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Revision 3879 by jmichalk, Mon Mar 18 21:20:12 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   \end{abstract}
90  
# Line 79 | Line 99 | Industrial catalysts usually consist of small particle
99   %       Sub: Also, easier to observe what is going on and provide reasons and explanations
100   %
101  
102 < Industrial catalysts usually consist of small particles exposing
103 < different atomic terminations that exhibit a high concentration of
104 < step, kink sites, and vacancies at the edges of the facets.  These
85 < sites are thought to be the locations of catalytic
102 > Industrial catalysts usually consist of small particles that exhibit a
103 > high concentration of steps, kink sites, and vacancies at the edges of
104 > the facets.  These sites are thought to be the locations of catalytic
105   activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now
106 < significant evidence to demonstrate that solid surfaces are often
107 < structurally, compositionally, and chemically {\it modified} by
108 < reactants under operating conditions.\cite{Tao2008,Tao:2010,Tao2011}
109 < The coupling between surface oxidation state and catalytic activity
110 < for CO oxidation on Pt, for instance, is widely
111 < documented.\cite{Ertl08,Hendriksen:2002} Despite the well-documented
112 < role of these effects on reactivity, the ability to capture or predict
113 < them in atomistic models is currently somewhat limited.  While these
114 < effects are perhaps unsurprising on the highly disperse, multi-faceted
115 < nanoscale particles that characterize industrial catalysts, they are
116 < manifest even on ordered, well-defined surfaces. The Pt(557) surface,
117 < for example, exhibits substantial and reversible restructuring under
118 < exposure to moderate pressures of carbon monoxide.\cite{Tao:2010}
106 > significant evidence that solid surfaces are often structurally,
107 > compositionally, and chemically modified by reactants under operating
108 > conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between
109 > surface oxidation states and catalytic activity for CO oxidation on
110 > Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002}
111 > Despite the well-documented role of these effects on reactivity, the
112 > ability to capture or predict them in atomistic models is somewhat
113 > limited.  While these effects are perhaps unsurprising on the highly
114 > disperse, multi-faceted nanoscale particles that characterize
115 > industrial catalysts, they are manifest even on ordered, well-defined
116 > surfaces. The Pt(557) surface, for example, exhibits substantial and
117 > reversible restructuring under exposure to moderate pressures of
118 > carbon monoxide.\cite{Tao:2010}
119  
120 < This work is part of an ongoing effort to understand the causes,
121 < mechanisms and timescales for surface restructuring using molecular
122 < simulation methods.  Since the dynamics of the process is of
123 < particular interest, we utilize classical molecular dynamic methods
124 < with force fields that represent a compromise between chemical
125 < accuracy and the computational efficiency necessary to observe the
126 < process of interest.
120 > This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557)
121 > surface restructuring using molecular simulations.  Since the dynamics
122 > of the process are of particular interest, we employ classical force
123 > fields that represent a compromise between chemical accuracy and the
124 > computational efficiency necessary to simulate the process of interest.
125 > Since restructuring typically occurs as a result of specific interactions of the
126 > catalyst with adsorbates, in this work, two metal systems exposed
127 > to carbon monoxide were examined. The Pt(557) surface has already been shown
128 > to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010}
129 > The Au(557) surface, because of a weaker interaction with CO, is less
130 > likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000}
131 > and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced
132 > reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the
133 > 22 x $\sqrt{3}$ cell. They argued that only a few Au atoms
134 > become adatoms, limiting the stress of this reconstruction, while
135 > allowing the rest to relax and approach the ideal (111)
136 > configuration. They did not see the usual herringbone pattern on Au(111) being greatly
137 > affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a
138 > disruption of the herringbone pattern as CO was adsorbed to the
139 > surface. Both groups suggested that the preference CO shows for
140 > low-coordinated Au atoms was the primary driving force for the reconstruction.
141  
142 < Since restructuring occurs as a result of specific interactions of the catalyst
143 < 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.
142 >
143 >
144   %Platinum molecular dynamics
145   %gold molecular dynamics
146  
117 –
118 –
119 –
120 –
121 –
147   \section{Simulation Methods}
148 < The challenge in modeling any solid/gas interface problem is the
148 > The challenge in modeling any solid/gas interface is the
149   development of a sufficiently general yet computationally tractable
150   model of the chemical interactions between the surface atoms and
151   adsorbates.  Since the interfaces involved are quite large (10$^3$ -
152 < 10$^6$ atoms) and respond slowly to perturbations, {\it ab initio}
152 > 10$^4$ atoms) and respond slowly to perturbations, {\it ab initio}
153   molecular dynamics
154   (AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello
155   methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum
# Line 133 | Line 158 | Coulomb potential.  For this work, we have been using
158   typically not well represented in terms of classical pairwise
159   interactions in the same way that bonds in a molecular material are,
160   nor are they captured by simple non-directional interactions like the
161 < Coulomb potential.  For this work, we have been using classical
162 < molecular dynamics with potential energy surfaces that are
163 < specifically tuned for transition metals.  In particular, we use the
164 < EAM potential for Au-Au and Pt-Pt interactions, while modeling the CO
165 < using a model developed by Straub and Karplus for studying
166 < photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and Pt-CO
167 < cross interactions were parameterized as part of this work.
161 > Coulomb potential.  For this work, we have used classical molecular
162 > dynamics with potential energy surfaces that are specifically tuned
163 > for transition metals.  In particular, we used the EAM potential for
164 > Au-Au and Pt-Pt interactions.\cite{EAM} The CO was modeled using a rigid
165 > three-site model developed by Straub and Karplus for studying
166 > photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and
167 > Pt-CO cross interactions were parameterized as part of this work.
168    
169   \subsection{Metal-metal interactions}
170 < Many of the potentials used for classical simulation of transition
171 < metals are based on a non-pairwise additive functional of the local
172 < electron density. The embedded atom method (EAM) is perhaps the best
173 < known of these
170 > Many of the potentials used for modeling transition metals are based
171 > on a non-pairwise additive functional of the local electron
172 > density. The embedded atom method (EAM) is perhaps the best known of
173 > these
174   methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98}
175   but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and
176   the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler
177 < parameter sets. The glue model of Ercolessi {\it et al.} is among the
177 > parameter sets. The glue model of Ercolessi {\it et al}. is among the
178   fastest of these density functional approaches.\cite{Ercolessi88} In
179 < all of these models, atoms are conceptualized as a positively charged
179 > all of these models, atoms are treated as a positively charged
180   core with a radially-decaying valence electron distribution. To
181   calculate the energy for embedding the core at a particular location,
182   the electron density due to the valence electrons at all of the other
183 < atomic sites is computed at atom $i$'s location,
183 > atomic sites is computed at atom $i$'s location,
184   \begin{equation*}
185   \bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
186   \end{equation*}
# Line 167 | Line 192 | $\phi_{ij}(r_{ij})$ is an pairwise term that is meant
192   V_i =  F[ \bar{\rho}_i ]  + \sum_{j \neq i} \phi_{ij}(r_{ij})
193   \end{equation*}
194   where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and
195 < $\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the
196 < overlap of the two positively charged cores.  
195 > $\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the
196 > repulsive overlap of the two positively charged cores.  
197  
198 < The {\it modified} embedded atom method (MEAM) adds angular terms to
199 < the electron density functions and an angular screening factor to the
200 < pairwise interaction between two
201 < atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
202 < MEAM has become widely used to simulate systems in which angular
203 < interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
204 < metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
205 < MEAM presents significant additional computational costs, however.
198 > % The {\it modified} embedded atom method (MEAM) adds angular terms to
199 > % the electron density functions and an angular screening factor to the
200 > % pairwise interaction between two
201 > % atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
202 > % MEAM has become widely used to simulate systems in which angular
203 > % interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
204 > % metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
205 > % MEAM presents significant additional computational costs, however.
206  
207 < The EAM, Finnis-Sinclair, MEAM, and the Quantum Sutton-Chen potentials
207 > The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials
208   have all been widely used by the materials simulation community for
209   simulations of bulk and nanoparticle
210   properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq}
211   melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
212   fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack
213   propagation,\cite{BECQUART:1993rg} and alloying
214 < dynamics.\cite{Shibata:2002hh} All of these potentials have their
215 < strengths and weaknesses.  One of the strengths common to all of the
216 < methods is the relatively large library of metals for which these
217 < potentials have been
218 < parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}
214 > dynamics.\cite{Shibata:2002hh} One of EAM's strengths
215 > is its sensitivity to small changes in structure. This arises
216 > because interactions
217 > up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a}
218 > Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88}
219 > which is only parameterized up to the nearest-neighbor
220 > interactions, EAM is a suitable choice for systems where
221 > the bulk properties are of secondary importance to low-index
222 > surface structures. Additionally, the similarity of EAM's functional
223 > treatment of the embedding energy to standard density functional
224 > theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier.
225 > \cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  
226  
227 < \subsection{CO}
228 < Since one explanation for the strong surface CO repulsion on metals is
229 < the large linear quadrupole moment of carbon monoxide, the model
230 < chosen for this molecule exhibits this property in an efficient
231 < manner.  We used a model first proposed by Karplus and Straub to study
232 < the photodissociation of CO from myoglobin.\cite{Straub} The Straub and
233 < Karplus model is a rigid three site model which places a massless M
234 < site at the center of mass along the CO bond.  The geometry used along
235 < with the interaction parameters are reproduced in Table 1. The effective
227 >
228 >
229 >
230 > \subsection{Carbon Monoxide model}
231 > Previous explanations for the surface rearrangements center on
232 > the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010}  
233 > We used a model first proposed by Karplus and Straub to study
234 > the photodissociation of CO from myoglobin because it reproduces
235 > the quadrupole moment well.\cite{Straub} The Straub and
236 > Karplus model treats CO as a rigid three site molecule with a massless M
237 > site at the molecular center of mass. The geometry and interaction
238 > parameters are reproduced in Table~\ref{tab:CO}. The effective
239   dipole moment, calculated from the assigned charges, is still
240   small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
241   to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
242   mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
243   %CO Table
244   \begin{table}[H]
245 < \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 $e$.}
245 >  \caption{Positions, Lennard-Jones parameters ($\sigma$ and
246 >    $\epsilon$), and charges for the CO-CO
247 >    interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are
248 >    in kcal/mol, and charges are in atomic units.}
249   \centering
250   \begin{tabular}{| c | c | ccc |}
251   \hline
214 – \multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\
215 – \hline
252   &  {\it z} & $\sigma$ & $\epsilon$ & q\\
253   \hline
254 < \textbf{C} & -0.6457 &  0.0262  & 3.83   &   -0.75 \\
255 < \textbf{O} &  0.4843 &   0.1591 &   3.12 &   -0.85 \\
254 > \textbf{C} & -0.6457 &  3.83 & 0.0262   &   -0.75 \\
255 > \textbf{O} &  0.4843 &  3.12 &  0.1591  &   -0.85 \\
256   \textbf{M} & 0.0 & -  &  -  &    1.6 \\
257   \hline
258   \end{tabular}
259 + \label{tab:CO}
260   \end{table}
261  
262 < \subsection{Cross-Interactions}
262 > \subsection{Cross-Interactions between the metals and carbon monoxide}
263  
264 < One hurdle that must be overcome in classical molecular simulations
265 < is the proper parameterization of the potential interactions present
266 < in the system. Since the adsorption of CO onto a platinum surface has been
267 < the focus of many experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
268 < and theoretical studies \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
269 < there is a large amount of data in the literature to fit too. We started with parameters
270 < reported by Korzeniewski et al. \cite{Pons:1986} and then
271 < modified them to ensure that the Pt-CO interaction favored
272 < an atop binding position for the CO upon the Pt surface. This
273 < constraint led to the binding energies being on the higher side
274 < of reported values. Following the method laid out by Korzeniewski,
275 < the Pt-C interaction was fit to a strong Lennard-Jones 12-6
276 < interaction to mimic binding, while the Pt-O interaction
277 < was parameterized to a Morse potential with a large $r_o$
278 < to contribute a weak repulsion. The resultant potential-energy
279 < surface suitably recovers the calculated Pt-C bond length ( 1.6\AA)\cite{Beurden:2002ys} and affinity
280 < for the atop binding position.\cite{Deshlahra:2012, Hopster:1978}
264 > Since the adsorption of CO onto a Pt surface has been the focus
265 > of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
266 > and theoretical work
267 > \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
268 > there is a significant amount of data on adsorption energies for CO on
269 > clean metal surfaces. An earlier model by Korzeniewski {\it et
270 >  al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were
271 > modified to ensure that the Pt-CO interaction favored the atop binding
272 > position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}.
273 > The modified parameters yield binding energies that are slightly higher
274 > than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski
275 > {\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
276 > Lennard-Jones interaction to mimic strong, but short-ranged, partial
277 > binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The
278 > Pt-O interaction was modeled with a Morse potential with a large
279 > equilibrium distance, ($r_o$).  These choices ensure that the C is preferred
280 > over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak
281 > repulsion which favors the atop site.  The resulting potential-energy
282 > surface suitably recovers the calculated Pt-C separation length
283 > (1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding
284 > position.\cite{Deshlahra:2012, Hopster:1978}
285  
286   %where did you actually get the functionals for citation?
287   %scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think
288   %same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there...
289 < The Au-C and Au-O interaction parameters were also fit to a Lennard-Jones
290 < and Morse potential respectively, to reproduce Au-CO binding energies.
291 < These energies were obtained from quantum calculations carried out using
292 < the PBE GGA exchange-correlation functionals\cite{Perdew_GGA} for gold, carbon, and oxygen
293 < constructed by Rappe, Rabe, Kaxiras, and Joannopoulos. \cite{RRKJ_PP}.
294 < All calculations were run using the {\sc Quantum ESPRESSO} package. \cite{QE-2009}  
295 < First, a four layer slab of gold comprised of 32 atoms displaying a (111) surface was
296 < converged using a 4X4X4 grid of Monkhorst-Pack \emph{k}-points.\cite{Monkhorst:1976}
297 < The kinetic energy of the wavefunctions were truncated at 20 Ry while the
298 < cutoff for the charge density and potential was set at 80 Ry. This relaxed
299 < gold slab was then used in numerous single point calculations  with CO at various heights
300 < to create a potential energy surface for the Au-CO interaction.
289 > The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and
290 > Morse potentials, respectively, to reproduce Au-CO binding energies.
291 > The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations.
292 > Adsorption energies were obtained from gas-surface DFT calculations with a
293 > periodic supercell plane-wave basis approach, as implemented in the
294 > {\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were
295 > described with the projector augmented-wave (PAW)
296 > method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
297 > included to an energy cutoff of 20 Ry. Electronic energies are
298 > computed with the PBE implementation of the generalized gradient
299 > approximation (GGA) for gold, carbon, and oxygen that was constructed
300 > by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
301 > In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4
302 > Au x 2 Au surface planes and separated from vertical images by six
303 > layers of vacuum space. The surface atoms were all allowed to relax
304 > before CO was added to the system. Electronic relaxations were
305 > performed until the energy difference between subsequent steps
306 > was less than $10^{-8}$ Ry.   Nonspin-polarized supercell calculations
307 > were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
308 > zone.\cite{Monkhorst:1976} The relaxed gold slab was
309 > then used in numerous single point calculations with CO at various
310 > heights (and angles relative to the surface) to allow fitting of the
311 > empirical force field.
312  
313   %Hint at future work
314 < The fit parameter sets employed in this work are shown in Table 2 and their
315 < reproduction of the binding energies are displayed in Table 3. Currently,
316 < charge transfer is not being treated in this system, however, that is a goal
317 < for future work as the effect has been seen to affect binding energies and
318 < binding site preferences. \cite{Deshlahra:2012}
314 > The parameters employed for the metal-CO cross-interactions in this work
315 > are shown in Table~\ref{tab:co_parameters} and the binding energies on the
316 > (111) surfaces are displayed in Table~\ref{tab:co_energies}.  Charge transfer
317 > and polarization are neglected in this model, although these effects could have
318 > an effect on  binding energies and binding site preferences.
319  
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 –
320   %Table  of Parameters
321   %Pt Parameter Set 9
322   %Au Parameter Set 35
323   \begin{table}[H]
324 < \caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol}
324 >  \caption{Best fit parameters for metal-CO cross-interactions. Metal-C
325 >    interactions are modeled with Lennard-Jones potentials. While the
326 >    metal-O interactions were fit to Morse
327 >    potentials.  Distances are given in \AA~and energies in kcal/mol. }
328   \centering
329   \begin{tabular}{| c | cc | c | ccc |}
330   \hline
331 < \multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\
331 > &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
332   \hline
308 – &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\
309 – \hline
333   \textbf{Pt-C} & 1.3 & 15  & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\
334   \textbf{Au-C} & 1.9 & 6.5  & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\
335  
336   \hline
337   \end{tabular}
338 + \label{tab:co_parameters}
339   \end{table}
340  
341   %Table of energies
342   \begin{table}[H]
343 < \caption{Adsorption energies in eV}
343 >  \caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials
344 >    described in this work.  All values are in eV.}
345   \centering
346   \begin{tabular}{| c | cc |}
347 < \hline
348 < & Calc. & Exp. \\
349 < \hline
350 < \textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\
351 < \textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\
352 < \hline
347 >  \hline
348 >  & Calculated & Experimental \\
349 >  \hline
350 >  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,}
351 >  (Ref. \protect\cite{Kelemen:1979}) \\
352 > & &  -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline
353 >  \textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,}  (Ref. \protect\cite{TPDGold}) \\
354 >  \hline
355   \end{tabular}
356 + \label{tab:co_energies}
357   \end{table}
358  
359 + \subsection{Pt(557) and Au(557) metal interfaces}
360 + Our Pt system is an orthorhombic periodic box of dimensions
361 + 54.482~x~50.046~x~120.88~\AA~while our Au system has
362 + dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs
363 + are 9 and 8 atoms deep respectively, corresponding to a slab
364 + thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
365 + The systems are arranged in a FCC crystal that have been cut
366 + along the (557) plane so that they are periodic in the {\it x} and
367 + {\it y} directions, and have been oriented to expose two aligned
368 + (557) cuts along the extended {\it z}-axis.  Simulations of the
369 + bare metal interfaces at temperatures ranging from 300~K to
370 + 1200~K were performed to confirm the relative
371 + stability of the surfaces without a CO overlayer.  
372  
373 + The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting}
374 + and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at
375 + different temperatures for the two metals.  The bare Au and Pt surfaces were
376 + initially run in the canonical (NVT) ensemble at 800~K and 1000~K
377 + respectively for 100 ps. The two surfaces were relatively stable at these
378 + temperatures when no CO was present, but experienced increased surface
379 + mobility on addition of CO. Each surface was then dosed with different concentrations of CO
380 + that was initially placed in the vacuum region.  Upon full adsorption,
381 + these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
382 + coverage. Higher coverages resulted in the formation of a double layer of CO,
383 + which introduces artifacts that are not relevant to (557) reconstruction.
384 + Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
385 + the Au surfaces often had a significant CO population in the gas
386 + phase.  These systems were allowed to reach thermal equilibrium (over
387 + 5~ns) before being run in the microcanonical (NVE) ensemble for
388 + data collection. All of the systems examined had at least 40~ns in the
389 + data collection stage, although simulation times for some Pt of the
390 + systems exceeded 200~ns.  Simulations were carried out using the open
391 + source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}
392  
393  
394  
395  
396 < % Just results, leave discussion for discussion section
396 > % RESULTS
397 > %
398   \section{Results}
399 < \subsection{Diffusion}
400 < While an ideal metallic surface is unlikely to experience much surface diffusion, high-index surfaces have large numbers of low-coordinated atoms which have a much easier time overcoming the energetic barriers limiting diffusion, leading to easier surface reconstructions. Surface movement was divided between the parallel ($\parallel$) and perpendicular ($\perp$) directions relative to the step edge. We were then able to calculate diffusion constants as a function of CO coverage. As can be seen in Table 4, the presence and amount of CO directly affects the diffusion constants of surface platinum atoms. The presence of two 50\% coverage systems is to show how the diffusion process is affected by time. The majority of the systems were run for approximately 50 ns while the half monolayer system been running continuously. The lowered diffusion constant at longer run times will be examined in-depth in the discussion section.
399 > \subsection{Structural remodeling}
400 > The bare metal surfaces experienced minor roughening of the
401 > step-edge because of the elevated temperatures, but the (557)
402 > face was stable throughout the simulations. The surface of both
403 > systems, upon dosage of CO, began to undergo extensive remodeling
404 > that was not observed in the bare systems. Reconstructions of
405 > the Au systems were limited to breakup of the step-edges and
406 > some step wandering. The lower coverage Pt systems experienced
407 > similar restructuring but to a greater extent. The 50\% coverage
408 > Pt system was unique among our simulations in that it formed
409 > well-defined and stable double layers through step coalescence,
410 > similar to results reported by Tao {\it et al}.\cite{Tao:2010}
411  
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}
412  
413 + \subsubsection{Step wandering}
414 + The 0\% coverage surfaces for both metals showed minimal
415 + step-wandering at their respective temperatures. As the CO
416 + coverage increased however, the mobility of the surface atoms,
417 + described through adatom diffusion and step-edge wandering,
418 + also increased.  Except for the 50\% Pt system where step
419 + coalescence occurred, the step-edges in the other simulations
420 + preferred to keep nearly the same distance between steps as in
421 + the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au.
422 + Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994}
423 + highlights the repulsion that exists between step-edges even
424 + when no direct interactions are present in the system. This
425 + repulsion is caused by an entropic barrier that arises from
426 + the fact that steps cannot cross over one another. This entropic
427 + repulsion does not completely define the interactions between
428 + steps, however, so it is possible to observe step coalescence
429 + on some surfaces.\cite{Williams:1991} The presence and
430 + concentration of adsorbates, as shown in this work, can
431 + affect step-step interactions, potentially leading to a new
432 + surface structure as the thermodynamic equilibrium.
433  
434 + \subsubsection{Double layers}
435 + Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface
436 + undergoes two separate reconstructions upon CO adsorption.
437 + The first involves a doubling of the step height and plateau length.
438 + Similar behavior has been seen on a number of surfaces
439 + at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl}
440 + Of the two systems we examined, the Pt system showed a greater
441 + propensity for reconstruction  
442 + because of the larger surface mobility and the greater extent of step wandering.
443 + The amount of reconstruction was strongly correlated to the amount of CO
444 + adsorbed upon the surface.  This appears to be related to the
445 + effect that adsorbate coverage has on edge breakup and on the
446 + surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the
447 + doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here.
448 + Over a longer time scale (150~ns) two more double layers formed
449 + on this surface. Although double layer formation did not occur
450 + in the other Pt systems, they exhibited more step-wandering and
451 + roughening compared to their Au counterparts. The
452 + 50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at
453 + various times along the simulation showing the evolution of a double layer step-edge.
454  
455 + The second reconstruction observed by
456 + Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched
457 + across the plateau between two step-edges. Neither metal, within
458 + the 40~ns time scale or the extended simulation time of 150~ns for
459 + the 50\% Pt system, experienced this reconstruction.
460 +
461 + %Evolution of surface
462 + \begin{figure}[H]
463 + \includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
464 + \caption{The Pt(557) / 50\% CO system at a sequence of times after
465 +  initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and
466 +  (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly.  The
467 +  doubling of the layers appears only after two adjacent step-edges
468 +  touch.  The circled spot in (b) nucleated the growth of the double
469 +  step observed in the later configurations.}
470 +  \label{fig:reconstruct}
471 + \end{figure}
472 +
473 + \subsection{Dynamics}
474 + Previous experimental work by Pearl and Sibener\cite{Pearl},
475 + using STM, has been able to capture the coalescence of steps
476 + on Ni(977). The time scale of the image acquisition, $\sim$70~s/image,
477 + provides an upper bound for the time required for the doubling
478 + to occur. By utilizing Molecular Dynamics we are able to probe
479 + the dynamics of these reconstructions at elevated temperatures
480 + and in this section we provide data on the timescales for transport
481 + properties, e.g. diffusion and layer formation time.
482 +
483 +
484 + \subsubsection{Transport of surface metal atoms}
485 + %forcedSystems/stepSeparation
486 + The wandering of a step-edge is a cooperative effect
487 + arising from the individual movements of the atoms making up the steps. An ideal metal surface
488 + displaying a low index facet, (111) or (100), is unlikely to experience
489 + much surface diffusion because of the large energetic barrier that must
490 + be overcome to lift an atom out of the surface. The presence of step-edges and other surface features
491 + on higher-index facets provides a lower energy source for mobile metal atoms.
492 + Single-atom break-away from a step-edge on a clean surface still imposes an
493 + energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting
494 + the same metal atom vertically out of the surface,  \textgreater~60 kcal/mol.
495 + The penalty lowers significantly when CO is present in sufficient quantities
496 + on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as
497 + $\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for
498 + diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then
499 + able to explore the terrace before rejoining either their original step-edge or
500 + becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom
501 + to traverse to a separate terrace although the presence of CO can lower the
502 + energy barrier required to lift or lower an adatom. By tracking the mobility of individual
503 + metal atoms on the Pt and Au surfaces we were able to determine the relative
504 + diffusion constants, as well as how varying coverages of CO affect the diffusion. Close
505 + observation of the mobile metal atoms showed that they were typically in
506 + equilibrium with the step-edges.
507 + At times, their motion was concerted and two or more adatoms would be
508 + observed moving together across the surfaces.
509 +
510 + A particle was considered ``mobile'' once it had traveled more than 2~\AA~
511 + between saved configurations of the system (typically 10-100 ps). A mobile atom
512 + would typically travel much greater distances than this, but the 2~\AA~cutoff
513 + was used to prevent swamping the diffusion data with the in-place vibrational
514 + movement of buried atoms. Diffusion on a surface is strongly affected by
515 + local structures and in this work, the presence of single and double layer
516 + step-edges causes the diffusion parallel to the step-edges to be larger than
517 + the diffusion perpendicular to these edges. Parallel and perpendicular
518 + diffusion constants are shown in Figure \ref{fig:diff}.
519 +
520 + %Diffusion graph
521 + \begin{figure}[H]
522 + \includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf}
523 + \caption{Diffusion constants for mobile surface atoms along directions
524 +  parallel ($\mathbf{D}_{\parallel}$) and perpendicular
525 +  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
526 +  surface coverage.  Diffusion parallel to the step-edge is higher
527 +  than that perpendicular to the edge because of the lower energy
528 +  barrier associated with traversing along the edge as compared to
529 +  completely breaking away. The two reported diffusion constants for
530 +  the 50\% Pt system arise from different sample sets. The lower values
531 +  correspond to the same 40~ns amount that all of the other systems were
532 +  examined at, while the larger values correspond to a 20~ns period }
533 + \label{fig:diff}
534 + \end{figure}
535 +
536 + The weaker Au-CO interaction is evident in the weak CO-coverage
537 + dependance of Au diffusion. This weak interaction leads to lower
538 + observed coverages when compared to dosage amounts. This further
539 + limits the effect the CO can have on surface diffusion. The correlation
540 + between coverage and Pt diffusion rates shows a near linear relationship
541 + at the earliest times in the simulations. Following double layer formation,
542 + however, there is a precipitous drop in adatom diffusion. As the double
543 + layer forms, many atoms that had been tracked for mobility data have
544 + now been buried resulting in a smaller reported diffusion constant. A
545 + secondary effect of higher coverages is CO-CO cross interactions that
546 + lower the effective mobility of the Pt adatoms that are bound to each CO.
547 + This effect would become evident only at higher coverages. A detailed
548 + account of Pt adatom energetics follows in the Discussion.
549 +
550 +
551 + \subsubsection{Dynamics of double layer formation}
552 + The increased diffusion on Pt at the higher CO coverages is the primary
553 + contributor to double layer formation. However, this is not a complete
554 + explanation -- the 33\%~Pt system has higher diffusion constants, but
555 + did not show any signs of edge doubling in 40~ns. On the 50\%~Pt
556 + system, one double layer formed within the first 40~ns of simulation time,
557 + while two more were formed as the system was allowed to run for an
558 + additional 110~ns (150~ns total). This suggests that this reconstruction
559 + is a rapid process and that the previously mentioned upper bound is a
560 + very large overestimate.\cite{Williams:1991,Pearl} In this system the first
561 + appearance of a double layer appears at 19~ns into the simulation.
562 + Within 12~ns of this nucleation event, nearly half of the step has formed
563 + the double layer and by 86~ns the complete layer has flattened out.
564 + From the appearance of the first nucleation event to the first observed
565 + double layer, the process took $\sim$20~ns. Another $\sim$40~ns was
566 + necessary for the layer to completely straighten. The other two layers in
567 + this simulation formed over periods of 22~ns and 42~ns respectively.
568 + A possible explanation for this rapid reconstruction is the elevated
569 + temperatures under which our systems were simulated. The process
570 + would almost certainly take longer at lower temperatures. Additionally,
571 + our measured times for completion of the doubling after the appearance
572 + of a nucleation site are likely affected by our periodic boxes. A longer
573 + step-edge will likely take longer to ``zipper''.
574 +
575 +
576   %Discussion
577   \section{Discussion}
578 < 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.
578 > We have shown that a classical potential model is able to model the
579 > initial reconstruction of the Pt(557) surface upon CO adsorption as
580 > shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were
581 > able to observe features of the dynamic processes necessary for
582 > this reconstruction. Here we discuss the features of the model that
583 > give rise to the observed dynamical properties of the (557) reconstruction.
584  
585   \subsection{Diffusion}
586 < 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?)
587 < \\
588 < \\
589 < %Evolution of surface
586 > The perpendicular diffusion constant
587 > appears to be the most important indicator of double layer
588 > formation. As highlighted in Figure \ref{fig:reconstruct}, the
589 > formation of the double layer did not begin until a nucleation
590 > site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994},
591 > the inability for edges to cross leads to an effective edge-edge repulsion that
592 > must be overcome to allow step coalescence.
593 > A greater $\textbf{D}_\perp$ implies more step-wandering
594 > and a larger chance for the stochastic meeting of two edges
595 > to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double
596 > layer. This helps explain why the time scale for formation after
597 > the appearance of a nucleation site was rapid, while the initial
598 > appearance of the nucleation site was unpredictable.
599 >
600 > \subsection{Mechanism for restructuring}
601 > Since the Au surface showed no large scale restructuring in any of
602 > our simulations, our discussion will focus on the 50\% Pt-CO system
603 > which did exhibit doubling featured in Figure \ref{fig:reconstruct}. A
604 > number of possible mechanisms exist to explain the role of adsorbed
605 > CO in restructuring the Pt surface. Quadrupolar repulsion between
606 > adjacent CO molecules adsorbed on the surface is one possibility.  
607 > However, the quadrupole-quadrupole interaction is short-ranged and
608 > is attractive for some orientations.  If the CO molecules are ``locked'' in
609 > a specific orientation relative to each other, through atop adsorption for
610 > example, this explanation would gain credence. The energetic repulsion
611 > between two CO molecules located a distance of 2.77~\AA~apart
612 > (nearest-neighbor distance of Pt) and both in a vertical orientation,
613 > is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance
614 > of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away
615 > from a purely vertical orientation also lowers the repulsion. When the
616 > carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is
617 > reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}.
618 > The barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so
619 > repulsion between adjacent CO molecules bound to Pt could increase the surface
620 > diffusion. However, the residence time of CO on Pt suggests that these
621 > molecules are extremely mobile, with diffusion constants 40 to 2500 times
622 > larger than surface Pt atoms. This mobility suggests that the CO are more
623 > likely to shift their positions without dragging the Pt along with them.
624 >
625 > A different interpretation of the above mechanism, taking into account the large
626 > mobility of the CO, looks at how instantaneous and short-lived configurations of
627 > CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge
628 > breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach
629 > an edge atom is $\sim$~43~kcal/mol, as is shown in configuration (a) in Figures
630 > \ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases
631 > (e), (g), and (h), the barrier can be lowered to $\sim$~23~kcal/mole. In these instances,
632 > it becomes quite energetically favorable to roughen the edge by introducing a small
633 > separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in
634 > simulations with significant CO populations, although it is present to a lesser extent
635 > on lower coverage surfaces and even on the bare surfaces. In these cases it is likely
636 > due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism
637 > of step-edge breakup suggested by these energy curves is one the most difficult
638 > processes, a complete break-away from the step-edge in one unbroken movement.
639 > Easier multistep mechanisms likely exist where an adatom moves laterally on the surface
640 > after being ejected so it is sitting on the edge. This provides the atom with 5 nearest
641 > neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher
642 > than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO
643 > quadrupolar repulsion is still playing a primary role, but for its importance in roughening
644 > the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not
645 > born out by their mobility data. The requirement for a large density of CO on the surface
646 > for some of the more favorable suggested mechanisms in Figure \ref{fig:SketchGraphic}
647 > correspond well with the increased mobility seen on higher coverage surfaces.
648 >
649 > %Sketch graphic of different configurations
650   \begin{figure}[H]
651 < \includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
652 < \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.}
651 > \includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf}
652 > \caption{The dark grey atoms refer to the upper ledge, while the white atoms are
653 > the lower terrace. The blue highlighted atoms had a CO in a vertical atop position
654 > upon them. These are a sampling of the configurations examined to gain a more
655 > complete understanding of the effects CO has on surface diffusion and edge breakup.
656 > Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.}
657 > \label{fig:SketchGraphic}
658   \end{figure}
659  
660 + %energy graph corresponding to sketch graphic
661 + \begin{figure}[H]
662 + \includegraphics[width=\linewidth]{stepSeparationComparison.pdf}
663 + \caption{The energy curves directly correspond to the labeled model
664 + surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative
665 + to their initial configuration so the energy of a and h do not have the
666 + same zero value. As is seen, certain arrangements of CO can lower
667 + the energetic barrier that must be overcome to create an adatom.
668 + However, it is the highest coverages where these higher-energy
669 + configurations of CO will be more likely. }
670 + \label{fig:SketchEnergies}
671 + \end{figure}
672  
673 + While configurations of CO on the surface are able to increase diffusion,
674 + this does not immediately provide an explanation for the formation of double
675 + layers. If adatoms were constrained to their terrace then doubling would be
676 + much less likely to occur. Nucleation sites could still potentially form, but there
677 + would not be enough atoms to finish the doubling. Real materials, where the
678 + step lengths can be taken as infinite, local doubling would be possible, but in
679 + our simulations with our periodic treatment of the system, this is not possible.
680 + Thus, there must be a mechanism that explains how adatoms are able to move
681 + amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate
682 + where an adatom along the step-edge with an adsorbed CO ``burrows'' into the
683 + edge displacing an atom onto the higher terrace. This mechanism was chosen
684 + because of similar events that were observed during the simulations. The barrier
685 + heights we obtained are only approximations because we constrained the movement
686 + of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s
687 + are the more interesting results from this investigation. When CO is not present and
688 + this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown
689 + in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol.
690 + While the barrier height is comparable to the non-CO case, that is a nearly a 20~kcal/mol
691 + difference in energies and moves the process from slightly unfavorable to energetically favorable.
692  
693 + %lambda progression of Pt -> shoving its way into the step
694 + \begin{figure}[H]
695 + \includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png}
696 + \caption{A model system of the Pt(557) surface was used as the framework
697 + for exploring energy barriers along a reaction coordinate. Various numbers,
698 + placements, and rotations of CO were examined as they affect Pt movement.
699 + The coordinate displayed in this Figure was a representative run.  relative to the energy of the system at 0\%, there
700 + is a slight decrease upon insertion of the Pt atom into the step-edge along
701 + with the resultant lifting of the other Pt atom when CO is present at certain positions.}
702 + \label{fig:lambda}
703 + \end{figure}
704  
705 + The mechanism for doubling on this surface appears to be a convolution of at least
706 + these two described processes. For complete doubling of a layer to occur there must
707 + be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from
708 + that terrace they must either rise up on the ledge above them or drop to the ledge below
709 + them. The presence of CO helps with both of these situations. There must be sufficient
710 + breakage of the step-edge to increase the concentration of adatoms on the surface.
711 + These adatoms must then undergo the burrowing highlighted above or some comparable
712 + mechanism to traverse the step-edge. Over time, these mechanisms working in concert
713 + led to the formation of a double layer.
714 +
715 + \subsection{CO Removal and double layer stability}
716 + Once a double layer had formed on the 50\%~Pt system it
717 + remained for the rest of the simulation time with minimal
718 + movement. There were configurations that showed small
719 + wells or peaks forming, but typically within a few nanoseconds
720 + the feature would smooth away. Within our simulation time,
721 + the formation of the double layer was irreversible and a double
722 + layer was never observed to split back into two single layer
723 + step-edges while CO was present. To further gauge the effect
724 + CO had on this system, additional simulations were run starting
725 + from a late configuration of the 50\%~Pt system that had formed
726 + double layers. These simulations then had their CO removed.
727 + The double layer breaks rapidly in these simulations, already
728 + showing a well-defined splitting after 100~ps. Configurations of
729 + this system are shown in Figure \ref{fig:breaking}. The coloring
730 + of the top and bottom layers helps to exhibit how much mixing
731 + the edges experience as they split. These systems were only
732 + examined briefly, 10~ns, and within that time despite the initial
733 + rapid splitting, the edges only moved another few \AA~apart.
734 + It is possible with longer simulation times that the
735 + (557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010}
736 +
737 +
738 +
739 + %breaking of the double layer upon removal of CO
740 + \begin{figure}[H]
741 + \includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png}
742 + \caption{(A)  0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO
743 + helped maintain the stability of the double layer and upon removal the two layers break
744 + and begin separating. The separation is not a simple pulling apart however, rather
745 + there is a mixing of the lower and upper atoms at the edge.}
746 + \label{fig:breaking}
747 + \end{figure}
748 +
749 +
750 +
751 +
752   %Peaks!
753 < \includegraphics[scale=0.25]{doublePeaks_noCO.png}
753 > %\begin{figure}[H]
754 > %\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
755 > %\caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
756 > %of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with
757 > %aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
758 > %\label{fig:peaks}
759 > %\end{figure}
760 >
761 >
762 > %Don't think I need this
763 > %clean surface...
764 > %\begin{figure}[H]
765 > %\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
766 > %\caption{}
767 >
768 > %\end{figure}
769 > %\label{fig:clean}
770 >
771 >
772   \section{Conclusion}
773 + In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in less than a $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems.
774  
775 + %Things I am not ready to remove yet
776  
777 < \section{Acknowledgments}
777 > %Table of Diffusion Constants
778 > %Add gold?M
779 > % \begin{table}[H]
780 > %   \caption{}
781 > %   \centering
782 > % \begin{tabular}{| c | cc | cc | }
783 > %   \hline
784 > %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
785 > %   \hline
786 > %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
787 > %   \hline
788 > %   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
789 > %   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
790 > %   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
791 > %   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
792 > %   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
793 > %   \hline
794 > % \end{tabular}
795 > % \end{table}
796 >
797 > \begin{acknowledgement}
798   Support for this project was provided by the National Science
799   Foundation under grant CHE-0848243 and by the Center for Sustainable
800   Energy at Notre Dame (cSEND). Computational time was provided by the
801   Center for Research Computing (CRC) at the University of Notre Dame.
802 <
802 > \end{acknowledgement}
803   \newpage
804   \bibliography{firstTryBibliography}
805 < \end{doublespace}
805 > %\end{doublespace}
806 >
807 > \begin{tocentry}
808 > %\includegraphics[height=3.5cm]{timelapse}
809 > \end{tocentry}
810 >
811   \end{document}

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