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Revision 3880 by jmichalk, Tue Mar 19 15:01:59 2013 UTC

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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}
14 < \usepackage[square, comma, sort&compress]{natbib}
22 > \usepackage{multicol}
23 >
24 > \usepackage[version=3]{mhchem}  % this is a great package for formatting chemical reactions
25 > % \usepackage[square, comma, sort&compress]{natbib}
26   \usepackage{url}
27   \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
28   \evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
29   9.0in \textwidth 6.5in \brokenpenalty=10000
30  
31   % double space list of tables and figures
32 < \AtBeginDelayedFloats{\renewcommand{\baselinestretch}{1.66}}
32 > %\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}}
33   \setlength{\abovecaptionskip}{20 pt}
34   \setlength{\belowcaptionskip}{30 pt}
35 + % \bibpunct{}{}{,}{s}{}{;}
36  
37 < %\renewcommand\citemid{\ } % no comma in optional reference note
38 < \bibpunct{[}{]}{,}{n}{}{;}
27 < \bibliographystyle{achemso}
37 > %\citestyle{nature}
38 > % \bibliographystyle{achemso}
39  
40 < \begin{document}
40 > \title{Molecular Dynamics simulations of the surface reconstructions
41 >  of Pt(557) and Au(557) under exposure to CO}
42  
43 + \author{Joseph R. Michalka}
44 + \author{Patrick W. McIntyre}
45 + \author{J. Daniel Gezelter}
46 + \email{gezelter@nd.edu}
47 + \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
48 +  Department of Chemistry and Biochemistry\\ University of Notre
49 +  Dame\\ Notre Dame, Indiana 46556}
50  
51 + \keywords{}
52 +
53 + \begin{document}
54 +
55 +
56   %%
57   %Introduction
58   %       Experimental observations
# Line 47 | Line 71
71   %Summary
72   %%
73  
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
74  
62 – % make the title
63 – \maketitle
64 –
65 – \begin{doublespace}
66 –
75   \begin{abstract}
76 + We examine surface reconstructions of Pt and Au(557) under
77 + various CO coverages using molecular dynamics in order to
78 + explore possible mechanisms for any observed reconstructions
79 + and their dynamics. The metal-CO interactions were parameterized
80 + as part of this work so that an efficient large-scale treatment of
81 + this system could be undertaken. The large difference in binding
82 + strengths of the metal-CO interactions was found to play a significant
83 + role with regards to step-edge stability and adatom diffusion. A
84 + small correlation between coverage and the diffusion constant
85 + was also determined. The energetics of CO adsorbed to the surface
86 + is sufficient to explain the reconstructions observed on the Pt
87 + systems and the lack  of reconstruction of the Au systems.
88  
89 +
90 + The mechanism and dynamics of surface reconstructions of Pt(557)
91 + and Au(557) exposed to various coverages of carbon monoxide (CO)
92 + were investigated using molecular dynamics simulations. Metal-CO
93 + interactions were parameterized from experimental data and plane-wave
94 + Density Functional Theory (DFT) calculations.  The large difference in
95 + binding strengths of the Pt-CO and Au-CO interactions was found to play
96 + a significant role in step-edge stability and adatom diffusion constants.
97 + The energetics of CO adsorbed to the surface is sufficient to explain the
98 + step-doubling reconstruction observed on Pt(557) and the lack of such
99 + a reconstruction on the Au(557) surface.
100   \end{abstract}
101  
102   \newpage
# Line 79 | Line 110 | Industrial catalysts usually consist of small particle
110   %       Sub: Also, easier to observe what is going on and provide reasons and explanations
111   %
112  
113 < Industrial catalysts usually consist of small particles exposing
114 < different atomic terminations that exhibit a high concentration of
115 < step, kink sites, and vacancies at the edges of the facets.  These
85 < sites are thought to be the locations of catalytic
113 > Industrial catalysts usually consist of small particles that exhibit a
114 > high concentration of steps, kink sites, and vacancies at the edges of
115 > the facets.  These sites are thought to be the locations of catalytic
116   activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now
117 < significant evidence to demonstrate that solid surfaces are often
118 < structurally, compositionally, and chemically {\it modified} by
119 < reactants under operating conditions.\cite{Tao2008,Tao:2010,Tao2011}
120 < The coupling between surface oxidation state and catalytic activity
121 < for CO oxidation on Pt, for instance, is widely
122 < documented.\cite{Ertl08,Hendriksen:2002} Despite the well-documented
123 < role of these effects on reactivity, the ability to capture or predict
124 < them in atomistic models is currently somewhat limited.  While these
125 < effects are perhaps unsurprising on the highly disperse, multi-faceted
126 < nanoscale particles that characterize industrial catalysts, they are
127 < manifest even on ordered, well-defined surfaces. The Pt(557) surface,
128 < for example, exhibits substantial and reversible restructuring under
129 < exposure to moderate pressures of carbon monoxide.\cite{Tao:2010}
117 > significant evidence that solid surfaces are often structurally,
118 > compositionally, and chemically modified by reactants under operating
119 > conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between
120 > surface oxidation states and catalytic activity for CO oxidation on
121 > Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002}
122 > Despite the well-documented role of these effects on reactivity, the
123 > ability to capture or predict them in atomistic models is somewhat
124 > limited.  While these effects are perhaps unsurprising on the highly
125 > disperse, multi-faceted nanoscale particles that characterize
126 > industrial catalysts, they are manifest even on ordered, well-defined
127 > surfaces. The Pt(557) surface, for example, exhibits substantial and
128 > reversible restructuring under exposure to moderate pressures of
129 > carbon monoxide.\cite{Tao:2010}
130  
131 < This work is part of an ongoing effort to understand the causes,
132 < mechanisms and timescales for surface restructuring using molecular
133 < simulation methods.  Since the dynamics of the process is of
134 < particular interest, we utilize classical molecular dynamic methods
135 < with force fields that represent a compromise between chemical
136 < accuracy and the computational efficiency necessary to observe the
137 < process of interest.
131 > This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557)
132 > surface restructuring using molecular simulations.  Since the dynamics
133 > of the process are of particular interest, we employ classical force
134 > fields that represent a compromise between chemical accuracy and the
135 > computational efficiency necessary to simulate the process of interest.
136 > Since restructuring typically occurs as a result of specific interactions of the
137 > catalyst with adsorbates, in this work, two metal systems exposed
138 > to carbon monoxide were examined. The Pt(557) surface has already been shown
139 > to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010}
140 > The Au(557) surface, because of a weaker interaction with CO, is less
141 > likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000}
142 > and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced
143 > reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the
144 > 22 x $\sqrt{3}$ cell. They argued that only a few Au atoms
145 > become adatoms, limiting the stress of this reconstruction, while
146 > allowing the rest to relax and approach the ideal (111)
147 > configuration. They did not see the usual herringbone pattern on Au(111) being greatly
148 > affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a
149 > disruption of the herringbone pattern as CO was adsorbed to the
150 > surface. Both groups suggested that the preference CO shows for
151 > low-coordinated Au atoms was the primary driving force for the reconstruction.
152  
153 < Since restructuring occurs as a result of specific interactions of the catalyst
154 < 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.
153 >
154 >
155   %Platinum molecular dynamics
156   %gold molecular dynamics
157  
117 –
118 –
119 –
120 –
121 –
158   \section{Simulation Methods}
159 < The challenge in modeling any solid/gas interface problem is the
159 > The challenge in modeling any solid/gas interface is the
160   development of a sufficiently general yet computationally tractable
161   model of the chemical interactions between the surface atoms and
162   adsorbates.  Since the interfaces involved are quite large (10$^3$ -
163 < 10$^6$ atoms) and respond slowly to perturbations, {\it ab initio}
163 > 10$^4$ atoms) and respond slowly to perturbations, {\it ab initio}
164   molecular dynamics
165   (AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello
166   methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum
# Line 133 | Line 169 | Coulomb potential.  For this work, we have been using
169   typically not well represented in terms of classical pairwise
170   interactions in the same way that bonds in a molecular material are,
171   nor are they captured by simple non-directional interactions like the
172 < Coulomb potential.  For this work, we have been using classical
173 < molecular dynamics with potential energy surfaces that are
174 < specifically tuned for transition metals.  In particular, we use the
175 < EAM potential for Au-Au and Pt-Pt interactions, while modeling the CO
176 < using a model developed by Straub and Karplus for studying
177 < photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and Pt-CO
178 < cross interactions were parameterized as part of this work.
172 > Coulomb potential.  For this work, we have used classical molecular
173 > dynamics with potential energy surfaces that are specifically tuned
174 > for transition metals.  In particular, we used the EAM potential for
175 > Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using a rigid
176 > three-site model developed by Straub and Karplus for studying
177 > photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and
178 > Pt-CO cross interactions were parameterized as part of this work.
179    
180   \subsection{Metal-metal interactions}
181 < Many of the potentials used for classical simulation of transition
182 < metals are based on a non-pairwise additive functional of the local
183 < electron density. The embedded atom method (EAM) is perhaps the best
184 < known of these
181 > Many of the potentials used for modeling transition metals are based
182 > on a non-pairwise additive functional of the local electron
183 > density. The embedded atom method (EAM) is perhaps the best known of
184 > these
185   methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98}
186   but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and
187   the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler
188 < parameter sets. The glue model of Ercolessi {\it et al.} is among the
189 < fastest of these density functional approaches.\cite{Ercolessi88} In
190 < all of these models, atoms are conceptualized as a positively charged
188 > parameter sets. The glue model of Ercolessi {\it et al}.\cite{Ercolessi88} is among the
189 > fastest of these density functional approaches. In
190 > all of these models, atoms are treated as a positively charged
191   core with a radially-decaying valence electron distribution. To
192   calculate the energy for embedding the core at a particular location,
193   the electron density due to the valence electrons at all of the other
194 < atomic sites is computed at atom $i$'s location,
194 > atomic sites is computed at atom $i$'s location,
195   \begin{equation*}
196   \bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
197   \end{equation*}
# Line 167 | Line 203 | $\phi_{ij}(r_{ij})$ is an pairwise term that is meant
203   V_i =  F[ \bar{\rho}_i ]  + \sum_{j \neq i} \phi_{ij}(r_{ij})
204   \end{equation*}
205   where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and
206 < $\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the
207 < overlap of the two positively charged cores.  
206 > $\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the
207 > repulsive overlap of the two positively charged cores.  
208  
209 < The {\it modified} embedded atom method (MEAM) adds angular terms to
210 < the electron density functions and an angular screening factor to the
211 < pairwise interaction between two
212 < atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
213 < MEAM has become widely used to simulate systems in which angular
214 < interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
215 < metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
216 < MEAM presents significant additional computational costs, however.
209 > % The {\it modified} embedded atom method (MEAM) adds angular terms to
210 > % the electron density functions and an angular screening factor to the
211 > % pairwise interaction between two
212 > % atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
213 > % MEAM has become widely used to simulate systems in which angular
214 > % interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
215 > % metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
216 > % MEAM presents significant additional computational costs, however.
217  
218 < The EAM, Finnis-Sinclair, MEAM, and the Quantum Sutton-Chen potentials
218 > The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials
219   have all been widely used by the materials simulation community for
220   simulations of bulk and nanoparticle
221   properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq}
222   melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
223   fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack
224   propagation,\cite{BECQUART:1993rg} and alloying
225 < dynamics.\cite{Shibata:2002hh} All of these potentials have their
226 < strengths and weaknesses.  One of the strengths common to all of the
227 < methods is the relatively large library of metals for which these
228 < potentials have been
229 < parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
225 > dynamics.\cite{Shibata:2002hh} One of EAM's strengths
226 > is its sensitivity to small changes in structure. This arises
227 > because interactions
228 > up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a}
229 > Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88}
230 > which is only parameterized up to the nearest-neighbor
231 > interactions, EAM is a suitable choice for systems where
232 > the bulk properties are of secondary importance to low-index
233 > surface structures. Additionally, the similarity of EAM's functional
234 > treatment of the embedding energy to standard density functional
235 > theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier.
236 > \cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  
237  
238 < \subsection{CO}
239 < Since one explanation for the strong surface CO repulsion on metals is
240 < the large linear quadrupole moment of carbon monoxide, the model
241 < chosen for this molecule exhibits this property in an efficient
242 < manner.  We used a model first proposed by Karplus and Straub to study
243 < the photodissociation of CO from myoglobin.\cite{Straub} The Straub and
244 < Karplus model is a rigid three site model which places a massless M
245 < site at the center of mass along the CO bond.  The geometry used along
246 < with the interaction parameters are reproduced in Table 1. The effective
238 >
239 >
240 >
241 > \subsection{Carbon Monoxide model}
242 > Previous explanations for the surface rearrangements center on
243 > the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010}  
244 > We used a model first proposed by Karplus and Straub to study
245 > the photodissociation of CO from myoglobin because it reproduces
246 > the quadrupole moment well.\cite{Straub} The Straub and
247 > Karplus model treats CO as a rigid three site molecule with a massless M
248 > site at the molecular center of mass. The geometry and interaction
249 > parameters are reproduced in Table~\ref{tab:CO}. The effective
250   dipole moment, calculated from the assigned charges, is still
251   small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
252   to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
253   mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
254   %CO Table
255   \begin{table}[H]
256 < \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 $e$.}
256 >  \caption{Positions, Lennard-Jones parameters ($\sigma$ and
257 >    $\epsilon$), and charges for the CO-CO
258 >    interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are
259 >    in kcal/mol, and charges are in atomic units.}
260   \centering
261   \begin{tabular}{| c | c | ccc |}
262   \hline
263 < \multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\
263 > &  {\it z} & $\sigma$ & $\epsilon$ & q\\
264   \hline
265 < &  r & $\sigma$ & $\epsilon$ & q\\
265 > \textbf{C} & -0.6457 &  3.83 & 0.0262   &   -0.75 \\
266 > \textbf{O} &  0.4843 &  3.12 &  0.1591  &   -0.85 \\
267 > \textbf{M} & 0.0 & -  &  -  &    1.6 \\
268   \hline
218 – \textbf{C} & 0.0 &  0.0262  & 3.83   &   -0.75 \\
219 – \textbf{O} &  1.13 &   0.1591 &   3.12 &   -0.85 \\
220 – \textbf{M} & 0.6457 & -  &  -  &    1.6 \\
221 – \hline
269   \end{tabular}
270 + \label{tab:CO}
271   \end{table}
272  
273 < \subsection{Cross-Interactions}
273 > \subsection{Cross-Interactions between the metals and carbon monoxide}
274  
275 < One hurdle that must be overcome in classical molecular simulations
276 < is the proper parameterization of the potential interactions present
277 < in the system. Since the adsorption of CO onto a platinum surface has been
278 < the focus of many experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
279 < and theoretical studies \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
280 < there is a large amount of data in the literature to fit too. We started with parameters
281 < reported by Korzeniewski et al. \cite{Pons:1986} and then
282 < modified them to ensure that the Pt-CO interaction favored
283 < an atop binding position for the CO upon the Pt surface. This
284 < constraint led to the binding energies being on the higher side
285 < of reported values. Following the method laid out by Korzeniewski,
286 < the Pt-C interaction was fit to a strong Lennard-Jones 12-6
287 < interaction to mimic binding, while the Pt-O interaction
288 < was parameterized to a Morse potential with a large $r_o$
289 < to contribute a weak repulsion. The resultant potential-energy
290 < surface suitably recovers the calculated Pt-C bond length ( 1.6\AA)\cite{Beurden:2002ys} and affinity
291 < for the atop binding position.\cite{Deshlahra:2012, Hopster:1978}
275 > Since the adsorption of CO onto a Pt surface has been the focus
276 > of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
277 > and theoretical work
278 > \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
279 > there is a significant amount of data on adsorption energies for CO on
280 > clean metal surfaces. An earlier model by Korzeniewski {\it et
281 >  al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were
282 > modified to ensure that the Pt-CO interaction favored the atop binding
283 > position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}.
284 > The modified parameters yield binding energies that are slightly higher
285 > than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski
286 > {\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
287 > Lennard-Jones interaction to mimic strong, but short-ranged, partial
288 > binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The
289 > Pt-O interaction was modeled with a Morse potential with a large
290 > equilibrium distance, ($r_o$).  These choices ensure that the C is preferred
291 > over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak
292 > repulsion which favors the atop site.  The resulting potential-energy
293 > surface suitably recovers the calculated Pt-C separation length
294 > (1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding
295 > position.\cite{Deshlahra:2012, Hopster:1978}
296  
297   %where did you actually get the functionals for citation?
298   %scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think
299   %same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there...
300 < The Au-C and Au-O interaction parameters were also fit to a Lennard-Jones
301 < and Morse potential respectively, to reproduce Au-CO binding energies.
302 < These energies were obtained from quantum calculations carried out using
303 < the PBE GGA exchange-correlation functionals\cite{Perdew_GGA} for gold, carbon, and oxygen
304 < constructed by Rappe, Rabe, Kaxiras, and Joannopoulos. \cite{RRKJ_PP}.
305 < All calculations were run using the {\sc Quantum ESPRESSO} package. \cite{QE-2009}  
306 < First, a four layer slab of gold comprised of 32 atoms displaying a (111) surface was
307 < converged using a 4X4X4 grid of Monkhorst-Pack \emph{k}-points.\cite{Monkhorst:1976}
308 < The kinetic energy of the wavefunctions were truncated at 20 Ry while the
309 < cutoff for the charge density and potential was set at 80 Ry. This relaxed
310 < gold slab was then used in numerous single point calculations  with CO at various heights
311 < to create a potential energy surface for the Au-CO interaction.
300 > The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and
301 > Morse potentials, respectively, to reproduce Au-CO binding energies.
302 > The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations.
303 > Adsorption energies were obtained from gas-surface DFT calculations with a
304 > periodic supercell plane-wave basis approach, as implemented in the
305 > {\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were
306 > described with the projector augmented-wave (PAW)
307 > method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
308 > included to an energy cutoff of 20 Ry. Electronic energies are
309 > computed with the PBE implementation of the generalized gradient
310 > approximation (GGA) for gold, carbon, and oxygen that was constructed
311 > by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
312 > In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4
313 > Au x 2 Au surface planes and separated from vertical images by six
314 > layers of vacuum space. The surface atoms were all allowed to relax
315 > before CO was added to the system. Electronic relaxations were
316 > performed until the energy difference between subsequent steps
317 > was less than $10^{-8}$ Ry.   Nonspin-polarized supercell calculations
318 > were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
319 > zone.\cite{Monkhorst:1976} The relaxed gold slab was
320 > then used in numerous single point calculations with CO at various
321 > heights (and angles relative to the surface) to allow fitting of the
322 > empirical force field.
323  
324   %Hint at future work
325 < The fit parameter sets employed in this work are shown in Table 2 and their
326 < reproduction of the binding energies are displayed in Table 3. Currently,
327 < charge transfer is not being treated in this system, however, that is a goal
328 < for future work as the effect has been seen to affect binding energies and
329 < binding site preferences. \cite{Deshlahra:2012}
325 > The parameters employed for the metal-CO cross-interactions in this work
326 > are shown in Table~\ref{tab:co_parameters} and the binding energies on the
327 > (111) surfaces are displayed in Table~\ref{tab:co_energies}.  Charge transfer
328 > and polarization are neglected in this model, although these effects could have
329 > an effect on  binding energies and binding site preferences.
330  
268 –
269 –
270 –
271 – \subsection{Construction and Equilibration of 557 Metal interfaces}
272 –
273 – Our model systems are composed of approximately 4000 metal atoms cut along the 557 plane so that they are periodic in the \it{x} and \it{y} directions exposing the 557 plane in the \it{z} direction. Runs at various temperatures ranging from 300~K to 1200~K were started with the intent of viewing relative stability of the surface when CO was not present in the system.  Owing to the different melting points (1337~K for Au and 2045~K for Pt), the bare crystal systems were initially run in the Canonical ensemble for at 800~K and 1000~K respectively for 100 ps. Various amounts of CO were placed in the vacuum portion which upon full adsorption to the surface corresponded to 5\%, 25\%, 33\%, and 50\% coverages. These systems were again allowed to reach thermal equilibrium before being run in the micro canonical ensemble. All of the systems examined were run for at least 40 ns. A subset that were undergoing interesting effects have been allowed to continue running with one system approaching 200 ns.em
274 –
275 –
276 –
277 –
278 –
279 –
280 – %\subsection{System}
281 – %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.
282 –
283 –
331   %Table  of Parameters
332   %Pt Parameter Set 9
333   %Au Parameter Set 35
334   \begin{table}[H]
335 < \caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol}
335 >  \caption{Best fit parameters for metal-CO cross-interactions. Metal-C
336 >    interactions are modeled with Lennard-Jones potentials. While the
337 >    metal-O interactions were fit to Morse
338 >    potentials.  Distances are given in \AA~and energies in kcal/mol. }
339   \centering
340   \begin{tabular}{| c | cc | c | ccc |}
341   \hline
342 < \multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\
342 > &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
343   \hline
294 – &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\
295 – \hline
344   \textbf{Pt-C} & 1.3 & 15  & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\
345   \textbf{Au-C} & 1.9 & 6.5  & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\
346  
347   \hline
348   \end{tabular}
349 + \label{tab:co_parameters}
350   \end{table}
351  
352   %Table of energies
353   \begin{table}[H]
354 < \caption{Adsorption energies in eV}
354 >  \caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials
355 >    described in this work.  All values are in eV.}
356   \centering
357   \begin{tabular}{| c | cc |}
358 < \hline
359 < & Calc. & Exp. \\
360 < \hline
361 < \textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\
362 < \textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\
363 < \hline
358 >  \hline
359 >  & Calculated & Experimental \\
360 >  \hline
361 >  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,}
362 >  (Ref. \protect\cite{Kelemen:1979}) \\
363 > & &  -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline
364 >  \textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,}  (Ref. \protect\cite{TPDGold}) \\
365 >  \hline
366   \end{tabular}
367 + \label{tab:co_energies}
368   \end{table}
369  
370 + \subsection{Pt(557) and Au(557) metal interfaces}
371 + Our Pt system is an orthorhombic periodic box of dimensions
372 + 54.482~x~50.046~x~120.88~\AA~while our Au system has
373 + dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs
374 + are 9 and 8 atoms deep respectively, corresponding to a slab
375 + thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
376 + The systems are arranged in a FCC crystal that have been cut
377 + along the (557) plane so that they are periodic in the {\it x} and
378 + {\it y} directions, and have been oriented to expose two aligned
379 + (557) cuts along the extended {\it z}-axis.  Simulations of the
380 + bare metal interfaces at temperatures ranging from 300~K to
381 + 1200~K were performed to confirm the relative
382 + stability of the surfaces without a CO overlayer.  
383  
384 + The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting}
385 + and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at
386 + different temperatures for the two metals.  The bare Au and Pt surfaces were
387 + initially run in the canonical (NVT) ensemble at 800~K and 1000~K
388 + respectively for 100 ps. The two surfaces were relatively stable at these
389 + temperatures when no CO was present, but experienced increased surface
390 + mobility on addition of CO. Each surface was then dosed with different concentrations of CO
391 + that was initially placed in the vacuum region.  Upon full adsorption,
392 + these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
393 + coverage. Higher coverages resulted in the formation of a double layer of CO,
394 + which introduces artifacts that are not relevant to (557) reconstruction.
395 + Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
396 + the Au surfaces often had a significant CO population in the gas
397 + phase.  These systems were allowed to reach thermal equilibrium (over
398 + 5~ns) before being run in the microcanonical (NVE) ensemble for
399 + data collection. All of the systems examined had at least 40~ns in the
400 + data collection stage, although simulation times for some Pt of the
401 + systems exceeded 200~ns.  Simulations were carried out using the open
402 + source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}
403  
404  
405  
406  
407 < % Just results, leave discussion for discussion section
407 > % RESULTS
408 > %
409   \section{Results}
410 < \subsection{Diffusion}
411 < 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.
410 > \subsection{Structural remodeling}
411 > The bare metal surfaces experienced minor roughening of the
412 > step-edge because of the elevated temperatures, but the (557)
413 > face was stable throughout the simulations. The surface of both
414 > systems, upon dosage of CO, began to undergo extensive remodeling
415 > that was not observed in the bare systems. Reconstructions of
416 > the Au systems were limited to breakup of the step-edges and
417 > some step wandering. The lower coverage Pt systems experienced
418 > similar restructuring but to a greater extent. The 50\% coverage
419 > Pt system was unique among our simulations in that it formed
420 > well-defined and stable double layers through step coalescence,
421 > similar to results reported by Tao {\it et al}.\cite{Tao:2010}
422  
327 – %Table of Diffusion Constants
328 – %Add gold?M
329 – \begin{table}[H]
330 – \caption{Platinum 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. There were two approaches of analysis. One looking at the surface atoms that had moved more than a prescribed amount over the run time and the other looking at all surface atoms. Units are \AA\textsuperscript{2}/ns}
331 – \centering
332 – \begin{tabular}{| c | ccc | ccc | c |}
333 – \hline
334 – \textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & \textbf{Time (ns)}\\
335 – \hline
336 – &\multicolumn{3}{c|}{\textbf{Mobile}}&\multicolumn{3}{c|}{\textbf{Surface Atoms}} & \\
337 – \hline
338 – 50\% & 3.74 & 0.89 & 497 & 2.05 & 0.49 & 912 & 116 \\
339 – 50\% & 5.81 & 1.59 & 365 & 2.41 & 0.68 & 912 & 46   \\
340 – 33\% & 6.73 & 2.47 & 332 & 2.51 & 0.93 & 912 & 46   \\
341 – 25\% & 5.38 & 2.04 & 361 & 2.18 & 0.84 & 912 & 46  \\
342 – 5\% & 5.54 & 0.63 & 230 & 1.44 & 0.19 & 912 & 46  \\
343 – 0\% & 3.53 & 0.61 & 282 & 1.11 & 0.22 & 912 & 56  \\
344 – \hline
345 – 50\%-r & 6.91 & 2.00 & 198 & 2.23 & 0.68  & 925 & 25\\
346 – 0\%-r  & 4.73 & 0.27 & 128 & 0.72 & 0.05 & 925 & 43\\
347 – \hline
348 – \end{tabular}
349 – \end{table}
423  
424 + \subsubsection{Step wandering}
425 + The 0\% coverage surfaces for both metals showed minimal
426 + step-wandering at their respective temperatures. As the CO
427 + coverage increased however, the mobility of the surface atoms,
428 + described through adatom diffusion and step-edge wandering,
429 + also increased.  Except for the 50\% Pt system where step
430 + coalescence occurred, the step-edges in the other simulations
431 + preferred to keep nearly the same distance between steps as in
432 + the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au.
433 + Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994}
434 + highlights the repulsion that exists between step-edges even
435 + when no direct interactions are present in the system. This
436 + repulsion is caused by an entropic barrier that arises from
437 + the fact that steps cannot cross over one another. This entropic
438 + repulsion does not completely define the interactions between
439 + steps, however, so it is possible to observe step coalescence
440 + on some surfaces.\cite{Williams:1991} The presence and
441 + concentration of adsorbates, as shown in this work, can
442 + affect step-step interactions, potentially leading to a new
443 + surface structure as the thermodynamic equilibrium.
444  
445 + \subsubsection{Double layers}
446 + Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface
447 + undergoes two separate reconstructions upon CO adsorption.
448 + The first involves a doubling of the step height and plateau length.
449 + Similar behavior has been seen on a number of surfaces
450 + at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl}
451 + Of the two systems we examined, the Pt system showed a greater
452 + propensity for reconstruction  
453 + because of the larger surface mobility and the greater extent of step wandering.
454 + The amount of reconstruction was strongly correlated to the amount of CO
455 + adsorbed upon the surface.  This appears to be related to the
456 + effect that adsorbate coverage has on edge breakup and on the
457 + surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the
458 + doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here.
459 + Over a longer time scale (150~ns) two more double layers formed
460 + on this surface. Although double layer formation did not occur
461 + in the other Pt systems, they exhibited more step-wandering and
462 + roughening compared to their Au counterparts. The
463 + 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
464 + various times along the simulation showing the evolution of a double layer step-edge.
465  
466 + The second reconstruction observed by
467 + Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched
468 + across the plateau between two step-edges. Neither metal, within
469 + the 40~ns time scale or the extended simulation time of 150~ns for
470 + the 50\% Pt system, experienced this reconstruction.
471 +
472 + %Evolution of surface
473 + \begin{figure}[H]
474 + \includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
475 + \caption{The Pt(557) / 50\% CO system at a sequence of times after
476 +  initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and
477 +  (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly.  The
478 +  doubling of the layers appears only after two adjacent step-edges
479 +  touch.  The circled spot in (b) nucleated the growth of the double
480 +  step observed in the later configurations.}
481 +  \label{fig:reconstruct}
482 + \end{figure}
483 +
484 + \subsection{Dynamics}
485 + Previous experimental work by Pearl and Sibener\cite{Pearl},
486 + using STM, has been able to capture the coalescence of steps
487 + on Ni(977). The time scale of the image acquisition, $\sim$70~s/image,
488 + provides an upper bound for the time required for the doubling
489 + to occur. By utilizing Molecular Dynamics we are able to probe
490 + the dynamics of these reconstructions at elevated temperatures
491 + and in this section we provide data on the timescales for transport
492 + properties, e.g. diffusion and layer formation time.
493 +
494 +
495 + \subsubsection{Transport of surface metal atoms}
496 + %forcedSystems/stepSeparation
497 + The wandering of a step-edge is a cooperative effect
498 + arising from the individual movements of the atoms making up the steps. An ideal metal surface
499 + displaying a low index facet, (111) or (100), is unlikely to experience
500 + much surface diffusion because of the large energetic barrier that must
501 + be overcome to lift an atom out of the surface. The presence of step-edges and other surface features
502 + on higher-index facets provides a lower energy source for mobile metal atoms.
503 + Single-atom break-away from a step-edge on a clean surface still imposes an
504 + energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting
505 + the same metal atom vertically out of the surface,  \textgreater~60 kcal/mol.
506 + The penalty lowers significantly when CO is present in sufficient quantities
507 + on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as
508 + $\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for
509 + diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then
510 + able to explore the terrace before rejoining either their original step-edge or
511 + becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom
512 + to traverse to a separate terrace although the presence of CO can lower the
513 + energy barrier required to lift or lower an adatom. By tracking the mobility of individual
514 + metal atoms on the Pt and Au surfaces we were able to determine the relative
515 + diffusion constants, as well as how varying coverages of CO affect the diffusion. Close
516 + observation of the mobile metal atoms showed that they were typically in
517 + equilibrium with the step-edges.
518 + At times, their motion was concerted and two or more adatoms would be
519 + observed moving together across the surfaces.
520 +
521 + A particle was considered ``mobile'' once it had traveled more than 2~\AA~
522 + between saved configurations of the system (typically 10-100 ps). A mobile atom
523 + would typically travel much greater distances than this, but the 2~\AA~cutoff
524 + was used to prevent swamping the diffusion data with the in-place vibrational
525 + movement of buried atoms. Diffusion on a surface is strongly affected by
526 + local structures and in this work, the presence of single and double layer
527 + step-edges causes the diffusion parallel to the step-edges to be larger than
528 + the diffusion perpendicular to these edges. Parallel and perpendicular
529 + diffusion constants are shown in Figure \ref{fig:diff}.
530 +
531 + %Diffusion graph
532 + \begin{figure}[H]
533 + \includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf}
534 + \caption{Diffusion constants for mobile surface atoms along directions
535 +  parallel ($\mathbf{D}_{\parallel}$) and perpendicular
536 +  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
537 +  surface coverage.  Diffusion parallel to the step-edge is higher
538 +  than that perpendicular to the edge because of the lower energy
539 +  barrier associated with traversing along the edge as compared to
540 +  completely breaking away. The two reported diffusion constants for
541 +  the 50\% Pt system arise from different sample sets. The lower values
542 +  correspond to the same 40~ns amount that all of the other systems were
543 +  examined at, while the larger values correspond to a 20~ns period }
544 + \label{fig:diff}
545 + \end{figure}
546 +
547 + The weaker Au-CO interaction is evident in the weak CO-coverage
548 + dependance of Au diffusion. This weak interaction leads to lower
549 + observed coverages when compared to dosage amounts. This further
550 + limits the effect the CO can have on surface diffusion. The correlation
551 + between coverage and Pt diffusion rates shows a near linear relationship
552 + at the earliest times in the simulations. Following double layer formation,
553 + however, there is a precipitous drop in adatom diffusion. As the double
554 + layer forms, many atoms that had been tracked for mobility data have
555 + now been buried resulting in a smaller reported diffusion constant. A
556 + secondary effect of higher coverages is CO-CO cross interactions that
557 + lower the effective mobility of the Pt adatoms that are bound to each CO.
558 + This effect would become evident only at higher coverages. A detailed
559 + account of Pt adatom energetics follows in the Discussion.
560 +
561 +
562 + \subsubsection{Dynamics of double layer formation}
563 + The increased diffusion on Pt at the higher CO coverages is the primary
564 + contributor to double layer formation. However, this is not a complete
565 + explanation -- the 33\%~Pt system has higher diffusion constants, but
566 + did not show any signs of edge doubling in 40~ns. On the 50\%~Pt
567 + system, one double layer formed within the first 40~ns of simulation time,
568 + while two more were formed as the system was allowed to run for an
569 + additional 110~ns (150~ns total). This suggests that this reconstruction
570 + is a rapid process and that the previously mentioned upper bound is a
571 + very large overestimate.\cite{Williams:1991,Pearl} In this system the first
572 + appearance of a double layer appears at 19~ns into the simulation.
573 + Within 12~ns of this nucleation event, nearly half of the step has formed
574 + the double layer and by 86~ns the complete layer has flattened out.
575 + From the appearance of the first nucleation event to the first observed
576 + double layer, the process took $\sim$20~ns. Another $\sim$40~ns was
577 + necessary for the layer to completely straighten. The other two layers in
578 + this simulation formed over periods of 22~ns and 42~ns respectively.
579 + A possible explanation for this rapid reconstruction is the elevated
580 + temperatures under which our systems were simulated. The process
581 + would almost certainly take longer at lower temperatures. Additionally,
582 + our measured times for completion of the doubling after the appearance
583 + of a nucleation site are likely affected by our periodic boxes. A longer
584 + step-edge will likely take longer to ``zipper''.
585 +
586 +
587   %Discussion
588   \section{Discussion}
589 < 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.
589 > We have shown that a classical potential model is able to model the
590 > initial reconstruction of the Pt(557) surface upon CO adsorption as
591 > shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were
592 > able to observe features of the dynamic processes necessary for
593 > this reconstruction. Here we discuss the features of the model that
594 > give rise to the observed dynamical properties of the (557) reconstruction.
595  
596   \subsection{Diffusion}
597 < 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?)
598 < \\
599 < \\
600 < %Evolution of surface
597 > The perpendicular diffusion constant
598 > appears to be the most important indicator of double layer
599 > formation. As highlighted in Figure \ref{fig:reconstruct}, the
600 > formation of the double layer did not begin until a nucleation
601 > site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994},
602 > the inability for edges to cross leads to an effective edge-edge repulsion that
603 > must be overcome to allow step coalescence.
604 > A greater $\textbf{D}_\perp$ implies more step-wandering
605 > and a larger chance for the stochastic meeting of two edges
606 > to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double
607 > layer. This helps explain why the time scale for formation after
608 > the appearance of a nucleation site was rapid, while the initial
609 > appearance of the nucleation site was unpredictable.
610 >
611 > \subsection{Mechanism for restructuring}
612 > Since the Au surface showed no large scale restructuring in any of
613 > our simulations, our discussion will focus on the 50\% Pt-CO system
614 > which did exhibit doubling. A
615 > number of possible mechanisms exist to explain the role of adsorbed
616 > CO in restructuring the Pt surface. Quadrupolar repulsion between
617 > adjacent CO molecules adsorbed on the surface is one possibility.  
618 > However, the quadrupole-quadrupole interaction is short-ranged and
619 > is attractive for some orientations.  If the CO molecules are ``locked'' in
620 > a specific orientation relative to each other, through atop adsorption for
621 > example, this explanation would gain credence. The calculated energetic repulsion
622 > between two CO molecules located a distance of 2.77~\AA~apart
623 > (nearest-neighbor distance of Pt) and both in a vertical orientation,
624 > is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance
625 > of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away
626 > from a purely vertical orientation also lowers the repulsion. When the
627 > carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is
628 > reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}.
629 > The calculated barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
630 > repulsion between adjacent CO molecules bound to Pt could increase the surface
631 > diffusion. However, the residence time of CO on Pt suggests that these
632 > molecules are extremely mobile, with diffusion constants 40 to 2500 times
633 > larger than surface Pt atoms. This mobility suggests that the CO molecules jump
634 > between different Pt atoms throughout the simulation, but will stay bound for
635 > significant periods of time.
636 >
637 > A different interpretation of the above mechanism, taking into account the large
638 > mobility of the CO, looks at how instantaneous and short-lived configurations of
639 > CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge
640 > breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach
641 > an edge atom is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures
642 > \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases
643 > (e), (g), and (h), the barrier can be lowered to $\sim$23~kcal/mole. In these instances,
644 > it becomes quite energetically favorable to roughen the edge by introducing a small
645 > separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in
646 > simulations with significant CO populations. The roughening is present to a lesser extent
647 > on lower coverage surfaces and even on the bare surfaces, although in these cases it is likely
648 > due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism
649 > of step-edge breakup suggested by these energy curves is one of the most difficult
650 > processes, a complete break-away from the step-edge in one unbroken movement.
651 > Easier multistep mechanisms likely exist where an adatom moves laterally on the surface
652 > after being ejected so it ends up alongside the ledge. This provides the atom with 5 nearest
653 > neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher
654 > than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO
655 > quadrupolar repulsion is still playing a primary role, but for its importance in roughening
656 > the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not
657 > born out by their mobility data. The requirement for a large density of CO on the surface
658 > for some of the more favorable suggested configurations in Figure \ref{fig:SketchGraphic}
659 > correspond well with the increased mobility seen on higher coverage surfaces.
660 >
661 > %Sketch graphic of different configurations
662   \begin{figure}[H]
663 < \includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
664 < \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.}
663 > \includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf}
664 > \caption{The dark grey atoms refer to the upper ledge, while the white atoms are
665 > the lower terrace. The blue highlighted atoms had a CO in a vertical atop position
666 > upon them. These are a sampling of the configurations examined to gain a more
667 > complete understanding of the effects CO has on surface diffusion and edge breakup.
668 > Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.}
669 > \label{fig:SketchGraphic}
670   \end{figure}
671  
672 + %energy graph corresponding to sketch graphic
673 + \begin{figure}[H]
674 + \includegraphics[width=\linewidth]{stepSeparationComparison.pdf}
675 + \caption{The energy curves directly correspond to the labeled model
676 + surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative
677 + to their initial configuration so the energy of a and h do not have the
678 + same zero value. As is seen, certain arrangements of CO can lower
679 + the energetic barrier that must be overcome to create an adatom.
680 + However, it is the highest coverages where these higher-energy
681 + configurations of CO will be more likely. }
682 + \label{fig:SketchEnergies}
683 + \end{figure}
684  
685 + While configurations of CO on the surface are able to increase diffusion,
686 + this does not immediately provide an explanation for the formation of double
687 + layers. If adatoms were constrained to their terrace then doubling would be
688 + much less likely to occur. Nucleation sites could still potentially form, but there
689 + would not be enough atoms to finish the doubling. For a non-simulated metal surface, where the
690 + step lengths can be assumed to be infinite relative to atomic sizes, local doubling would be possible, but in
691 + our simulations with our periodic treatment of the system, the system is not large enough to experience this effect.
692 + Thus, there must be a mechanism that explains how adatoms are able to move
693 + amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate
694 + where an adatom along the step-edge with an adsorbed CO ``burrows'' into the
695 + edge displacing an atom onto the higher terrace. This mechanism was chosen
696 + because of similar events that were observed during the simulations. The barrier
697 + heights we obtained are only approximations because we constrained the movement
698 + of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s
699 + are provide a strong energetic support for this modeled lifting mechanism. When CO is not present and
700 + this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown
701 + in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol.
702 + While the barrier height is comparable for both cases, there is nearly a 20~kcal/mol
703 + difference in energies and makes the process energetically favorable.
704  
705 + %lambda progression of Pt -> shoving its way into the step
706 + \begin{figure}[H]
707 + \includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png}
708 + \caption{ Various points along a reaction coordinate are displayed in the figure.
709 + The mechanism of edge traversal is examined in the presence of CO. The approximate
710 + barrier for the displayed process is 20~kcal/mol. However, the $\Delta E$ of this process
711 + is -15~kcal/mol making it an energetically favorable process.}
712 + \label{fig:lambda}
713 + \end{figure}
714  
715 + The mechanism for doubling on this surface appears to require the cooperation of at least
716 + these two described processes. For complete doubling of a layer to occur there must
717 + be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from
718 + that terrace they must either rise up on the ledge above them or drop to the ledge below
719 + them. The presence of CO helps with the energetics of both of these situations. There must be sufficient
720 + breakage of the step-edge to increase the concentration of adatoms on the surface and
721 + these adatoms must then undergo the burrowing highlighted above or some comparable
722 + mechanism to traverse the step-edge. Over time, these mechanisms working in concert
723 + lead to the formation of a double layer.
724 +
725 + \subsection{CO Removal and double layer stability}
726 + Once a double layer had formed on the 50\%~Pt system it
727 + remained for the rest of the simulation time with minimal
728 + movement. There were configurations that showed small
729 + wells or peaks forming, but typically within a few nanoseconds
730 + the feature would smooth away. Within our simulation time,
731 + the formation of the double layer was irreversible and a double
732 + layer was never observed to split back into two single layer
733 + step-edges while CO was present. To further gauge the effect
734 + CO had on this system, additional simulations were run starting
735 + from a late configuration of the 50\%~Pt system that had formed
736 + double layers. These simulations then had their CO removed.
737 + The double layer breaks rapidly in these simulations, already
738 + showing a well-defined splitting after 100~ps. Configurations of
739 + this system are shown in Figure \ref{fig:breaking}. The coloring
740 + of the top and bottom layers helps to exhibit how much mixing
741 + the edges experience as they split. These systems were only
742 + examined briefly, 10~ns, and within that time despite the initial
743 + rapid splitting, the edges only moved another few \AA~apart.
744 + It is possible with longer simulation times that the
745 + (557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010}
746 +
747 +
748 +
749 + %breaking of the double layer upon removal of CO
750 + \begin{figure}[H]
751 + \includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png}
752 + \caption{(A)  0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO
753 + helped maintain the stability of the double layer and its microfaceting of the double layer
754 + into a (111) configuration. This microfacet immediately reverts to the original (100) step
755 + edge which is a hallmark of the (557) surface. The separation is not a simple sliding apart, rather
756 + there is a mixing of the lower and upper atoms at the edge.}
757 + \label{fig:breaking}
758 + \end{figure}
759 +
760 +
761 +
762 +
763   %Peaks!
764 < \includegraphics[scale=0.25]{doublePeaks_noCO.png}
764 > %\begin{figure}[H]
765 > %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
766 > %\caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
767 > %of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with
768 > %aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
769 > %\label{fig:peaks}
770 > %\end{figure}
771 >
772 >
773 > %Don't think I need this
774 > %clean surface...
775 > %\begin{figure}[H]
776 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
777 > %\caption{}
778 >
779 > %\end{figure}
780 > %\label{fig:clean}
781 >
782 >
783   \section{Conclusion}
784 + The strength of the Pt-CO binding interaction as well as the large
785 + quadrupolar repulsion between CO molecules are sufficient to
786 + explain the observed increase in surface mobility and the resultant
787 + reconstructions at the highest simulated coverage. The weaker
788 + Au-CO interaction results in lower diffusion constants, less step-wandering,
789 + and a lack of the double layer reconstruction. An in-depth examination
790 + of the energetics shows the important role CO plays in increasing
791 + step-breakup and in facilitating edge traversal which are both
792 + necessary for double layer formation.
793  
794  
795 < \section{Acknowledgments}
795 >
796 > %Things I am not ready to remove yet
797 >
798 > %Table of Diffusion Constants
799 > %Add gold?M
800 > % \begin{table}[H]
801 > %   \caption{}
802 > %   \centering
803 > % \begin{tabular}{| c | cc | cc | }
804 > %   \hline
805 > %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
806 > %   \hline
807 > %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
808 > %   \hline
809 > %   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
810 > %   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
811 > %   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
812 > %   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
813 > %   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
814 > %   \hline
815 > % \end{tabular}
816 > % \end{table}
817 >
818 > \begin{acknowledgement}
819   Support for this project was provided by the National Science
820   Foundation under grant CHE-0848243 and by the Center for Sustainable
821   Energy at Notre Dame (cSEND). Computational time was provided by the
822   Center for Research Computing (CRC) at the University of Notre Dame.
823 <
823 > \end{acknowledgement}
824   \newpage
825   \bibliography{firstTryBibliography}
826 < \end{doublespace}
826 > %\end{doublespace}
827 >
828 > \begin{tocentry}
829 > %\includegraphics[height=3.5cm]{timelapse}
830 > \end{tocentry}
831 >
832   \end{document}

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