PtPd/tex/draft.tex

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\title{CO-induced island formation on Pt@Pd(557) subsurface alloys: A
  molecular dynamics study}
  

\author{Joseph R. Michalka}
\author{J. Daniel Gezelter}
\email{gezelter@nd.edu}
\affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
  Department of Chemistry and Biochemistry\\ University of Notre
  Dame\\ Notre Dame, Indiana 46556}

\keywords{}

\begin{document}

%%
% Introduction
%   
% Materials/Methods
%
% Results/Discussion
%
% Conclusion
%% 


\begin{abstract}


\end{abstract}

\newpage


\section{Introduction}
Bimetallic alloys, subsurface alloys, and core-shell nanostructures are
currently under intense investigation\cite{a} because of their large accesible
design space for various catalytic processes.  The presence of two (or more)
components in these structures allows for a high degree of tuning of the
specific characteristics, whether that be catalytic activity\cite{a}, thermal
stability\cite{a}, or resistance to deactivation\cite{a}. As seen in many
experimental\cite{Ertl:1989} and theoretical studies\cite{a}, the potential
energy landscape of the surface is often modified by the presence of adsorbates
leading to large-scale reconstructions of the surface. This reconstruction
could be a simple refaceting or a more complicated process that leads to the
formation of significant nano-features. Both situations will provide additional
or different active sites, chaning the activity and selectivity of the
catalyst.

Tuning catalyst work...

This work is an investigation into the effect of CO adsorption on surface
restructuring of a Pd(557) and Pt@Pd(557) shell surface using molecular
simulation. Since the mechanism and dynamics of the restructuring are of
particular interest, classical force fields which balance computational
efficiency against chemical accuracy were employed. A more complete
understanding of a catalyst's structural response to industrial conditions
brings us ever closer to the end goal of catalytic design.


\section{Methodology}
\subsection{Interaction Potentials}
Modeling large metallic interfaces (10\textsuperscript{3}-
10\textsuperscript{4} atoms) over relatively long time scales (10-100
ns) requires the use of empirical potentials.  Metallic cohesive and
surface energies are not reproduced with purely pairwise interactions,
so a number of empirical potentials have been developed for modeling
transition metals.  These include the embedded atom method
(EAM)\cite{EAM}, Finnis-Sinclair\cite{Finnis84}, and Sutton-Chen-based
models like QSC\cite{QSC}.  These models are fairly similar in that
they describe an atom as a positively charged core with a radially
decaying valence electron distribution.  Refinements include angle
dependent EAM implementations,\cite{Baskes:1987} that treat BCC metals
more accurately.

In EAM, the energy for embedding a metallic atom at a specific
location in the system requires the electron density at that location,
\begin{equation*}
\bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij}).
\end{equation*}
This density depends on the contributions to the electron density from
all other atoms in the system.  Here, $\rho_j(r)$ describes the
distance dependence of the valence electron distribution of atom $j$.
Atom $i$'s contribution to the potential energy is obtained from an
embedding functional, $F_i\left[ \bar{\rho}_i \right]$, as well as a sum
of pairwise interactions,
\begin{equation*}
V_i =  F[ \bar{\rho}_i ]  + \sum_{j \neq i} \phi_{ij}(r_{ij})
\end{equation*}

The energy functional is parameterized for each metallic atom type,
and depends only on the local electron density, $\bar{\rho_i}$.  Thus,
the cohesive energy felt by atom $i$ depends on collective
contributions from all of the surrounding metal atoms, and is an
explicitly non-pairwise additive quantity.

The short-ranged repulsions are treated as a pairwise contribution
that models the repulsive overlap of the positive cores.  For alloyed
metallic systems, mixing rules as outlined by Johnson \cite{johnson89}
were used to compute the heterogenous pair potential,
\begin{equation*} 
\phi_{ab}(r) = \frac{1}{2}
\bigg\{ \bigg(
\frac{\rho_b(r)}{\rho_a(r)}
\bigg) \phi_{aa}(r)
+ \bigg(
\frac{\rho_a(r)}{\rho_b(r)}
\bigg)\phi_{bb}(r) 
\bigg\}
\end{equation*} 

One of EAM's strengths is its sensitivity to small changes in
structure which is due to the inclusion of second and third nearest
neighbor interactions during parameterization.\cite{a}

In this work, we have employed the embedded atom method (EAM) to
describe the Pt-Pt, Pt-Pd, and Pd-Pd electron density, embedding
functionals, and pair potentials,\cite{EAM} utilizing the Johnson
mixing rules for the Pt-Pd cross-interactions.\cite{johnson89}

The CO self-interactions were modeled using a rigid three-site model
developed by Straub and Karplus for studying photodissociation of CO
from myoglobin.\cite{Straub} This model accurately captures the large
linear quadrupole (and weak dipole) of the CO molecule.  

The Pt-CO interactions have been modified from our previous
work\cite{Michalka:2013} to include additional experimental
data,\cite{Deshlahra:2012} resulting in a slightly weaker binding of
the Pt-CO interaction.  The Pd-CO interactions were parameterized as
part of this work.  Refitting the Pt-CO interaction gives the correct
energetic ordering and site-preferences for both the Pd-CO and Pt-CO
interactions on 111 surfaces.

Specifically, --- show CO binding to Pd to be stronger than Pt with an
absolute value between ---\cite{} and ---\cite{} and a binding site
preference of --- when the coverage is greater than a ---
monolayer. As in our previous work, we use a model by Korzeniewski
\textit{et al.}\cite{Pons:1986} as a starting point for our fits.

The parameters were then modified to accurately reproduce binding
energy and binding site preference on the M(111) surfaces.  One key
difference between the previous model and this one is that the M-O
bond is now modeled using a purely repulsive Morse potential, $D
e^{-2\gamma(r-r_e)}$.  The functional forms and the broad repulsive
M-O contribution are flexible enough to reproduce the atop preference
for Pt-CO as well as the bridge-site preference for Pd-CO.  Parameters
for the potentials are given in Table~\ref{tab:CO_parameters} and the
calculated binding energies at various binding sites are shown in
Table~\ref{tab:CO_energies}.
\begin{table}
  \caption{Parameters for the metal-CO cross-interactions. Metal-Carbon
    interactions are modeled with Lennard-Jones potentials, while the
    metal-Oxygen interactions are fit using repulsive Morse-like
    potentials.  Distances are given in \AA~and energies in kcal/mol. }
\centering
\begin{tabular}{| c | cc | c | ccc |}
\hline
 &  $\sigma$ & $\epsilon$ & & $r_e$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
\hline
\textbf{Pt-C} & 1.41 & 45  & \textbf{Pt-O} & 4.4  & 0.05 & 1.8 \\
\textbf{Pd-C} & 1.6 &  40  & \textbf{Pd-O} & 4.95 & 0.05 & 1.45\\
\hline
\end{tabular}
\label{tab:CO_parameters}
\end{table}

%Table of energies
\begin{table}
  \caption{Adsorption energies for a CO molecule at the three special sites
    on M(111) using the potentials described in table
    \ref{tab:CO_parameters}.   These values are compared with DFT
    calculations of XXX along with relevant experimental desorption
    data. Reference \citenum{Deshlahra:2012} values are reported at $\frac{1}{4}$ ML. All values are in eV.}
\centering
\begin{tabular}{| cc | ccc |}
  \hline
  & Site & This Model & DFT & Experimental \\
  \hline
  \textbf{Pt-CO} & atop   & -1.47 & -1.48\cite{Deshlahra:2012} & -1.39\cite{Kelemen:1979}, -1.43\cite{Ertl:1977}, -1.90\cite{Yeo:1997} \\
                 & bridge & -1.13 & -1.47\cite{Deshlahra:2012} &  \\
                 & hollow & -1.02 & -1.45\cite{Deshlahra:2012} &  \\
  \textbf{Pd-CO} & atop   & -1.54 & -1.25\cite{McDonough:unpublished} &  \\
                 & bridge & -1.65 & -1.58\cite{McDonough:unpublished} &  \\
                 & hollow & -1.60 & -1.70\cite{McDonough:unpublished} & -1.47\cite{Ertl:1970}, -1.54\cite{Guo:1989} \\
  \hline
\end{tabular}
\label{tab:CO_energies}
\end{table}

\subsection{557 interfaces and subsurface alloys}
Our Pd(557) system is an orthorhombic periodic box with dimensions of
55.09~x~49.48~x~120.00~\AA~ while our subsurface alloys (Pt(557)
surface layers, with Pd bulk) have dimensions of
54.875~x~49.235~x~120.00~\AA.  The Pd system consists of 9 layers of
Pd while our subsurface alloys consist of 7 layers of Pd sandwiched
between 2 layers of Pt.  Both the pure Pd slab and the subsurface
alloy systems are $\sim$22~\AA~ thick. The lattice constants for Pd
and Pt (3.89 and 3.92~\AA) provide minimal strain energy in the alloy
(and the relaxed geometries of the two interfaces are therefore quite
similar).

The systems are cut from a FCC crystal along the 557 plane, and are
rotated so that they are periodic in the $x$ and $y$ directions, while
exposing 557 facets on both the positive and negative sides of the
$z$-axis of the box.

Simulations of the metal without any adsorbate present were performed
at temperatures ranging from 300 to 900~K to establish the stability
of the surface without a CO overlayer.  The bare systems were
initially run in the canonical (NVT) ensemble at 850~K for 200 ps and
the microcanonical (NVE) ensemble for 1 ns, and displayed no changes
in the 557 structure during this period.


Ten systems were constructed corresponding to five dosage levels for each
metallic system. The amounts of CO added to each system (0,48,240,320,480), assuming every CO
absorbs, would result in an approximately 0.00, 0.05, 0.25, 0.33, and 0.5 monolayer (ML)
coverage.  Simulation boxes of the same sizes as the metallic systems were
constructed with varying densities of CO and equilibrated to 850~K. The CO and
metallic boxes were then combined, with a 5~\AA~ cutoff between metallic atoms
and CO to prevent overlap. The remaining CO was further pared down to match the
needed number for the system and then had its velocities resampled from a
Boltzmann distribution to zero out any net momentum. The combined
systems were run for 1 ns in the NVT ensemble, before being run in the NVE
ensemble for data collection.


All of the Pd systems were run in the microcanonical ensemble for 40 ns while
the Pt@Pd systems which were observed to undergo greater amounts of
restructuring were run for 110 ns.  All simulations were carried out with the
open source molecular dynamics package,
OpenMD.\cite{openmd,a,a}
 
 % RESULTS
%
\section{Results}
Similar to our previous work, we focused on measuring the dynamics and
structural changes that the Pd and Pt@Pd systems underwent as a function of CO
coverage. Specifically, we measured the mobility of surface metal atoms on both
systems and the structural reconstruction that was observed for the shell
systems. The Pd system, regardless of coverage, retained the characteristic
plateaus and steps of the (557) cut with only minimal adatom movement. The Pt@Pd
system showed much greater reconstruction and clustering and is the focus of
most of our discussion. 


Upon introduction of CO to the system, the surface mobility increased.
As in our previous work we dosed the surfaces with 0\%, 5\%, 25\%,
33\%, and 50\% monolayers of CO to test the effect of coverage on
various dynamical processes and structural reconstructions. Higher
coverages appeared to have minimal effect on the pure Pd systems,
however, on the Pt@Pd systems, increasing coverage of CO did result in
increased structural remodeling of the surface. These systems were run
in the canonical ensemble for an additional 1 ns before transitioning
to the microcanonical (NVE) ensemble for data collection.

The stronger Pd-CO binding energy when compared to Pt-CO is hypothesized to
play a role in disrupting the surface and in the case of the shell system in
revealing the underlying Pd by causing clustering and island formation of the
Pt shell. However, when we examine representative selections of the systems in
Figure \ref{fig:systems}, we see that the Pd system highlighted in A, has
undergone nearly no restructuring.  The other three images highlight the effect
of varying CO concentrations on the Pt@Pd systems where the surface does
undergo large amounts of structural modification.

\begin{figure}
\includegraphics[width=\linewidth]{../figures/SystemFigures/systems_ochre2.png}
\caption{(A) is the $\frac{1}{3}$ monolayer (ML) Pd system after $\sim$40 ns of run
time. (B)-(D) are the 0, $\frac{1}{3}$, and $\frac{1}{2}$ ML Pt@Pd
systems after $\sim$80 ns of run time. Platinum atoms are gray, Palladium
ochre, Carbon black, and Oxygen are red. The minor restructuring in B is due to
the energy benefit gained when Pt maximizes Pt-Pt bonds. (C) and (D) have undergone greater
remodeling because the presence of CO helps speed up adatom mobility and
enables the vertical displacement of Pt adatoms leading to more clustering.}
\label{fig:systems}
\end{figure}


\subsection{Dynamics}

\subsubsection{Diffusion of Surface Metal Atoms}

As Tao et al.\cite{Tao:2010} showed and we modeled\cite{Michalka:2013}, the
steps of the Pt(557) system when exposed to a CO atmosphere undergo doubling.
To the extent of our knowledge there has been no similar work done with CO on
Pd(557) and this work is an attempt to explore that system as well as what
happens to a bimetallic system containing both Pt and Pd. As we examine the
surface mobility of these two systems, Figure \ref{fig:systems} immediately
suggests that there is limited to no mobility on the pure Pd systems whereas
there is significant movement of Pt in the shell systems.  There were not
enough mobile atoms in the bulk Pd systems to perform diffusion analysis and
since they underwent no noticable structural modifications in their 40~ns run
times our focus will be on the shell systems.  

The calculated diffusion constants of mobile Pt atoms from the Pt@Pd systems
are shown in Figure/Table \ref{fig:diffusion}.  The absolute number of mobile Pt
atoms was similar between all coverage systems ($\sim600$), where mobile is
defined as the atom having moved at least 2~\AA~during the simulation.  Of
immediate interest is the slight correlation between increasing CO coverage and
Pt diffusion rates.


\begin{figure}
\includegraphics[width=\linewidth]{../figures/diffusion/DiffusionConstants_Pt_error.pdf}
\caption{Diffusion constants of mobile Pt atoms for the Pt@Pd systems. The
dotted line is drawn as a guide. The errors bars are obtained from deviations
of the linear fits against the raw diffusion data.}
\label{fig:diffusion}
\end{figure}

\begin{table}
\centering
\begin{tabular}{| c | c |}
\hline
CO ML & Diffusion Constant (\AA\textsuperscript{2}/ns) \\
\hline
0\% & 2.779 $\pm$ 0.002 \\
5\% & 3.992 $\pm$ 0.006 \\
25\% & 3.436 $\pm$ 0.005 \\
33\% & 4.180 $\pm$ 0.007 \\
50\% & 3.935 $\pm$ 0.005 \\
\hline
\end{tabular}
\caption{Diffusion constants of mobile Pt atoms for the Pt@Pd systems. The
errors bars are obtained from deviations of the linear fits against the raw
diffusion data.}
\label{tab:diffusion}
\end{table}


\subsection{Structural}
As in our previous work, the structural reconstructions that occurred are of
considerable interest and our focus will be on the Pt@Pd shell systems which
underwent significant restructuring. As can be see in Figure
\ref{fig:domainAreasPd}, over the 110~ns run time the amount of exposed Pd
increases both over time, and as a function of CO coverage. The appearance of
the underlying Pd necessitates a loss of surface area of the outer Pt shell.
Two likely scenarios, burying of Pt atoms, or island formation both would explain the
decreased surface area of Pt as seen in Figure \ref{fig:domainAreasPt}. A closer examination of Figure
\ref{fig:systems} suggests that the primary loss of surface area is due to Pt
clustering into islands and this argument is further supported with Figure
\ref{fig:nearestNeighbors}, where we see the increase in Pt with 9 Pt nearest
neighbors along with the concomittant decrease in Pt with only 6 Pt nearest
neighbors. This along with Figure \ref{fig:systems} is strong evidence for the formation of multi-layer Pt features
since single layers of Pt are restricted to having 6 Pt nearest neighbors.

\begin{figure}
\includegraphics[width=\linewidth]{../figures/domainAreas/domain_Pd_110ns.pdf}
\caption{Distributions of Pd domain size as a function of time and CO coverage.
Data is averaged over $\sim$20~ns segments to help show progression,
additionally, the data is shown as a percentage of the total surface area of
the Pt@Pd system with the integration of the curves equaling the percentage
surface area of Pd, shown in Table \ref{tab:integratedArea}. The presence of CO
leads to more exposure of the underlying Pd, which is quantified here by an
increasing number and increasing size of Pd domains. The bare Pt@Pd surface,
as seen in Figure \ref{fig:systems}.B, undergoes some restructuring, however, the
extent is much less when compared to the 25\% and 50\% monolayer (ML) systems.}
\label{fig:domainAreasPd} 
\end{figure}

\begin{figure}
\includegraphics[width=\linewidth]{../figures/domainAreas/domain_Pt_110ns.pdf}
\caption{Distributions of Pt domain size as a function of time and CO coverage.
Here the presence of CO facilitates the clustering of Pt into smaller domains
by forming multilayer features which leads to a reduction of Pt surface coverage and concomitant increased exposure of the Pd.}
\label{fig:domainAreasPt}
\end{figure}


\begin{figure}
\includegraphics[width=\linewidth]{../figures/nearestNeighbor/NearestNeighbor_110ns.pdf}
\caption{Population of Pt atoms with either 6 (solid) or 9 (hollow) Pt nearest
neighbors averaged over similar blocks of time as in Figure
\ref{fig:domainAreasPd} and \ref{fig:domainAreasPt}. At time 0, the majority ($\frac{2}{3}$) of
Pt is located in the (111) plateaus where the number of Pt nearest neighbors is 6.
A sizeable minority ($\frac{1}{3}$) is located at the step edge, or beneath a step edge with a
nearest neighbor number of 5. The decrease in Pt with 6
nearest neighbors, while Pt with 9 nearest neighbors rises implies that Pt
atoms are being incorporated into multilayer features. 
}
\label{fig:nearestNeighbors}
\end{figure}

The small amount of restructuring observed in the zero coverage system suggests
that there are two driving forces for restructuring, with the CO playing one
role. 


\begin{table}
  \caption{Percent Pd surface coverage as a function of time. The following values were obtained by integrating the data in Figure \ref{fig:domainAreasPd}.}
  \begin{tabular}{| c || c | c | c | c | c | c |}
  \hline
  & 0-18 ns & 19-37 ns & 38-56 ns & 57-75 ns & 76-94 ns & 95-113 ns \\
  \hline
  0.00 &  6.6 & 16.2 & 20.1 & 21.7 & 23.5 & 25.2 \\
  0.05 &  8.0 & 15.8 & 20.2 & 25.1 & 27.6 & 30.9 \\
  0.25 &  8.5 & 17.3 & 23.7 & 27.8 & 30.5 & 31.0 \\
  0.33 &  8.8 & 17.8 & 21.9 & 26.2 & 30.3 & 35.4 \\
  0.50 & 11.8 & 19.2 & 25.9 & 29.8 & 31.1 & 32.6 \\
  \hline
  \end{tabular}
\label{tab:integratedArea}
\end{table}

%Discussion
\section{Discussion}

\subsection{Diffusion}
As noted above, their is limited movement of Pd in any of the systems we
examined. In a few instances, inversion is observed where a Pd and a Pt atom
are swapped in the shell systems. But on the whole the Pd is overwhelmingly
stationary. Time scales and kinetic barriers are possible explanations for the
lack of movement, but for the shell systems what seems to be the most likely is
that the Pt is acting as a protective layer. Even with significant
restructuring of the Pt overlayer, the underlying Pd is unlikely to be located
in a position where an energetically easier break from a step-edge will be
possible. However, this explanation does not explain the stability of the pure
Pd systems and is an area for further exploration.

An analysis of Pt's perpendicular (across the plateaus) and parallel (along the
steps) diffusion constants on the various shell systems is shown in the
supporting information. Unlike in our previous work\cite{Michalka:2013}, where
the step-edges were maintained throughout the restructuring of the surface from
a single step motif to a double step, the surfaces of the shell systems quickly
start to cluster, breaking the steps and limiting the usefulness of
deconvoluting the diffusion data. Instead only the total 2-dimensional (i.e.
surface) diffusion constants are shown in Figure \ref{fig:diffusion}. The
diffusion constants obtained here are slightly lower than those obtained in our
previous work which is easily explained by the lower temperature these systems
were run at (850~K compared to 1000~K). While the 5\% data is abnormally high,
the other coverages show a strong correlation of increasing diffusion with
increasing CO coverage. This correlation likely stems from the same mechanism
we reported previously, where the presence of CO, coupled with its large
quadrupolar moment assists in the initial break-up of the step-edges allowing
for consistent adatom formation.  Once the Pt adatoms are formed, the barrier
for diffusion is negligible ($<$4 kcal/mol using the EAM forcefield) and the
adatom will continue to diffuse until it is reincorporated, with most diffusion
occuring along the front of the step edges. Thus, the more CO present on the
surface, the more likely adatoms will form and explore the surface before
reaching a more stable state.

\subsection{Relative Metallic Binding Energies}
The presence and amount of CO is one of the driving forces for the observed
reconstruction, however, this doesn't explain the minor restructuring observed
for the shell system that had no CO present. Rather, there appears to be two
factors that are both responsible for aspects of the restructuring. This other
driving force is that Pt-Pt interactions are stronger and thus more favored
when compared to Pt-Pd interactions, as established by the EAM forcefield.
Removing a Pt surface atom from a (111) plateau on a pure Pt (557) surface,
shows that the Pt was contributing (-$\infty$ kcal/mol) to the energy of the
system, while a Pt taken from a similar spot in our shell system was only
contributing (-$\infty$ kcal/mol).  In the first instance, the Pt had 9
nearest neighbors, all Pt, while in the second the three atoms underneath the
surface are now Pd, which contribute a smaller electron density, leading to a
weaker binding between the Pt and Pd. As Figure \ref{fig:nearestNeighbors}
shows, over the 110 ns of the simulation, the number of Pt with increasing
number of Pt-Pt nearest neighbors grows. Thus, the restructuring of the surface
for the 0\%~coverage system can be explained by the stronger Pt-Pt binding
interaction, while the presence of CO is what appears to allow or speed up the
mechanism of step traversal, leading to larger scale reconstructions and for
the shell systems, clustering and island formation.

\subsection{Domain Sizes}
The lack of a clear feature (e.g. a double step) in any of the shell systems
after a significant amount of restructuring led us to analyze the sizes and
compositions of the various domains we observed. To perform this analysis, the
exposed surfaces were first simplified by projecting the 3-dimensional surface
onto a 2-dimensional grid (with two grids per system to capture the surfaces on
both sides of the system). The grids could only have one of two values at each
site, Pt or Pd. The resulting Ising-like grids were then deconvoluted into
separate domains based on nearest-neighbor connectivity (up, down, left, right;
corners were not included). The resulting data was aggregated and normalized
and is presented in Figures \ref{fig:domainAreasPd} and
\ref{fig:domainAreasPt}. Representative examples of the grids can be seen in
the supporting information. 

This analysis allows us to focus on collective motion of the surface atoms as
measured by the domain sizes, rather than individual adatom movement.  At the
beginning of the simulations, the surface layer of Pt makes up one domain of
size $\sim$2625~\AA\textsuperscript{2}. This domain begins to shrink relatively
quickly and is matched by a growth in the number and size of Pd domains.  The
presence of CO in the system allows further clustering
of the Pt domains, which requires a larger amount of exposed
Pd of various domain sizes. For clarity purposes, there is a small peak in the
Pt graphs around 0-100~\AA~that is not shown in Figure \ref{fig:domainAreasPt}
but can be seen in the supporting information. These data poins arise from 1 to
2 atom clusters of Pt embedded in the Pd.

The quantification of the surface composition that these figures display is
helpful, but is more easily seen when the curves are integrated, which is shown
in Table \ref{tab:integratedArea}. 


\subsection{Equilibrium state}
As shown in Figure \ref{fig:systems}.B, the 0\% coverage system has undergone a
small but significant amount of restructuring, despite no CO being present.
This is due to the stronger Pt-Pt compared to Pt-Pd binding energy.  Movement
of Pt from one layer onto the top of another layer without vertical
displacement benefits both layers of Pt, and the small energy barrier
preventing it is overcome by the increased thermal motion at elevated
temperatures. The now underlying Pt has approximately 9 nearest neighbors of Pt
and 3 of Pd and is essentially in bulk.  The upper layer of Pt also benefits
because it is now experiencing 9 nearest neighbor interactions, all with other
Pt. The ideal case would involve the majority of Pt maximizing their Pt-Pt
interactions which could lead to massive disruption without any need for CO,
but as seen in Figure \ref{fig:systems}.B, the (557) crystal facet is still
present, just with Pt plateaus moved slightly forward and backward. Without the
presence of CO, very little vertical displacement is observed, which is what is
hypothesized to facilite the multiple layer features observed in the higher
coverage systems. The systems were run for approximately 110 nanoseconds and
then stopped, primarily because, large scale changes had drastically slowed.
Additionally, results from various analyses were converging (see
Figures~\ref{fig:domainAreasPd},~\ref{fig:domainAreasPt}, and
\ref{fig:nearestNeighbors}), suggesting that we were close to a equilibrium
state, at least for the time scales we were able to explore. Increased run time
while possible, was not judged to be useful at this time.

\subsection{Role of CO: Presence and Absence} 
As shown in the previous sections, the presence of CO plays a large role in the
restructuring of the Pt@Pd shell systems. The small amount of restructuring due
to favorable Pt-Pt interactions is greatly enhanced when CO is added to the
system. As concluded in our previous paper\cite{Michalka:2013}, CO helps enable
vertical displacement of adatoms between layers, which is also seen here by
examining the degree of clustering that occurred for various CO coverages. 

%One
%final test we performed, already mentioned in Figure \ref{fig:domainAreasNoCO},
%is the removal of CO from the 25\% and 50\% systems. Figure
%\ref{fig:domainAreasNoCO} shows a slight increase in the Pt domain size, which
%would require the multi-layer Pt cluster to lose some of its stability and
%spread out. This is very similar to our previous work, where the removal of CO,
%led to the double-layer beginning to split back into individual steps. These ``No-CO''
%systems were run for an additional 50 ns and despite the initial destablizing
%of the Pt clusters, appear to have ended up in a local thermodynamic minimum. It is
%possible that a slower removal of CO would remove the stability while still
%enabling the vertical displacement that CO assists with and allow these
%systems to approach the equilibrium 0\% coverage system, but this would likely
%require a much longer and complicated approach outside the focus of this study. 


\section{Conclusion}
The favorable Pt-Pt interactions, coupled with the stronger Pd-CO binding
energy help to explain the clustering seen on the Pt@Pd (557) systems. The lack
of any surface disruption on the Pd (557) surfaces at all coverages, suggests
that the presence of CO is not enough of a perturbation to overcome the
thermodynamic barriers hindering reconstruction.

This work suggests that bimetallic and subsurface alloys could be tailored to
create and or expose active catalytic sites as a result of an adsorbates
presence or absence. 


\begin{acknowledgement}
  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.
\end{acknowledgement}
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% Some prelimary work on (111) and (100) surfaces of bimetallic systems
% (representative images in the SI) showed minimal restructuring when the
% low-energy (111) facet was exposed. The (100) surface did show a moderate
% amount of remodeling, but primarily to a more compact (111) surface while
% exposing the underlying (100) layer of the other element. There was a small
% amount of individual atom exchanges between layers on both
% surfaces, but over $\sim$50~ns run times there was essentially no
% reconstruction. In our previous work, we established that the primary mechanism
% for the double layer formation involved the ``lifting'' or ``falling'' of
% surface atoms to the ledge above or below them, respectively. This mechanism
% was seen to be vastly enhanced as the amount of CO in the system was increased.
% Additionally, this vertical traversal was only observed to happen near a
% step-edge, not from one of the larger (111) plateaus.  This suggested to us
% that the energetic barrier for lifting an atom out from a surface ( > $\inf$) was
% sufficient to prevent restructuring for our preliminary (111) and (100) systems
% at the time scales and temperatures we were exploring. As such, we again began
% using the (557) system which alleviates the energetic barrier by exhibiting
% repeated high-index edges to act as a source for adatoms and provides sites for
% ``lifting'' and ``falling''. 
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