffusion,
749 < this does not immediately provide an explanation for the formation of double
750 < layers. If adatoms were constrained to their terrace then doubling would be
751 < much less likely to occur. Nucleation sites could still potentially form, but there
752 < would not be enough atoms to finish the doubling. Real materials, where the
753 < 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.
748 > While configurations of CO on the surface are able to increase
749 > diffusion and the likelihood of edge wandering, this does not provide
750 > a complete explanation for the formation of double layers. If adatoms
751 > were constrained to their original terraces then doubling could not
752 > occur.  A mechanism for vertical displacement of adatoms at the
753 > step-edge is required to explain the doubling.
754  
755 + We have discovered one possible mechanism for a CO-mediated vertical
756 + displacement of Pt atoms at the step edge. Figure \ref{fig:lambda}
757 + shows four points along a reaction coordinate in which a CO-bound
758 + adatom along the step-edge ``burrows'' into the edge and displaces the
759 + original edge atom onto the higher terrace.  A number of events
760 + similar to this mechanism were observed during the simulations.  We
761 + predict an energetic barrier of 20~kcal/mol for this process (in which
762 + the displaced edge atom follows a curvilinear path into an adjacent
763 + 3-fold hollow site).  The barrier heights we obtain for this reaction
764 + coordinate are approximate because the exact path is unknown, but the
765 + calculated energy barriers would be easily accessible at operating
766 + conditions.  Additionally, this mechanism is exothermic, with a final
767 + energy 15~kcal/mol below the original $\lambda = 0$ configuration.
768 + When CO is not present and this reaction coordinate is followed, the
769 + process is endothermic by 3~kcal/mol.  The difference in the relative
770 + energies for the $\lambda=0$ and $\lambda=1$ case when CO is present
771 + provides strong support for CO-mediated Pt-Pt interactions giving rise
772 + to the doubling reconstruction.
773 +
774   %lambda progression of Pt -> shoving its way into the step
775   \begin{figure}[H]
776 < \includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png}
777 < \caption{A model system of the Pt(557) surface was used as the framework
778 < for exploring energy barriers along a reaction coordinate. Various numbers,
779 < placements, and rotations of CO were examined as they affect Pt movement.
780 < The coordinate displayed in this Figure was a representative run.  relative to the energy of the system at 0\%, there
781 < is a slight decrease upon insertion of the Pt atom into the step-edge along
782 < with the resultant lifting of the other Pt atom when CO is present at certain positions.}
776 > \includegraphics[width=\linewidth]{EPS_rxnCoord}
777 > \caption{Points along a possible reaction coordinate for CO-mediated
778 >  edge doubling. Here, a CO-bound adatom burrows into an established
779 >  step edge and displaces an edge atom onto the upper terrace along a
780 >  curvilinear path.  The approximate barrier for the process is
781 >  20~kcal/mol, and the complete process is exothermic by 15~kcal/mol
782 >  in the presence of CO, but is endothermic by 3~kcal/mol without CO.}
783   \label{fig:lambda}
784   \end{figure}
785  
786 < The mechanism for doubling on this surface appears to be a convolution of at least
787 < these two described processes. For complete doubling of a layer to occur there must
788 < be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from
789 < that terrace they must either rise up on the ledge above them or drop to the ledge below
790 < them. The presence of CO helps with both of these situations. There must be sufficient
791 < breakage of the step-edge to increase the concentration of adatoms on the surface.
792 < These adatoms must then undergo the burrowing highlighted above or some comparable
793 < mechanism to traverse the step-edge. Over time, these mechanisms working in concert
794 < led to the formation of a double layer.
786 > The mechanism for doubling on the Pt(557) surface appears to require
787 > the cooperation of at least two distinct processes. For complete
788 > doubling of a layer to occur there must be a breakup of one
789 > terrace. These atoms must then ``disappear'' from that terrace, either
790 > by travelling to the terraces above or below their original levels.
791 > The presence of CO helps explain mechanisms for both of these
792 > situations. There must be sufficient breakage of the step-edge to
793 > increase the concentration of adatoms on the surface and these adatoms
794 > must then undergo the burrowing highlighted above (or a comparable
795 > mechanism) to create the double layer.  With sufficient time, these
796 > mechanisms working in concert lead to the formation of a double layer.
797  
798   \subsection{CO Removal and double layer stability}
799 < Once a double layer had formed on the 50\%~Pt system it
800 < remained for the rest of the simulation time with minimal
801 < movement. There were configurations that showed small
802 < wells or peaks forming, but typically within a few nanoseconds
803 < the feature would smooth away. Within our simulation time,
804 < the formation of the double layer was irreversible and a double
805 < layer was never observed to split back into two single layer
806 < 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}
799 > Once the double layers had formed on the 50\%~Pt system, they remained
800 > stable for the rest of the simulation time with minimal movement.
801 > Random fluctuations that involved small clusters or divots were
802 > observed, but these features typically healed within a few
803 > nanoseconds.  Within our simulations, the formation of the double
804 > layer appeared to be irreversible and a double layer was never
805 > observed to split back into two single layer step-edges while CO was
806 > present.
807  
808 + To further gauge the effect CO has on this surface, additional
809 + simulations were run starting from a late configuration of the 50\%~Pt
810 + system that had already formed double layers. These simulations then
811 + had their CO molecules suddenly removed.  The double layer broke apart
812 + rapidly in these simulations, showing a well-defined edge-splitting
813 + after 100~ps. Configurations of this system are shown in Figure
814 + \ref{fig:breaking}. The coloring of the top and bottom layers helps to
815 + show how much mixing the edges experience as they split. These systems
816 + were only examined for 10~ns, and within that time despite the initial
817 + rapid splitting, the edges only moved another few \AA~apart. It is
818 + possible that with longer simulation times, the (557) surface recovery
819 + observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered.
820  
738 –
821   %breaking of the double layer upon removal of CO
822   \begin{figure}[H]
823 < \includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png}
824 < \caption{(A)  0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO
825 < helped maintain the stability of the double layer and upon removal the two layers break
826 < and begin separating. The separation is not a simple pulling apart however, rather
827 < there is a mixing of the lower and upper atoms at the edge.}
823 > \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking}
824 > \caption{Behavior of an established (111) double step after removal of
825 >  the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the
826 >  removal of CO.  Nearly immediately after the CO is removed, the
827 >  step edge reforms in a (100) configuration, which is also the step
828 >  type seen on clean (557) surfaces. The step separation involves
829 >  significant mixing of the lower and upper atoms at the edge.}
830   \label{fig:breaking}
831   \end{figure}
832  
833  
750 –
751 –
834   %Peaks!
835   %\begin{figure}[H]
836   %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
# Line 762 | Line 844 | It is possible with longer simulation times that the
844   %Don't think I need this
845   %clean surface...
846   %\begin{figure}[H]
847 < %\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
847 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF}
848   %\caption{}
849  
850   %\end{figure}
# Line 770 | Line 852 | In this work we have shown the reconstruction of the P
852  
853  
854   \section{Conclusion}
855 < 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.
855 > The strength and directionality of the Pt-CO binding interaction, as
856 > well as the large quadrupolar repulsion between atop-bound CO
857 > molecules, help to explain the observed increase in surface mobility
858 > of Pt(557) and the resultant reconstruction into a double-layer
859 > configuration at the highest simulated CO-coverages.  The weaker Au-CO
860 > interaction results in significantly lower adataom diffusion
861 > constants, less step-wandering, and a lack of the double layer
862 > reconstruction on the Au(557) surface.
863  
864 + An in-depth examination of the energetics shows the important role CO
865 + plays in increasing step-breakup and in facilitating edge traversal
866 + which are both necessary for double layer formation.
867 +
868   %Things I am not ready to remove yet
869  
870   %Table of Diffusion Constants
# Line 795 | Line 888 | Support for this project was provided by the National
888   % \end{table}
889  
890   \begin{acknowledgement}
891 < Support for this project was provided by the National Science
892 < Foundation under grant CHE-0848243 and by the Center for Sustainable
893 < Energy at Notre Dame (cSEND). Computational time was provided by the
894 < Center for Research Computing (CRC) at the University of Notre Dame.
891 >  We gratefully acknowledge conversations with Dr. William
892 >  F. Schneider and Dr. Feng Tao.  Support for this project was
893 >  provided by the National Science Foundation under grant CHE-0848243
894 >  and by the Center for Sustainable Energy at Notre Dame
895 >  (cSEND). Computational time was provided by the Center for Research
896 >  Computing (CRC) at the University of Notre Dame.
897   \end{acknowledgement}
898   \newpage
899 < \bibliography{firstTryBibliography}
899 > \bibstyle{achemso}
900 > \bibliography{COonPtAu}
901   %\end{doublespace}
902  
903   \begin{tocentry}
904 < %\includegraphics[height=3.5cm]{timelapse}
904 > \begin{wrapfigure}{l}{0.5\textwidth}
905 > \begin{center}
906 > \includegraphics[width=\linewidth]{TOC_doubleLayer}
907 > \end{center}
908 > \end{wrapfigure}
909 > A reconstructed Pt(557) surface after 86~ns exposure to a half a
910 > monolayer of CO.  The double layer that forms is a result of
911 > CO-mediated step-edge wandering as well as a burrowing mechanism that
912 > helps lift edge atoms onto an upper terrace.
913   \end{tocentry}
914  
915   \end{document}

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