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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}
7 < \usepackage{epstopdf}
6 > \usepackage{wrapfig}
7 > \usepackage{fixltx2e}
8 > %\mciteErrorOnUnknownfalse
9  
10   \usepackage[version=3]{mhchem}  % this is a great package for formatting chemical reactions
26 – % \usepackage[square, comma, sort&compress]{natbib}
11   \usepackage{url}
28 – \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
29 – \evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
30 – 9.0in \textwidth 6.5in \brokenpenalty=1110000
12  
32 – % double space list of tables and figures
33 – %\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}}
34 – \setlength{\abovecaptionskip}{20 pt}
35 – \setlength{\belowcaptionskip}{30 pt}
36 – % \bibpunct{}{}{,}{s}{}{;}
37 –
38 – %\citestyle{nature}
39 – % \bibliographystyle{achemso}
40 –
13   \title{Molecular Dynamics simulations of the surface reconstructions
14    of Pt(557) and Au(557) under exposure to CO}
15  
# Line 74 | 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 <
62 <
63 < The mechanism and dynamics of surface reconstructions of Pt(557)
92 < and Au(557) exposed to various coverages of carbon monoxide (CO)
93 < were investigated using molecular dynamics simulations. Metal-CO
94 < interactions were parameterized from experimental data and plane-wave
95 < Density Functional Theory (DFT) calculations.  The large difference in
96 < binding strengths of the Pt-CO and Au-CO interactions was found to play
97 < a significant role in step-edge stability and adatom diffusion constants.
98 < The energetics of CO adsorbed to the surface is sufficient to explain the
99 < step-doubling reconstruction observed on Pt(557) and the lack of such
100 < a reconstruction on the Au(557) surface.
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 129 | 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.
116 <
117 <
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  
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 173 | Line 139 | Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO wa
139   Coulomb potential.  For this work, we have used classical molecular
140   dynamics with potential energy surfaces that are specifically tuned
141   for transition metals.  In particular, we used the EAM potential for
142 < Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using 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 186 | 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}.\cite{Ercolessi88} is among the
156 < fastest of these density functional approaches. 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 219 | 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  
239 –
240 –
241 –
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 303 | 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 327 | 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 366 | Line 331 | an effect on  binding energies and binding site prefer
331    \hline
332   \end{tabular}
333   \label{tab:co_energies}
334 + \end{table}
335 +
336 +
337 + \subsection{Validation of forcefield selections}
338 + By calculating minimum energies for commensurate systems of
339 + single and double layer Pt and Au systems with 0 and 50\% coverages
340 + (arranged in a c(2x4) pattern), our forcefield selections were able to be
341 + indirectly compared to results shown in the supporting information of Tao
342 + {\it et al.} \cite{Tao:2010}. Five layer thick systems, displaying a 557 facet
343 + were constructed, each composed of 480 metal atoms. Double layers systems
344 + were constructed from six layer thick systems where an entire layer was
345 + removed from both displayed facets to create a double step. By design, the
346 + double step system also contains 480 atoms, five layers thick, so energy
347 + comparisons between the arrangements can be made directly. The positions
348 + of the atoms were allowed to relax, along with the box sizes, before a
349 + minimum energy was calculated. Carbon monoxide, equivalent to 50\%
350 + coverage on one side of the metal system was added in a c(2x4) arrangement
351 + and again allowed to relax before a minimum energy was calculated.
352 +
353 + Energies for the various systems are displayed in Table ~\ref{tab:steps}. Examining
354 + the Pt systems first, it is apparent that the double layer system is slightly less stable
355 + then the original single step. However, upon addition of carbon monoxide, the
356 + stability is reversed and the double layer system becomes more stable. This result
357 + is in agreement with DFT calculations in Tao {\it et al.}\cite{Tao:2010}, who also show
358 + that the addition of CO leads to a reversal in the most stable system. While our
359 + results agree qualitatively, quantitatively, they are approximately an order of magnitude
360 + different. Looking at additional stability per atom in kcal/mol, the DFT calculations suggest
361 + an increased stability of 0.1 kcal/mol per Pt atom, whereas we are seeing closer to a 0.4 kcal/mol
362 + increase in stability per Pt atom.
363 +
364 + The gold systems show a much smaller energy difference between the single and double
365 + systems, likely arising from their lower energy per atom values. Additionally, the weaker
366 + binding of CO to Au is evidenced by the much smaller energy change between the two systems,
367 + when compared to the Pt results. This limited change helps explain our lack of any reconstruction
368 + on the Au systems.
369 +
370 +
371 + %Table of single step double step calculations
372 + \begin{table}[H]
373 + \caption{Minimized single point energies of unit cell crystals displaying (S)ingle or (D)double steps. Systems are periodic along and perpendicular to the step-edge axes with a large vacuum above the displayed 557 facet. The addition of CO in a 50\% c(2x4) coverage acts as a stabilizing presence and suggests a driving force for the observed reconstruction on the highest coverage Pt system. All energies are in kcal/mol.}
374 + \centering
375 + \begin{tabular}{| c | c | c | c | c | c | c |}
376 + \hline
377 + \textbf{Step} & \textbf{N}\textsubscript{M} & \textbf{N\textsubscript{CO}} & \textbf{Unit-Cell Energy} & \textbf{Energy per M} & \textbf{Energy per CO} & \textbf{Difference per M} \\
378 + \hline
379 + Pt(557)-S & 480 & 0 & -61142.624 & -127.381 & - & 0 \\
380 + Pt(557)-D & 480 & 0 & -61027.841 & -127.141 & - & 0.240 \\
381 + \hline
382 + Pt(557)-S & 480 & 40 & -62960.289 & -131.167 & -45.442 & 0 \\
383 + Pt(557)-D & 480 & 44 & -63040.007 & -131.333 & -45.731 & -0.166\\
384 + \hline
385 + \hline
386 + Au(557)-S & 480 & 0 & -41879.286 & -87.249 & - &0 \\
387 + Au(557)-D & 480 & 0 & -41799.714 & -87.084 & - & 0.165 \\
388 + \hline
389 + Au(557)-S & 480 & 40 & -42423.899 & -88.381 & -13.615 & 0 \\
390 + Au(557)-D & 480 & 44 & -42428.738 & -88.393 & -14.296 & -0.012 \\
391 + \hline
392 + \end{tabular}
393 + \label{tab:steps}
394   \end{table}
395  
396 +
397   \subsection{Pt(557) and Au(557) metal interfaces}
398   Our Pt system is an orthorhombic periodic box of dimensions
399   54.482~x~50.046~x~120.88~\AA~while our Au system has
# Line 382 | Line 408 | The different bulk melting temperatures predicted by E
408   1200~K were performed to confirm the relative
409   stability of the surfaces without a CO overlayer.  
410  
411 < The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting}
412 < and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at
413 < different temperatures for the two metals.  The bare Au and Pt surfaces were
414 < initially run in the canonical (NVT) ensemble at 800~K and 1000~K
415 < respectively for 100 ps. The two surfaces were relatively stable at these
416 < temperatures when no CO was present, but experienced increased surface
417 < mobility on addition of CO. Each surface was then dosed with different concentrations of CO
418 < that was initially placed in the vacuum region.  Upon full adsorption,
419 < these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
420 < coverage. Higher coverages resulted in the formation of a double layer of CO,
421 < which introduces artifacts that are not relevant to (557) reconstruction.
422 < Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
423 < the Au surfaces often had a significant CO population in the gas
424 < phase.  These systems were allowed to reach thermal equilibrium (over
425 < 5~ns) before being run in the microcanonical (NVE) ensemble for
426 < data collection. All of the systems examined had at least 40~ns in the
427 < data collection stage, although simulation times for some Pt of the
428 < systems exceeded 200~ns.  Simulations were carried out using the open
429 < source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}
411 > The different bulk melting temperatures predicted by EAM
412 > (1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for
413 > Pt\cite{Pt:melting}) suggest that any reconstructions should happen at
414 > different temperatures for the two metals.  The bare Au and Pt
415 > surfaces were initially run in the canonical (NVT) ensemble at 800~K
416 > and 1000~K respectively for 100 ps. The two surfaces were relatively
417 > stable at these temperatures when no CO was present, but experienced
418 > increased surface mobility on addition of CO. Each surface was then
419 > dosed with different concentrations of CO that was initially placed in
420 > the vacuum region.  Upon full adsorption, these concentrations
421 > correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher
422 > coverages resulted in the formation of a double layer of CO, which
423 > introduces artifacts that are not relevant to (557) reconstruction.
424 > Because of the difference in binding energies, nearly all of the CO
425 > was bound to the Pt surface, while the Au surfaces often had a
426 > significant CO population in the gas phase.  These systems were
427 > allowed to reach thermal equilibrium (over 5~ns) before being run in
428 > the microcanonical (NVE) ensemble for data collection. All of the
429 > systems examined had at least 40~ns in the data collection stage,
430 > although simulation times for some Pt of the systems exceeded 200~ns.
431 > Simulations were carried out using the open source molecular dynamics
432 > package, OpenMD.\cite{Ewald,OOPSE,openmd}
433  
434  
406 –
407 –
435   % RESULTS
436   %
437   \section{Results}
438   \subsection{Structural remodeling}
439 < The bare metal surfaces experienced minor roughening of the
440 < step-edge because of the elevated temperatures, but the (557)
441 < face was stable throughout the simulations. The surface of both
442 < systems, upon dosage of CO, began to undergo extensive remodeling
443 < that was not observed in the bare systems. Reconstructions of
444 < the Au systems were limited to breakup of the step-edges and
445 < some step wandering. The lower coverage Pt systems experienced
446 < similar restructuring but to a greater extent. The 50\% coverage
447 < Pt system was unique among our simulations in that it formed
448 < well-defined and stable double layers through step coalescence,
449 < similar to results reported by Tao {\it et al}.\cite{Tao:2010}
439 > The bare metal surfaces experienced minor roughening of the step-edge
440 > because of the elevated temperatures, but the (557) face was stable
441 > throughout the simulations. The surfaces of both systems, upon dosage
442 > of CO, began to undergo extensive remodeling that was not observed in
443 > the bare systems. Reconstructions of the Au systems were limited to
444 > breakup of the step-edges and some step wandering. The lower coverage
445 > Pt systems experienced similar step edge wandering but to a greater
446 > extent. The 50\% coverage Pt system was unique among our simulations
447 > in that it formed well-defined and stable double layers through step
448 > coalescence, similar to results reported by Tao {\it et
449 >  al}.\cite{Tao:2010}
450  
424 –
451   \subsubsection{Step wandering}
452 < The 0\% coverage surfaces for both metals showed minimal
453 < step-wandering at their respective temperatures. As the CO
454 < coverage increased however, the mobility of the surface atoms,
455 < described through adatom diffusion and step-edge wandering,
456 < also increased.  Except for the 50\% Pt system where step
457 < coalescence occurred, the step-edges in the other simulations
458 < preferred to keep nearly the same distance between steps as in
459 < the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au.
460 < Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994}
461 < highlights the repulsion that exists between step-edges even
462 < when no direct interactions are present in the system. This
463 < repulsion is caused by an entropic barrier that arises from
464 < the fact that steps cannot cross over one another. This entropic
465 < repulsion does not completely define the interactions between
466 < steps, however, so it is possible to observe step coalescence
467 < on some surfaces.\cite{Williams:1991} The presence and
468 < concentration of adsorbates, as shown in this work, can
469 < affect step-step interactions, potentially leading to a new
444 < surface structure as the thermodynamic equilibrium.
452 > The bare surfaces for both metals showed minimal step-wandering at
453 > their respective temperatures. As the CO coverage increased however,
454 > the mobility of the surface atoms, described through adatom diffusion
455 > and step-edge wandering, also increased.  Except for the 50\% Pt
456 > system where step coalescence occurred, the step-edges in the other
457 > simulations preferred to keep nearly the same distance between steps
458 > as in the original (557) lattice, $\sim$13\AA~for Pt and
459 > $\sim$14\AA~for Au.  Previous work by Williams {\it et
460 >  al}.\cite{Williams:1991, Williams:1994} highlights the repulsion
461 > that exists between step-edges even when no direct interactions are
462 > present in the system. This repulsion is caused by an entropic barrier
463 > that arises from the fact that steps cannot cross over one
464 > another. This entropic repulsion does not completely define the
465 > interactions between steps, however, so it is possible to observe step
466 > coalescence on some surfaces.\cite{Williams:1991} The presence and
467 > concentration of adsorbates, as shown in this work, can affect
468 > step-step interactions, potentially leading to a new surface structure
469 > as the thermodynamic equilibrium.
470  
471   \subsubsection{Double layers}
472 < Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface
473 < undergoes two separate reconstructions upon CO adsorption.
474 < The first involves a doubling of the step height and plateau length.
475 < Similar behavior has been seen on a number of surfaces
476 < at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl}
477 < Of the two systems we examined, the Pt system showed a greater
478 < propensity for reconstruction  
479 < because of the larger surface mobility and the greater extent of step wandering.
480 < The amount of reconstruction was strongly correlated to the amount of CO
481 < adsorbed upon the surface.  This appears to be related to the
482 < effect that adsorbate coverage has on edge breakup and on the
483 < surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the
484 < doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here.
485 < Over a longer time scale (150~ns) two more double layers formed
486 < on this surface. Although double layer formation did not occur
487 < in the other Pt systems, they exhibited more step-wandering and
488 < roughening compared to their Au counterparts. The
489 < 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
490 < various times along the simulation showing the evolution of a double layer step-edge.
472 > Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the
473 > Pt(557) surface undergoes two separate reconstructions upon CO
474 > adsorption.  The first involves a doubling of the step height and
475 > plateau length.  Similar behavior has been seen on a number of
476 > surfaces at varying conditions, including Ni(977) and
477 > Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we
478 > examined, the Pt system showed a greater propensity for reconstruction
479 > because of the larger surface mobility and the greater extent of step
480 > wandering.  The amount of reconstruction was strongly correlated to
481 > the amount of CO adsorbed upon the surface.  This appears to be
482 > related to the effect that adsorbate coverage has on edge breakup and
483 > on the surface diffusion of metal adatoms. Only the 50\% Pt surface
484 > underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within
485 > the time scales studied here.  Over a longer time scale (150~ns) two
486 > more double layers formed on this surface. Although double layer
487 > formation did not occur in the other Pt systems, they exhibited more
488 > step-wandering and roughening compared to their Au counterparts. The
489 > 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
490 > various times along the simulation showing the evolution of a double
491 > layer step-edge.
492  
493 < The second reconstruction observed by
494 < Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched
495 < across the plateau between two step-edges. Neither metal, within
496 < the 40~ns time scale or the extended simulation time of 150~ns for
497 < the 50\% Pt system, experienced this reconstruction.
493 > The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010}
494 > involved the formation of triangular clusters that stretched across
495 > the plateau between two step-edges. Neither of the simulated metal
496 > interfaces, within the 40~ns time scale or the extended time of 150~ns
497 > for the 50\% Pt system, experienced this reconstruction.
498  
499   %Evolution of surface
500   \begin{figure}[H]
501 < \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation.pdf}
502 < \caption{The Pt(557) / 50\% CO system at a sequence of times after
503 <  initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and
504 <  (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly.  The
501 > \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation}
502 > \caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a)
503 >  258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after
504 >  exposure. Disruption of the (557) step-edges occurs quickly.  The
505    doubling of the layers appears only after two adjacent step-edges
506    touch.  The circled spot in (b) nucleated the growth of the double
507    step observed in the later configurations.}
# Line 483 | Line 509 | Previous experimental work by Pearl and Sibener\cite{P
509   \end{figure}
510  
511   \subsection{Dynamics}
512 < Previous experimental work by Pearl and Sibener\cite{Pearl},
513 < using STM, has been able to capture the coalescence of steps
514 < on Ni(977). The time scale of the image acquisition, $\sim$70~s/image,
515 < provides an upper bound for the time required for the doubling
516 < to occur. By utilizing Molecular Dynamics we are able to probe
517 < the dynamics of these reconstructions at elevated temperatures
518 < and in this section we provide data on the timescales for transport
519 < properties, e.g. diffusion and layer formation time.
512 > Previous experimental work by Pearl and Sibener\cite{Pearl}, using
513 > STM, has been able to capture the coalescence of steps on Ni(977). The
514 > time scale of the image acquisition, $\sim$70~s/image, provides an
515 > upper bound for the time required for the doubling to occur. By
516 > utilizing Molecular Dynamics we are able to probe the dynamics of
517 > these reconstructions at elevated temperatures and in this section we
518 > provide data on the timescales for transport properties,
519 > e.g. diffusion and layer formation time.
520  
521  
522   \subsubsection{Transport of surface metal atoms}
523   %forcedSystems/stepSeparation
524 < The wandering of a step-edge is a cooperative effect
525 < arising from the individual movements of the atoms making up the steps. An ideal metal surface
526 < displaying a low index facet, (111) or (100), is unlikely to experience
527 < much surface diffusion because of the large energetic barrier that must
528 < be overcome to lift an atom out of the surface. The presence of step-edges and other surface features
529 < on higher-index facets provides a lower energy source for mobile metal atoms.
530 < Single-atom break-away from a step-edge on a clean surface still imposes an
531 < energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting
532 < the same metal atom vertically out of the surface,  \textgreater~60 kcal/mol.
533 < The penalty lowers significantly when CO is present in sufficient quantities
534 < on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as
535 < $\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for
536 < diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then
537 < able to explore the terrace before rejoining either their original step-edge or
538 < becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom
539 < to traverse to a separate terrace although the presence of CO can lower the
540 < energy barrier required to lift or lower an adatom. By tracking the mobility of individual
515 < metal atoms on the Pt and Au surfaces we were able to determine the relative
516 < diffusion constants, as well as how varying coverages of CO affect the diffusion. Close
517 < observation of the mobile metal atoms showed that they were typically in
518 < equilibrium with the step-edges.
519 < At times, their motion was concerted and two or more adatoms would be
520 < observed moving together across the surfaces.
524 >
525 > The wandering of a step-edge is a cooperative effect arising from the
526 > individual movements of the atoms making up the steps. An ideal metal
527 > surface displaying a low index facet, (111) or (100), is unlikely to
528 > experience much surface diffusion because of the large energetic
529 > barrier that must be overcome to lift an atom out of the surface. The
530 > presence of step-edges and other surface features on higher-index
531 > facets provides a lower energy source for mobile metal atoms.  Using
532 > our potential model, single-atom break-away from a step-edge on a
533 > clean surface still imposes an energetic penalty around
534 > $\sim$~45~kcal/mol, but this is certainly easier than lifting the same
535 > metal atom vertically out of the surface, \textgreater~60~kcal/mol.
536 > The penalty lowers significantly when CO is present in sufficient
537 > quantities on the surface. For certain distributions of CO, the
538 > energetic penalty can fall to as low as $\sim$~20~kcal/mol. The
539 > configurations that create these lower barriers are detailed in the
540 > discussion section below.
541  
542 < A particle was considered ``mobile'' once it had traveled more than 2~\AA~
543 < between saved configurations of the system (typically 10-100 ps). A mobile atom
544 < would typically travel much greater distances than this, but the 2~\AA~cutoff
545 < was used to prevent swamping the diffusion data with the in-place vibrational
546 < movement of buried atoms. Diffusion on a surface is strongly affected by
547 < local structures and in this work, the presence of single and double layer
548 < step-edges causes the diffusion parallel to the step-edges to be larger than
549 < the diffusion perpendicular to these edges. Parallel and perpendicular
550 < diffusion constants are shown in Figure \ref{fig:diff}.
542 > Once an adatom exists on the surface, the barrier for diffusion is
543 > negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are
544 > then able to explore the terrace before rejoining either their
545 > original step-edge or becoming a part of a different edge. It is an
546 > energetically unfavorable process with a high barrier for an atom to
547 > traverse to a separate terrace although the presence of CO can lower
548 > the energy barrier required to lift or lower an adatom. By tracking
549 > the mobility of individual metal atoms on the Pt and Au surfaces we
550 > were able to determine the relative diffusion constants, as well as
551 > how varying coverages of CO affect the diffusion. Close observation of
552 > the mobile metal atoms showed that they were typically in equilibrium
553 > with the step-edges.  At times, their motion was concerted, and two or
554 > more adatoms would be observed moving together across the surfaces.
555  
556 + A particle was considered ``mobile'' once it had traveled more than
557 + 2~\AA~ between saved configurations of the system (typically 10-100
558 + ps). A mobile atom would typically travel much greater distances than
559 + this, but the 2~\AA~cutoff was used to prevent swamping the diffusion
560 + data with the in-place vibrational movement of buried atoms. Diffusion
561 + on a surface is strongly affected by local structures and the presence
562 + of single and double layer step-edges causes the diffusion parallel to
563 + the step-edges to be larger than the diffusion perpendicular to these
564 + edges. Parallel and perpendicular diffusion constants are shown in
565 + Figure \ref{fig:diff}.  Diffusion parallel to the step-edge is higher
566 + than diffusion perpendicular to the edge because of the lower energy
567 + barrier associated with sliding along an edge compared to breaking
568 + away to form an isolated adatom.
569 +
570   %Diffusion graph
571   \begin{figure}[H]
572 < \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1.pdf}
572 > \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1}
573   \caption{Diffusion constants for mobile surface atoms along directions
574    parallel ($\mathbf{D}_{\parallel}$) and perpendicular
575    ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
576 <  surface coverage.  Diffusion parallel to the step-edge is higher
577 <  than that perpendicular to the edge because of the lower energy
578 <  barrier associated with traversing along the edge as compared to
579 <  completely breaking away. The two reported diffusion constants for
542 <  the 50\% Pt system arise from different sample sets. The lower values
543 <  correspond to the same 40~ns amount that all of the other systems were
544 <  examined at, while the larger values correspond to a 20~ns period }
576 >  surface coverage.  The two reported diffusion constants for the 50\%
577 >  Pt system correspond to a 20~ns period before the formation of the
578 >  double layer (upper points), and to the full 40~ns sampling period
579 >  (lower points).}
580   \label{fig:diff}
581   \end{figure}
582  
# Line 553 | Line 588 | now been buried resulting in a smaller reported diffus
588   at the earliest times in the simulations. Following double layer formation,
589   however, there is a precipitous drop in adatom diffusion. As the double
590   layer forms, many atoms that had been tracked for mobility data have
591 < now been buried resulting in a smaller reported diffusion constant. A
591 > now been buried, resulting in a smaller reported diffusion constant. A
592   secondary effect of higher coverages is CO-CO cross interactions that
593   lower the effective mobility of the Pt adatoms that are bound to each CO.
594   This effect would become evident only at higher coverages. A detailed
595   account of Pt adatom energetics follows in the Discussion.
596  
562 –
597   \subsubsection{Dynamics of double layer formation}
598   The increased diffusion on Pt at the higher CO coverages is the primary
599   contributor to double layer formation. However, this is not a complete
# Line 587 | Line 621 | We have shown that a classical potential model is able
621  
622   %Discussion
623   \section{Discussion}
624 < We have shown that a classical potential model is able to model the
625 < initial reconstruction of the Pt(557) surface upon CO adsorption as
626 < shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were
627 < able to observe features of the dynamic processes necessary for
628 < this reconstruction. Here we discuss the features of the model that
629 < give rise to the observed dynamical properties of the (557) reconstruction.
624 > We have shown that a classical potential is able to model the initial
625 > reconstruction of the Pt(557) surface upon CO adsorption, and have
626 > reproduced the double layer structure observed by Tao {\it et
627 >  al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be
628 > rapid -- occurring within 100 ns of the initial exposure to CO.  Here
629 > we discuss the features of the classical potential that are
630 > contributing to the stability and speed of the Pt(557) reconstruction.
631  
632   \subsection{Diffusion}
633 < The perpendicular diffusion constant
634 < appears to be the most important indicator of double layer
635 < formation. As highlighted in Figure \ref{fig:reconstruct}, the
636 < formation of the double layer did not begin until a nucleation
637 < site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994},
638 < the inability for edges to cross leads to an effective edge-edge repulsion that
639 < must be overcome to allow step coalescence.
640 < A greater $\textbf{D}_\perp$ implies more step-wandering
641 < and a larger chance for the stochastic meeting of two edges
642 < to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double
643 < layer. This helps explain why the time scale for formation after
644 < the appearance of a nucleation site was rapid, while the initial
645 < appearance of the nucleation site was unpredictable.
633 > The perpendicular diffusion constant appears to be the most important
634 > indicator of double layer formation. As highlighted in Figure
635 > \ref{fig:reconstruct}, the formation of the double layer did not begin
636 > until a nucleation site appeared.  Williams {\it et
637 >  al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge
638 > repulsion arising from the inability of edge crossing.  This repulsion
639 > must be overcome to allow step coalescence.  A larger
640 > $\textbf{D}_\perp$ value implies more step-wandering and a larger
641 > chance for the stochastic meeting of two edges to create a nucleation
642 > point.  Diffusion parallel to the step-edge can help ``zipper'' up a
643 > nascent double layer. This helps explain the rapid time scale for
644 > double layer completion after the appearance of a nucleation site, while
645 > the initial appearance of the nucleation site was unpredictable.
646  
647   \subsection{Mechanism for restructuring}
648 < Since the Au surface showed no large scale restructuring in any of
649 < our simulations, our discussion will focus on the 50\% Pt-CO system
650 < which did exhibit doubling. A
651 < number of possible mechanisms exist to explain the role of adsorbed
652 < CO in restructuring the Pt surface. Quadrupolar repulsion between
653 < adjacent CO molecules adsorbed on the surface is one possibility.  
654 < However, the quadrupole-quadrupole interaction is short-ranged and
655 < is attractive for some orientations.  If the CO molecules are ``locked'' in
656 < a specific orientation relative to each other, through atop adsorption for
657 < example, this explanation would gain credence. The calculated energetic repulsion
658 < between two CO molecules located a distance of 2.77~\AA~apart
659 < (nearest-neighbor distance of Pt) and both in a vertical orientation,
660 < is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance
661 < of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away
662 < from a purely vertical orientation also lowers the repulsion. When the
663 < carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is
664 < reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}.
665 < The calculated barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
666 < repulsion between adjacent CO molecules bound to Pt could increase the surface
667 < diffusion. However, the residence time of CO on Pt suggests that these
668 < molecules are extremely mobile, with diffusion constants 40 to 2500 times
669 < larger than surface Pt atoms. This mobility suggests that the CO molecules jump
670 < between different Pt atoms throughout the simulation, but will stay bound for
671 < significant periods of time.
648 > Since the Au surface showed no large scale restructuring in any of our
649 > simulations, our discussion will focus on the 50\% Pt-CO system which
650 > did exhibit doubling. A number of possible mechanisms exist to explain
651 > the role of adsorbed CO in restructuring the Pt surface. Quadrupolar
652 > repulsion between adjacent CO molecules adsorbed on the surface is one
653 > possibility.  However, the quadrupole-quadrupole interaction is
654 > short-ranged and is attractive for some orientations.  If the CO
655 > molecules are ``locked'' in a vertical orientation, through atop
656 > adsorption for example, this explanation would gain credence. Within
657 > the framework of our classical potential, the calculated energetic
658 > repulsion between two CO molecules located a distance of
659 > 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a
660 > vertical orientation, is 8.62 kcal/mol. Moving the CO to the second
661 > nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly
662 > 0. Allowing the CO to rotate away from a purely vertical orientation
663 > also lowers the repulsion. When the carbons are locked at a distance
664 > of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle
665 > between the 2 CO is $\sim$24\textsuperscript{o}.  The calculated
666 > barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
667 > repulsion between adjacent CO molecules bound to Pt could indeed
668 > increase the surface diffusion. However, the residence time of CO on
669 > Pt suggests that the CO molecules are extremely mobile, with diffusion
670 > constants 40 to 2500 times larger than surface Pt atoms. This mobility
671 > suggests that the CO molecules jump between different Pt atoms
672 > throughout the simulation.  However, they do stay bound to individual
673 > Pt atoms for long enough to modify the local energy landscape for the
674 > mobile adatoms.
675  
676 < A different interpretation of the above mechanism, taking into account the large
677 < mobility of the CO, looks at how instantaneous and short-lived configurations of
678 < CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge
679 < breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach
680 < an edge atom is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
681 < \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases
682 < (e), (g), and (h), the barrier can be lowered to $\sim$23~kcal/mole. In these instances,
683 < it becomes quite energetically favorable to roughen the edge by introducing a small
684 < separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in
685 < simulations with significant CO populations. The roughening is present to a lesser extent
686 < on lower coverage surfaces and even on the bare surfaces, although in these cases it is likely
687 < due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism
688 < of step-edge breakup suggested by these energy curves is one of the most difficult
689 < processes, a complete break-away from the step-edge in one unbroken movement.
690 < Easier multistep mechanisms likely exist where an adatom moves laterally on the surface
691 < after being ejected so it ends up alongside the ledge. This provides the atom with 5 nearest
692 < neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher
693 < than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO
694 < quadrupolar repulsion is still playing a primary role, but for its importance in roughening
695 < the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not
696 < born out by their mobility data. The requirement for a large density of CO on the surface
697 < for some of the more favorable suggested configurations in Figure \ref{fig:SketchGraphic}
698 < correspond well with the increased mobility seen on higher coverage surfaces.
676 > A different interpretation of the above mechanism which takes the
677 > large mobility of the CO into account, would be in the destabilization
678 > of Pt-Pt interactions due to bound CO.  Destabilizing Pt-Pt bonds at
679 > the edges could lead to increased step-edge breakup and diffusion. On
680 > the bare Pt(557) surface the barrier to completely detach an edge atom
681 > is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
682 > \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain
683 > configurations, cases (e), (g), and (h), the barrier can be lowered to
684 > $\sim$23~kcal/mol by the presence of bound CO molecules. In these
685 > instances, it becomes energetically favorable to roughen the edge by
686 > introducing a small separation of 0.5 to 1.0~\AA. This roughening
687 > becomes immediately obvious in simulations with significant CO
688 > populations. The roughening is present to a lesser extent on surfaces
689 > with lower CO coverage (and even on the bare surfaces), although in
690 > these cases it is likely due to random fluctuations that squeeze out
691 > step-edge atoms. Step-edge breakup by direct single-atom translations
692 > (as suggested by these energy curves) is probably a worst-case
693 > scenario.  Multistep mechanisms in which an adatom moves laterally on
694 > the surface after being ejected would be more energetically favorable.
695 > This would leave the adatom alongside the ledge, providing it with
696 > five nearest neighbors.  While fewer than the seven neighbors it had
697 > as part of the step-edge, it keeps more Pt neighbors than the three
698 > neighbors an isolated adatom has on the terrace. In this proposed
699 > mechanism, the CO quadrupolar repulsion still plays a role in the
700 > initial roughening of the step-edge, but not in any long-term bonds
701 > with individual Pt atoms.  Higher CO coverages create more
702 > opportunities for the crowded CO configurations shown in Figure
703 > \ref{fig:SketchGraphic}, and this is likely to cause an increased
704 > propensity for step-edge breakup.
705  
706   %Sketch graphic of different configurations
707   \begin{figure}[H]
708 < \includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf}
709 < \caption{The dark grey atoms refer to the upper ledge, while the white atoms are
710 < the lower terrace. The blue highlighted atoms had a CO in a vertical atop position
711 < upon them. These are a sampling of the configurations examined to gain a more
712 < complete understanding of the effects CO has on surface diffusion and edge breakup.
713 < Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.}
708 > \includegraphics[width=\linewidth]{COpaths}
709 > \caption{Configurations used to investigate the mechanism of step-edge
710 >  breakup on Pt(557). In each case, the central (starred) atom was
711 >  pulled directly across the surface away from the step edge.  The Pt
712 >  atoms on the upper terrace are colored dark grey, while those on the
713 >  lower terrace are in white.  In each of these configurations, some
714 >  of the atoms (highlighted in blue) had CO molecules bound in the
715 >  vertical atop position.  The energies of these configurations as a
716 >  function of central atom displacement are displayed in Figure
717 >  \ref{fig:SketchEnergies}.}
718   \label{fig:SketchGraphic}
719   \end{figure}
720  
721   %energy graph corresponding to sketch graphic
722   \begin{figure}[H]
723 < \includegraphics[width=\linewidth]{Portrait_SeparationComparison.pdf}
724 < \caption{The energy curves directly correspond to the labeled model
725 < surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative
726 < to their initial configuration so the energy of a and h do not have the
727 < same zero value. As is seen, certain arrangements of CO can lower
728 < the energetic barrier that must be overcome to create an adatom.
729 < However, it is the highest coverages where these higher-energy
730 < configurations of CO will be more likely. }
723 > \includegraphics[width=\linewidth]{Portrait_SeparationComparison}
724 > \caption{Energies for displacing a single edge atom perpendicular to
725 >  the step edge as a function of atomic displacement. Each of the
726 >  energy curves corresponds to one of the labeled configurations in
727 >  Figure \ref{fig:SketchGraphic}, and the energies are referenced to
728 >  the unperturbed step-edge.  Certain arrangements of bound CO
729 >  (notably configurations g and h) can lower the energetic barrier for
730 >  creating an adatom relative to the bare surface (configuration a).}
731   \label{fig:SketchEnergies}
732   \end{figure}
733  
734 < While configurations of CO on the surface are able to increase diffusion,
735 < this does not immediately provide an explanation for the formation of double
736 < layers. If adatoms were constrained to their terrace then doubling would be
737 < much less likely to occur. Nucleation sites could still potentially form, but there
738 < would not be enough atoms to finish the doubling. For a non-simulated metal surface, where the
739 < step lengths can be assumed to be infinite relative to atomic sizes, local doubling would be possible, but in
692 < our simulations with our periodic treatment of the system, the system is not large enough to experience this effect.
693 < Thus, there must be a mechanism that explains how adatoms are able to move
694 < amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate
695 < where an adatom along the step-edge with an adsorbed CO ``burrows'' into the
696 < edge displacing an atom onto the higher terrace. This mechanism was chosen
697 < because of similar events that were observed during the simulations. The barrier
698 < heights we obtained are only approximations because we constrained the movement
699 < of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s
700 < are provide a strong energetic support for this modeled lifting mechanism. When CO is not present and
701 < this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown
702 < in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol.
703 < While the barrier height is comparable for both cases, there is nearly a 20~kcal/mol
704 < difference in energies and makes the process energetically favorable.
734 > While configurations of CO on the surface are able to increase
735 > diffusion and the likelihood of edge wandering, this does not provide
736 > a complete explanation for the formation of double layers. If adatoms
737 > were constrained to their original terraces then doubling could not
738 > occur.  A mechanism for vertical displacement of adatoms at the
739 > step-edge is required to explain the doubling.
740  
741 + We have discovered one possible mechanism for a CO-mediated vertical
742 + displacement of Pt atoms at the step edge. Figure \ref{fig:lambda}
743 + shows four points along a reaction coordinate in which a CO-bound
744 + adatom along the step-edge ``burrows'' into the edge and displaces the
745 + original edge atom onto the higher terrace.  A number of events
746 + similar to this mechanism were observed during the simulations.  We
747 + predict an energetic barrier of 20~kcal/mol for this process (in which
748 + the displaced edge atom follows a curvilinear path into an adjacent
749 + 3-fold hollow site).  The barrier heights we obtain for this reaction
750 + coordinate are approximate because the exact path is unknown, but the
751 + calculated energy barriers would be easily accessible at operating
752 + conditions.  Additionally, this mechanism is exothermic, with a final
753 + energy 15~kcal/mol below the original $\lambda = 0$ configuration.
754 + When CO is not present and this reaction coordinate is followed, the
755 + process is endothermic by 3~kcal/mol.  The difference in the relative
756 + energies for the $\lambda=0$ and $\lambda=1$ case when CO is present
757 + provides strong support for CO-mediated Pt-Pt interactions giving rise
758 + to the doubling reconstruction.
759 +
760   %lambda progression of Pt -> shoving its way into the step
761   \begin{figure}[H]
762 < \includegraphics[width=\linewidth]{EPS_rxnCoord.pdf}
763 < \caption{ Various points along a reaction coordinate are displayed in the figure.
764 < The mechanism of edge traversal is examined in the presence of CO. The approximate
765 < barrier for the displayed process is 20~kcal/mol. However, the $\Delta E$ of this process
766 < is -15~kcal/mol making it an energetically favorable process.}
762 > \includegraphics[width=\linewidth]{EPS_rxnCoord}
763 > \caption{Points along a possible reaction coordinate for CO-mediated
764 >  edge doubling. Here, a CO-bound adatom burrows into an established
765 >  step edge and displaces an edge atom onto the upper terrace along a
766 >  curvilinear path.  The approximate barrier for the process is
767 >  20~kcal/mol, and the complete process is exothermic by 15~kcal/mol
768 >  in the presence of CO, but is endothermic by 3~kcal/mol without CO.}
769   \label{fig:lambda}
770   \end{figure}
771  
772 < The mechanism for doubling on this surface appears to require the cooperation of at least
773 < these two described processes. For complete doubling of a layer to occur there must
774 < be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from
775 < that terrace they must either rise up on the ledge above them or drop to the ledge below
776 < them. The presence of CO helps with the energetics of both of these situations. There must be sufficient
777 < breakage of the step-edge to increase the concentration of adatoms on the surface and
778 < these adatoms must then undergo the burrowing highlighted above or some comparable
779 < mechanism to traverse the step-edge. Over time, these mechanisms working in concert
780 < lead to the formation of a double layer.
772 > The mechanism for doubling on the Pt(557) surface appears to require
773 > the cooperation of at least two distinct processes. For complete
774 > doubling of a layer to occur there must be a breakup of one
775 > terrace. These atoms must then ``disappear'' from that terrace, either
776 > by travelling to the terraces above or below their original levels.
777 > The presence of CO helps explain mechanisms for both of these
778 > situations. There must be sufficient breakage of the step-edge to
779 > increase the concentration of adatoms on the surface and these adatoms
780 > must then undergo the burrowing highlighted above (or a comparable
781 > mechanism) to create the double layer.  With sufficient time, these
782 > mechanisms working in concert lead to the formation of a double layer.
783  
784   \subsection{CO Removal and double layer stability}
785 < Once a double layer had formed on the 50\%~Pt system it
786 < remained for the rest of the simulation time with minimal
787 < movement. There were configurations that showed small
788 < wells or peaks forming, but typically within a few nanoseconds
789 < the feature would smooth away. Within our simulation time,
790 < the formation of the double layer was irreversible and a double
791 < layer was never observed to split back into two single layer
792 < step-edges while CO was present. To further gauge the effect
735 < CO had on this system, additional simulations were run starting
736 < from a late configuration of the 50\%~Pt system that had formed
737 < double layers. These simulations then had their CO removed.
738 < The double layer breaks rapidly in these simulations, already
739 < showing a well-defined splitting after 100~ps. Configurations of
740 < this system are shown in Figure \ref{fig:breaking}. The coloring
741 < of the top and bottom layers helps to exhibit how much mixing
742 < the edges experience as they split. These systems were only
743 < examined briefly, 10~ns, and within that time despite the initial
744 < rapid splitting, the edges only moved another few \AA~apart.
745 < It is possible with longer simulation times that the
746 < (557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010}
785 > Once the double layers had formed on the 50\%~Pt system, they remained
786 > stable for the rest of the simulation time with minimal movement.
787 > Random fluctuations that involved small clusters or divots were
788 > observed, but these features typically healed within a few
789 > nanoseconds.  Within our simulations, the formation of the double
790 > layer appeared to be irreversible and a double layer was never
791 > observed to split back into two single layer step-edges while CO was
792 > present.
793  
794 + To further gauge the effect CO has on this surface, additional
795 + simulations were run starting from a late configuration of the 50\%~Pt
796 + system that had already formed double layers. These simulations then
797 + had their CO molecules suddenly removed.  The double layer broke apart
798 + rapidly in these simulations, showing a well-defined edge-splitting
799 + after 100~ps. Configurations of this system are shown in Figure
800 + \ref{fig:breaking}. The coloring of the top and bottom layers helps to
801 + show how much mixing the edges experience as they split. These systems
802 + were only examined for 10~ns, and within that time despite the initial
803 + rapid splitting, the edges only moved another few \AA~apart. It is
804 + possible that with longer simulation times, the (557) surface recovery
805 + observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered.
806  
749 –
807   %breaking of the double layer upon removal of CO
808   \begin{figure}[H]
809 < \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking.pdf}
810 < \caption{(A)  0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO
811 < helped maintain the stability of the double layer and its microfaceting of the double layer
812 < into a (111) configuration. This microfacet immediately reverts to the original (100) step
813 < edge which is a hallmark of the (557) surface. The separation is not a simple sliding apart, rather
814 < there is a mixing of the lower and upper atoms at the edge.}
809 > \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking}
810 > \caption{Behavior of an established (111) double step after removal of
811 >  the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the
812 >  removal of CO.  Nearly immediately after the CO is removed, the
813 >  step edge reforms in a (100) configuration, which is also the step
814 >  type seen on clean (557) surfaces. The step separation involves
815 >  significant mixing of the lower and upper atoms at the edge.}
816   \label{fig:breaking}
817   \end{figure}
818  
819  
762 –
763 –
820   %Peaks!
821   %\begin{figure}[H]
822   %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
# Line 774 | Line 830 | there is a mixing of the lower and upper atoms at the
830   %Don't think I need this
831   %clean surface...
832   %\begin{figure}[H]
833 < %\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
833 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF}
834   %\caption{}
835  
836   %\end{figure}
# Line 782 | Line 838 | The strength of the Pt-CO binding interaction as well
838  
839  
840   \section{Conclusion}
841 < The strength of the Pt-CO binding interaction as well as the large
842 < quadrupolar repulsion between CO molecules are sufficient to
843 < explain the observed increase in surface mobility and the resultant
844 < reconstructions at the highest simulated coverage. The weaker
845 < Au-CO interaction results in lower diffusion constants, less step-wandering,
846 < and a lack of the double layer reconstruction. An in-depth examination
847 < of the energetics shows the important role CO plays in increasing
848 < step-breakup and in facilitating edge traversal which are both
793 < necessary for double layer formation.
841 > The strength and directionality of the Pt-CO binding interaction, as
842 > well as the large quadrupolar repulsion between atop-bound CO
843 > molecules, help to explain the observed increase in surface mobility
844 > of Pt(557) and the resultant reconstruction into a double-layer
845 > configuration at the highest simulated CO-coverages.  The weaker Au-CO
846 > interaction results in significantly lower adataom diffusion
847 > constants, less step-wandering, and a lack of the double layer
848 > reconstruction on the Au(557) surface.
849  
850 + An in-depth examination of the energetics shows the important role CO
851 + plays in increasing step-breakup and in facilitating edge traversal
852 + which are both necessary for double layer formation.
853  
796 –
854   %Things I am not ready to remove yet
855  
856   %Table of Diffusion Constants
# Line 817 | Line 874 | Support for this project was provided by the National
874   % \end{table}
875  
876   \begin{acknowledgement}
877 < Support for this project was provided by the National Science
878 < Foundation under grant CHE-0848243 and by the Center for Sustainable
879 < Energy at Notre Dame (cSEND). Computational time was provided by the
880 < Center for Research Computing (CRC) at the University of Notre Dame.
877 >  We gratefully acknowledge conversations with Dr. William
878 >  F. Schneider and Dr. Feng Tao.  Support for this project was
879 >  provided by the National Science Foundation under grant CHE-0848243
880 >  and by the Center for Sustainable Energy at Notre Dame
881 >  (cSEND). Computational time was provided by the Center for Research
882 >  Computing (CRC) at the University of Notre Dame.
883   \end{acknowledgement}
884   \newpage
885 < \bibliography{firstTryBibliography}
885 > \bibstyle{achemso}
886 > \bibliography{COonPtAu}
887   %\end{doublespace}
888  
889   \begin{tocentry}
890 < %\includegraphics[height=3.5cm]{timelapse}
890 > \begin{wrapfigure}{l}{0.5\textwidth}
891 > \begin{center}
892 > \includegraphics[width=\linewidth]{TOC_doubleLayer}
893 > \end{center}
894 > \end{wrapfigure}
895 > A reconstructed Pt(557) surface after 86~ns exposure to a half a
896 > monolayer of CO.  The double layer that forms is a result of
897 > CO-mediated step-edge wandering as well as a burrowing mechanism that
898 > helps lift edge atoms onto an upper terrace.
899   \end{tocentry}
900  
901   \end{document}

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