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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 > \usepackage{epstopdf}
24 >
25 > \usepackage[version=3]{mhchem}  % this is a great package for formatting chemical reactions
26 > % \usepackage[square, comma, sort&compress]{natbib}
27   \usepackage{url}
28   \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
29   \evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
30 < 9.0in \textwidth 6.5in \brokenpenalty=10000
30 > 9.0in \textwidth 6.5in \brokenpenalty=1110000
31  
32   % double space list of tables and figures
33 < \AtBeginDelayedFloats{\renewcommand{\baselinestretch}{1.66}}
33 > %\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}}
34   \setlength{\abovecaptionskip}{20 pt}
35   \setlength{\belowcaptionskip}{30 pt}
36 + % \bibpunct{}{}{,}{s}{}{;}
37  
38 < %\renewcommand\citemid{\ } % no comma in optional reference note
39 < \bibpunct{[}{]}{,}{n}{}{;}
27 < \bibliographystyle{achemso}
38 > %\citestyle{nature}
39 > % \bibliographystyle{achemso}
40  
41 < \begin{document}
41 > \title{Molecular Dynamics simulations of the surface reconstructions
42 >  of Pt(557) and Au(557) under exposure to CO}
43  
44 + \author{Joseph R. Michalka}
45 + \author{Patrick W. McIntyre}
46 + \author{J. Daniel Gezelter}
47 + \email{gezelter@nd.edu}
48 + \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
49 +  Department of Chemistry and Biochemistry\\ University of Notre
50 +  Dame\\ Notre Dame, Indiana 46556}
51  
52 + \keywords{}
53 +
54 + \begin{document}
55 +
56 +
57   %%
58   %Introduction
59   %       Experimental observations
# Line 47 | Line 72
72   %Summary
73   %%
74  
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
75  
62 – % make the title
63 – \maketitle
64 –
65 – \begin{doublespace}
66 –
76   \begin{abstract}
77 + We examine surface reconstructions of Pt and Au(557) under
78 + various CO coverages using molecular dynamics in order to
79 + explore possible mechanisms for any observed reconstructions
80 + and their dynamics. The metal-CO interactions were parameterized
81 + as part of this work so that an efficient large-scale treatment of
82 + this system could be undertaken. The large difference in binding
83 + strengths of the metal-CO interactions was found to play a significant
84 + role with regards to step-edge stability and adatom diffusion. A
85 + small correlation between coverage and the diffusion constant
86 + was also determined. The energetics of CO adsorbed to the surface
87 + is sufficient to explain the reconstructions observed on the Pt
88 + systems and the lack  of reconstruction of the Au systems.
89  
90 +
91 + The mechanism and dynamics of surface reconstructions of Pt(557)
92 + and Au(557) exposed to various coverages of carbon monoxide (CO)
93 + were investigated using molecular dynamics simulations. Metal-CO
94 + interactions were parameterized from experimental data and plane-wave
95 + Density Functional Theory (DFT) calculations.  The large difference in
96 + binding strengths of the Pt-CO and Au-CO interactions was found to play
97 + a significant role in step-edge stability and adatom diffusion constants.
98 + The energetics of CO adsorbed to the surface is sufficient to explain the
99 + step-doubling reconstruction observed on Pt(557) and the lack of such
100 + a reconstruction on the Au(557) surface.
101   \end{abstract}
102  
103   \newpage
# Line 79 | Line 111 | Industrial catalysts usually consist of small particle
111   %       Sub: Also, easier to observe what is going on and provide reasons and explanations
112   %
113  
114 < Industrial catalysts usually consist of small particles exposing
115 < different atomic terminations that exhibit a high concentration of
116 < step, kink sites, and vacancies at the edges of the facets.  These
85 < sites are thought to be the locations of catalytic
114 > Industrial catalysts usually consist of small particles that exhibit a
115 > high concentration of steps, kink sites, and vacancies at the edges of
116 > the facets.  These sites are thought to be the locations of catalytic
117   activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now
118 < significant evidence to demonstrate that solid surfaces are often
119 < structurally, compositionally, and chemically {\it modified} by
120 < reactants under operating conditions.\cite{Tao2008,Tao:2010,Tao2011}
121 < The coupling between surface oxidation state and catalytic activity
122 < for CO oxidation on Pt, for instance, is widely
123 < documented.\cite{Ertl08,Hendriksen:2002} Despite the well-documented
124 < role of these effects on reactivity, the ability to capture or predict
125 < them in atomistic models is currently somewhat limited.  While these
126 < effects are perhaps unsurprising on the highly disperse, multi-faceted
127 < nanoscale particles that characterize industrial catalysts, they are
128 < manifest even on ordered, well-defined surfaces. The Pt(557) surface,
129 < for example, exhibits substantial and reversible restructuring under
130 < exposure to moderate pressures of carbon monoxide.\cite{Tao:2010}
118 > significant evidence that solid surfaces are often structurally,
119 > compositionally, and chemically modified by reactants under operating
120 > conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between
121 > surface oxidation states and catalytic activity for CO oxidation on
122 > Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002}
123 > Despite the well-documented role of these effects on reactivity, the
124 > ability to capture or predict them in atomistic models is somewhat
125 > limited.  While these effects are perhaps unsurprising on the highly
126 > disperse, multi-faceted nanoscale particles that characterize
127 > industrial catalysts, they are manifest even on ordered, well-defined
128 > surfaces. The Pt(557) surface, for example, exhibits substantial and
129 > reversible restructuring under exposure to moderate pressures of
130 > carbon monoxide.\cite{Tao:2010}
131  
132 < This work is part of an ongoing effort to understand the causes,
133 < mechanisms and timescales for surface restructuring using molecular
134 < simulation methods.  Since the dynamics of the process is of
135 < particular interest, we utilize classical molecular dynamic methods
136 < with force fields that represent a compromise between chemical
137 < accuracy and the computational efficiency necessary to observe the
138 < process of interest.
132 > This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557)
133 > surface restructuring using molecular simulations.  Since the dynamics
134 > of the process are of particular interest, we employ classical force
135 > fields that represent a compromise between chemical accuracy and the
136 > computational efficiency necessary to simulate the process of interest.
137 > Since restructuring typically occurs as a result of specific interactions of the
138 > catalyst with adsorbates, in this work, two metal systems exposed
139 > to carbon monoxide were examined. The Pt(557) surface has already been shown
140 > to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010}
141 > The Au(557) surface, because of a weaker interaction with CO, is less
142 > likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000}
143 > and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced
144 > reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the
145 > 22 x $\sqrt{3}$ cell. They argued that only a few Au atoms
146 > become adatoms, limiting the stress of this reconstruction, while
147 > allowing the rest to relax and approach the ideal (111)
148 > configuration. They did not see the usual herringbone pattern on Au(111) being greatly
149 > affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a
150 > disruption of the herringbone pattern as CO was adsorbed to the
151 > surface. Both groups suggested that the preference CO shows for
152 > low-coordinated Au atoms was the primary driving force for the reconstruction.
153  
154 < Since restructuring occurs as a result of specific interactions of the catalyst
155 < 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.
154 >
155 >
156   %Platinum molecular dynamics
157   %gold molecular dynamics
158  
117 –
118 –
119 –
120 –
121 –
159   \section{Simulation Methods}
160 < The challenge in modeling any solid/gas interface problem is the
160 > The challenge in modeling any solid/gas interface is the
161   development of a sufficiently general yet computationally tractable
162   model of the chemical interactions between the surface atoms and
163   adsorbates.  Since the interfaces involved are quite large (10$^3$ -
164 < 10$^6$ atoms) and respond slowly to perturbations, {\it ab initio}
164 > 10$^4$ atoms) and respond slowly to perturbations, {\it ab initio}
165   molecular dynamics
166   (AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello
167   methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum
# Line 133 | Line 170 | Coulomb potential.  For this work, we have been using
170   typically not well represented in terms of classical pairwise
171   interactions in the same way that bonds in a molecular material are,
172   nor are they captured by simple non-directional interactions like the
173 < Coulomb potential.  For this work, we have been using classical
174 < molecular dynamics with potential energy surfaces that are
175 < specifically tuned for transition metals.  In particular, we use the
176 < EAM potential for Au-Au and Pt-Pt interactions, while modeling the CO
177 < using a model developed by Straub and Karplus for studying
178 < photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and Pt-CO
179 < cross interactions were parameterized as part of this work.
173 > Coulomb potential.  For this work, we have used classical molecular
174 > dynamics with potential energy surfaces that are specifically tuned
175 > for transition metals.  In particular, we used the EAM potential for
176 > Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using a rigid
177 > three-site model developed by Straub and Karplus for studying
178 > photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and
179 > Pt-CO cross interactions were parameterized as part of this work.
180    
181   \subsection{Metal-metal interactions}
182 < Many of the potentials used for classical simulation of transition
183 < metals are based on a non-pairwise additive functional of the local
184 < electron density. The embedded atom method (EAM) is perhaps the best
185 < known of these
182 > Many of the potentials used for modeling transition metals are based
183 > on a non-pairwise additive functional of the local electron
184 > density. The embedded atom method (EAM) is perhaps the best known of
185 > these
186   methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98}
187   but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and
188   the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler
189 < parameter sets. The glue model of Ercolessi {\it et al.} is among the
190 < fastest of these density functional approaches.\cite{Ercolessi88} In
191 < all of these models, atoms are conceptualized as a positively charged
189 > parameter sets. The glue model of Ercolessi {\it et al}.\cite{Ercolessi88} is among the
190 > fastest of these density functional approaches. In
191 > all of these models, atoms are treated as a positively charged
192   core with a radially-decaying valence electron distribution. To
193   calculate the energy for embedding the core at a particular location,
194   the electron density due to the valence electrons at all of the other
195 < atomic sites is computed at atom $i$'s location,
195 > atomic sites is computed at atom $i$'s location,
196   \begin{equation*}
197   \bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
198   \end{equation*}
# Line 167 | Line 204 | $\phi_{ij}(r_{ij})$ is an pairwise term that is meant
204   V_i =  F[ \bar{\rho}_i ]  + \sum_{j \neq i} \phi_{ij}(r_{ij})
205   \end{equation*}
206   where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and
207 < $\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the
208 < overlap of the two positively charged cores.  
207 > $\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the
208 > repulsive overlap of the two positively charged cores.  
209  
210 < The {\it modified} embedded atom method (MEAM) adds angular terms to
211 < the electron density functions and an angular screening factor to the
212 < pairwise interaction between two
213 < atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
214 < MEAM has become widely used to simulate systems in which angular
215 < interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
216 < metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
217 < MEAM presents significant additional computational costs, however.
210 > % The {\it modified} embedded atom method (MEAM) adds angular terms to
211 > % the electron density functions and an angular screening factor to the
212 > % pairwise interaction between two
213 > % atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
214 > % MEAM has become widely used to simulate systems in which angular
215 > % interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
216 > % metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
217 > % MEAM presents significant additional computational costs, however.
218  
219 < The EAM, Finnis-Sinclair, MEAM, and the Quantum Sutton-Chen potentials
219 > The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials
220   have all been widely used by the materials simulation community for
221   simulations of bulk and nanoparticle
222   properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq}
223   melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
224   fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack
225   propagation,\cite{BECQUART:1993rg} and alloying
226 < dynamics.\cite{Shibata:2002hh} All of these potentials have their
227 < strengths and weaknesses.  One of the strengths common to all of the
228 < methods is the relatively large library of metals for which these
229 < potentials have been
230 < parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
226 > dynamics.\cite{Shibata:2002hh} One of EAM's strengths
227 > is its sensitivity to small changes in structure. This arises
228 > because interactions
229 > up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a}
230 > Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88}
231 > which is only parameterized up to the nearest-neighbor
232 > interactions, EAM is a suitable choice for systems where
233 > the bulk properties are of secondary importance to low-index
234 > surface structures. Additionally, the similarity of EAM's functional
235 > treatment of the embedding energy to standard density functional
236 > theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier.
237 > \cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  
238  
239 < \subsection{CO}
240 < Since one explanation for the strong surface CO repulsion on metals is
241 < the large linear quadrupole moment of carbon monoxide, the model
242 < chosen for this molecule exhibits this property in an efficient
243 < manner.  We used a model first proposed by Karplus and Straub to study
244 < the photodissociation of CO from myoglobin.\cite{Straub} The Straub and
245 < Karplus model is a rigid three site model which places a massless M
246 < site at the center of mass along the CO bond.  The geometry used along
247 < with the interaction parameters are reproduced in Table 1. The effective
239 >
240 >
241 >
242 > \subsection{Carbon Monoxide model}
243 > Previous explanations for the surface rearrangements center on
244 > the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010}  
245 > We used a model first proposed by Karplus and Straub to study
246 > the photodissociation of CO from myoglobin because it reproduces
247 > the quadrupole moment well.\cite{Straub} The Straub and
248 > Karplus model treats CO as a rigid three site molecule with a massless M
249 > site at the molecular center of mass. The geometry and interaction
250 > parameters are reproduced in Table~\ref{tab:CO}. The effective
251   dipole moment, calculated from the assigned charges, is still
252   small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
253   to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
254   mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
255   %CO Table
256   \begin{table}[H]
257 < \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 $e$.}
257 >  \caption{Positions, Lennard-Jones parameters ($\sigma$ and
258 >    $\epsilon$), and charges for the CO-CO
259 >    interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are
260 >    in kcal/mol, and charges are in atomic units.}
261   \centering
262   \begin{tabular}{| c | c | ccc |}
263   \hline
214 – \multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\
215 – \hline
264   &  {\it z} & $\sigma$ & $\epsilon$ & q\\
265   \hline
266 < \textbf{C} & -0.6457 &  0.0262  & 3.83   &   -0.75 \\
267 < \textbf{O} &  0.4843 &   0.1591 &   3.12 &   -0.85 \\
266 > \textbf{C} & -0.6457 &  3.83 & 0.0262   &   -0.75 \\
267 > \textbf{O} &  0.4843 &  3.12 &  0.1591  &   -0.85 \\
268   \textbf{M} & 0.0 & -  &  -  &    1.6 \\
269   \hline
270   \end{tabular}
271 + \label{tab:CO}
272   \end{table}
273  
274 < \subsection{Cross-Interactions}
274 > \subsection{Cross-Interactions between the metals and carbon monoxide}
275  
276 < One hurdle that must be overcome in classical molecular simulations
277 < is the proper parameterization of the potential interactions present
278 < in the system. Since the adsorption of CO onto a platinum surface has been
279 < the focus of many experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
280 < and theoretical studies \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
281 < there is a large amount of data in the literature to fit too. We started with parameters
282 < reported by Korzeniewski et al. \cite{Pons:1986} and then
283 < modified them to ensure that the Pt-CO interaction favored
284 < an atop binding position for the CO upon the Pt surface. This
285 < constraint led to the binding energies being on the higher side
286 < of reported values. Following the method laid out by Korzeniewski,
287 < the Pt-C interaction was fit to a strong Lennard-Jones 12-6
288 < interaction to mimic binding, while the Pt-O interaction
289 < was parameterized to a Morse potential with a large $r_o$
290 < to contribute a weak repulsion. The resultant potential-energy
291 < surface suitably recovers the calculated Pt-C bond length ( 1.6\AA)\cite{Beurden:2002ys} and affinity
292 < for the atop binding position.\cite{Deshlahra:2012, Hopster:1978}
276 > Since the adsorption of CO onto a Pt surface has been the focus
277 > of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
278 > and theoretical work
279 > \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
280 > there is a significant amount of data on adsorption energies for CO on
281 > clean metal surfaces. An earlier model by Korzeniewski {\it et
282 >  al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were
283 > modified to ensure that the Pt-CO interaction favored the atop binding
284 > position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}.
285 > The modified parameters yield binding energies that are slightly higher
286 > than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski
287 > {\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
288 > Lennard-Jones interaction to mimic strong, but short-ranged, partial
289 > binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The
290 > Pt-O interaction was modeled with a Morse potential with a large
291 > equilibrium distance, ($r_o$).  These choices ensure that the C is preferred
292 > over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak
293 > repulsion which favors the atop site.  The resulting potential-energy
294 > surface suitably recovers the calculated Pt-C separation length
295 > (1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding
296 > position.\cite{Deshlahra:2012, Hopster:1978}
297  
298   %where did you actually get the functionals for citation?
299   %scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think
300   %same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there...
301 < The Au-C and Au-O interaction parameters were also fit to a Lennard-Jones
302 < and Morse potential respectively, to reproduce Au-CO binding energies.
303 < These energies were obtained from quantum calculations carried out using
304 < the PBE GGA exchange-correlation functionals\cite{Perdew_GGA} for gold, carbon, and oxygen
305 < constructed by Rappe, Rabe, Kaxiras, and Joannopoulos. \cite{RRKJ_PP}.
306 < All calculations were run using the {\sc Quantum ESPRESSO} package. \cite{QE-2009}  
307 < First, a four layer slab of gold comprised of 32 atoms displaying a (111) surface was
308 < converged using a 4X4X4 grid of Monkhorst-Pack \emph{k}-points.\cite{Monkhorst:1976}
309 < The kinetic energy of the wavefunctions were truncated at 20 Ry while the
310 < cutoff for the charge density and potential was set at 80 Ry. This relaxed
311 < gold slab was then used in numerous single point calculations  with CO at various heights
312 < to create a potential energy surface for the Au-CO interaction.
301 > The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and
302 > Morse potentials, respectively, to reproduce Au-CO binding energies.
303 > The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations.
304 > Adsorption energies were obtained from gas-surface DFT calculations with a
305 > periodic supercell plane-wave basis approach, as implemented in the
306 > {\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were
307 > described with the projector augmented-wave (PAW)
308 > method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
309 > included to an energy cutoff of 20 Ry. Electronic energies are
310 > computed with the PBE implementation of the generalized gradient
311 > approximation (GGA) for gold, carbon, and oxygen that was constructed
312 > by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
313 > In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4
314 > Au x 2 Au surface planes and separated from vertical images by six
315 > layers of vacuum space. The surface atoms were all allowed to relax
316 > before CO was added to the system. Electronic relaxations were
317 > performed until the energy difference between subsequent steps
318 > was less than $10^{-8}$ Ry.   Nonspin-polarized supercell calculations
319 > were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
320 > zone.\cite{Monkhorst:1976} The relaxed gold slab was
321 > then used in numerous single point calculations with CO at various
322 > heights (and angles relative to the surface) to allow fitting of the
323 > empirical force field.
324  
325   %Hint at future work
326 < The fit parameter sets employed in this work are shown in Table 2 and their
327 < reproduction of the binding energies are displayed in Table 3. Currently,
328 < charge transfer is not being treated in this system, however, that is a goal
329 < for future work as the effect has been seen to affect binding energies and
330 < binding site preferences. \cite{Deshlahra:2012}
326 > The parameters employed for the metal-CO cross-interactions in this work
327 > are shown in Table~\ref{tab:co_parameters} and the binding energies on the
328 > (111) surfaces are displayed in Table~\ref{tab:co_energies}.  Charge transfer
329 > and polarization are neglected in this model, although these effects could have
330 > an effect on  binding energies and binding site preferences.
331  
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 –
332   %Table  of Parameters
333   %Pt Parameter Set 9
334   %Au Parameter Set 35
335   \begin{table}[H]
336 < \caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol}
336 >  \caption{Best fit parameters for metal-CO cross-interactions. Metal-C
337 >    interactions are modeled with Lennard-Jones potentials. While the
338 >    metal-O interactions were fit to Morse
339 >    potentials.  Distances are given in \AA~and energies in kcal/mol. }
340   \centering
341   \begin{tabular}{| c | cc | c | ccc |}
342   \hline
343 < \multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\
343 > &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
344   \hline
308 – &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\
309 – \hline
345   \textbf{Pt-C} & 1.3 & 15  & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\
346   \textbf{Au-C} & 1.9 & 6.5  & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\
347  
348   \hline
349   \end{tabular}
350 + \label{tab:co_parameters}
351   \end{table}
352  
353   %Table of energies
354   \begin{table}[H]
355 < \caption{Adsorption energies in eV}
355 >  \caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials
356 >    described in this work.  All values are in eV.}
357   \centering
358   \begin{tabular}{| c | cc |}
359 < \hline
360 < & Calc. & Exp. \\
361 < \hline
362 < \textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\
363 < \textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\
364 < \hline
359 >  \hline
360 >  & Calculated & Experimental \\
361 >  \hline
362 >  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,}
363 >  (Ref. \protect\cite{Kelemen:1979}) \\
364 > & &  -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline
365 >  \textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,}  (Ref. \protect\cite{TPDGold}) \\
366 >  \hline
367   \end{tabular}
368 + \label{tab:co_energies}
369   \end{table}
370  
371 + \subsection{Pt(557) and Au(557) metal interfaces}
372 + Our Pt system is an orthorhombic periodic box of dimensions
373 + 54.482~x~50.046~x~120.88~\AA~while our Au system has
374 + dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs
375 + are 9 and 8 atoms deep respectively, corresponding to a slab
376 + thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
377 + The systems are arranged in a FCC crystal that have been cut
378 + along the (557) plane so that they are periodic in the {\it x} and
379 + {\it y} directions, and have been oriented to expose two aligned
380 + (557) cuts along the extended {\it z}-axis.  Simulations of the
381 + bare metal interfaces at temperatures ranging from 300~K to
382 + 1200~K were performed to confirm the relative
383 + stability of the surfaces without a CO overlayer.  
384  
385 + The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting}
386 + and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at
387 + different temperatures for the two metals.  The bare Au and Pt surfaces were
388 + initially run in the canonical (NVT) ensemble at 800~K and 1000~K
389 + respectively for 100 ps. The two surfaces were relatively stable at these
390 + temperatures when no CO was present, but experienced increased surface
391 + mobility on addition of CO. Each surface was then dosed with different concentrations of CO
392 + that was initially placed in the vacuum region.  Upon full adsorption,
393 + these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
394 + coverage. Higher coverages resulted in the formation of a double layer of CO,
395 + which introduces artifacts that are not relevant to (557) reconstruction.
396 + Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
397 + the Au surfaces often had a significant CO population in the gas
398 + phase.  These systems were allowed to reach thermal equilibrium (over
399 + 5~ns) before being run in the microcanonical (NVE) ensemble for
400 + data collection. All of the systems examined had at least 40~ns in the
401 + data collection stage, although simulation times for some Pt of the
402 + systems exceeded 200~ns.  Simulations were carried out using the open
403 + source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}
404  
405  
406  
407  
408 < % Just results, leave discussion for discussion section
408 > % RESULTS
409 > %
410   \section{Results}
411 < \subsection{Diffusion}
412 < 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.
411 > \subsection{Structural remodeling}
412 > The bare metal surfaces experienced minor roughening of the
413 > step-edge because of the elevated temperatures, but the (557)
414 > face was stable throughout the simulations. The surface of both
415 > systems, upon dosage of CO, began to undergo extensive remodeling
416 > that was not observed in the bare systems. Reconstructions of
417 > the Au systems were limited to breakup of the step-edges and
418 > some step wandering. The lower coverage Pt systems experienced
419 > similar restructuring but to a greater extent. The 50\% coverage
420 > Pt system was unique among our simulations in that it formed
421 > well-defined and stable double layers through step coalescence,
422 > similar to results reported by Tao {\it et al}.\cite{Tao:2010}
423  
341 – %Table of Diffusion Constants
342 – %Add gold?M
343 – \begin{table}[H]
344 – \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}
345 – \centering
346 – \begin{tabular}{| c | cc | cc | c |}
347 – \hline
348 – \textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  & \textbf{Time (ns)}\\
349 – \hline
350 – &\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}
424  
425 + \subsubsection{Step wandering}
426 + The 0\% coverage surfaces for both metals showed minimal
427 + step-wandering at their respective temperatures. As the CO
428 + coverage increased however, the mobility of the surface atoms,
429 + described through adatom diffusion and step-edge wandering,
430 + also increased.  Except for the 50\% Pt system where step
431 + coalescence occurred, the step-edges in the other simulations
432 + preferred to keep nearly the same distance between steps as in
433 + the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au.
434 + Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994}
435 + highlights the repulsion that exists between step-edges even
436 + when no direct interactions are present in the system. This
437 + repulsion is caused by an entropic barrier that arises from
438 + the fact that steps cannot cross over one another. This entropic
439 + repulsion does not completely define the interactions between
440 + steps, however, so it is possible to observe step coalescence
441 + on some surfaces.\cite{Williams:1991} The presence and
442 + concentration of adsorbates, as shown in this work, can
443 + affect step-step interactions, potentially leading to a new
444 + surface structure as the thermodynamic equilibrium.
445  
446 + \subsubsection{Double layers}
447 + Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface
448 + undergoes two separate reconstructions upon CO adsorption.
449 + The first involves a doubling of the step height and plateau length.
450 + Similar behavior has been seen on a number of surfaces
451 + at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl}
452 + Of the two systems we examined, the Pt system showed a greater
453 + propensity for reconstruction  
454 + because of the larger surface mobility and the greater extent of step wandering.
455 + The amount of reconstruction was strongly correlated to the amount of CO
456 + adsorbed upon the surface.  This appears to be related to the
457 + effect that adsorbate coverage has on edge breakup and on the
458 + surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the
459 + doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here.
460 + Over a longer time scale (150~ns) two more double layers formed
461 + on this surface. Although double layer formation did not occur
462 + in the other Pt systems, they exhibited more step-wandering and
463 + roughening compared to their Au counterparts. The
464 + 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
465 + various times along the simulation showing the evolution of a double layer step-edge.
466  
467 + The second reconstruction observed by
468 + Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched
469 + across the plateau between two step-edges. Neither metal, within
470 + the 40~ns time scale or the extended simulation time of 150~ns for
471 + the 50\% Pt system, experienced this reconstruction.
472 +
473 + %Evolution of surface
474 + \begin{figure}[H]
475 + \includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation.pdf}
476 + \caption{The Pt(557) / 50\% CO system at a sequence of times after
477 +  initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and
478 +  (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly.  The
479 +  doubling of the layers appears only after two adjacent step-edges
480 +  touch.  The circled spot in (b) nucleated the growth of the double
481 +  step observed in the later configurations.}
482 +  \label{fig:reconstruct}
483 + \end{figure}
484 +
485 + \subsection{Dynamics}
486 + Previous experimental work by Pearl and Sibener\cite{Pearl},
487 + using STM, has been able to capture the coalescence of steps
488 + on Ni(977). The time scale of the image acquisition, $\sim$70~s/image,
489 + provides an upper bound for the time required for the doubling
490 + to occur. By utilizing Molecular Dynamics we are able to probe
491 + the dynamics of these reconstructions at elevated temperatures
492 + and in this section we provide data on the timescales for transport
493 + properties, e.g. diffusion and layer formation time.
494 +
495 +
496 + \subsubsection{Transport of surface metal atoms}
497 + %forcedSystems/stepSeparation
498 + The wandering of a step-edge is a cooperative effect
499 + arising from the individual movements of the atoms making up the steps. An ideal metal surface
500 + displaying a low index facet, (111) or (100), is unlikely to experience
501 + much surface diffusion because of the large energetic barrier that must
502 + be overcome to lift an atom out of the surface. The presence of step-edges and other surface features
503 + on higher-index facets provides a lower energy source for mobile metal atoms.
504 + Single-atom break-away from a step-edge on a clean surface still imposes an
505 + energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting
506 + the same metal atom vertically out of the surface,  \textgreater~60 kcal/mol.
507 + The penalty lowers significantly when CO is present in sufficient quantities
508 + on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as
509 + $\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for
510 + diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then
511 + able to explore the terrace before rejoining either their original step-edge or
512 + becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom
513 + to traverse to a separate terrace although the presence of CO can lower the
514 + energy barrier required to lift or lower an adatom. By tracking the mobility of individual
515 + metal atoms on the Pt and Au surfaces we were able to determine the relative
516 + diffusion constants, as well as how varying coverages of CO affect the diffusion. Close
517 + observation of the mobile metal atoms showed that they were typically in
518 + equilibrium with the step-edges.
519 + At times, their motion was concerted and two or more adatoms would be
520 + observed moving together across the surfaces.
521 +
522 + A particle was considered ``mobile'' once it had traveled more than 2~\AA~
523 + between saved configurations of the system (typically 10-100 ps). A mobile atom
524 + would typically travel much greater distances than this, but the 2~\AA~cutoff
525 + was used to prevent swamping the diffusion data with the in-place vibrational
526 + movement of buried atoms. Diffusion on a surface is strongly affected by
527 + local structures and in this work, the presence of single and double layer
528 + step-edges causes the diffusion parallel to the step-edges to be larger than
529 + the diffusion perpendicular to these edges. Parallel and perpendicular
530 + diffusion constants are shown in Figure \ref{fig:diff}.
531 +
532 + %Diffusion graph
533 + \begin{figure}[H]
534 + \includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1.pdf}
535 + \caption{Diffusion constants for mobile surface atoms along directions
536 +  parallel ($\mathbf{D}_{\parallel}$) and perpendicular
537 +  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
538 +  surface coverage.  Diffusion parallel to the step-edge is higher
539 +  than that perpendicular to the edge because of the lower energy
540 +  barrier associated with traversing along the edge as compared to
541 +  completely breaking away. The two reported diffusion constants for
542 +  the 50\% Pt system arise from different sample sets. The lower values
543 +  correspond to the same 40~ns amount that all of the other systems were
544 +  examined at, while the larger values correspond to a 20~ns period }
545 + \label{fig:diff}
546 + \end{figure}
547 +
548 + The weaker Au-CO interaction is evident in the weak CO-coverage
549 + dependance of Au diffusion. This weak interaction leads to lower
550 + observed coverages when compared to dosage amounts. This further
551 + limits the effect the CO can have on surface diffusion. The correlation
552 + between coverage and Pt diffusion rates shows a near linear relationship
553 + at the earliest times in the simulations. Following double layer formation,
554 + however, there is a precipitous drop in adatom diffusion. As the double
555 + layer forms, many atoms that had been tracked for mobility data have
556 + now been buried resulting in a smaller reported diffusion constant. A
557 + secondary effect of higher coverages is CO-CO cross interactions that
558 + lower the effective mobility of the Pt adatoms that are bound to each CO.
559 + This effect would become evident only at higher coverages. A detailed
560 + account of Pt adatom energetics follows in the Discussion.
561 +
562 +
563 + \subsubsection{Dynamics of double layer formation}
564 + The increased diffusion on Pt at the higher CO coverages is the primary
565 + contributor to double layer formation. However, this is not a complete
566 + explanation -- the 33\%~Pt system has higher diffusion constants, but
567 + did not show any signs of edge doubling in 40~ns. On the 50\%~Pt
568 + system, one double layer formed within the first 40~ns of simulation time,
569 + while two more were formed as the system was allowed to run for an
570 + additional 110~ns (150~ns total). This suggests that this reconstruction
571 + is a rapid process and that the previously mentioned upper bound is a
572 + very large overestimate.\cite{Williams:1991,Pearl} In this system the first
573 + appearance of a double layer appears at 19~ns into the simulation.
574 + Within 12~ns of this nucleation event, nearly half of the step has formed
575 + the double layer and by 86~ns the complete layer has flattened out.
576 + From the appearance of the first nucleation event to the first observed
577 + double layer, the process took $\sim$20~ns. Another $\sim$40~ns was
578 + necessary for the layer to completely straighten. The other two layers in
579 + this simulation formed over periods of 22~ns and 42~ns respectively.
580 + A possible explanation for this rapid reconstruction is the elevated
581 + temperatures under which our systems were simulated. The process
582 + would almost certainly take longer at lower temperatures. Additionally,
583 + our measured times for completion of the doubling after the appearance
584 + of a nucleation site are likely affected by our periodic boxes. A longer
585 + step-edge will likely take longer to ``zipper''.
586 +
587 +
588   %Discussion
589   \section{Discussion}
590 < 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.
590 > We have shown that a classical potential model is able to model the
591 > initial reconstruction of the Pt(557) surface upon CO adsorption as
592 > shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were
593 > able to observe features of the dynamic processes necessary for
594 > this reconstruction. Here we discuss the features of the model that
595 > give rise to the observed dynamical properties of the (557) reconstruction.
596  
597   \subsection{Diffusion}
598 < 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?)
599 < \\
600 < \\
601 < %Evolution of surface
598 > The perpendicular diffusion constant
599 > appears to be the most important indicator of double layer
600 > formation. As highlighted in Figure \ref{fig:reconstruct}, the
601 > formation of the double layer did not begin until a nucleation
602 > site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994},
603 > the inability for edges to cross leads to an effective edge-edge repulsion that
604 > must be overcome to allow step coalescence.
605 > A greater $\textbf{D}_\perp$ implies more step-wandering
606 > and a larger chance for the stochastic meeting of two edges
607 > to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double
608 > layer. This helps explain why the time scale for formation after
609 > the appearance of a nucleation site was rapid, while the initial
610 > appearance of the nucleation site was unpredictable.
611 >
612 > \subsection{Mechanism for restructuring}
613 > Since the Au surface showed no large scale restructuring in any of
614 > our simulations, our discussion will focus on the 50\% Pt-CO system
615 > which did exhibit doubling. A
616 > number of possible mechanisms exist to explain the role of adsorbed
617 > CO in restructuring the Pt surface. Quadrupolar repulsion between
618 > adjacent CO molecules adsorbed on the surface is one possibility.  
619 > However, the quadrupole-quadrupole interaction is short-ranged and
620 > is attractive for some orientations.  If the CO molecules are ``locked'' in
621 > a specific orientation relative to each other, through atop adsorption for
622 > example, this explanation would gain credence. The calculated energetic repulsion
623 > between two CO molecules located a distance of 2.77~\AA~apart
624 > (nearest-neighbor distance of Pt) and both in a vertical orientation,
625 > is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance
626 > of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away
627 > from a purely vertical orientation also lowers the repulsion. When the
628 > carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is
629 > reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}.
630 > The calculated barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
631 > repulsion between adjacent CO molecules bound to Pt could increase the surface
632 > diffusion. However, the residence time of CO on Pt suggests that these
633 > molecules are extremely mobile, with diffusion constants 40 to 2500 times
634 > larger than surface Pt atoms. This mobility suggests that the CO molecules jump
635 > between different Pt atoms throughout the simulation, but will stay bound for
636 > significant periods of time.
637 >
638 > A different interpretation of the above mechanism, taking into account the large
639 > mobility of the CO, looks at how instantaneous and short-lived configurations of
640 > CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge
641 > breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach
642 > an edge atom is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
643 > \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases
644 > (e), (g), and (h), the barrier can be lowered to $\sim$23~kcal/mole. In these instances,
645 > it becomes quite energetically favorable to roughen the edge by introducing a small
646 > separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in
647 > simulations with significant CO populations. The roughening is present to a lesser extent
648 > on lower coverage surfaces and even on the bare surfaces, although in these cases it is likely
649 > due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism
650 > of step-edge breakup suggested by these energy curves is one of the most difficult
651 > processes, a complete break-away from the step-edge in one unbroken movement.
652 > Easier multistep mechanisms likely exist where an adatom moves laterally on the surface
653 > after being ejected so it ends up alongside the ledge. This provides the atom with 5 nearest
654 > neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher
655 > than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO
656 > quadrupolar repulsion is still playing a primary role, but for its importance in roughening
657 > the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not
658 > born out by their mobility data. The requirement for a large density of CO on the surface
659 > for some of the more favorable suggested configurations in Figure \ref{fig:SketchGraphic}
660 > correspond well with the increased mobility seen on higher coverage surfaces.
661 >
662 > %Sketch graphic of different configurations
663   \begin{figure}[H]
664 < \includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
665 < \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.}
664 > \includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf}
665 > \caption{The dark grey atoms refer to the upper ledge, while the white atoms are
666 > the lower terrace. The blue highlighted atoms had a CO in a vertical atop position
667 > upon them. These are a sampling of the configurations examined to gain a more
668 > complete understanding of the effects CO has on surface diffusion and edge breakup.
669 > Energies associated with each configuration are displayed in Figure \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.pdf}
676 + \caption{The energy curves directly correspond to the labeled model
677 + surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative
678 + to their initial configuration so the energy of a and h do not have the
679 + same zero value. As is seen, certain arrangements of CO can lower
680 + the energetic barrier that must be overcome to create an adatom.
681 + However, it is the highest coverages where these higher-energy
682 + configurations of CO will be more likely. }
683 + \label{fig:SketchEnergies}
684 + \end{figure}
685  
686 + While configurations of CO on the surface are able to increase diffusion,
687 + this does not immediately provide an explanation for the formation of double
688 + layers. If adatoms were constrained to their terrace then doubling would be
689 + much less likely to occur. Nucleation sites could still potentially form, but there
690 + would not be enough atoms to finish the doubling. For a non-simulated metal surface, where the
691 + step lengths can be assumed to be infinite relative to atomic sizes, local doubling would be possible, but in
692 + our simulations with our periodic treatment of the system, the system is not large enough to experience this effect.
693 + Thus, there must be a mechanism that explains how adatoms are able to move
694 + amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate
695 + where an adatom along the step-edge with an adsorbed CO ``burrows'' into the
696 + edge displacing an atom onto the higher terrace. This mechanism was chosen
697 + because of similar events that were observed during the simulations. The barrier
698 + heights we obtained are only approximations because we constrained the movement
699 + of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s
700 + are provide a strong energetic support for this modeled lifting mechanism. When CO is not present and
701 + this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown
702 + in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol.
703 + While the barrier height is comparable for both cases, there is nearly a 20~kcal/mol
704 + difference in energies and makes the process energetically favorable.
705  
706 + %lambda progression of Pt -> shoving its way into the step
707 + \begin{figure}[H]
708 + \includegraphics[width=\linewidth]{EPS_rxnCoord.pdf}
709 + \caption{ Various points along a reaction coordinate are displayed in the figure.
710 + The mechanism of edge traversal is examined in the presence of CO. The approximate
711 + barrier for the displayed process is 20~kcal/mol. However, the $\Delta E$ of this process
712 + is -15~kcal/mol making it an energetically favorable process.}
713 + \label{fig:lambda}
714 + \end{figure}
715  
716 + The mechanism for doubling on this surface appears to require the cooperation of at least
717 + these two described processes. For complete doubling of a layer to occur there must
718 + be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from
719 + that terrace they must either rise up on the ledge above them or drop to the ledge below
720 + them. The presence of CO helps with the energetics of both of these situations. There must be sufficient
721 + breakage of the step-edge to increase the concentration of adatoms on the surface and
722 + these adatoms must then undergo the burrowing highlighted above or some comparable
723 + mechanism to traverse the step-edge. Over time, these mechanisms working in concert
724 + lead to the formation of a double layer.
725 +
726 + \subsection{CO Removal and double layer stability}
727 + Once a double layer had formed on the 50\%~Pt system it
728 + remained for the rest of the simulation time with minimal
729 + movement. There were configurations that showed small
730 + wells or peaks forming, but typically within a few nanoseconds
731 + the feature would smooth away. Within our simulation time,
732 + the formation of the double layer was irreversible and a double
733 + layer was never observed to split back into two single layer
734 + step-edges while CO was present. To further gauge the effect
735 + CO had on this system, additional simulations were run starting
736 + from a late configuration of the 50\%~Pt system that had formed
737 + double layers. These simulations then had their CO removed.
738 + The double layer breaks rapidly in these simulations, already
739 + showing a well-defined splitting after 100~ps. Configurations of
740 + this system are shown in Figure \ref{fig:breaking}. The coloring
741 + of the top and bottom layers helps to exhibit how much mixing
742 + the edges experience as they split. These systems were only
743 + examined briefly, 10~ns, and within that time despite the initial
744 + rapid splitting, the edges only moved another few \AA~apart.
745 + It is possible with longer simulation times that the
746 + (557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010}
747 +
748 +
749 +
750 + %breaking of the double layer upon removal of CO
751 + \begin{figure}[H]
752 + \includegraphics[width=\linewidth]{EPS_doubleLayerBreaking.pdf}
753 + \caption{(A)  0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO
754 + helped maintain the stability of the double layer and its microfaceting of the double layer
755 + into a (111) configuration. This microfacet immediately reverts to the original (100) step
756 + edge which is a hallmark of the (557) surface. The separation is not a simple sliding apart, rather
757 + there is a mixing of the lower and upper atoms at the edge.}
758 + \label{fig:breaking}
759 + \end{figure}
760 +
761 +
762 +
763 +
764   %Peaks!
765 < \includegraphics[scale=0.25]{doublePeaks_noCO.png}
765 > %\begin{figure}[H]
766 > %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
767 > %\caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
768 > %of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with
769 > %aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
770 > %\label{fig:peaks}
771 > %\end{figure}
772 >
773 >
774 > %Don't think I need this
775 > %clean surface...
776 > %\begin{figure}[H]
777 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
778 > %\caption{}
779 >
780 > %\end{figure}
781 > %\label{fig:clean}
782 >
783 >
784   \section{Conclusion}
785 + The strength of the Pt-CO binding interaction as well as the large
786 + quadrupolar repulsion between CO molecules are sufficient to
787 + explain the observed increase in surface mobility and the resultant
788 + reconstructions at the highest simulated coverage. The weaker
789 + Au-CO interaction results in lower diffusion constants, less step-wandering,
790 + and a lack of the double layer reconstruction. An in-depth examination
791 + of the energetics shows the important role CO plays in increasing
792 + step-breakup and in facilitating edge traversal which are both
793 + necessary for double layer formation.
794  
795  
796 < \section{Acknowledgments}
796 >
797 > %Things I am not ready to remove yet
798 >
799 > %Table of Diffusion Constants
800 > %Add gold?M
801 > % \begin{table}[H]
802 > %   \caption{}
803 > %   \centering
804 > % \begin{tabular}{| c | cc | cc | }
805 > %   \hline
806 > %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
807 > %   \hline
808 > %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
809 > %   \hline
810 > %   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
811 > %   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
812 > %   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
813 > %   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
814 > %   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
815 > %   \hline
816 > % \end{tabular}
817 > % \end{table}
818 >
819 > \begin{acknowledgement}
820   Support for this project was provided by the National Science
821   Foundation under grant CHE-0848243 and by the Center for Sustainable
822   Energy at Notre Dame (cSEND). Computational time was provided by the
823   Center for Research Computing (CRC) at the University of Notre Dame.
824 <
824 > \end{acknowledgement}
825   \newpage
826   \bibliography{firstTryBibliography}
827 < \end{doublespace}
827 > %\end{doublespace}
828 >
829 > \begin{tocentry}
830 > %\includegraphics[height=3.5cm]{timelapse}
831 > \end{tocentry}
832 >
833   \end{document}

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