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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 > %\mciteErrorOnUnknownfalse
8  
9   \usepackage[version=3]{mhchem}  % this is a great package for formatting chemical reactions
25 – % \usepackage[square, comma, sort&compress]{natbib}
10   \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
11  
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 –
12   \title{Molecular Dynamics simulations of the surface reconstructions
13    of Pt(557) and Au(557) under exposure to CO}
14  
# Line 73 | Line 45 | We examine surface reconstructions of Pt and Au(557) u
45  
46  
47   \begin{abstract}
48 < We examine surface reconstructions of Pt and Au(557) under
49 < various CO coverages using molecular dynamics in order to
50 < explore possible mechanisms for any observed reconstructions
51 < and their dynamics. The metal-CO interactions were parameterized
52 < as part of this work so that an efficient large-scale treatment of
53 < this system could be undertaken. The large difference in binding
54 < strengths of the metal-CO interactions was found to play a significant
55 < role with regards to step-edge stability and adatom diffusion. A
56 < small correlation between coverage and the diffusion constant
57 < was also determined. The energetics of CO adsorbed to the surface
58 < is sufficient to explain the reconstructions observed on the Pt
59 < systems and the lack  of reconstruction of the Au systems.
60 <
48 >  The mechanism and dynamics of surface reconstructions of Pt(557) and
49 >  Au(557) exposed to various coverages of carbon monoxide (CO) were
50 >  investigated using molecular dynamics simulations.  Metal-CO
51 >  interactions were parameterized from experimental data and
52 >  plane-wave Density Functional Theory (DFT) calculations.  The large
53 >  difference in binding strengths of the Pt-CO and Au-CO interactions
54 >  was found to play a significant role in step-edge stability and
55 >  adatom diffusion constants.  Various mechanisms for CO-mediated step
56 >  wandering and step doubling were investigated on the Pt(557)
57 >  surface.  We find that the energetics of CO adsorbed to the surface
58 >  can explain the step-doubling reconstruction observed on Pt(557) and
59 >  the lack of such a reconstruction on the Au(557) surface.  However,
60 >  more complicated reconstructions into triangular clusters that have
61 >  been seen in recent experiments were not observed in these
62 >  simulations.
63   \end{abstract}
64  
65   \newpage
# Line 117 | Line 91 | This work is an investigation into the mechanism and t
91   reversible restructuring under exposure to moderate pressures of
92   carbon monoxide.\cite{Tao:2010}
93  
94 < This work is an investigation into the mechanism and timescale for
95 < surface restructuring using molecular simulations.  Since the dynamics
96 < of the process are of particular interest, we employ classical force
97 < fields that represent a compromise between chemical accuracy and the
98 < computational efficiency necessary to simulate the process of interest.
99 < Since restructuring typically occurs as a result of specific interactions of the
100 < catalyst with adsorbates, in this work, two metal systems exposed
101 < to carbon monoxide were examined. The Pt(557) surface has already been shown
102 < to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010}
103 < The Au(557) surface, because of a weaker interaction with CO, is seen as less
104 < likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000}
105 < and Piccolo et al.\cite{Piccolo:2004} have both observed CO-induced
106 < reconstruction of a Au(111) surface. Peters et al. saw a relaxation to the
107 < 22 x $\sqrt{3}$ cell. They argued that only a few Au atoms
108 < become adatoms, limiting the stress of this reconstruction while
109 < allowing the rest to relax and approach the ideal (111)
110 < configuration. They did not see the usual herringbone pattern being greatly
111 < affected by this relaxation. Piccolo et al. on the other hand, did see a
112 < disruption of the herringbone pattern as CO was adsorbed to the
113 < surface. Both groups suggested that the preference CO shows for
114 < low-coordinated Au atoms was the primary driving force for the reconstruction.
94 > This work is an investigation into the mechanism and timescale for the
95 > Pt(557) \& Au(557) surface restructuring using molecular simulation.
96 > Since the dynamics of the process are of particular interest, we
97 > employ classical force fields that represent a compromise between
98 > chemical accuracy and the computational efficiency necessary to
99 > simulate the process of interest.  Since restructuring typically
100 > occurs as a result of specific interactions of the catalyst with
101 > adsorbates, in this work, two metal systems exposed to carbon monoxide
102 > were examined. The Pt(557) surface has already been shown to undergo a
103 > large scale reconstruction under certain conditions.\cite{Tao:2010}
104 > The Au(557) surface, because of weaker interactions with CO, is less
105 > likely to undergo this kind of reconstruction. However, Peters {\it et
106 >  al}.\cite{Peters:2000} and Piccolo {\it et al}.\cite{Piccolo:2004}
107 > have both observed CO-induced modification of reconstructions to the
108 > Au(111) surface. Peters {\it et al}. observed the Au(111)-($22 \times
109 > \sqrt{3}$) ``herringbone'' reconstruction relaxing slightly under CO
110 > adsorption. They argued that only a few Au atoms become adatoms,
111 > limiting the stress of this reconstruction, while allowing the rest to
112 > relax and approach the ideal (111) configuration.  Piccolo {\it et
113 >  al}. on the other hand, saw a more significant disruption of the
114 > Au(111)-($22 \times \sqrt{3}$) herringbone pattern as CO adsorbed on
115 > the surface. Both groups suggested that the preference CO shows for
116 > low-coordinated Au atoms was the primary driving force for the
117 > relaxation.  Although the Au(111) reconstruction was not the primary
118 > goal of our work, the classical models we have fit may be of future
119 > use in simulating this reconstruction.
120  
142 –
143 –
121   %Platinum molecular dynamics
122   %gold molecular dynamics
123  
124   \section{Simulation Methods}
125 < The challenge in modeling any solid/gas interface is the
126 < development of a sufficiently general yet computationally tractable
127 < model of the chemical interactions between the surface atoms and
128 < adsorbates.  Since the interfaces involved are quite large (10$^3$ -
129 < 10$^6$ atoms) and respond slowly to perturbations, {\it ab initio}
125 > The challenge in modeling any solid/gas interface is the development
126 > of a sufficiently general yet computationally tractable model of the
127 > chemical interactions between the surface atoms and adsorbates.  Since
128 > the interfaces involved are quite large (10$^3$ - 10$^4$ atoms), have
129 > many electrons, and respond slowly to perturbations, {\it ab initio}
130   molecular dynamics
131   (AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello
132   methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum
# Line 161 | Line 138 | Au-Au and Pt-Pt interactions.\cite{EAM} The CO was mod
138   Coulomb potential.  For this work, we have used classical molecular
139   dynamics with potential energy surfaces that are specifically tuned
140   for transition metals.  In particular, we used the EAM potential for
141 < Au-Au and Pt-Pt interactions.\cite{EAM} The CO was modeled using a rigid
142 < three-site model developed by Straub and Karplus for studying
141 > Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using
142 > a rigid three-site model developed by Straub and Karplus for studying
143   photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and
144   Pt-CO cross interactions were parameterized as part of this work.
145    
# Line 174 | Line 151 | parameter sets. The glue model of Ercolessi et al. is
151   methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98}
152   but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and
153   the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler
154 < parameter sets. The glue model of Ercolessi et al. is among the
155 < fastest of these density functional approaches.\cite{Ercolessi88} In
156 < all of these models, atoms are conceptualized as a positively charged
157 < core with a radially-decaying valence electron distribution. To
158 < calculate the energy for embedding the core at a particular location,
159 < the electron density due to the valence electrons at all of the other
160 < atomic sites is computed at atom $i$'s location,
154 > parameter sets. The glue model of Ercolessi {\it et
155 >  al}.\cite{Ercolessi88} is among the fastest of these density
156 > functional approaches. In all of these models, atoms are treated as a
157 > positively charged core with a radially-decaying valence electron
158 > distribution. To calculate the energy for embedding the core at a
159 > particular location, the electron density due to the valence electrons
160 > at all of the other atomic sites is computed at atom $i$'s location,
161   \begin{equation*}
162   \bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
163   \end{equation*}
# Line 207 | Line 184 | properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007
184   The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials
185   have all been widely used by the materials simulation community for
186   simulations of bulk and nanoparticle
187 < properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq}
187 > properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq,mishin99:_inter}
188   melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
189 < fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack
190 < propagation,\cite{BECQUART:1993rg} and alloying
191 < dynamics.\cite{Shibata:2002hh} One of EAM's strengths
192 < is its sensitivity to small changes in structure. This arises
193 < from the original parameterization, where the interactions
194 < up to the third nearest neighbor were taken into account.\cite{Voter95a}
195 < Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88}
196 < which is only parameterized up to the nearest-neighbor
197 < interactions, EAM is a suitable choice for systems where
198 < the bulk properties are of secondary importance to low-index
199 < surface structures. Additionally, the similarity of EAMs functional
200 < treatment of the embedding energy to standard density functional
201 < theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier.
202 < \cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  
189 > fracture,\cite{Shastry:1996qg,Shastry:1998dx,mishin01:cu} crack
190 > propagation,\cite{BECQUART:1993rg,Rifkin1992} and alloying
191 > dynamics.\cite{Shibata:2002hh,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
192 > One of EAM's strengths is its sensitivity to small changes in
193 > structure. This is due to the inclusion of up to the third nearest
194 > neighbor interactions during fitting of the parameters.\cite{Voter95a}
195 > In comparison, the glue model of Ercolessi {\it et
196 >  al}.\cite{Ercolessi88} was only parameterized to include
197 > nearest-neighbor interactions, EAM is a suitable choice for systems
198 > where the bulk properties are of secondary importance to low-index
199 > surface structures. Additionally, the similarity of EAM's functional
200 > treatment of the embedding energy to standard density functional
201 > theory (DFT) makes fitting DFT-derived cross potentials with
202 > adsorbates somewhat easier.
203  
227 –
228 –
229 –
204   \subsection{Carbon Monoxide model}
205 < Previous explanations for the surface rearrangements center on
206 < the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010}  
207 < We used a model first proposed by Karplus and Straub to study
208 < the photodissociation of CO from myoglobin because it reproduces
209 < the quadrupole moment well.\cite{Straub} The Straub and
210 < Karplus model treats CO as a rigid three site molecule with a massless M
211 < site at the molecular center of mass. The geometry and interaction
212 < parameters are reproduced in Table~\ref{tab:CO}. The effective
213 < dipole moment, calculated from the assigned charges, is still
214 < small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
215 < to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
205 > Previous explanations for the surface rearrangements center on the
206 > large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} We
207 > used a model first proposed by Karplus and Straub to study the
208 > photodissociation of CO from myoglobin because it reproduces the
209 > quadrupole moment well.\cite{Straub} The Straub and Karplus model
210 > treats CO as a rigid three site molecule with a massless
211 > charge-carrying ``M'' site at the center of mass. The geometry and
212 > interaction parameters are reproduced in Table~\ref{tab:CO}. The
213 > effective dipole moment, calculated from the assigned charges, is
214 > still small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is
215 > close to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
216   mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
217   %CO Table
218   \begin{table}[H]
219    \caption{Positions, Lennard-Jones parameters ($\sigma$ and
220 <    $\epsilon$), and charges for the CO-CO
221 <    interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are
222 <    in kcal/mol, and charges are in atomic units.}
220 >    $\epsilon$), and charges for CO-CO
221 >    interactions. Distances are in \AA, energies are
222 >    in kcal/mol, and charges are in atomic units.  The CO model
223 >    from Ref.\bibpunct{}{}{,}{n}{}{,}
224 >    \protect\cite{Straub} was used without modification.}
225   \centering
226   \begin{tabular}{| c | c | ccc |}
227   \hline
# Line 272 | Line 248 | et al.,\cite{Pons:1986} the Pt-C interaction was fit t
248   position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}.
249   The modified parameters yield binding energies that are slightly higher
250   than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski
251 < et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
252 < Lennard-Jones interaction to mimic strong, but short-ranged partial
251 > {\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
252 > Lennard-Jones interaction to mimic strong, but short-ranged, partial
253   binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The
254   Pt-O interaction was modeled with a Morse potential with a large
255   equilibrium distance, ($r_o$).  These choices ensure that the C is preferred
256 < over O as the surface-binding atom. In most cases, the Pt-O parameterization contributes a weak
256 > over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak
257   repulsion which favors the atop site.  The resulting potential-energy
258   surface suitably recovers the calculated Pt-C separation length
259   (1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding
# Line 291 | Line 267 | periodic supercell plane-wave basis approach, as imple
267   The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations.
268   Adsorption energies were obtained from gas-surface DFT calculations with a
269   periodic supercell plane-wave basis approach, as implemented in the
270 < {\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were
270 > Quantum ESPRESSO package.\cite{QE-2009} Electron cores were
271   described with the projector augmented-wave (PAW)
272   method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
273   included to an energy cutoff of 20 Ry. Electronic energies are
# Line 314 | Line 290 | and polarization are neglected in this model, although
290   The parameters employed for the metal-CO cross-interactions in this work
291   are shown in Table~\ref{tab:co_parameters} and the binding energies on the
292   (111) surfaces are displayed in Table~\ref{tab:co_energies}.  Charge transfer
293 < and polarization are neglected in this model, although these effects are likely to
294 < affect binding energies and binding site preferences, and will be addressed in
319 < future work.
293 > and polarization are neglected in this model, although these effects could have
294 > an effect on binding energies and binding site preferences.
295  
296   %Table  of Parameters
297   %Pt Parameter Set 9
298   %Au Parameter Set 35
299   \begin{table}[H]
300 <  \caption{Best fit parameters for metal-CO cross-interactions. Metal-C
301 <    interactions are modeled with Lennard-Jones potentials. While the
302 <    metal-O interactions were fit to Morse
300 >  \caption{Parameters for the metal-CO cross-interactions. Metal-C
301 >    interactions are modeled with Lennard-Jones potentials, while the
302 >    metal-O interactions were fit to broad Morse
303      potentials.  Distances are given in \AA~and energies in kcal/mol. }
304   \centering
305   \begin{tabular}{| c | cc | c | ccc |}
# Line 360 | Line 335 | dimensions of 57.4~x~51.9285~x~100~\AA.
335   \subsection{Pt(557) and Au(557) metal interfaces}
336   Our Pt system is an orthorhombic periodic box of dimensions
337   54.482~x~50.046~x~120.88~\AA~while our Au system has
338 < dimensions of 57.4~x~51.9285~x~100~\AA.
338 > dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs
339 > are 9 and 8 atoms deep respectively, corresponding to a slab
340 > thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
341   The systems are arranged in a FCC crystal that have been cut
342   along the (557) plane so that they are periodic in the {\it x} and
343   {\it y} directions, and have been oriented to expose two aligned
# Line 369 | Line 346 | The different bulk melting temperatures (1345~$\pm$~10
346   1200~K were performed to confirm the relative
347   stability of the surfaces without a CO overlayer.  
348  
349 < The different bulk melting temperatures (1345~$\pm$~10~K for Au\cite{Au:melting}
350 < and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at
351 < different temperatures for the two metals.  The bare Au and Pt surfaces were
352 < initially run in the canonical (NVT) ensemble at 800~K and 1000~K
353 < respectively for 100 ps. The two surfaces were relatively stable at these
354 < temperatures when no CO was present, but experienced increased surface
355 < mobility on addition of CO. Each surface was then dosed with different concentrations of CO
356 < that was initially placed in the vacuum region.  Upon full adsorption,
357 < these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
358 < coverage. Higher coverages resulted in the formation of a double layer of CO,
359 < which introduces artifacts that are not relevant to (557) reconstruction.
360 < Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
361 < the Au surfaces often had a significant CO population in the gas
362 < phase.  These systems were allowed to reach thermal equilibrium (over
363 < 5~ns) before being run in the microcanonical (NVE) ensemble for
364 < data collection. All of the systems examined had at least 40~ns in the
365 < data collection stage, although simulation times for some Pt of the
366 < systems exceeded 200~ns.  Simulations were carried out using the open
367 < source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}
349 > The different bulk melting temperatures predicted by EAM
350 > (1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for
351 > Pt\cite{Pt:melting}) suggest that any reconstructions should happen at
352 > different temperatures for the two metals.  The bare Au and Pt
353 > surfaces were initially run in the canonical (NVT) ensemble at 800~K
354 > and 1000~K respectively for 100 ps. The two surfaces were relatively
355 > stable at these temperatures when no CO was present, but experienced
356 > increased surface mobility on addition of CO. Each surface was then
357 > dosed with different concentrations of CO that was initially placed in
358 > the vacuum region.  Upon full adsorption, these concentrations
359 > correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher
360 > coverages resulted in the formation of a double layer of CO, which
361 > introduces artifacts that are not relevant to (557) reconstruction.
362 > Because of the difference in binding energies, nearly all of the CO
363 > was bound to the Pt surface, while the Au surfaces often had a
364 > significant CO population in the gas phase.  These systems were
365 > allowed to reach thermal equilibrium (over 5~ns) before being run in
366 > the microcanonical (NVE) ensemble for data collection. All of the
367 > systems examined had at least 40~ns in the data collection stage,
368 > although simulation times for some Pt of the systems exceeded 200~ns.
369 > Simulations were carried out using the open source molecular dynamics
370 > package, OpenMD.\cite{Ewald,OOPSE,openmd}
371  
372  
393 –
394 –
373   % RESULTS
374   %
375   \section{Results}
376   \subsection{Structural remodeling}
377 < The surfaces of both systems, upon dosage of CO, began
378 < to undergo extensive remodeling that was not observed in the bare
379 < systems. The bare metal surfaces
380 < experienced minor roughening of the step-edge because
381 < of the elevated temperatures, but the
382 < (557) lattice was well-maintained throughout the simulation
383 < time. The Au systems were limited to greater amounts of
384 < roughening, i.e. breakup of the step-edge, and some step
385 < wandering. The lower coverage Pt systems experienced
386 < similar restructuring but to a greater extent when
387 < compared to the Au systems. The 50\% coverage
410 < Pt system was unique among our simulations in that it
411 < formed numerous double layers through step coalescence,
412 < similar to results reported by Tao et al.\cite{Tao:2010}
377 > The bare metal surfaces experienced minor roughening of the step-edge
378 > because of the elevated temperatures, but the (557) face was stable
379 > throughout the simulations. The surfaces of both systems, upon dosage
380 > of CO, began to undergo extensive remodeling that was not observed in
381 > the bare systems. Reconstructions of the Au systems were limited to
382 > breakup of the step-edges and some step wandering. The lower coverage
383 > Pt systems experienced similar step edge wandering but to a greater
384 > extent. The 50\% coverage Pt system was unique among our simulations
385 > in that it formed well-defined and stable double layers through step
386 > coalescence, similar to results reported by Tao {\it et
387 >  al}.\cite{Tao:2010}
388  
414 –
389   \subsubsection{Step wandering}
390 < The 0\% coverage surfaces for both metals showed minimal
391 < movement at their respective run temperatures. As the CO
392 < coverage increased however, the mobility of the surface,
393 < described through adatom diffusion and step-edge wandering,
394 < also increased.  Except for the 50\% Pt system, the step-edges
395 < did not coalesce in any of the other simulations, instead
396 < preferring to keep nearly the same distance between steps
397 < as in the original (557) lattice, $\sim$13\AA for Pt and $\sim$14\AA for Au.
398 < Previous work by Williams et al.\cite{Williams:1991, Williams:1994}
399 < highlights the repulsion that exists between step-edges even
400 < when no direct interactions are present in the system. This
401 < repulsion arises because step-edge crossing is not allowed
402 < which constrains the entropy. This entropic repulsion does
403 < not completely define the interactions between steps, which
404 < is why some surfaces will undergo step coalescence, where
405 < additional attractive interactions can overcome the repulsion.\cite{Williams:1991}
406 < The presence and concentration of adsorbates, as shown in
407 < this work, can affect these step interactions, potentially leading
434 < to a new surface structure as the thermodynamic minimum.
390 > The bare surfaces for both metals showed minimal step-wandering at
391 > their respective temperatures. As the CO coverage increased however,
392 > the mobility of the surface atoms, described through adatom diffusion
393 > and step-edge wandering, also increased.  Except for the 50\% Pt
394 > system where step coalescence occurred, the step-edges in the other
395 > simulations preferred to keep nearly the same distance between steps
396 > as in the original (557) lattice, $\sim$13\AA~for Pt and
397 > $\sim$14\AA~for Au.  Previous work by Williams {\it et
398 >  al}.\cite{Williams:1991, Williams:1994} highlights the repulsion
399 > that exists between step-edges even when no direct interactions are
400 > present in the system. This repulsion is caused by an entropic barrier
401 > that arises from the fact that steps cannot cross over one
402 > another. This entropic repulsion does not completely define the
403 > interactions between steps, however, so it is possible to observe step
404 > coalescence on some surfaces.\cite{Williams:1991} The presence and
405 > concentration of adsorbates, as shown in this work, can affect
406 > step-step interactions, potentially leading to a new surface structure
407 > as the thermodynamic equilibrium.
408  
409   \subsubsection{Double layers}
410 < Tao et al.\cite{Tao:2010} have shown experimentally that the Pt(557) surface
411 < undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010}
412 < The first involves a doubling of the step height and plateau length.
413 < Similar behavior has been seen on numerous surfaces
414 < at varying conditions: Ni(977), Si(111).\cite{Williams:1994,Williams:1991,Pearl}
415 < Of the two systems we examined, the Pt system showed a greater
416 < propensity for reconstruction when compared to the Au system
417 < because of the larger surface mobility and extent of step wandering.
418 < The amount of reconstruction is strongly correlated to the amount of CO
419 < adsorbed upon the surface.  This appears to be related to the
420 < effect that adsorbate coverage has on edge breakup and on the
421 < surface diffusion of metal adatoms. While both systems displayed
422 < step-edge wandering, only the 50\% Pt surface underwent the
423 < doubling seen by Tao et al.\cite{Tao:2010} within the time scales studied here.
424 < Over longer periods, (150~ns) two more double layers formed
425 < on this interface. Although double layer formation did not occur
426 < in the other Pt systems, they show more step-wandering and
427 < general roughening compared to their Au counterparts. The
428 < 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
429 < various times along the simulation showing the evolution of a double layer step-edge.
410 > Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the
411 > Pt(557) surface undergoes two separate reconstructions upon CO
412 > adsorption.  The first involves a doubling of the step height and
413 > plateau length.  Similar behavior has been seen on a number of
414 > surfaces at varying conditions, including Ni(977) and
415 > Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we
416 > examined, the Pt system showed a greater propensity for reconstruction
417 > because of the larger surface mobility and the greater extent of step
418 > wandering.  The amount of reconstruction was strongly correlated to
419 > the amount of CO adsorbed upon the surface.  This appears to be
420 > related to the effect that adsorbate coverage has on edge breakup and
421 > on the surface diffusion of metal adatoms. Only the 50\% Pt surface
422 > underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within
423 > the time scales studied here.  Over a longer time scale (150~ns) two
424 > more double layers formed on this surface. Although double layer
425 > formation did not occur in the other Pt systems, they exhibited more
426 > step-wandering and roughening compared to their Au counterparts. The
427 > 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
428 > various times along the simulation showing the evolution of a double
429 > layer step-edge.
430  
431 < The second reconstruction on the Pt(557) surface observed by
432 < Tao involved the formation of triangular clusters that stretched
433 < across the plateau between two step-edges. Neither system, within
434 < the 40~ns time scale or the extended simulation time of 150~ns for
435 < the 50\% Pt system, experienced this reconstruction.
431 > The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010}
432 > involved the formation of triangular clusters that stretched across
433 > the plateau between two step-edges. Neither of the simulated metal
434 > interfaces, within the 40~ns time scale or the extended time of 150~ns
435 > for the 50\% Pt system, experienced this reconstruction.
436  
437   %Evolution of surface
438   \begin{figure}[H]
439 < \includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
440 < \caption{The Pt(557) / 50\% CO system at a sequence of times after
441 <  initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and
442 <  (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly.  The
439 > \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation}
440 > \caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a)
441 >  258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after
442 >  exposure. Disruption of the (557) step-edges occurs quickly.  The
443    doubling of the layers appears only after two adjacent step-edges
444    touch.  The circled spot in (b) nucleated the growth of the double
445    step observed in the later configurations.}
# Line 474 | Line 447 | Previous atomistic simulations of stepped surfaces dea
447   \end{figure}
448  
449   \subsection{Dynamics}
450 < Previous atomistic simulations of stepped surfaces dealt largely
451 < with the energetics and structures at different conditions.
452 < \cite{Williams:1991,Williams:1994} Consequently, the most common
453 < technique utilized to date has been Monte Carlo sampling. Monte Carlo approaches give an efficient
454 < sampling of the equilibrium thermodynamic landscape at the expense
455 < of ignoring the dynamics of the system. Previous experimental work by Pearl and
456 < Sibener\cite{Pearl}, using STM, has been able to capture the coalescing
457 < of steps on Ni(977). The time scale of the image acquisition,
485 < $\sim$70~s/image provides an upper bound for the time required for
486 < the doubling to occur. By utilizing Molecular Dynamics we were able to probe the dynamics of these reconstructions and in this section we give data on dynamic and
487 < transport properties, e.g. diffusion, layer formation time, etc.
450 > Previous experimental work by Pearl and Sibener\cite{Pearl}, using
451 > STM, has been able to capture the coalescence of steps on Ni(977). The
452 > time scale of the image acquisition, $\sim$70~s/image, provides an
453 > upper bound for the time required for the doubling to occur. By
454 > utilizing Molecular Dynamics we are able to probe the dynamics of
455 > these reconstructions at elevated temperatures and in this section we
456 > provide data on the timescales for transport properties,
457 > e.g. diffusion and layer formation time.
458  
459  
460   \subsubsection{Transport of surface metal atoms}
461   %forcedSystems/stepSeparation
492 – The movement or wandering of a step-edge is a cooperative effect
493 – arising from the individual movements of the atoms making up the steps. An ideal metal surface
494 – displaying a low index facet, (111) or (100), is unlikely to experience
495 – much surface diffusion because of the large energetic barrier that must
496 – be overcome to lift an atom out of the surface. The presence of step-edges and other surface features
497 – on higher-index facets provides a lower energy source for mobile metal atoms.
498 – Breaking away from the step-edge on a clean surface still imposes an
499 – energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting
500 – the same metal atom vertically out of the surface,  \textgreater~60 kcal/mol.
501 – The penalty lowers significantly when CO is present in sufficient quantities
502 – on the surface. For certain distributions of CO, see Figures \ref{fig:SketchGraphic} and \ref{fig:SketchEnergies}, the penalty can fall to as low as
503 – $\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for
504 – diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are then
505 – able to explore the terrace before rejoining either their original step-edge or
506 – becoming a part of a different edge. It is a difficult process for an atom
507 – to traverse to a separate terrace although the presence of CO can lower the
508 – energy barrier required to lift or lower an adatom. By tracking the mobility of individual
509 – metal atoms on the Pt and Au surfaces we were able to determine the relative
510 – diffusion constants, as well as how varying coverages of CO affect the diffusion. Close
511 – observation of the mobile metal atoms showed that they were typically in
512 – equilibrium with the step-edges, dynamically breaking apart and rejoining the edges.
513 – At times, their motion was concerted and two or more adatoms would be
514 – observed moving together across the surfaces.
462  
463 < A particle was considered ``mobile'' once it had traveled more than 2~\AA~
464 < between saved configurations of the system (typically 10-100 ps). An atom that was
465 < truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff
466 < was used to prevent swamping the diffusion data with the in-place vibrational
467 < movement of buried atoms. Diffusion on a surface is strongly affected by
468 < local structures and in this work, the presence of single and double layer
469 < step-edges causes the diffusion parallel to the step-edges to be larger than
470 < the diffusion perpendicular to these edges. Parallel and perpendicular
471 < diffusion constants are shown in Figure \ref{fig:diff}.
463 > The wandering of a step-edge is a cooperative effect arising from the
464 > individual movements of the atoms making up the steps. An ideal metal
465 > surface displaying a low index facet, (111) or (100), is unlikely to
466 > experience much surface diffusion because of the large energetic
467 > barrier that must be overcome to lift an atom out of the surface. The
468 > presence of step-edges and other surface features on higher-index
469 > facets provides a lower energy source for mobile metal atoms.  Using
470 > our potential model, single-atom break-away from a step-edge on a
471 > clean surface still imposes an energetic penalty around
472 > $\sim$~45~kcal/mol, but this is certainly easier than lifting the same
473 > metal atom vertically out of the surface, \textgreater~60~kcal/mol.
474 > The penalty lowers significantly when CO is present in sufficient
475 > quantities on the surface. For certain distributions of CO, the
476 > energetic penalty can fall to as low as $\sim$~20~kcal/mol. The
477 > configurations that create these lower barriers are detailed in the
478 > discussion section below.
479  
480 + Once an adatom exists on the surface, the barrier for diffusion is
481 + negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are
482 + then able to explore the terrace before rejoining either their
483 + original step-edge or becoming a part of a different edge. It is an
484 + energetically unfavorable process with a high barrier for an atom to
485 + traverse to a separate terrace although the presence of CO can lower
486 + the energy barrier required to lift or lower an adatom. By tracking
487 + the mobility of individual metal atoms on the Pt and Au surfaces we
488 + were able to determine the relative diffusion constants, as well as
489 + how varying coverages of CO affect the diffusion. Close observation of
490 + the mobile metal atoms showed that they were typically in equilibrium
491 + with the step-edges.  At times, their motion was concerted, and two or
492 + more adatoms would be observed moving together across the surfaces.
493 +
494 + A particle was considered ``mobile'' once it had traveled more than
495 + 2~\AA~ between saved configurations of the system (typically 10-100
496 + ps). A mobile atom would typically travel much greater distances than
497 + this, but the 2~\AA~cutoff was used to prevent swamping the diffusion
498 + data with the in-place vibrational movement of buried atoms. Diffusion
499 + on a surface is strongly affected by local structures and the presence
500 + of single and double layer step-edges causes the diffusion parallel to
501 + the step-edges to be larger than the diffusion perpendicular to these
502 + edges. Parallel and perpendicular diffusion constants are shown in
503 + Figure \ref{fig:diff}.  Diffusion parallel to the step-edge is higher
504 + than diffusion perpendicular to the edge because of the lower energy
505 + barrier associated with sliding along an edge compared to breaking
506 + away to form an isolated adatom.
507 +
508   %Diffusion graph
509   \begin{figure}[H]
510 < \includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf}
510 > \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1}
511   \caption{Diffusion constants for mobile surface atoms along directions
512    parallel ($\mathbf{D}_{\parallel}$) and perpendicular
513    ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
514 <  surface coverage.  Diffusion parallel to the step-edge is higher
515 <  than that perpendicular to the edge because of the lower energy
516 <  barrier associated with traversing along the edge as compared to
517 <  completely breaking away. The two reported diffusion constants for
536 <  the 50\% Pt system arise from different sample sets. The lower values
537 <  correspond to the same 40~ns amount that all of the other systems were
538 <  examined at, while the larger values correspond to a 20~ns period }
514 >  surface coverage.  The two reported diffusion constants for the 50\%
515 >  Pt system correspond to a 20~ns period before the formation of the
516 >  double layer (upper points), and to the full 40~ns sampling period
517 >  (lower points).}
518   \label{fig:diff}
519   \end{figure}
520  
521 < The lack of a definite trend in the Au diffusion data in Figure \ref{fig:diff} is likely due
522 < to the weaker bonding between Au and CO. This leads to a lower observed
523 < coverage ({\it x}-axis) when compared to dosage amount, which
524 < then further limits the effect the CO can have on surface diffusion. The correlation
525 < between coverage and Pt diffusion rates conversely shows a
526 < definite trend marred by the highest coverage surface. Two
527 < explanations arise for this drop. First, upon a visual inspection of
528 < the system, after a double layer has been formed, it maintains its
529 < stability strongly and many atoms that had been tracked for mobility
530 < data have now been buried. By performing the same diffusion
531 < calculation but on a shorter run time (20~ns), only including data
532 < before the formation of the first double layer, we obtain the larger
533 < values for both $\mathbf{D}_{\parallel}$ and $\mathbf{D}_{\perp}$
534 < at the 50\% coverage as seen in Figure \ref{fig:diff}.
556 < This places the parallel diffusion constant more closely in line with the
557 < expected trend, while the perpendicular diffusion constant does not
558 < drop as far. A secondary explanation arising from our analysis of the
559 < mechanism of double layer formation focuses on the effect that CO on the
560 < surface has with respect to overcoming surface diffusion of Pt. If the
561 < coverage is too sparse, the Pt engages in minimal interactions and
562 < thus minimal diffusion. As coverage increases, there are more favorable
563 < arrangements of CO on the surface allowing for the formation of a path,
564 < a minimum energy trajectory, for the adatom to explore the surface.
565 < As the CO is constantly moving on the surface, this path is constantly
566 < changing. If the coverage becomes too great, the paths could
567 < potentially be clogged leading to a decrease in diffusion despite
568 < their being more adatoms and step-wandering.
569 <
570 <
571 <
521 > The weaker Au-CO interaction is evident in the weak CO-coverage
522 > dependance of Au diffusion. This weak interaction leads to lower
523 > observed coverages when compared to dosage amounts. This further
524 > limits the effect the CO can have on surface diffusion. The correlation
525 > between coverage and Pt diffusion rates shows a near linear relationship
526 > at the earliest times in the simulations. Following double layer formation,
527 > however, there is a precipitous drop in adatom diffusion. As the double
528 > layer forms, many atoms that had been tracked for mobility data have
529 > now been buried, resulting in a smaller reported diffusion constant. A
530 > secondary effect of higher coverages is CO-CO cross interactions that
531 > lower the effective mobility of the Pt adatoms that are bound to each CO.
532 > This effect would become evident only at higher coverages. A detailed
533 > account of Pt adatom energetics follows in the Discussion.
534 >
535   \subsubsection{Dynamics of double layer formation}
536 < The increased diffusion on Pt at the higher CO coverages
537 < plays a primary role in double layer formation. However,
538 < this is not a complete explanation -- the 33\%~Pt system
539 < has higher diffusion constants but did not show any signs
540 < of edge doubling in the observed run time. On the
541 < 50\%~Pt system, one layer formed within the first 40~ns
542 < of simulation time, while two more were formed as the
543 < system was allowed to run for an additional
544 < 110~ns (150~ns total). This suggests that this reconstruction is
545 < a rapid process and that the previously mentioned upper bound
546 < will be lowered as experimental techniques continue to improve.\cite{Williams:1991,Pearl}
547 < In this system, as seen in Figure \ref{fig:reconstruct}, the first
548 < appearance of a double layer, appears at 19~ns
549 < into the simulation. Within 12~ns of this nucleation event, nearly half of the step has
550 < formed the double layer and by 86~ns, the complete layer
551 < has been flattened out. The double layer could be considered
552 < ``complete" by 37~ns but remains a bit rough. From the
553 < appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another
554 < $\sim$40~ns was necessary for the layer to completely straighten.
555 < The other two layers in this simulation formed over periods of
556 < 22~ns and 42~ns respectively. A possible explanation
557 < for this rapid reconstruction is the elevated temperatures
595 < under which our systems were simulated. It is probable that the process would
596 < take longer at lower temperatures. Additionally, our measured times for completion
597 < of the doubling after the appearance of a nucleation site are likely affected by our
598 < constrained axes. A longer step-edge will likely take longer to ``zipper''. However,
599 < the first appearance of a nucleation site will likely occur more quickly due to its stochastic nature.
536 > The increased diffusion on Pt at the higher CO coverages is the primary
537 > contributor to double layer formation. However, this is not a complete
538 > explanation -- the 33\%~Pt system has higher diffusion constants, but
539 > did not show any signs of edge doubling in 40~ns. On the 50\%~Pt
540 > system, one double layer formed within the first 40~ns of simulation time,
541 > while two more were formed as the system was allowed to run for an
542 > additional 110~ns (150~ns total). This suggests that this reconstruction
543 > is a rapid process and that the previously mentioned upper bound is a
544 > very large overestimate.\cite{Williams:1991,Pearl} In this system the first
545 > appearance of a double layer appears at 19~ns into the simulation.
546 > Within 12~ns of this nucleation event, nearly half of the step has formed
547 > the double layer and by 86~ns the complete layer has flattened out.
548 > From the appearance of the first nucleation event to the first observed
549 > double layer, the process took $\sim$20~ns. Another $\sim$40~ns was
550 > necessary for the layer to completely straighten. The other two layers in
551 > this simulation formed over periods of 22~ns and 42~ns respectively.
552 > A possible explanation for this rapid reconstruction is the elevated
553 > temperatures under which our systems were simulated. The process
554 > would almost certainly take longer at lower temperatures. Additionally,
555 > our measured times for completion of the doubling after the appearance
556 > of a nucleation site are likely affected by our periodic boxes. A longer
557 > step-edge will likely take longer to ``zipper''.
558  
559  
560 + %Discussion
561 + \section{Discussion}
562 + We have shown that a classical potential is able to model the initial
563 + reconstruction of the Pt(557) surface upon CO adsorption, and have
564 + reproduced the double layer structure observed by Tao {\it et
565 +  al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be
566 + rapid -- occurring within 100 ns of the initial exposure to CO.  Here
567 + we discuss the features of the classical potential that are
568 + contributing to the stability and speed of the Pt(557) reconstruction.
569  
570 + \subsection{Diffusion}
571 + The perpendicular diffusion constant appears to be the most important
572 + indicator of double layer formation. As highlighted in Figure
573 + \ref{fig:reconstruct}, the formation of the double layer did not begin
574 + until a nucleation site appeared.  Williams {\it et
575 +  al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge
576 + repulsion arising from the inability of edge crossing.  This repulsion
577 + must be overcome to allow step coalescence.  A larger
578 + $\textbf{D}_\perp$ value implies more step-wandering and a larger
579 + chance for the stochastic meeting of two edges to create a nucleation
580 + point.  Diffusion parallel to the step-edge can help ``zipper'' up a
581 + nascent double layer. This helps explain the rapid time scale for
582 + double layer completion after the appearance of a nucleation site, while
583 + the initial appearance of the nucleation site was unpredictable.
584  
585 + \subsection{Mechanism for restructuring}
586 + Since the Au surface showed no large scale restructuring in any of our
587 + simulations, our discussion will focus on the 50\% Pt-CO system which
588 + did exhibit doubling. A number of possible mechanisms exist to explain
589 + the role of adsorbed CO in restructuring the Pt surface. Quadrupolar
590 + repulsion between adjacent CO molecules adsorbed on the surface is one
591 + possibility.  However, the quadrupole-quadrupole interaction is
592 + short-ranged and is attractive for some orientations.  If the CO
593 + molecules are ``locked'' in a vertical orientation, through atop
594 + adsorption for example, this explanation would gain credence. Within
595 + the framework of our classical potential, the calculated energetic
596 + repulsion between two CO molecules located a distance of
597 + 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a
598 + vertical orientation, is 8.62 kcal/mol. Moving the CO to the second
599 + nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly
600 + 0. Allowing the CO to rotate away from a purely vertical orientation
601 + also lowers the repulsion. When the carbons are locked at a distance
602 + of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle
603 + between the 2 CO is $\sim$24\textsuperscript{o}.  The calculated
604 + barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
605 + repulsion between adjacent CO molecules bound to Pt could indeed
606 + increase the surface diffusion. However, the residence time of CO on
607 + Pt suggests that the CO molecules are extremely mobile, with diffusion
608 + constants 40 to 2500 times larger than surface Pt atoms. This mobility
609 + suggests that the CO molecules jump between different Pt atoms
610 + throughout the simulation.  However, they do stay bound to individual
611 + Pt atoms for long enough to modify the local energy landscape for the
612 + mobile adatoms.
613  
614 + A different interpretation of the above mechanism which takes the
615 + large mobility of the CO into account, would be in the destabilization
616 + of Pt-Pt interactions due to bound CO.  Destabilizing Pt-Pt bonds at
617 + the edges could lead to increased step-edge breakup and diffusion. On
618 + the bare Pt(557) surface the barrier to completely detach an edge atom
619 + is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
620 + \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain
621 + configurations, cases (e), (g), and (h), the barrier can be lowered to
622 + $\sim$23~kcal/mol by the presence of bound CO molecules. In these
623 + instances, it becomes energetically favorable to roughen the edge by
624 + introducing a small separation of 0.5 to 1.0~\AA. This roughening
625 + becomes immediately obvious in simulations with significant CO
626 + populations. The roughening is present to a lesser extent on surfaces
627 + with lower CO coverage (and even on the bare surfaces), although in
628 + these cases it is likely due to random fluctuations that squeeze out
629 + step-edge atoms. Step-edge breakup by direct single-atom translations
630 + (as suggested by these energy curves) is probably a worst-case
631 + scenario.  Multistep mechanisms in which an adatom moves laterally on
632 + the surface after being ejected would be more energetically favorable.
633 + This would leave the adatom alongside the ledge, providing it with
634 + five nearest neighbors.  While fewer than the seven neighbors it had
635 + as part of the step-edge, it keeps more Pt neighbors than the three
636 + neighbors an isolated adatom has on the terrace. In this proposed
637 + mechanism, the CO quadrupolar repulsion still plays a role in the
638 + initial roughening of the step-edge, but not in any long-term bonds
639 + with individual Pt atoms.  Higher CO coverages create more
640 + opportunities for the crowded CO configurations shown in Figure
641 + \ref{fig:SketchGraphic}, and this is likely to cause an increased
642 + propensity for step-edge breakup.
643  
644   %Sketch graphic of different configurations
645   \begin{figure}[H]
646 < \includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf}
647 < \caption{The dark grey atoms refer to the upper ledge, while the white atoms are
648 < the lower terrace. The blue highlighted atoms had a CO in a vertical atop position
649 < upon them. These are a sampling of the configurations examined to gain a more
650 < complete understanding of the effects CO has on surface diffusion and edge breakup.
651 < Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.}
646 > \includegraphics[width=\linewidth]{COpaths}
647 > \caption{Configurations used to investigate the mechanism of step-edge
648 >  breakup on Pt(557). In each case, the central (starred) atom was
649 >  pulled directly across the surface away from the step edge.  The Pt
650 >  atoms on the upper terrace are colored dark grey, while those on the
651 >  lower terrace are in white.  In each of these configurations, some
652 >  of the atoms (highlighted in blue) had CO molecules bound in the
653 >  vertical atop position.  The energies of these configurations as a
654 >  function of central atom displacement are displayed in Figure
655 >  \ref{fig:SketchEnergies}.}
656   \label{fig:SketchGraphic}
657   \end{figure}
658  
659   %energy graph corresponding to sketch graphic
660   \begin{figure}[H]
661 < \includegraphics[width=\linewidth]{stepSeparationComparison.pdf}
662 < \caption{The energy curves directly correspond to the labeled model
663 < surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative
664 < to their initial configuration so the energy of a and h do not have the
665 < same zero value. As is seen, certain arrangements of CO can lower
666 < the energetic barrier that must be overcome to create an adatom.
667 < However, it is the highest coverages where these higher-energy
668 < configurations of CO will be more likely. }
661 > \includegraphics[width=\linewidth]{Portrait_SeparationComparison}
662 > \caption{Energies for displacing a single edge atom perpendicular to
663 >  the step edge as a function of atomic displacement. Each of the
664 >  energy curves corresponds to one of the labeled configurations in
665 >  Figure \ref{fig:SketchGraphic}, and the energies are referenced to
666 >  the unperturbed step-edge.  Certain arrangements of bound CO
667 >  (notably configurations g and h) can lower the energetic barrier for
668 >  creating an adatom relative to the bare surface (configuration a).}
669   \label{fig:SketchEnergies}
670   \end{figure}
671  
672 < %Discussion
673 < \section{Discussion}
674 < We have shown that the classical potential models are able to model the initial reconstruction of the
675 < Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we
676 < were able to observe features of the dynamic processes necessary for this reconstruction.
672 > While configurations of CO on the surface are able to increase
673 > diffusion and the likelihood of edge wandering, this does not provide
674 > a complete explanation for the formation of double layers. If adatoms
675 > were constrained to their original terraces then doubling could not
676 > occur.  A mechanism for vertical displacement of adatoms at the
677 > step-edge is required to explain the doubling.
678  
679 < \subsection{Diffusion}
680 < As shown in Figure \ref{fig:diff}, for the Pt systems, there
681 < is a strong trend toward higher diffusion constants as
682 < surface coverage of CO increases. The drop for the 50\%
683 < case being explained as double layer formation already
684 < beginning to occur in the analyzed 40~ns, which lowered
685 < the calculated diffusion rates. Between the parallel and
686 < perpendicular rates, the perpendicular diffusion constant
687 < appears to be the most important indicator of double layer
688 < formation. As highlighted in Figure \ref{fig:reconstruct}, the
689 < formation of the double layer did not begin until a nucleation
690 < site appeared. And as mentioned by Williams et al.\cite{Williams:1991, Williams:1994},
691 < the inability for edges to cross leads to an effective repulsion.
692 < This repulsion must be overcome to allow step coalescence.
693 < A greater $\textbf{D}_\perp$ implies more step-wandering
694 < and a larger chance for the stochastic meeting of two edges
695 < to form the nucleation point. Upon that appearance, parallel
696 < diffusion along the step-edge can help ``zipper'' up the double
654 < layer. This helps explain why the time scale for formation after
655 < the appearance of a nucleation site was rapid, while the initial
656 < appearance of said site was unpredictable.
679 > We have discovered one possible mechanism for a CO-mediated vertical
680 > displacement of Pt atoms at the step edge. Figure \ref{fig:lambda}
681 > shows four points along a reaction coordinate in which a CO-bound
682 > adatom along the step-edge ``burrows'' into the edge and displaces the
683 > original edge atom onto the higher terrace.  A number of events
684 > similar to this mechanism were observed during the simulations.  We
685 > predict an energetic barrier of 20~kcal/mol for this process (in which
686 > the displaced edge atom follows a curvilinear path into an adjacent
687 > 3-fold hollow site).  The barrier heights we obtain for this reaction
688 > coordinate are approximate because the exact path is unknown, but the
689 > calculated energy barriers would be easily accessible at operating
690 > conditions.  Additionally, this mechanism is exothermic, with a final
691 > energy 15~kcal/mol below the original $\lambda = 0$ configuration.
692 > When CO is not present and this reaction coordinate is followed, the
693 > process is endothermic by 3~kcal/mol.  The difference in the relative
694 > energies for the $\lambda=0$ and $\lambda=1$ case when CO is present
695 > provides strong support for CO-mediated Pt-Pt interactions giving rise
696 > to the doubling reconstruction.
697  
658 – \subsection{Mechanism for restructuring}
659 – Since the Au surface showed no large scale restructuring throughout
660 – our simulation time our discussion will focus on the 50\% Pt-CO system
661 – which did undergo the doubling featured in Figure \ref{fig:reconstruct}.
662 – Similarities of our results to those reported previously by Tao et al.\cite{Tao:2010}
663 – are quite strong. The simulated Pt system exposed to a large dosage
664 – of CO readily restructures by doubling the terrace widths and step heights.
665 – The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a
666 – time, but is rapid on experimental timescales. The adatoms either break
667 – away from the step-edge and stay on the lower terrace or they lift up onto
668 – a higher terrace. Once ``free'', they diffuse on the terrace until reaching
669 – another step-edge or rejoining their original edge. This combination of
670 – growth and decay of the step-edges is in a state of dynamic equilibrium.
671 – However, once two previously separated edges meet as shown in Figure 1.B,
672 – this nucleates the rest of the edge to meet up, forming a double layer.
673 – From simulations which exhibit a double layer, the time delay from the
674 – initial appearance of a nucleation point to a fully formed double layer is $\sim$35~ns.
675 –
676 – A number of possible mechanisms exist to explain the role of adsorbed
677 – CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent
678 – CO molecules adsorbed on the surface is one possibility.  However,
679 – the quadrupole-quadrupole interaction is short-ranged and is attractive for
680 – some orientations.  If the CO molecules are ``locked'' in a specific orientation
681 – relative to each other, through atop adsorption for example, this explanation
682 – gains some credence. The energetic repulsion between two CO located a
683 – distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in
684 – a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second
685 – nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to
686 – nearly 0 kcal/mol. Allowing the CO to rotate away from a purely vertical orientation
687 – also lowers the repulsion. A minimum of 6.2 kcal/mol is reached at when the
688 – angle between the 2 CO is $\sim$24\textsuperscript{o}, when the carbons are
689 – locked at a distance of 2.77 \AA apart. As mentioned above, the energy barrier
690 – for surface diffusion of a Pt adatom is only 4 kcal/mol. So this repulsion between
691 – neighboring CO molecules can increase the surface diffusion. However, the
692 – residence time of CO on Pt was examined and while the majority of the CO is
693 – on or near the surface throughout the run, the molecules are extremely mobile,
694 – with diffusion constants 40 to 2500 times larger, depending on coverage. This
695 – mobility suggests that the CO are more likely to shift their positions without
696 – necessarily the Pt along with them.
697 –
698 – Another possible and more likely mechanism for the restructuring is in the
699 – destabilization of strong Pt-Pt interactions by CO adsorbed on surface
700 – Pt atoms. To test this hypothesis, numerous configurations of
701 – CO in varying quantities were arranged on the higher and lower plateaus
702 – around a step on a otherwise clean Pt(557) surface. A few sample
703 – configurations are displayed in Figure \ref{fig:SketchGraphic}, with
704 – energies at various positions along the path displayed in Table
705 – NO TABLE. Certain configurations of CO, cases B and D for
706 – example, can have quite strong energetic reasons for breaking
707 – away from the step-edge. Although the packing of these configurations
708 – is unlikely until CO coverage has reached a high enough value.
709 – These examples are showing the most difficult cases, immediate
710 – adatom formation through breakage away from the step-edge, which
711 – is why their energies at large distances are relatively high. There are
712 – mechanistic paths where an edge atom could get shifted to onto the
713 – step-edge to form a small peak before fully breaking away. And again,
714 – once the adatom is formed, the barrier for diffusion on the surface is
715 – negligible. These sample configurations help explain CO's effect on
716 – general surface mobility and step wandering, but they are lacking in
717 – providing a mechanism for the formation of double layers. One possible
718 – mechanism is elucidated in Figure \ref{fig:lambda}, where a burrowing
719 – and lifting process of an adatom and step-edge atom respectively is
720 – examined. The system, without CO present, is nearly energetically
721 – neutral, whereas with CO present there is a $\sim$ 15 kcal/mol drop
722 – in the energy of the system.
723 –
698   %lambda progression of Pt -> shoving its way into the step
699   \begin{figure}[H]
700 < \includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png}
701 < \caption{A model system of the Pt(557) surface was used as the framework
702 < for exploring energy barriers along a reaction coordinate. Various numbers,
703 < placements, and rotations of CO were examined as they affect Pt movement.
704 < The coordinate displayed in this Figure was a representative run.  relative to the energy of the system at 0\%, there
705 < is a slight decrease upon insertion of the Pt atom into the step-edge along
706 < with the resultant lifting of the other Pt atom when CO is present at certain positions.}
700 > \includegraphics[width=\linewidth]{EPS_rxnCoord}
701 > \caption{Points along a possible reaction coordinate for CO-mediated
702 >  edge doubling. Here, a CO-bound adatom burrows into an established
703 >  step edge and displaces an edge atom onto the upper terrace along a
704 >  curvilinear path.  The approximate barrier for the process is
705 >  20~kcal/mol, and the complete process is exothermic by 15~kcal/mol
706 >  in the presence of CO, but is endothermic by 3~kcal/mol without CO.}
707   \label{fig:lambda}
708   \end{figure}
709  
710 + The mechanism for doubling on the Pt(557) surface appears to require
711 + the cooperation of at least two distinct processes. For complete
712 + doubling of a layer to occur there must be a breakup of one
713 + terrace. These atoms must then ``disappear'' from that terrace, either
714 + by travelling to the terraces above or below their original levels.
715 + The presence of CO helps explain mechanisms for both of these
716 + situations. There must be sufficient breakage of the step-edge to
717 + increase the concentration of adatoms on the surface and these adatoms
718 + must then undergo the burrowing highlighted above (or a comparable
719 + mechanism) to create the double layer.  With sufficient time, these
720 + mechanisms working in concert lead to the formation of a double layer.
721  
722 + \subsection{CO Removal and double layer stability}
723 + Once the double layers had formed on the 50\%~Pt system, they remained
724 + stable for the rest of the simulation time with minimal movement.
725 + Random fluctuations that involved small clusters or divots were
726 + observed, but these features typically healed within a few
727 + nanoseconds.  Within our simulations, the formation of the double
728 + layer appeared to be irreversible and a double layer was never
729 + observed to split back into two single layer step-edges while CO was
730 + present.
731  
732 + To further gauge the effect CO has on this surface, additional
733 + simulations were run starting from a late configuration of the 50\%~Pt
734 + system that had already formed double layers. These simulations then
735 + had their CO molecules suddenly removed.  The double layer broke apart
736 + rapidly in these simulations, showing a well-defined edge-splitting
737 + after 100~ps. Configurations of this system are shown in Figure
738 + \ref{fig:breaking}. The coloring of the top and bottom layers helps to
739 + show how much mixing the edges experience as they split. These systems
740 + were only examined for 10~ns, and within that time despite the initial
741 + rapid splitting, the edges only moved another few \AA~apart. It is
742 + possible that with longer simulation times, the (557) surface recovery
743 + observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered.
744  
739 –
745   %breaking of the double layer upon removal of CO
746   \begin{figure}[H]
747 < \includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png}
748 < \caption{(A)  0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO
749 < helped maintain the stability of the double layer and upon removal the two layers break
750 < and begin separating. The separation is not a simple pulling apart however, rather
751 < there is a mixing of the lower and upper atoms at the edge.}
747 > \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking}
748 > \caption{Behavior of an established (111) double step after removal of
749 >  the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the
750 >  removal of CO.  Nearly immediately after the CO is removed, the
751 >  step edge reforms in a (100) configuration, which is also the step
752 >  type seen on clean (557) surfaces. The step separation involves
753 >  significant mixing of the lower and upper atoms at the edge.}
754   \label{fig:breaking}
755   \end{figure}
756  
757  
751 –
752 –
758   %Peaks!
759   %\begin{figure}[H]
760   %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
# Line 763 | Line 768 | in the energy of the system.
768   %Don't think I need this
769   %clean surface...
770   %\begin{figure}[H]
771 < %\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
771 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF}
772   %\caption{}
773  
774   %\end{figure}
# Line 771 | Line 776 | In this work we have shown the reconstruction of the P
776  
777  
778   \section{Conclusion}
779 < 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.
779 > The strength and directionality of the Pt-CO binding interaction, as
780 > well as the large quadrupolar repulsion between atop-bound CO
781 > molecules, help to explain the observed increase in surface mobility
782 > of Pt(557) and the resultant reconstruction into a double-layer
783 > configuration at the highest simulated CO-coverages.  The weaker Au-CO
784 > interaction results in significantly lower adataom diffusion
785 > constants, less step-wandering, and a lack of the double layer
786 > reconstruction on the Au(557) surface.
787  
788 + An in-depth examination of the energetics shows the important role CO
789 + plays in increasing step-breakup and in facilitating edge traversal
790 + which are both necessary for double layer formation.
791 +
792   %Things I am not ready to remove yet
793  
794   %Table of Diffusion Constants
# Line 796 | Line 812 | Support for this project was provided by the National
812   % \end{table}
813  
814   \begin{acknowledgement}
815 < Support for this project was provided by the National Science
816 < Foundation under grant CHE-0848243 and by the Center for Sustainable
817 < Energy at Notre Dame (cSEND). Computational time was provided by the
818 < Center for Research Computing (CRC) at the University of Notre Dame.
815 >  We gratefully acknowledge conversations with Dr. William
816 >  F. Schneider and Dr. Feng Tao.  Support for this project was
817 >  provided by the National Science Foundation under grant CHE-0848243
818 >  and by the Center for Sustainable Energy at Notre Dame
819 >  (cSEND). Computational time was provided by the Center for Research
820 >  Computing (CRC) at the University of Notre Dame.
821   \end{acknowledgement}
822   \newpage
823 < \bibliography{firstTryBibliography}
823 > \bibstyle{achemso}
824 > \bibliography{COonPtAu}
825   %\end{doublespace}
826  
827   \begin{tocentry}
828 < %\includegraphics[height=3.5cm]{timelapse}
828 > \begin{wrapfigure}{l}{0.5\textwidth}
829 > \begin{center}
830 > \includegraphics[width=\linewidth]{TOC_doubleLayer}
831 > \end{center}
832 > \end{wrapfigure}
833 > A reconstructed Pt(557) surface after 86~ns exposure to a half a
834 > monolayer of CO.  The double layer that forms is a result of
835 > CO-mediated step-edge wandering as well as a burrowing mechanism that
836 > helps lift edge atoms onto an upper terrace.
837   \end{tocentry}
838  
839   \end{document}

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