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1 < \documentclass[11pt]{article}
1 > \documentclass[journal = jpccck, manuscript = article]{achemso}
2 > \setkeys{acs}{usetitle = true}
3 > \usepackage{achemso}
4 > \usepackage{caption}
5 > \usepackage{float}
6 > \usepackage{geometry}
7 > \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}
18 > \usepackage{tabularx}
19 > \usepackage{longtable}
20   \usepackage{graphicx}
21   \usepackage{multirow}
22 < %\usepackage{booktabs}
23 < %\usepackage{bibentry}
24 < %\usepackage{mathrsfs}
25 < %\usepackage[ref]{overcite}
26 < \usepackage[square, comma, sort&compress]{natbib}
22 > \usepackage{multicol}
23 > \mciteErrorOnUnknownfalse
24 > %\usepackage{epstopdf}
25 >
26 > \usepackage[version=3]{mhchem}  % this is a great package for formatting chemical reactions
27 > % \usepackage[square, comma, sort&compress]{natbib}
28   \usepackage{url}
29   \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
30   \evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
31 < 9.0in \textwidth 6.5in \brokenpenalty=10000
31 > 9.0in \textwidth 6.5in \brokenpenalty=1110000
32  
33   % double space list of tables and figures
34 < \AtBeginDelayedFloats{\renewcommand{\baselinestretch}{1.66}}
34 > %\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}}
35   \setlength{\abovecaptionskip}{20 pt}
36   \setlength{\belowcaptionskip}{30 pt}
37 + % \bibpunct{}{}{,}{s}{}{;}
38  
39 < %\renewcommand\citemid{\ } % no comma in optional reference note
40 < \bibpunct{[}{]}{,}{n}{}{;}
27 < \bibliographystyle{achemso}
39 > %\citestyle{nature}
40 > % \bibliographystyle{achemso}
41  
42 < \begin{document}
42 > \title{Molecular Dynamics simulations of the surface reconstructions
43 >  of Pt(557) and Au(557) under exposure to CO}
44  
45 + \author{Joseph R. Michalka}
46 + \author{Patrick W. McIntyre}
47 + \author{J. Daniel Gezelter}
48 + \email{gezelter@nd.edu}
49 + \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
50 +  Department of Chemistry and Biochemistry\\ University of Notre
51 +  Dame\\ Notre Dame, Indiana 46556}
52  
53 + \keywords{}
54 +
55 + \begin{document}
56 +
57 +
58   %%
59   %Introduction
60   %       Experimental observations
# Line 47 | Line 73
73   %Summary
74   %%
75  
50 – %Title
51 – \title{Investigation of the Pt and Au 557 Surface Reconstructions
52 –  under a CO Atmosphere}
53 – \author{Joseph R. Michalka, Patrick W. MacIntyre and J. Daniel
54 – Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\
55 – Department of Chemistry and Biochemistry,\\
56 – University of Notre Dame\\
57 – Notre Dame, Indiana 46556}
58 – %Date
59 – \date{Dec 15,  2012}
60 – %authors
76  
62 – % make the title
63 – \maketitle
64 –
65 – \begin{doublespace}
66 –
77   \begin{abstract}
78 <
78 >  The mechanism and dynamics of surface reconstructions of Pt(557) and
79 >  Au(557) exposed to various coverages of carbon monoxide (CO) were
80 >  investigated using molecular dynamics simulations. Metal-CO
81 >  interactions were parameterized from experimental data and
82 >  plane-wave Density Functional Theory (DFT) calculations.  The large
83 >  difference in binding strengths of the Pt-CO and Au-CO interactions
84 >  was found to play a significant role in step-edge stability and
85 >  adatom diffusion constants.  Various mechanisms for CO-mediated step
86 >  wandering and step doubling were investigated on the Pt(557)
87 >  surface.  We find that the energetics of CO adsorbed to the surface
88 >  can explain the step-doubling reconstruction observed on Pt(557) and
89 >  the lack of such a reconstruction on the Au(557) surface.
90   \end{abstract}
91  
92   \newpage
# Line 79 | Line 100 | Industrial catalysts usually consist of small particle
100   %       Sub: Also, easier to observe what is going on and provide reasons and explanations
101   %
102  
103 < Industrial catalysts usually consist of small particles exposing
104 < different atomic terminations that exhibit a high concentration of
105 < step, kink sites, and vacancies at the edges of the facets.  These
85 < sites are thought to be the locations of catalytic
103 > Industrial catalysts usually consist of small particles that exhibit a
104 > high concentration of steps, kink sites, and vacancies at the edges of
105 > the facets.  These sites are thought to be the locations of catalytic
106   activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now
107 < significant evidence to demonstrate that solid surfaces are often
108 < structurally, compositionally, and chemically {\it modified} by
109 < reactants under operating conditions.\cite{Tao2008,Tao:2010,Tao2011}
110 < The coupling between surface oxidation state and catalytic activity
111 < for CO oxidation on Pt, for instance, is widely
112 < documented.\cite{Ertl08,Hendriksen:2002} Despite the well-documented
113 < role of these effects on reactivity, the ability to capture or predict
114 < them in atomistic models is currently somewhat limited.  While these
115 < effects are perhaps unsurprising on the highly disperse, multi-faceted
116 < nanoscale particles that characterize industrial catalysts, they are
117 < manifest even on ordered, well-defined surfaces. The Pt(557) surface,
118 < for example, exhibits substantial and reversible restructuring under
119 < exposure to moderate pressures of carbon monoxide.\cite{Tao:2010}
107 > significant evidence that solid surfaces are often structurally,
108 > compositionally, and chemically modified by reactants under operating
109 > conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between
110 > surface oxidation states and catalytic activity for CO oxidation on
111 > Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002}
112 > Despite the well-documented role of these effects on reactivity, the
113 > ability to capture or predict them in atomistic models is somewhat
114 > limited.  While these effects are perhaps unsurprising on the highly
115 > disperse, multi-faceted nanoscale particles that characterize
116 > industrial catalysts, they are manifest even on ordered, well-defined
117 > surfaces. The Pt(557) surface, for example, exhibits substantial and
118 > reversible restructuring under exposure to moderate pressures of
119 > carbon monoxide.\cite{Tao:2010}
120  
121 < This work is part of an ongoing effort to understand the causes,
122 < mechanisms and timescales for surface restructuring using molecular
123 < simulation methods.  Since the dynamics of the process is of
124 < particular interest, we utilize classical molecular dynamic methods
125 < with force fields that represent a compromise between chemical
126 < accuracy and the computational efficiency necessary to observe the
127 < process of interest.
121 > This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557)
122 > surface restructuring using molecular simulations.  Since the dynamics
123 > of the process are of particular interest, we employ classical force
124 > fields that represent a compromise between chemical accuracy and the
125 > computational efficiency necessary to simulate the process of interest.
126 > Since restructuring typically occurs as a result of specific interactions of the
127 > catalyst with adsorbates, in this work, two metal systems exposed
128 > to carbon monoxide were examined. The Pt(557) surface has already been shown
129 > to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010}
130 > The Au(557) surface, because of a weaker interaction with CO, is less
131 > likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000}
132 > and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced
133 > reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the
134 > 22 x $\sqrt{3}$ cell. They argued that only a few Au atoms
135 > become adatoms, limiting the stress of this reconstruction, while
136 > allowing the rest to relax and approach the ideal (111)
137 > configuration. They did not see the usual herringbone pattern on Au(111) being greatly
138 > affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a
139 > disruption of the herringbone pattern as CO was adsorbed to the
140 > surface. Both groups suggested that the preference CO shows for
141 > low-coordinated Au atoms was the primary driving force for the reconstruction.
142  
143 < Since restructuring occurs as a result of specific interactions of the catalyst
144 < with adsorbates, two metals systems exposed to the same adsorbate, CO,
111 < were examined in this work. The Pt(557) surface has already been shown to
112 < reconstruct under certain conditions. The Au(557) surface, because of gold's
113 < weaker interaction with CO, is less likely to undergo such a large reconstruction.
143 >
144 >
145   %Platinum molecular dynamics
146   %gold molecular dynamics
147  
117 –
118 –
119 –
120 –
121 –
148   \section{Simulation Methods}
149 < The challenge in modeling any solid/gas interface problem is the
149 > The challenge in modeling any solid/gas interface is the
150   development of a sufficiently general yet computationally tractable
151   model of the chemical interactions between the surface atoms and
152   adsorbates.  Since the interfaces involved are quite large (10$^3$ -
153 < 10$^6$ atoms) and respond slowly to perturbations, {\it ab initio}
153 > 10$^4$ atoms) and respond slowly to perturbations, {\it ab initio}
154   molecular dynamics
155   (AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello
156   methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum
# Line 133 | Line 159 | Coulomb potential.  For this work, we have been using
159   typically not well represented in terms of classical pairwise
160   interactions in the same way that bonds in a molecular material are,
161   nor are they captured by simple non-directional interactions like the
162 < Coulomb potential.  For this work, we have been using classical
163 < molecular dynamics with potential energy surfaces that are
164 < specifically tuned for transition metals.  In particular, we use the
165 < EAM potential for Au-Au and Pt-Pt interactions, while modeling the CO
166 < using a model developed by Straub and Karplus for studying
167 < photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and Pt-CO
168 < cross interactions were parameterized as part of this work.
162 > Coulomb potential.  For this work, we have used classical molecular
163 > dynamics with potential energy surfaces that are specifically tuned
164 > for transition metals.  In particular, we used the EAM potential for
165 > Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using a rigid
166 > three-site model developed by Straub and Karplus for studying
167 > photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and
168 > Pt-CO cross interactions were parameterized as part of this work.
169    
170   \subsection{Metal-metal interactions}
171 < Many of the potentials used for classical simulation of transition
172 < metals are based on a non-pairwise additive functional of the local
173 < electron density. The embedded atom method (EAM) is perhaps the best
174 < known of these
171 > Many of the potentials used for modeling transition metals are based
172 > on a non-pairwise additive functional of the local electron
173 > density. The embedded atom method (EAM) is perhaps the best known of
174 > these
175   methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98}
176   but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and
177   the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler
178 < parameter sets. The glue model of Ercolessi {\it et al.} is among the
179 < fastest of these density functional approaches.\cite{Ercolessi88} In
180 < all of these models, atoms are conceptualized as a positively charged
178 > parameter sets. The glue model of Ercolessi {\it et al}.\cite{Ercolessi88} is among the
179 > fastest of these density functional approaches. In
180 > all of these models, atoms are treated as a positively charged
181   core with a radially-decaying valence electron distribution. To
182   calculate the energy for embedding the core at a particular location,
183   the electron density due to the valence electrons at all of the other
184 < atomic sites is computed at atom $i$'s location,
184 > atomic sites is computed at atom $i$'s location,
185   \begin{equation*}
186   \bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
187   \end{equation*}
# Line 167 | Line 193 | $\phi_{ij}(r_{ij})$ is an pairwise term that is meant
193   V_i =  F[ \bar{\rho}_i ]  + \sum_{j \neq i} \phi_{ij}(r_{ij})
194   \end{equation*}
195   where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and
196 < $\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the
197 < overlap of the two positively charged cores.  
196 > $\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the
197 > repulsive overlap of the two positively charged cores.  
198  
199 < The {\it modified} embedded atom method (MEAM) adds angular terms to
200 < the electron density functions and an angular screening factor to the
201 < pairwise interaction between two
202 < atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
203 < MEAM has become widely used to simulate systems in which angular
204 < interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
205 < metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
206 < MEAM presents significant additional computational costs, however.
199 > % The {\it modified} embedded atom method (MEAM) adds angular terms to
200 > % the electron density functions and an angular screening factor to the
201 > % pairwise interaction between two
202 > % atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
203 > % MEAM has become widely used to simulate systems in which angular
204 > % interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
205 > % metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
206 > % MEAM presents significant additional computational costs, however.
207  
208 < The EAM, Finnis-Sinclair, MEAM, and the Quantum Sutton-Chen potentials
208 > The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials
209   have all been widely used by the materials simulation community for
210   simulations of bulk and nanoparticle
211   properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq}
212   melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
213   fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack
214   propagation,\cite{BECQUART:1993rg} and alloying
215 < dynamics.\cite{Shibata:2002hh} All of these potentials have their
216 < strengths and weaknesses.  One of the strengths common to all of the
217 < methods is the relatively large library of metals for which these
218 < potentials have been
219 < parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
215 > dynamics.\cite{Shibata:2002hh} One of EAM's strengths
216 > is its sensitivity to small changes in structure. This arises
217 > because interactions
218 > up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a}
219 > Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88}
220 > which is only parameterized up to the nearest-neighbor
221 > interactions, EAM is a suitable choice for systems where
222 > the bulk properties are of secondary importance to low-index
223 > surface structures. Additionally, the similarity of EAM's functional
224 > treatment of the embedding energy to standard density functional
225 > theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier.
226 > \cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  
227  
228 < \subsection{CO}
229 < Since one explanation for the strong surface CO repulsion on metals is
230 < the large linear quadrupole moment of carbon monoxide, the model
231 < chosen for this molecule exhibits this property in an efficient
232 < manner.  We used a model first proposed by Karplus and Straub to study
233 < the photodissociation of CO from myoglobin.\cite{Straub} The Straub and
234 < Karplus model is a rigid three site model which places a massless M
235 < site at the center of mass along the CO bond.  The geometry used along
236 < with the interaction parameters are reproduced in Table 1. The effective
228 >
229 >
230 >
231 > \subsection{Carbon Monoxide model}
232 > Previous explanations for the surface rearrangements center on
233 > the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010}  
234 > We used a model first proposed by Karplus and Straub to study
235 > the photodissociation of CO from myoglobin because it reproduces
236 > the quadrupole moment well.\cite{Straub} The Straub and
237 > Karplus model treats CO as a rigid three site molecule with a massless M
238 > site at the molecular center of mass. The geometry and interaction
239 > parameters are reproduced in Table~\ref{tab:CO}. The effective
240   dipole moment, calculated from the assigned charges, is still
241   small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
242   to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
243   mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
244   %CO Table
245   \begin{table}[H]
246 < \caption{Positions, $\sigma$, $\epsilon$ and charges for CO geometry and self-interactions\cite{Straub}. Distances are in \AA~, energies are in kcal/mol, and charges are in $e$.}
246 >  \caption{Positions, Lennard-Jones parameters ($\sigma$ and
247 >    $\epsilon$), and charges for the CO-CO
248 >    interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are
249 >    in kcal/mol, and charges are in atomic units.}
250   \centering
251   \begin{tabular}{| c | c | ccc |}
252   \hline
214 – \multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\
215 – \hline
253   &  {\it z} & $\sigma$ & $\epsilon$ & q\\
254   \hline
255 < \textbf{C} & -0.6457 &  0.0262  & 3.83   &   -0.75 \\
256 < \textbf{O} &  0.4843 &   0.1591 &   3.12 &   -0.85 \\
255 > \textbf{C} & -0.6457 &  3.83 & 0.0262   &   -0.75 \\
256 > \textbf{O} &  0.4843 &  3.12 &  0.1591  &   -0.85 \\
257   \textbf{M} & 0.0 & -  &  -  &    1.6 \\
258   \hline
259   \end{tabular}
260 + \label{tab:CO}
261   \end{table}
262  
263 < \subsection{Cross-Interactions}
263 > \subsection{Cross-Interactions between the metals and carbon monoxide}
264  
265 < One hurdle that must be overcome in classical molecular simulations
266 < is the proper parameterization of the potential interactions present
267 < in the system. Since the adsorption of CO onto a platinum surface has been
268 < the focus of many experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
269 < and theoretical studies \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
270 < there is a large amount of data in the literature to fit too. We started with parameters
271 < reported by Korzeniewski et al. \cite{Pons:1986} and then
272 < modified them to ensure that the Pt-CO interaction favored
273 < an atop binding position for the CO upon the Pt surface. This
274 < constraint led to the binding energies being on the higher side
275 < of reported values. Following the method laid out by Korzeniewski,
276 < the Pt-C interaction was fit to a strong Lennard-Jones 12-6
277 < interaction to mimic binding, while the Pt-O interaction
278 < was parameterized to a Morse potential with a large $r_o$
279 < to contribute a weak repulsion. The resultant potential-energy
280 < surface suitably recovers the calculated Pt-C bond length ( 1.6\AA)\cite{Beurden:2002ys} and affinity
281 < for the atop binding position.\cite{Deshlahra:2012, Hopster:1978}
265 > Since the adsorption of CO onto a Pt surface has been the focus
266 > of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
267 > and theoretical work
268 > \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
269 > there is a significant amount of data on adsorption energies for CO on
270 > clean metal surfaces. An earlier model by Korzeniewski {\it et
271 >  al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were
272 > modified to ensure that the Pt-CO interaction favored the atop binding
273 > position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}.
274 > The modified parameters yield binding energies that are slightly higher
275 > than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski
276 > {\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
277 > Lennard-Jones interaction to mimic strong, but short-ranged, partial
278 > binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The
279 > Pt-O interaction was modeled with a Morse potential with a large
280 > equilibrium distance, ($r_o$).  These choices ensure that the C is preferred
281 > over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak
282 > repulsion which favors the atop site.  The resulting potential-energy
283 > surface suitably recovers the calculated Pt-C separation length
284 > (1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding
285 > position.\cite{Deshlahra:2012, Hopster:1978}
286  
287   %where did you actually get the functionals for citation?
288   %scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think
289   %same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there...
290 < The Au-C and Au-O interaction parameters were also fit to a Lennard-Jones
291 < and Morse potential respectively, to reproduce Au-CO binding energies.
292 < These energies were obtained from quantum calculations carried out using
293 < the PBE GGA exchange-correlation functionals\cite{Perdew_GGA} for gold, carbon, and oxygen
294 < constructed by Rappe, Rabe, Kaxiras, and Joannopoulos. \cite{RRKJ_PP}.
295 < All calculations were run using the {\sc Quantum ESPRESSO} package. \cite{QE-2009}  
296 < First, a four layer slab of gold comprised of 32 atoms displaying a (111) surface was
297 < converged using a 4X4X4 grid of Monkhorst-Pack \emph{k}-points.\cite{Monkhorst:1976}
298 < The kinetic energy of the wavefunctions were truncated at 20 Ry while the
299 < cutoff for the charge density and potential was set at 80 Ry. This relaxed
300 < gold slab was then used in numerous single point calculations  with CO at various heights
301 < to create a potential energy surface for the Au-CO interaction.
290 > The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and
291 > Morse potentials, respectively, to reproduce Au-CO binding energies.
292 > The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations.
293 > Adsorption energies were obtained from gas-surface DFT calculations with a
294 > periodic supercell plane-wave basis approach, as implemented in the
295 > {\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were
296 > described with the projector augmented-wave (PAW)
297 > method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
298 > included to an energy cutoff of 20 Ry. Electronic energies are
299 > computed with the PBE implementation of the generalized gradient
300 > approximation (GGA) for gold, carbon, and oxygen that was constructed
301 > by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
302 > In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4
303 > Au x 2 Au surface planes and separated from vertical images by six
304 > layers of vacuum space. The surface atoms were all allowed to relax
305 > before CO was added to the system. Electronic relaxations were
306 > performed until the energy difference between subsequent steps
307 > was less than $10^{-8}$ Ry.   Nonspin-polarized supercell calculations
308 > were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
309 > zone.\cite{Monkhorst:1976} The relaxed gold slab was
310 > then used in numerous single point calculations with CO at various
311 > heights (and angles relative to the surface) to allow fitting of the
312 > empirical force field.
313  
314   %Hint at future work
315 < The fit parameter sets employed in this work are shown in Table 2 and their
316 < reproduction of the binding energies are displayed in Table 3. Currently,
317 < charge transfer is not being treated in this system, however, that is a goal
318 < for future work as the effect has been seen to affect binding energies and
319 < binding site preferences. \cite{Deshlahra:2012}
315 > The parameters employed for the metal-CO cross-interactions in this work
316 > are shown in Table~\ref{tab:co_parameters} and the binding energies on the
317 > (111) surfaces are displayed in Table~\ref{tab:co_energies}.  Charge transfer
318 > and polarization are neglected in this model, although these effects could have
319 > an effect on  binding energies and binding site preferences.
320  
268 –
269 –
270 –
271 – \subsection{Construction and Equilibration of 557 Metal interfaces}
272 –
273 – Our model systems are composed of approximately 4000 metal atoms
274 – cut along the 557 plane so that they are periodic in the {\it x} and {\it y}
275 – directions exposing the 557 plane in the {\it z} direction. Runs at various
276 – temperatures ranging from 300~K to 1200~K were started with the intent
277 – of viewing relative stability of the surface when CO was not present in the
278 – system.  Owing to the different melting points (1337~K for Au and 2045~K for Pt),
279 – the bare crystal systems were initially run in the Canonical ensemble at
280 – 800~K and 1000~K respectively for 100 ps. Various amounts of CO were
281 – placed in the vacuum region, which upon full adsorption to the surface
282 – corresponded to 5\%, 25\%, 33\%, and 50\% coverages. These systems
283 – were again allowed to reach thermal equilibrium before being run in the
284 – microcanonical ensemble. All of the systems examined in this work were
285 – run for at least 40 ns. A subset that were undergoing interesting effects
286 – have been allowed to continue running with one system approaching 200 ns.
287 – All simulations were run using the open source molecular dynamics package, OpenMD. \cite{Ewald, OOPSE}
288 –
289 –
290 –
291 –
292 –
293 –
294 – %\subsection{System}
295 – %Once equilibration was reached, the systems were exposed to various sub-monolayer coverage of CO: $0, \frac{1}{10}, \frac{1}{4}, \frac{1}{3},\frac{1}{2}$. The CO was started many \AA~above the surface with random velocity and rotational velocity vectors sampling from a Gaussian distribution centered on the temperature of the equilibrated metal block.  Full adsorption occurred over the period of approximately 10 ps for Pt, while the binding energy between Au and CO is smaller and led to an incomplete adsorption. The metal-metal interactions were treated using the Embedded Atom Method while the Pt-CO and Au-CO interactions were fit to experimental data and quantum calculations. The raised temperature helped shorten the length of the simulations by allowing the activation barrier of reconstruction to be more easily overcome. A few runs at lower temperatures showed the very beginnings of reconstructions, but their simulation lengths limited their usefulness.
296 –
297 –
321   %Table  of Parameters
322   %Pt Parameter Set 9
323   %Au Parameter Set 35
324   \begin{table}[H]
325 < \caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol}
325 >  \caption{Best fit parameters for metal-CO cross-interactions. Metal-C
326 >    interactions are modeled with Lennard-Jones potentials. While the
327 >    metal-O interactions were fit to Morse
328 >    potentials.  Distances are given in \AA~and energies in kcal/mol. }
329   \centering
330   \begin{tabular}{| c | cc | c | ccc |}
331   \hline
332 < \multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\
332 > &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
333   \hline
308 – &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\
309 – \hline
334   \textbf{Pt-C} & 1.3 & 15  & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\
335   \textbf{Au-C} & 1.9 & 6.5  & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\
336  
337   \hline
338   \end{tabular}
339 + \label{tab:co_parameters}
340   \end{table}
341  
342   %Table of energies
343   \begin{table}[H]
344 < \caption{Adsorption energies in eV}
344 >  \caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials
345 >    described in this work.  All values are in eV.}
346   \centering
347   \begin{tabular}{| c | cc |}
348 < \hline
349 < & Calc. & Exp. \\
350 < \hline
351 < \textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\
352 < \textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\
353 < \hline
348 >  \hline
349 >  & Calculated & Experimental \\
350 >  \hline
351 >  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,}
352 >  (Ref. \protect\cite{Kelemen:1979}) \\
353 > & &  -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline
354 >  \textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,}  (Ref. \protect\cite{TPDGold}) \\
355 >  \hline
356   \end{tabular}
357 + \label{tab:co_energies}
358   \end{table}
359  
360 + \subsection{Pt(557) and Au(557) metal interfaces}
361 + Our Pt system is an orthorhombic periodic box of dimensions
362 + 54.482~x~50.046~x~120.88~\AA~while our Au system has
363 + dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs
364 + are 9 and 8 atoms deep respectively, corresponding to a slab
365 + thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
366 + The systems are arranged in a FCC crystal that have been cut
367 + along the (557) plane so that they are periodic in the {\it x} and
368 + {\it y} directions, and have been oriented to expose two aligned
369 + (557) cuts along the extended {\it z}-axis.  Simulations of the
370 + bare metal interfaces at temperatures ranging from 300~K to
371 + 1200~K were performed to confirm the relative
372 + stability of the surfaces without a CO overlayer.  
373  
374 + The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting}
375 + and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at
376 + different temperatures for the two metals.  The bare Au and Pt surfaces were
377 + initially run in the canonical (NVT) ensemble at 800~K and 1000~K
378 + respectively for 100 ps. The two surfaces were relatively stable at these
379 + temperatures when no CO was present, but experienced increased surface
380 + mobility on addition of CO. Each surface was then dosed with different concentrations of CO
381 + that was initially placed in the vacuum region.  Upon full adsorption,
382 + these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
383 + coverage. Higher coverages resulted in the formation of a double layer of CO,
384 + which introduces artifacts that are not relevant to (557) reconstruction.
385 + Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
386 + the Au surfaces often had a significant CO population in the gas
387 + phase.  These systems were allowed to reach thermal equilibrium (over
388 + 5~ns) before being run in the microcanonical (NVE) ensemble for
389 + data collection. All of the systems examined had at least 40~ns in the
390 + data collection stage, although simulation times for some Pt of the
391 + systems exceeded 200~ns.  Simulations were carried out using the open
392 + source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,openmd}
393  
394  
395  
396  
397 < % Just results, leave discussion for discussion section
398 < \section{Results}
399 < \subsection{Diffusion}
400 < While an ideal metallic surface is unlikely to experience much surface diffusion, high-index surfaces have large numbers of low-coordinated atoms which have a much easier time overcoming the energetic barriers limiting diffusion, leading to easier surface reconstructions. Surface movement was divided between the parallel ($\parallel$) and perpendicular ($\perp$) directions relative to the step edge. We were then able to calculate diffusion constants as a function of CO coverage. As can be seen in Table 4, the presence and amount of CO directly affects the diffusion constants of surface platinum atoms. The presence of two 50\% coverage systems is to show how the diffusion process is affected by time. The majority of the systems were run for approximately 50 ns while the half monolayer system been running continuously. The lowered diffusion constant at longer run times will be examined in-depth in the discussion section.
401 <
402 < %Table of Diffusion Constants
403 < %Add gold?M
404 < \begin{table}[H]
405 < \caption{Platinum and gold diffusion constants parallel and perpendicular to the 557 step edge. As the coverage increases, the diffusion constants parallel and  perpendicular to the step edge both initially increase and then decrease slightly. Units are \AA\textsuperscript{2}/ns}
406 < \centering
407 < \begin{tabular}{| c | cc | cc | c |}
408 < \hline
409 < \textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  & \textbf{Time (ns)}\\
410 < \hline
411 < &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} & \\
351 < \hline
352 < 50\% & 4.32 $\pm$ 0.02 & 1.185 $\pm$ 0.008 & 1.72 $\pm$ 0.02 & 0.455 $\pm$ 0.006 & 40 \\
353 < 33\% & 5.18 $\pm$ 0.03 & 1.999 $\pm$ 0.005 & 1.95 $\pm$ 0.02 & 0.337 $\pm$ 0.004 & 40   \\
354 < 25\% & 5.01 $\pm$ 0.02 & 1.574 $\pm$ 0.004 & 1.26 $\pm$ 0.03 & 0.377 $\pm$ 0.006 & 40  \\
355 < 5\%   & 3.61 $\pm$ 0.02 & 0.355 $\pm$ 0.002 & 1.84 $\pm$ 0.03 & 0.169 $\pm$ 0.004 & 40  \\
356 < 0\%   & 3.27 $\pm$ 0.02 & 0.147 $\pm$ 0.004 & 1.50 $\pm$ 0.02 & 0.194 $\pm$ 0.002  & 40  \\
357 < \hline
358 < \end{tabular}
359 < \end{table}
397 > % RESULTS
398 > %
399 > \section{Results}
400 > \subsection{Structural remodeling}
401 > The bare metal surfaces experienced minor roughening of the
402 > step-edge because of the elevated temperatures, but the (557)
403 > face was stable throughout the simulations. The surface of both
404 > systems, upon dosage of CO, began to undergo extensive remodeling
405 > that was not observed in the bare systems. Reconstructions of
406 > the Au systems were limited to breakup of the step-edges and
407 > some step wandering. The lower coverage Pt systems experienced
408 > similar restructuring but to a greater extent. The 50\% coverage
409 > Pt system was unique among our simulations in that it formed
410 > well-defined and stable double layers through step coalescence,
411 > similar to results reported by Tao {\it et al}.\cite{Tao:2010}
412  
413  
414 + \subsubsection{Step wandering}
415 + The 0\% coverage surfaces for both metals showed minimal
416 + step-wandering at their respective temperatures. As the CO
417 + coverage increased however, the mobility of the surface atoms,
418 + described through adatom diffusion and step-edge wandering,
419 + also increased.  Except for the 50\% Pt system where step
420 + coalescence occurred, the step-edges in the other simulations
421 + preferred to keep nearly the same distance between steps as in
422 + the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au.
423 + Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994}
424 + highlights the repulsion that exists between step-edges even
425 + when no direct interactions are present in the system. This
426 + repulsion is caused by an entropic barrier that arises from
427 + the fact that steps cannot cross over one another. This entropic
428 + repulsion does not completely define the interactions between
429 + steps, however, so it is possible to observe step coalescence
430 + on some surfaces.\cite{Williams:1991} The presence and
431 + concentration of adsorbates, as shown in this work, can
432 + affect step-step interactions, potentially leading to a new
433 + surface structure as the thermodynamic equilibrium.
434  
435 + \subsubsection{Double layers}
436 + Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface
437 + undergoes two separate reconstructions upon CO adsorption.
438 + The first involves a doubling of the step height and plateau length.
439 + Similar behavior has been seen on a number of surfaces
440 + at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl}
441 + Of the two systems we examined, the Pt system showed a greater
442 + propensity for reconstruction  
443 + because of the larger surface mobility and the greater extent of step wandering.
444 + The amount of reconstruction was strongly correlated to the amount of CO
445 + adsorbed upon the surface.  This appears to be related to the
446 + effect that adsorbate coverage has on edge breakup and on the
447 + surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the
448 + doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here.
449 + Over a longer time scale (150~ns) two more double layers formed
450 + on this surface. Although double layer formation did not occur
451 + in the other Pt systems, they exhibited more step-wandering and
452 + roughening compared to their Au counterparts. The
453 + 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
454 + various times along the simulation showing the evolution of a double layer step-edge.
455 +
456 + The second reconstruction observed by
457 + Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched
458 + across the plateau between two step-edges. Neither metal, within
459 + the 40~ns time scale or the extended simulation time of 150~ns for
460 + the 50\% Pt system, experienced this reconstruction.
461 +
462 + %Evolution of surface
463 + \begin{figure}[H]
464 + \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation}
465 + \caption{The Pt(557) / 50\% CO system at a sequence of times after
466 +  initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and
467 +  (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly.  The
468 +  doubling of the layers appears only after two adjacent step-edges
469 +  touch.  The circled spot in (b) nucleated the growth of the double
470 +  step observed in the later configurations.}
471 +  \label{fig:reconstruct}
472 + \end{figure}
473 +
474 + \subsection{Dynamics}
475 + Previous experimental work by Pearl and Sibener\cite{Pearl},
476 + using STM, has been able to capture the coalescence of steps
477 + on Ni(977). The time scale of the image acquisition, $\sim$70~s/image,
478 + provides an upper bound for the time required for the doubling
479 + to occur. By utilizing Molecular Dynamics we are able to probe
480 + the dynamics of these reconstructions at elevated temperatures
481 + and in this section we provide data on the timescales for transport
482 + properties, e.g. diffusion and layer formation time.
483 +
484 +
485 + \subsubsection{Transport of surface metal atoms}
486 + %forcedSystems/stepSeparation
487 + The wandering of a step-edge is a cooperative effect
488 + arising from the individual movements of the atoms making up the steps. An ideal metal surface
489 + displaying a low index facet, (111) or (100), is unlikely to experience
490 + much surface diffusion because of the large energetic barrier that must
491 + be overcome to lift an atom out of the surface. The presence of step-edges and other surface features
492 + on higher-index facets provides a lower energy source for mobile metal atoms.
493 + Single-atom break-away from a step-edge on a clean surface still imposes an
494 + energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting
495 + the same metal atom vertically out of the surface,  \textgreater~60 kcal/mol.
496 + The penalty lowers significantly when CO is present in sufficient quantities
497 + on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as
498 + $\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for
499 + diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then
500 + able to explore the terrace before rejoining either their original step-edge or
501 + becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom
502 + to traverse to a separate terrace although the presence of CO can lower the
503 + energy barrier required to lift or lower an adatom. By tracking the mobility of individual
504 + metal atoms on the Pt and Au surfaces we were able to determine the relative
505 + diffusion constants, as well as how varying coverages of CO affect the diffusion. Close
506 + observation of the mobile metal atoms showed that they were typically in
507 + equilibrium with the step-edges.
508 + At times, their motion was concerted and two or more adatoms would be
509 + observed moving together across the surfaces.
510 +
511 + A particle was considered ``mobile'' once it had traveled more than 2~\AA~
512 + between saved configurations of the system (typically 10-100 ps). A mobile atom
513 + would typically travel much greater distances than this, but the 2~\AA~cutoff
514 + was used to prevent swamping the diffusion data with the in-place vibrational
515 + movement of buried atoms. Diffusion on a surface is strongly affected by
516 + local structures and in this work, the presence of single and double layer
517 + step-edges causes the diffusion parallel to the step-edges to be larger than
518 + the diffusion perpendicular to these edges. Parallel and perpendicular
519 + diffusion constants are shown in Figure \ref{fig:diff}.
520 +
521 + %Diffusion graph
522 + \begin{figure}[H]
523 + \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1}
524 + \caption{Diffusion constants for mobile surface atoms along directions
525 +  parallel ($\mathbf{D}_{\parallel}$) and perpendicular
526 +  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
527 +  surface coverage.  Diffusion parallel to the step-edge is higher
528 +  than that perpendicular to the edge because of the lower energy
529 +  barrier associated with traversing along the edge as compared to
530 +  completely breaking away. The two reported diffusion constants for
531 +  the 50\% Pt system arise from different sample sets. The lower values
532 +  correspond to the same 40~ns amount that all of the other systems were
533 +  examined at, while the larger values correspond to a 20~ns period }
534 + \label{fig:diff}
535 + \end{figure}
536 +
537 + The weaker Au-CO interaction is evident in the weak CO-coverage
538 + dependance of Au diffusion. This weak interaction leads to lower
539 + observed coverages when compared to dosage amounts. This further
540 + limits the effect the CO can have on surface diffusion. The correlation
541 + between coverage and Pt diffusion rates shows a near linear relationship
542 + at the earliest times in the simulations. Following double layer formation,
543 + however, there is a precipitous drop in adatom diffusion. As the double
544 + layer forms, many atoms that had been tracked for mobility data have
545 + now been buried resulting in a smaller reported diffusion constant. A
546 + secondary effect of higher coverages is CO-CO cross interactions that
547 + lower the effective mobility of the Pt adatoms that are bound to each CO.
548 + This effect would become evident only at higher coverages. A detailed
549 + account of Pt adatom energetics follows in the Discussion.
550 +
551 +
552 + \subsubsection{Dynamics of double layer formation}
553 + The increased diffusion on Pt at the higher CO coverages is the primary
554 + contributor to double layer formation. However, this is not a complete
555 + explanation -- the 33\%~Pt system has higher diffusion constants, but
556 + did not show any signs of edge doubling in 40~ns. On the 50\%~Pt
557 + system, one double layer formed within the first 40~ns of simulation time,
558 + while two more were formed as the system was allowed to run for an
559 + additional 110~ns (150~ns total). This suggests that this reconstruction
560 + is a rapid process and that the previously mentioned upper bound is a
561 + very large overestimate.\cite{Williams:1991,Pearl} In this system the first
562 + appearance of a double layer appears at 19~ns into the simulation.
563 + Within 12~ns of this nucleation event, nearly half of the step has formed
564 + the double layer and by 86~ns the complete layer has flattened out.
565 + From the appearance of the first nucleation event to the first observed
566 + double layer, the process took $\sim$20~ns. Another $\sim$40~ns was
567 + necessary for the layer to completely straighten. The other two layers in
568 + this simulation formed over periods of 22~ns and 42~ns respectively.
569 + A possible explanation for this rapid reconstruction is the elevated
570 + temperatures under which our systems were simulated. The process
571 + would almost certainly take longer at lower temperatures. Additionally,
572 + our measured times for completion of the doubling after the appearance
573 + of a nucleation site are likely affected by our periodic boxes. A longer
574 + step-edge will likely take longer to ``zipper''.
575 +
576 +
577   %Discussion
578   \section{Discussion}
579 < Comparing the results from simulation to those reported previously by Tao et al. the similarities in the platinum and CO system are quite strong. As shown in figure 1, the simulated platinum system under a CO atmosphere will restructure slightly by doubling the terrace heights. The restructuring appears to occur slowly, one to two platinum atoms at a time. Looking at individual snapshots, these adatoms tend to either rise on top of the plateau or break away from the step edge and then diffuse perpendicularly to the step direction until reaching another step edge. This combination of growth and decay of the step edges appears to be in somewhat of a state of dynamic equilibrium. However, once two previously separated edges meet as shown in figure 1.B, this point tends to act as a focus or growth point for the rest of the edge to meet up, akin to that of a zipper. From the handful of cases where a double layer was formed during the simulation. Measuring from the initial appearance of a growth point, the double layer tends to be fully formed within $\sim$~35 ns.
579 > We have shown that a classical potential is able to model the initial
580 > reconstruction of the Pt(557) surface upon CO adsorption, and have
581 > reproduced the double layer structure observed by Tao {\it et
582 >  al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be
583 > rapid -- occurring within 100 ns of the initial exposure to CO.  Here
584 > we discuss the features of the classical potential that are
585 > contributing to the stability and speed of the Pt(557) reconstruction.
586  
587   \subsection{Diffusion}
588 < As shown in the results section, the diffusion parallel to the step edge tends to be much faster than that perpendicular to the step edge. Additionally, the coverage of CO appears to play a slight role in relative rates of diffusion, as shown in Table 4. Thus, the bottleneck of the double layer formation appears to be the initial formation of this growth point, which seems to be somewhat of a stochastic event. Once it appears, parallel diffusion, along the now slightly angled step edge, will allow for a faster formation of the double layer than if the entire process were dependent on only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the more likely a growth point is to be formed. One driving force behind this reconstruction appears to be the lowering of surface energy that occurs by doubling the terrace widths. (I'm not really proving this... I have the surface flatness to show it, but surface energy?)
589 < \\
590 < \\
591 < %Evolution of surface
588 > The perpendicular diffusion constant appears to be the most important
589 > indicator of double layer formation. As highlighted in Figure
590 > \ref{fig:reconstruct}, the formation of the double layer did not begin
591 > until a nucleation site appeared.  Williams {\it et
592 >  al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge
593 > repulsion arising from the inability of edge crossing.  This repulsion
594 > must be overcome to allow step coalescence.  A larger
595 > $\textbf{D}_\perp$ value implies more step-wandering and a larger
596 > chance for the stochastic meeting of two edges to create a nucleation
597 > point.  Diffusion parallel to the step-edge can help ``zipper'' up a
598 > nascent double layer. This helps explain the rapid time scale for
599 > double layer completion after the appearance of a nucleation site, while
600 > the initial appearance of the nucleation site was unpredictable.
601 >
602 > \subsection{Mechanism for restructuring}
603 > Since the Au surface showed no large scale restructuring in any of our
604 > simulations, our discussion will focus on the 50\% Pt-CO system which
605 > did exhibit doubling. A number of possible mechanisms exist to explain
606 > the role of adsorbed CO in restructuring the Pt surface. Quadrupolar
607 > repulsion between adjacent CO molecules adsorbed on the surface is one
608 > possibility.  However, the quadrupole-quadrupole interaction is
609 > short-ranged and is attractive for some orientations.  If the CO
610 > molecules are ``locked'' in a vertical orientation, through atop
611 > adsorption for example, this explanation would gain credence. The
612 > calculated energetic repulsion between two CO molecules located a
613 > distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both
614 > in a vertical orientation, is 8.62 kcal/mol. Moving the CO to the
615 > second nearest-neighbor distance of 4.8~\AA~drops the repulsion to
616 > nearly 0. Allowing the CO to rotate away from a purely vertical
617 > orientation also lowers the repulsion. When the carbons are locked at
618 > a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the
619 > angle between the 2 CO is $\sim$24\textsuperscript{o}.  The calculated
620 > barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
621 > repulsion between adjacent CO molecules bound to Pt could increase the
622 > surface diffusion. However, the residence time of CO on Pt suggests
623 > that the CO molecules are extremely mobile, with diffusion constants 40
624 > to 2500 times larger than surface Pt atoms. This mobility suggests
625 > that the CO molecules jump between different Pt atoms throughout the
626 > simulation, but can stay bound for significant periods of time.
627 >
628 > A different interpretation of the above mechanism which takes the
629 > large mobility of the CO into account, would be in the destabilization
630 > of Pt-Pt interactions due to bound CO.  Destabilizing Pt-Pt bonds at
631 > the edges could lead to increased step-edge breakup and diffusion. On
632 > the bare Pt(557) surface the barrier to completely detach an edge atom
633 > is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
634 > \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain
635 > configurations, cases (e), (g), and (h), the barrier can be lowered to
636 > $\sim$23~kcal/mol by the presence of bound CO molecules. In these
637 > instances, it becomes energetically favorable to roughen the edge by
638 > introducing a small separation of 0.5 to 1.0~\AA. This roughening
639 > becomes immediately obvious in simulations with significant CO
640 > populations. The roughening is present to a lesser extent on surfaces
641 > with lower CO coverage (and even on the bare surfaces), although in
642 > these cases it is likely due to random fluctuations that squeeze out
643 > step-edge atoms. Step-edge breakup by continuous single-atom
644 > translations (as suggested by these energy curves) is probably a
645 > worst-case scenario.  Multistep mechanisms in which an adatom moves
646 > laterally on the surface after being ejected would be more
647 > energetically favorable.  This would leave the adatom alongside the
648 > ledge, providing it with 5 nearest neighbors.  While fewer than the 7
649 > neighbors it had as part of the step-edge, it keeps more Pt neighbors
650 > than the 3 an isolated adatom would have on the terrace. In this
651 > proposed mechanism, the CO quadrupolar repulsion still plays a role in
652 > the initial roughening of the step-edge, but not in any long-term
653 > bonds with individual Pt atoms.  Higher CO coverages create more
654 > opportunities for the crowded CO configurations shown in Figure
655 > \ref{fig:SketchGraphic}, and this is likely to cause an increased
656 > propensity for step-edge breakup.
657 >
658 > %Sketch graphic of different configurations
659   \begin{figure}[H]
660 < \includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
661 < \caption{Four snapshots at various times a) 258 ps b) 19 ns c) 31.2 ns d) 86.1 ns. Slight disruption of the surface occurs fairly quickly. However, the doubling of the layers seems to be very dependent on the initial linking of two separate step edges. The focal point in b, appears to be a growth spot for the rest of the double layer.}
660 > \includegraphics[width=\linewidth]{COpaths}
661 > \caption{Configurations used to investigate the mechanism of step-edge
662 >  breakup on Pt(557). In each case, the central (starred) atom is
663 >  pulled directly across the surface away from the step edge.  The Pt
664 >  atoms on the upper terrace are colored dark grey, while those on the
665 >  lower terrace are in white.  In each of these configurations, some
666 >  number of the atoms (highlighted in blue) had a CO molecule bound in
667 >  a vertical atop position.  The energies of these configurations as a
668 >  function of central atom displacement are displayed in Figure
669 >  \ref{fig:SketchEnergies}.}
670 > \label{fig:SketchGraphic}
671   \end{figure}
672  
673 + %energy graph corresponding to sketch graphic
674 + \begin{figure}[H]
675 + \includegraphics[width=\linewidth]{Portrait_SeparationComparison}
676 + \caption{Energies for displacing a single edge atom perpendicular to
677 +  the step edge as a function of atomic displacement. Each of the
678 +  energy curves corresponds to one of the labeled configurations in
679 +  Figure \ref{fig:SketchGraphic}, and are referenced to the
680 +  unperturbed step-edge.  Certain arrangements of bound CO (notably
681 +  configurations g and h) can lower the energetic barrier for creating
682 +  an adatom relative to the bare surface (configuration a).}
683 + \label{fig:SketchEnergies}
684 + \end{figure}
685  
686 + While configurations of CO on the surface are able to increase
687 + diffusion and the likelihood of edge wandering, this does not provide
688 + a complete explanation for the formation of double layers. If adatoms
689 + were constrained to their original terraces then doubling could not
690 + occur.  A mechanism for vertical displacement of adatoms at the
691 + step-edge is required to explain the doubling.
692  
693 + We have discovered one possible mechanism for a CO-mediated vertical
694 + displacement of Pt atoms at the step edge. Figure \ref{fig:lambda}
695 + shows four points along a reaction coordinate in which a CO-bound
696 + adatom along the step-edge ``burrows'' into the edge and displaces the
697 + original edge atom onto the higher terrace. A number of events similar
698 + to this mechanism were observed during the simulations.  We predict an
699 + energetic barrier of 20~kcal/mol for this process (in which the
700 + displaced edge atom follows a curvilinear path into an adjacent 3-fold
701 + hollow site).  The barrier heights we obtain for this reaction
702 + coordinate are approximate because the exact path is unknown, but the
703 + calculated energy barriers would be easily accessible at operating
704 + conditions.  Additionally, this mechanism is exothermic, with a final
705 + energy 15~kcal/mol below the original $\lambda = 0$ configuration.
706 + When CO is not present and this reaction coordinate is followed, the
707 + process is endothermic by 3~kcal/mol.  The difference in the relative
708 + energies for the $\lambda=0$ and $\lambda=1$ case when CO is present
709 + provides strong support for CO-mediated Pt-Pt interactions giving rise
710 + to the doubling reconstruction.
711  
712 + %lambda progression of Pt -> shoving its way into the step
713 + \begin{figure}[H]
714 + \includegraphics[width=\linewidth]{EPS_rxnCoord}
715 + \caption{Points along a possible reaction coordinate for CO-mediated
716 +  edge doubling. Here, a CO-bound adatom burrows into an established
717 +  step edge and displaces an edge atom onto the upper terrace along a
718 +  curvilinear path.  The approximate barrier for the process is
719 +  20~kcal/mol, and the complete process is exothermic by 15~kcal/mol
720 +  in the presence of CO, but is endothermic by 3~kcal/mol without.}
721 + \label{fig:lambda}
722 + \end{figure}
723 +
724 + The mechanism for doubling on the Pt(557) surface appears to require
725 + the cooperation of at least two distinct processes. For complete
726 + doubling of a layer to occur there must be a breakup of one
727 + terrace. These atoms must then ``disappear'' from that terrace, either
728 + by travelling to the terraces above of below their original levels.
729 + The presence of CO helps explain mechanisms for both of these
730 + situations. There must be sufficient breakage of the step-edge to
731 + increase the concentration of adatoms on the surface and these adatoms
732 + must then undergo the burrowing highlighted above (or a comparable
733 + mechanism) to create the double layer.  With sufficient time, these
734 + mechanisms working in concert lead to the formation of a double layer.
735 +
736 + \subsection{CO Removal and double layer stability}
737 + Once a double layer had formed on the 50\%~Pt system, it remained for
738 + the rest of the simulation time with minimal movement.  Random
739 + fluctuations that involved small clusters or divots were observed, but
740 + these features typically healed within a few nanoseconds.  Within our
741 + simulations, the formation of the double layer appeared to be
742 + irreversible and a double layer was never observed to split back into
743 + two single layer step-edges while CO was present.
744 +
745 + To further gauge the effect CO has on this surface, additional
746 + simulations were run starting from a late configuration of the 50\%~Pt
747 + system that had already formed double layers. These simulations then
748 + had their CO forcibly removed.  The double layer broke apart rapidly
749 + in these simulations, showing a well-defined edge-splitting after
750 + 100~ps. Configurations of this system are shown in Figure
751 + \ref{fig:breaking}. The coloring of the top and bottom layers helps to
752 + exhibit how much mixing the edges experience as they split. These
753 + systems were only examined for 10~ns, and within that time despite the
754 + initial rapid splitting, the edges only moved another few
755 + \AA~apart. It is possible that with longer simulation times, the (557)
756 + surface recovery observed by Tao {\it et al}.\cite{Tao:2010} could
757 + also be recovered.
758 +
759 + %breaking of the double layer upon removal of CO
760 + \begin{figure}[H]
761 + \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking}
762 + \caption{Dynamics of an established (111) double step after removal of
763 +  the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the removal
764 +  of CO. The presence of the CO helped maintain the stability of the
765 +  double step.  Nearly immediately after the CO is removed, the step
766 +  edge reforms in a (100) configuration, which is also the step type
767 +  seen on clean (557) surfaces. The step separation involves
768 +  significant mixing of the lower and upper atoms at the edge.}
769 + \label{fig:breaking}
770 + \end{figure}
771 +
772 +
773   %Peaks!
774 < \includegraphics[scale=0.25]{doublePeaks_noCO.png}
774 > %\begin{figure}[H]
775 > %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
776 > %\caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
777 > %of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with
778 > %aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
779 > %\label{fig:peaks}
780 > %\end{figure}
781 >
782 >
783 > %Don't think I need this
784 > %clean surface...
785 > %\begin{figure}[H]
786 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF}
787 > %\caption{}
788 >
789 > %\end{figure}
790 > %\label{fig:clean}
791 >
792 >
793   \section{Conclusion}
794 + The strength and directionality of the Pt-CO binding interaction, as
795 + well as the large quadrupolar repulsion between atop-bound CO
796 + molecules, help to explain the observed increase in surface mobility
797 + of Pt(557) and the resultant reconstruction into a double-layer
798 + configuration at the highest simulated CO-coverages.  The weaker Au-CO
799 + interaction results in significantly lower adataom diffusion
800 + constants, less step-wandering, and a lack of the double layer
801 + reconstruction on the Au(557) surface.
802  
803 + An in-depth examination of the energetics shows the important role CO
804 + plays in increasing step-breakup and in facilitating edge traversal
805 + which are both necessary for double layer formation.
806  
807 < \section{Acknowledgments}
386 < Support for this project was provided by the National Science
387 < Foundation under grant CHE-0848243 and by the Center for Sustainable
388 < Energy at Notre Dame (cSEND). Computational time was provided by the
389 < Center for Research Computing (CRC) at the University of Notre Dame.
807 > %Things I am not ready to remove yet
808  
809 + %Table of Diffusion Constants
810 + %Add gold?M
811 + % \begin{table}[H]
812 + %   \caption{}
813 + %   \centering
814 + % \begin{tabular}{| c | cc | cc | }
815 + %   \hline
816 + %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
817 + %   \hline
818 + %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
819 + %   \hline
820 + %   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
821 + %   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
822 + %   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
823 + %   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
824 + %   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
825 + %   \hline
826 + % \end{tabular}
827 + % \end{table}
828 +
829 + \begin{acknowledgement}
830 +  We gratefully acknowledge conversations with Dr. William
831 +  F. Schneider and Dr. Feng Tao.  Support for this project was
832 +  provided by the National Science Foundation under grant CHE-0848243
833 +  and by the Center for Sustainable Energy at Notre Dame
834 +  (cSEND). Computational time was provided by the Center for Research
835 +  Computing (CRC) at the University of Notre Dame.
836 + \end{acknowledgement}
837   \newpage
838   \bibliography{firstTryBibliography}
839 < \end{doublespace}
839 > %\end{doublespace}
840 >
841 > \begin{tocentry}
842 > %\includegraphics[height=3.5cm]{timelapse}
843 > \includegraphics[height=3.5cm]{TOC_doubleLayer.pdf}
844 > \end{tocentry}
845 >
846   \end{document}

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