trunk/COonPt/firstTry.tex

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%%
%Introduction
%       Experimental observations
%       Previous work on Pt, CO, etc.
%
%Simulation Methodology
%       FF (fits and parameters)
%       MD (setup, equilibration, collection)
%
%       Analysis of trajectories!!!
%Discussion
%       CO preferences for specific locales
%       CO-CO interactions
%       Differences between Au & Pt
%       Causes of 2_layer reordering in Pt
%Summary
%%

%Title
\title{Molecular Dynamics simulations of the surface reconstructions
  of Pt(557) and Au(557) under exposure to CO}

\author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel
Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\
Department of Chemistry and Biochemistry,\\
University of Notre Dame\\
Notre Dame, Indiana 46556}

%Date
\date{Mar 5, 2013}

%authors

% make the title
\maketitle

\begin{doublespace}

\begin{abstract}
We examine surface reconstructions of Pt and Au(557) under
various CO coverages using molecular dynamics in order to 
explore possible mechanisms for any observed reconstructions 
and their dynamics. The metal-CO interactions were parameterized 
as part of this work so that an efficient large-scale treatment of 
this system could be undertaken. The large difference in binding 
strengths of the metal-CO interactions was found to play a significant 
role with regards to step-edge stability and adatom diffusion. A 
small correlation between coverage and the diffusion constant 
was also determined. The energetics of CO adsorbed to the surface 
is sufficient to explain the reconstructions observed on the Pt 
systems and the lack  of reconstruction of the Au systems.

\end{abstract}

\newpage


\section{Introduction}
% Importance: catalytically active metals are important
%       Sub: Knowledge of how their surface structure affects their ability to catalytically facilitate certain reactions is growing, but is more reactionary than predictive
%       Sub: Designing catalysis is the future, and will play an important role in numerous processes (ones that are currently seen to be impractical, or at least inefficient)
% Theory can explore temperatures and pressures which are difficult to work with in experiments
%       Sub: Also, easier to observe what is going on and provide reasons and explanations
%

Industrial catalysts usually consist of small particles that exhibit a
high concentration of steps, kink sites, and vacancies at the edges of
the facets.  These sites are thought to be the locations of catalytic
activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now
significant evidence that solid surfaces are often structurally,
compositionally, and chemically modified by reactants under operating
conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between
surface oxidation states and catalytic activity for CO oxidation on
Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002}
Despite the well-documented role of these effects on reactivity, the
ability to capture or predict them in atomistic models is somewhat
limited.  While these effects are perhaps unsurprising on the highly
disperse, multi-faceted nanoscale particles that characterize
industrial catalysts, they are manifest even on ordered, well-defined
surfaces. The Pt(557) surface, for example, exhibits substantial and
reversible restructuring under exposure to moderate pressures of
carbon monoxide.\cite{Tao:2010}

This work is an investigation into the mechanism and timescale for
surface restructuring using molecular simulations.  Since the dynamics
of the process are of particular interest, we employ classical force
fields that represent a compromise between chemical accuracy and the
computational efficiency necessary to simulate the process of interest.
Since restructuring typically occurs as a result of specific interactions of the
catalyst with adsorbates, in this work, two metal systems exposed 
to carbon monoxide were examined. The Pt(557) surface has already been shown
to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010} 
The Au(557) surface, because of a weaker interaction with CO, is seen as less 
likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000} 
and Piccolo et al.\cite{Piccolo:2004} have both observed CO-induced 
reconstruction of a Au(111) surface. Peters et al. saw a relaxation to the 
22 x $\sqrt{3}$ cell. They argued that only a few Au atoms
become adatoms, limiting the stress of this reconstruction while 
allowing the rest to relax and approach the ideal (111) 
configuration. They did not see the usual herringbone pattern being greatly 
affected by this relaxation. Piccolo et al. on the other hand, did see a 
disruption of the herringbone pattern as CO was adsorbed to the 
surface. Both groups suggested that the preference CO shows for 
low-coordinated Au atoms was the primary driving force for the reconstruction.


%Platinum molecular dynamics
%gold molecular dynamics

\section{Simulation Methods}
The challenge in modeling any solid/gas interface is the
development of a sufficiently general yet computationally tractable
model of the chemical interactions between the surface atoms and
adsorbates.  Since the interfaces involved are quite large (10$^3$ -
10$^6$ atoms) and respond slowly to perturbations, {\it ab initio}
molecular dynamics
(AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello
methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum
mechanical potential energy surfaces remain out of reach.
Additionally, the ``bonds'' between metal atoms at a surface are
typically not well represented in terms of classical pairwise
interactions in the same way that bonds in a molecular material are,
nor are they captured by simple non-directional interactions like the
Coulomb potential.  For this work, we have used classical molecular
dynamics with potential energy surfaces that are specifically tuned
for transition metals.  In particular, we used the EAM potential for
Au-Au and Pt-Pt interactions\cite{EAM}. The CO was modeled using a rigid
three-site model developed by Straub and Karplus for studying
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and
Pt-CO cross interactions were parameterized as part of this work.
  
\subsection{Metal-metal interactions}
Many of the potentials used for modeling transition metals are based
on a non-pairwise additive functional of the local electron
density. The embedded atom method (EAM) is perhaps the best known of
these
methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98}
but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and
the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler
parameter sets. The glue model of Ercolessi et al. is among the
fastest of these density functional approaches.\cite{Ercolessi88} In
all of these models, atoms are conceptualized as a positively charged
core with a radially-decaying valence electron distribution. To
calculate the energy for embedding the core at a particular location,
the electron density due to the valence electrons at all of the other
atomic sites is computed at atom $i$'s location,
\begin{equation*}
\bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
\end{equation*}
Here, $\rho_j(r_{ij})$ is the function that describes the distance
dependence of the valence electron distribution of atom $j$. The
contribution to the potential that comes from placing atom $i$ at that
location is then
\begin{equation*}
V_i =  F[ \bar{\rho}_i ]  + \sum_{j \neq i} \phi_{ij}(r_{ij})
\end{equation*}
where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and
$\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the
repulsive overlap of the two positively charged cores.  

% The {\it modified} embedded atom method (MEAM) adds angular terms to
% the electron density functions and an angular screening factor to the
% pairwise interaction between two
% atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve}
% MEAM has become widely used to simulate systems in which angular
% interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc
% metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys})
% MEAM presents significant additional computational costs, however.

The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials
have all been widely used by the materials simulation community for
simulations of bulk and nanoparticle
properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq}
melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack
propagation,\cite{BECQUART:1993rg} and alloying
dynamics.\cite{Shibata:2002hh} One of EAM's strengths
is its sensitivity to small changes in structure. This arises
from the original parameterization, where the interactions
up to the third nearest neighbor were taken into account.\cite{Voter95a}
Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88}
which is only parameterized up to the nearest-neighbor
interactions, EAM is a suitable choice for systems where 
the bulk properties are of secondary importance to low-index 
surface structures. Additionally, the similarity of EAMs functional 
treatment of the embedding energy to standard density functional 
theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier.
\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  


\subsection{Carbon Monoxide model}
Previous explanations for the surface rearrangements center on
the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010}  
We used a model first proposed by Karplus and Straub to study
the photodissociation of CO from myoglobin because it reproduces 
the quadrupole moment well.\cite{Straub} The Straub and
Karplus model treats CO as a rigid three site molecule with a massless M
site at the molecular center of mass. The geometry and interaction 
parameters are reproduced in Table~\ref{tab:CO}. The effective 
dipole moment, calculated from the assigned charges, is still
small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum 
mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
%CO Table
\begin{table}[H]
  \caption{Positions, Lennard-Jones parameters ($\sigma$ and
    $\epsilon$), and charges for the CO-CO 
    interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are 
    in kcal/mol, and charges are in atomic units.}
\centering
\begin{tabular}{| c | c | ccc |}
\hline
&  {\it z} & $\sigma$ & $\epsilon$ & q\\
\hline
\textbf{C} & -0.6457 &  3.83 & 0.0262   &   -0.75 \\
\textbf{O} &  0.4843 &  3.12 &  0.1591  &   -0.85 \\
\textbf{M} & 0.0 & -  &  -  &    1.6 \\
\hline
\end{tabular}
\label{tab:CO}
\end{table}

\subsection{Cross-Interactions between the metals and carbon monoxide}

Since the adsorption of CO onto a Pt surface has been the focus
of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979}
and theoretical work
\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
there is a significant amount of data on adsorption energies for CO on
clean metal surfaces. An earlier model by Korzeniewski {\it et
  al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were
modified to ensure that the Pt-CO interaction favored the atop binding
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}.
The modified parameters yield binding energies that are slightly higher
than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski
et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
Lennard-Jones interaction to mimic strong, but short-ranged partial
binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The
Pt-O interaction was modeled with a Morse potential with a large
equilibrium distance, ($r_o$).  These choices ensure that the C is preferred
over O as the surface-binding atom. In most cases, the Pt-O parameterization contributes a weak
repulsion which favors the atop site.  The resulting potential-energy
surface suitably recovers the calculated Pt-C separation length
(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding
position.\cite{Deshlahra:2012, Hopster:1978}

%where did you actually get the functionals for citation?
%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think
%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there...
The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and
Morse potentials, respectively, to reproduce Au-CO binding energies.
The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations.
Adsorption energies were obtained from gas-surface DFT calculations with a
periodic supercell plane-wave basis approach, as implemented in the
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were
described with the projector augmented-wave (PAW)
method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
included to an energy cutoff of 20 Ry. Electronic energies are
computed with the PBE implementation of the generalized gradient
approximation (GGA) for gold, carbon, and oxygen that was constructed
by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4
Au x 2 Au surface planes and separated from vertical images by six
layers of vacuum space. The surface atoms were all allowed to relax 
before CO was added to the system. Electronic relaxations were 
performed until the energy difference between subsequent steps 
was less than $10^{-8}$ Ry.   Nonspin-polarized supercell calculations 
were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was
then used in numerous single point calculations with CO at various
heights (and angles relative to the surface) to allow fitting of the
empirical force field.

%Hint at future work
The parameters employed for the metal-CO cross-interactions in this work 
are shown in Table~\ref{tab:co_parameters} and the binding energies on the 
(111) surfaces are displayed in Table~\ref{tab:co_energies}.  Charge transfer
and polarization are neglected in this model, although these effects are likely to
affect binding energies and binding site preferences, and will be addressed in
future work.

%Table  of Parameters
%Pt Parameter Set 9
%Au Parameter Set 35
\begin{table}[H]
  \caption{Best fit parameters for metal-CO cross-interactions. Metal-C
    interactions are modeled with Lennard-Jones potentials. While the
    metal-O interactions were fit to Morse
    potentials.  Distances are given in \AA~and energies in kcal/mol. }
\centering
\begin{tabular}{| c | cc | c | ccc |}
\hline
 &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
\hline
\textbf{Pt-C} & 1.3 & 15  & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\
\textbf{Au-C} & 1.9 & 6.5  & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\

\hline
\end{tabular}
\label{tab:co_parameters}
\end{table}

%Table of energies
\begin{table}[H]
  \caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials
    described in this work.  All values are in eV.}
\centering
\begin{tabular}{| c | cc |}
  \hline
  & Calculated & Experimental \\
  \hline
  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,}
  (Ref. \protect\cite{Kelemen:1979}) \\
 & &  -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline
  \textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,}  (Ref. \protect\cite{TPD_Gold}) \\
  \hline
\end{tabular}
\label{tab:co_energies}
\end{table}

\subsection{Pt(557) and Au(557) metal interfaces}
Our Pt system is an orthorhombic periodic box of dimensions
54.482~x~50.046~x~120.88~\AA~while our Au system has 
dimensions of 57.4~x~51.9285~x~100~\AA.
The systems are arranged in a FCC crystal that have been cut
along the (557) plane so that they are periodic in the {\it x} and
{\it y} directions, and have been oriented to expose two aligned
(557) cuts along the extended {\it z}-axis.  Simulations of the 
bare metal interfaces at temperatures ranging from 300~K to
1200~K were performed to confirm the relative
stability of the surfaces without a CO overlayer.  

The different bulk melting temperatures (1337~K for Au
and 2045~K for Pt) suggest that any possible reconstruction should happen at
different temperatures for the two metals.  The bare Au and Pt surfaces were
initially run in the canonical (NVT) ensemble at 800~K and 1000~K
respectively for 100 ps. The two surfaces were relatively stable at these 
temperatures when no CO was present, but experienced increased surface 
mobility on addition of CO. Each surface was then dosed with different concentrations of CO
that was initially placed in the vacuum region.  Upon full adsorption,
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
coverage. Higher coverages resulted in the formation of a double layer of CO,
which introduces artifacts that are not relevant to (557) reconstruction.
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
the Au surfaces often had a significant CO population in the gas
phase.  These systems were allowed to reach thermal equilibrium (over
5~ns) before being run in the microcanonical (NVE) ensemble for
data collection. All of the systems examined had at least 40~ns in the
data collection stage, although simulation times for some Pt of the
systems exceeded 200~ns.  Simulations were carried out using the open
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}


% RESULTS
%
\section{Results}
\subsection{Structural remodeling}
The surfaces of both systems, upon dosage of CO, began 
to undergo remodeling that was not observed in the bare 
metal system. The surfaces which were not exposed to CO 
did experience minor roughening of the step-edge because 
of the elevated temperatures, but the 
(557) lattice was well-maintained throughout the simulation 
time. The Au systems were limited to greater amounts of 
roughening, i.e. breakup of the step-edge, and some step 
wandering. The lower coverage Pt systems experienced 
similar restructuring but to a greater extent when 
compared to the Au systems. The 50\% coverage 
Pt system was unique among our simulations in that it 
formed numerous double layers through step coalescence, 
similar to results reported by Tao et al.\cite{Tao:2010}


\subsubsection{Step wandering}
The 0\% coverage surfaces for both metals showed minimal 
movement at their respective run temperatures. As the CO 
coverage increased however, the mobility of the surface, 
adatoms and step-edges alike, also increased. Additionally, 
at the higher coverages on both metals, there was more 
step-wandering. Except for the 50\% Pt system, the step-edges 
did not coalesce in any of the other simulations, instead preferring 
to keep nearly the same distance between steps as in the 
original (557) lattice. Previous work by Williams et al.\cite{Williams:1991, Williams:1994} 
highlights the repulsion that exists between step-edges even 
when no direct interactions are present in the system. This 
repulsion exists because the entropy of the step-edges is constrained 
since step-edge crossing is not allowed. This entropic repulsion 
does not completely define the interactions between steps, 
which is why some surfaces will undergo step coalescence, 
where additional attractive interactions can overcome the 
repulsion\cite{Williams:1991} and others will not. The presence 
of adsorbates can affect these step interactions, potentially 
leading to a new surface structure as the thermodynamic minimum.

\subsubsection{Double layers}
Tao et al. have shown experimentally that the Pt(557) surface 
undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} 
The first involves a doubling of the step height and plateau length. 
Similar behavior has been seen to occur on numerous surfaces 
at varying conditions: Ni(977), Si(111).\cite{Williams:1994,Williams:1991,Pearl} 
Of the two systems we examined, the Pt system showed a greater 
propensity for reconstruction when compared to the Au system 
because of the larger surface mobility and extent of step wandering. 
The amount of reconstruction is correlated to the amount of CO 
adsorbed upon the surface.  This appears to be related to the 
effect that adsorbate coverage has on edge breakup and on the 
surface diffusion of metal adatoms. While both systems displayed 
step-edge wandering, only the 50\% Pt surface underwent the 
doubling seen by Tao et al. within the time scales studied here. 
Over longer periods (150~ns) two more double layers formed 
on this interface. Although double layer formation did not occur 
in the other Pt systems, they show more step-wandering and 
general roughening compared to their Au counterparts. The 
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at 
various times along the simulation showing the evolution of a step-edge.

The second reconstruction on the Pt(557) surface observed by 
Tao involved the formation of triangular clusters that stretched 
across the plateau between two step-edges. Neither system, within 
the 40~ns time scale or the extended simulation time of 150~ns for 
the 50\% Pt system, experienced this reconstruction.

\subsection{Dynamics}
Previous atomistic simulations of stepped surfaces dealt largely
with the energetics and structures at different conditions
\cite{Williams:1991,Williams:1994}. Consequently, the most common 
technique utilized to date has been Monte Carlo sampling. Monte Carlo gives an efficient 
sampling of the equilibrium thermodynamic landscape at the expense 
of ignoring the dynamics of the system. Previous experimental work by Pearl and 
Sibener\cite{Pearl}, using STM, has been able to capture the coalescing 
of steps on Ni(977). The time scale of the image acquisition, 
$\sim$70 s/image provides an upper bound for the time required for 
the doubling to occur. In this section we give data on dynamic and 
transport properties, e.g. diffusion, layer formation time, etc.


\subsubsection{Transport of surface metal atoms}
%forcedSystems/stepSeparation
The movement or wandering of a step-edge is a cooperative effect 
arising from the individual movements of the atoms making up the steps. An ideal metal surface 
displaying a low index facet, (111) or (100), is unlikely to experience 
much surface diffusion because of the large energetic barrier that must 
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features
on higher-index facets provide a lower energy source for mobile metal atoms. 
Breaking away from the step-edge on a clean surface still imposes an 
energetic penalty around $\sim$~40 kcal/mol, but this is significantly easier than lifting 
the same metal atom vertically out of the surface,  \textgreater~60 kcal/mol. 
The penalty lowers significantly when CO is present in sufficient quantities 
on the surface. For certain distributions of CO, the penalty can fall as low as 
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for 
diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are 
able to explore the terrace before rejoining either the original step-edge or 
becoming a part of a different edge. It is a more difficult process for an atom 
to traverse to a separate terrace although the presence of CO can lower the 
energy barrier required to lift or lower the adatom. By tracking the mobility of individual 
metal atoms on the Pt and Au surfaces we were able to determine the relative 
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close 
observation of the mobile metal atoms showed that they were typically in 
equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. 
At times, their motion was concerted and two or more adatoms would be 
observed moving together across the surfaces. 

A particle was considered ``mobile'' once it had traveled more than 2~\AA~
between saved configurations of the system (typically 10-100 ps). An atom that was 
truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff 
was used to prevent swamping the diffusion data with the in-place vibrational 
movement of buried atoms. Diffusion on a surface is strongly affected by 
local structures and in this work, the presence of single and double layer 
step-edges causes the diffusion parallel to the step-edges to be different 
from the diffusion perpendicular to these edges. Parallel and perpendicular
diffusion constants are shown in Figure \ref{fig:diff}.

The lack of a definite trend in the Au diffusion data is likely due 
to the weaker bonding between Au and CO. This leads to a lower 
coverage ({\it x}-axis) when compared to dosage amount, which 
then further limits the affects of the surface diffusion. The correlation 
between coverage and Pt diffusion rates conversely shows a 
definite trend marred by the highest coverage surface. Two 
explanations arise for this drop. First, upon a visual inspection of 
the system, after a double layer has been formed, it maintains its 
stability strongly and is no longer a good source for adatoms. By 
performing the same diffusion calculation but on a shorter run time 
(20~ns), only including data before the formation of the double layer, 
provides a $\mathbf{D}_{\perp}$ diffusion constant of $1.69~\pm~0.08$ 
and a $\mathbf{D}_{\parallel}$ diffusion constant of $6.30~\pm~0.08$. 
This places the parallel diffusion constant more closely in line with the 
expected trend, while the perpendicular diffusion constant does not 
drop as far. A secondary explanation arising from our analysis of the 
mechanism of double layer formation show the affect that CO on the 
surface has with respect to overcoming surface diffusion of Pt. If the 
coverage is too sparse, the Pt engages in minimal interactions and 
thus minimal diffusion. As coverage increases, there are more favorable 
arrangements of CO on the surface allowing the formation of a path, 
a minimum energy trajectory, for the adatom to explore the surface. 
As the CO is constantly moving on the surface, this path is constantly 
changing. If the coverage becomes too great, the paths could 
potentially be clogged leading to a decrease in diffusion despite 
their being more adatoms and step-wandering.

\subsubsection{Dynamics of double layer formation}
The increased diffusion on Pt at the higher 
CO coverages plays a primary role in double layer formation. However, this is not 
a complete explanation -- the 33\%~Pt system 
has higher diffusion constants but did not show 
any signs of edge doubling in the observed run time. On the 
50\%~Pt system, one layer formed within the first 40~ns of simulation time, while two more were formed as the system was run for an additional
110~ns (150~ns total). Previous experimental 
work gives insight into the upper bounds of the 
time required for step coalescence.\cite{Williams:1991,Pearl} 
In this system, as seen in Figure \ref{fig:reconstruct}, the first 
appearance of a double layer, appears at 19~ns 
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has 
formed the double layer and by 86~ns, the complete layer 
has been flattened out. The double layer could be considered 
``complete" by 37~ns but remains a bit rough. From the 
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another 
$\sim$40~ns was necessary for the layer to completely straighten. 
The other two layers in this simulation formed over periods of
22~ns and 42~ns respectively. Comparing this to the upper 
bounds of the image scan, it is likely that most aspects of this 
reconstruction occur very rapidly. A possible explanation 
for this rapid reconstruction is the elevated temperatures 
under which our systems were simulated. It is probable that the process would 
take longer at lower temperatures.

%Evolution of surface
\begin{figure}[H]
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
\caption{The Pt(557) / 50\% CO system at a sequence of times after
  initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and
  (d) 86.1~ns. Disruption of the (557) step-edges occurs quickly.  The
  doubling of the layers appears only after two adjacent step-edges
  touch.  The circled spot in (b) nucleated the growth of the double
  step observed in the later configurations.}
  \label{fig:reconstruct}
\end{figure}

\begin{figure}[H]
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf}
\caption{Diffusion constants for mobile surface atoms along directions
  parallel ($\mathbf{D}_{\parallel}$) and perpendicular
  ($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO
  surface coverage.  Diffusion parallel to the step-edge is higher
  than that perpendicular to the edge because of the lower energy
  barrier associated with traversing along the edge as compared to
  completely breaking away. Additionally, the observed
  maximum and subsequent decrease for the Pt system suggests that the
  CO self-interactions are playing a significant role with regards to
  movement of the Pt atoms around and across the surface. }
\label{fig:diff}
\end{figure}


%Discussion
\section{Discussion}
We have shown that the classical potential models are able to model the initial reconstruction of the
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we
were able to observe features of the dynamic processes necessary for this reconstruction. 

\subsection{Mechanism for restructuring}
Since the Au surface showed no large scale restructuring throughout
our simulation time our discussion will focus on the 50\% Pt-CO system
which did undergo the doubling featured in Figure \ref{fig:reconstruct}.
Similarities of our results to those reported previously by 
Tao et al.\cite{Tao:2010} are quite 
strong. The simulated Pt 
system exposed to a large dosage of CO readily restructures by doubling the terrace 
widths and step heights. The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a time, but is rapid on experimental timescales. 
The adatoms either 
break away from the step-edge and stay on the lower terrace or they lift 
up onto a higher terrace. Once ``free'', they diffuse on the terrace 
until reaching another step-edge or rejoining their original edge.  
This combination of growth and decay of the step-edges is in a state of 
dynamic equilibrium. However, once two previously separated edges 
meet as shown in Figure 1.B, this nucleates the rest of the edge to meet up, forming a double layer.
From simulations which exhibit a double layer, the time delay from the initial appearance of a nucleation point to a fully formed double layer is $\sim$35~ns.

A number of possible mechanisms exist to explain the role of adsorbed 
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent 
CO molecules adsorbed on the surface is one possibility.  However, 
the quadrupole-quadrupole interaction is short-ranged and is attractive for 
some orientations.  If the CO molecules are ``locked'' in a specific orientation 
relative to each other, through atop adsorption for example, this explanation 
gains some credence.  The energetic repulsion between two CO located a 
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in 
a  vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second 
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to 
nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation 
also quickly drops the repulsion, a minimum of 6.2 kcal/mol is reached at $\sim$24 degrees between the 2 CO when the carbons are locked at a distance of 2.77 \AA apart.
As mentioned above, the energy barrier for surface diffusion 
of a Pt adatom is only 4 kcal/mol. So this repulsion between neighboring CO molecules can 
increase the surface diffusion. However, the residence time of CO on Pt was 
examined and while the majority of the CO is on or near the surface throughout 
the run, most molecules are mobile. This mobility suggests that the CO are more 
likely to shift their positions without necessarily the Pt along with them.

Another possible and more likely mechanism for the restructuring is in the
destabilization of strong Pt-Pt interactions by CO adsorbed on surface
Pt atoms.  This would then have the effect of increasing surface mobility
of these atoms.  To test this hypothesis, numerous configurations of 
CO in varying quantities were arranged on the higher and lower plateaus
around a step on a otherwise clean Pt(557) surface. One representative
configuration is displayed in Figure \ref{fig:lambda}. Single or concerted movement
of Pt atoms was then examined to determine possible barriers. Because
the movement was forced along a pre-defined reaction coordinate that may differ
from the true minimum of this path, only the beginning and ending energies
are displayed in Table \ref{tab:energies} with the corresponding beginning and ending reaction coordinates in Figure \ref{fig:lambdaTable}. These values suggest that the presence of CO at suitable
locations can lead to lowered barriers for Pt breaking apart from the step-edge.
Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the
burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral
in terms of energetics.

%lambda progression of Pt -> shoving its way into the step
\begin{figure}[H]
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png}
\caption{A model system of the Pt(557) surface was used as the framework
 for exploring energy barriers along a reaction coordinate. Various numbers,
 placements, and rotations of CO were examined as they affect Pt movement.
 The coordinate displayed in this Figure was a representative run. As shown
 in Table \ref{tab:rxcoord}, relative to the energy of the system at 0\%, there
 is a slight decrease upon insertion of the Pt atom into the step-edge along
 with the resultant lifting of the other Pt atom when CO is present at certain positions.}
\label{fig:lambda}
\end{figure}

\begin{figure}[H]
\includegraphics[totalheight=0.9\textheight]{lambdaTable.png}
\caption{}
\label{fig:lambdaTable}
\end{figure}


\subsection{Diffusion}
The diffusion parallel to the step-edge tends to be 
much larger than that perpendicular to the step-edge. The dynamic 
equilibrium that is established between the step-edge and adatom interface. The coverage 
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}.
The 
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. 
\\


%breaking of the double layer upon removal of CO
\begin{figure}[H]
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png}
\caption{(A)  0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO
 helped maintain the stability of the double layer and upon removal the two layers break
 and begin separating. The separation is not a simple pulling apart however, rather 
 there is a mixing of the lower and upper atoms at the edge.}
\label{fig:breaking}
\end{figure}


%Peaks!
%\begin{figure}[H]
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
%\caption{At the initial formation of this double layer  ( $\sim$ 37 ns) there is a degree
 %of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with 
 %aspects of waviness and by 80 ns the double layer is completely formed and smooth. }
%\label{fig:peaks}
%\end{figure}


%Don't think I need this
%clean surface...
%\begin{figure}[H]
%\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
%\caption{}

%\end{figure}
%\label{fig:clean}


\section{Conclusion}
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. 

%Things I am not ready to remove yet

%Table of Diffusion Constants
%Add gold?M
% \begin{table}[H]
%   \caption{}
%   \centering
% \begin{tabular}{| c | cc | cc | }
%   \hline
%   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
%   \hline
%   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
%   \hline
%   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
%   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
%   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
%   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
%   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
%   \hline 
% \end{tabular}
% \end{table}

\section{Acknowledgments}
Support for this project was provided by the National Science
Foundation under grant CHE-0848243 and by the Center for Sustainable
Energy at Notre Dame (cSEND). Computational time was provided by the
Center for Research Computing (CRC) at the University of Notre Dame.

\newpage
\bibliography{firstTryBibliography}
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\end{document}
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