PtPd/tex/draft.tex

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\title{\ce{CO}-induced island formation on \ce{Pt}/\ce{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}

Pt-based and Pd-based bimetallic materials are crucial catalysts in
oxygen reduction reactions (ORR),\cite{Lim:2009fk} and oxygen
evolution reactions (OER),\cite{Reier:2012uq} that are important in
charging and discharging of Li-air batteries\cite{Lu:2011vn} and in
fuel cell processes.\cite{Bliznakov:2012kx} Oxide-supported noble
metal particles are also important in the water-gas shift
reaction.\cite{Bunluesin:1998ys}


Bimetallic alloys, subsurface alloys, and core-shell nanostructures are
currently under intense investigation\cite{Kim:2013jt, Gao:2009oj, Gao:2009wo}
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{Kim:2013jt}, 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, changing the activity and selectivity of the catalyst.

Tuning catalyst work...

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 \ce{CO} atmosphere undergo
doubling.  To the extent of our knowledge there has been no similar work done
with \ce{CO} on \ce{Pd}(557) and this work is an attempt to explore that system
as well as what happens to a bimetallic system containing both \ce{Pt} and
\ce{Pd}. 

This work is an investigation into the effect of \ce{CO} adsorption on surface
restructuring of a \ce{Pd}(557) and \ce{Pt}/\ce{Pd} (557) subsurface alloy
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.  Cohesive and surface energies in
metals 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 describe an atom as a positively charged core with
a radially-decaying valence electron density.  Refinements include angle
dependent EAM implementations,\cite{Baskes:1987} that treat BCC metals more
accurately.

In EAM, the energy for embedding a metallic atom $i$ at a specific
location in the system requires the electron density at that location,
\begin{equation*}
\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, $F_i\left[ \rho_i \right]$, as well as a sum of
pairwise interactions,
\begin{equation*}
  V_i =  F[ \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, $\rho_i$.  Thus, the
cohesive energy for 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 positively-charged cores.
For alloys, 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 \ce{Pt} and \ce{Pd} electron densities, embedding
functionals, and pair potentials,\cite{EAM} utilizing the Johnson
mixing rules for the \ce{Pt\bond{-}Pd}
cross-interactions.\cite{johnson89}

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

The \ce{Pt\bond{-}CO} interactions have been modified from previous fits to
account for recently-published DFT
data.\cite{Michalka:2013,Deshlahra:2012} This modification yields a
slightly weaker \ce{Pt\bond{-}CO} binding energy.

The \ce{Pd\bond{-}CO} interaction potential was parameterized as part
of this work, and uses similar functional forms to the
\ce{Pt\bond{-}CO} model.\cite{Michalka:2013} Our starting point is a
model introduced by Korzeniewski \textit{et al.}\cite{Pons:1986} The
parameters were modified to reflect binding energies and binding site
preferences on the \ce{M} (111) surfaces.  One key difference from the
potential in Ref.  \citenum{Michalka:2013} is that the \ce{M\bond{-}O}
bond is modeled using a purely repulsive Morse potential, $D
e^{-2\gamma(r-r_e)}$.  The functional forms and the broad repulsive
\ce{M\bond{-}O} contribution are flexible enough to reproduce the atop
preference for \ce{Pt\bond{-}CO} as well as the bridge/hollow -
preference for \ce{Pd\bond{-}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-\ce{CO} cross-interactions. Metal-Carbon
  interactions are modeled with Lennard-Jones potentials, while the
  metal-Oxygen interactions are fit using repulsive Morse potentials.
  Distances are given in \AA~and energies in
  kcal/mol.\label{tab:CO_parameters}}  
\centering
\begin{tabular}{| c | cc | c | ccc |}
\hline
 &  $\sigma$ & $\epsilon$ & & $r_e$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
\hline
\textbf{\ce{Pt\bond{-}C}} & 1.41 & 45  & \textbf{\ce{Pt\bond{-}O}} & 4.4  & 0.05 & 1.8 \\
\textbf{\ce{Pd\bond{-}C}} & 1.6 &  40  & \textbf{\ce{Pd\bond{-}O}} & 4.95 & 0.05 & 1.45\\
\hline
\end{tabular}
\end{table}

%Table of energies
\begin{table}
  \caption{Adsorption energies for a \ce{CO} molecule at the three special sites
    on \ce{M} (111) using the potentials described in table
    \ref{tab:CO_parameters}.   These values are compared with DFT
    calculations of XXX along with experimental desorption
    data when available. 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{\ce{Pt\bond{-}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{\ce{Pd\bond{-}CO}} & atop   & -1.54 & -1.44\cite{Honkala:2001sf} &  \\
                 & bridge & -1.65 & -1.83\cite{Honkala:2001sf} &  \\
                 & hollow & -1.60 & -1.99\cite{Honkala:2001sf} & -1.47\cite{Ertl:1970}, -1.54\cite{Guo:1989} \\
  \hline
\end{tabular}
\label{tab:CO_energies}
\end{table}

This \ce{Pd\bond{-}CO} model does not have a strong preference for
either the bridge or hollow binding sites, so it may overestimate the
bridge-site binding at low coverages, but at higher coverages, the
situation is somewhat less clear.\cite{Wong:1991ta} Studies using
low-energy elecron diffraction (LEED) and \ce{C\bond{-}O} stretching
frequencies of \ce{CO} bound to \ce{Pd}(111) suggest that the 3-fold
hollow sites are preferred at low
coverages,\cite{Bradshaw:1978uf,Conrad:1978fx,Ohtani:1987zh} where it
forms a $(\sqrt{3} \times \sqrt{3}) R~30^{\circ}$ pattern.  These
observations are supported by temperature desorption
spectroscopy,\cite{Guo:1989} and infrared absorption
spectroscopy~\cite{Szanyi:1992} where binding energies have been
reported to lie between 1.3 and 1.54 eV.

At higher \ce{CO} coverages (e.g. $> 0.5$ ML), the preferred binding
of \ce{CO} on \ce{Pd}(111) appears to be a $c(4\times2)$ ordered
structure with the \ce{CO} bound to the bridge
sites.\cite{Bradshaw:1978uf}

Theoretical work by Honkala \textit{et al.}\cite{Honkala:2001sf} using
DFT with the generalized gradient approximation (GGA) to describe
electron exchange correlation and pseudopotentials for the \ce{Pd}
atoms also reported the fcc site as the most favorable binding
position with a binding energy of 2.00 eV compared to the bridge site
binding energy of 1.83 eV at $1/3$ monolayer.

High resolution x-ray photoelectron spectroscopy (XPS) results from
Surnev \textit{et al.}\cite{Surnev:2000uk} confirm that the preferred
low coverage (< 0.1 ML) binding site is the fcc hollow, but also
suggest a competition between hollow and bridge binding for coverages
between 0.1 and 0.32 ML, suggesting similar binding energies for these
two sites. Additional DFT calculations from Loffreda et
al.\cite{Loffreda:1999vl} suggest that as the coverage increases, the
binding energy difference shrinks, as at $1/2$ ML the hollow to bridge
energy difference is 0.06 eV (-1.85 hollow, -1.79 bridge).

Although the weak preference for hollow vs. bridge sites is not
captured by the \ce{Pd\bond{-}CO} fit, the slight favoring of the
bridge adsorption site in this model does result in an accurate
reproduction of the $c(4\times2)$ adsorption structure at higher
coverages, which would be the most relevant regime for catalytic
behavior.

\subsection{557 interfaces and subsurface alloys}
The \ce{Pd}(557) model is an orthorhombic periodic box with dimensions
of $55.09 \times 49.48 \times 120$~\AA~ while the subsurface alloys
(Pt(557) surface layers, with Pd bulk) have dimensions of $54.875
\times 49.235 \times 120$~\AA.  The \ce{Pd} system consists of 9
layers of \ce{Pd} while our subsurface alloys consist of 7 layers of
\ce{Pd} sandwiched between 2 layers of \ce{Pt}.  Both the pure \ce{Pd}
slab and the subsurface alloy systems are $\sim$22~\AA~ thick. The
lattice constants for \ce{Pd} and \ce{Pt}, 3.89 and 3.92~\AA,
respectively, 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,
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 557 surface without a \ce{CO} overlayer.  The bare systems were 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 \ce{CO}-coverage levels
for each metallic system.  The number of \ce{CO} molecules (0, 48, 240,
320, and 480) yield surface coverages of 0, 0.05, 0.25, 0.33, and 0.5
monolayers (ML) assuming that every \ce{CO} adsorbs on the surface.

Simulation boxes of the same sizes as the metallic systems were
constructed with appropriate densities of \ce{CO} and equilibrated to
850~K. The gas-phase \ce{CO} and surface simulation boxes were then
combined, using a 5~\AA~ cutoff between metallic atoms and \ce{CO} to
prevent overlap. The remaining \ce{CO} population was further reduced to
match the required number for the correct surface coverage.
Velocities were resampled from a Boltzmann distribution, and any net
linear momentum was subtracted from the entire system.  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 \ce{Pd} systems were run in the microcanonical ensemble for a
minimum of 40 ns to collect statistics. The \ce{Pt/Pd} subsurface alloy
systems, which were observed to undergo significant restructuring,
were each run for a total simulation time of 110 ns.  All simulations
were carried out with the open source molecular dynamics package,
OpenMD.\cite{openmd,OOPSE}
 
\section{Results}
In our earlier work on \ce{Pt}(557), we observed \ce{CO}-induced
restructuring into relatively clean double-layer structures. For the
pure \ce{Pd}(557) studied here, the 557 facet retains the plateaus and
steps with only minimal adatom movement, and with almost no surface
reconstruction.  Higher \ce{CO} coverages appear to have minimal
effect on the pure \ce{Pd}(557) systems.

However, the \ce{Pt}-coated \ce{Pd} alloy exhibits a \ce{CO}-induced
speedup of the diffusion of surface metal atoms, as well as a
large-scale restructuring of the well-ordered surface into
\ce{Pt}-rich islands, and will therefore be the focus of most of our
analysis.

\begin{figure}
  \includegraphics[width=\linewidth]{../figures/SystemFigures/systems_ochre2.png}
  \caption{Snapshots of the some of the simulated systems. Panel A is the
    pure \ce{Pd}(557) $\sim$40 ns after being dosed with  $\frac{1}{3}$
    monolayer of {CO}.  Panels B-D are the subsurface alloy 80 ns after
    being dosed with 0, $\frac{1}{3}$, and
    $\frac{1}{2}$ ML of \ce{CO}, respectively.  \ce{Pt} atoms are shown in gray,
    \ce{Pd} in orange, while the \ce{CO} molecules are shown in black / red. }
\label{fig:systems}
\end{figure}

Figure \ref{fig:systems} shows representative configurations of the
various systems after significant exposure to the \ce{CO}. We see that
the Pd system highlighted in panel A has undergone no surface
restructuring. The other three panels highlight the effect of varying
\ce{CO} concentrations on the surface alloys, which do exhibit
structural reorganization.

\subsection{Diffusion of Surface Metal Atoms in the Surface Alloy}

Figure \ref{fig:systems} suggests that there is limited to no mobility
on the pure Pd systems. Analysis of the surface atom mobility showed
that there were fewer than 50 Pd atoms that made $> 2$\AA\ hops in any
10 ps window during the entire 40 ns run. As most of these atoms
immediately hopped back to their starting points, surface mobility
estimates give diffusion constants as close to zero as can be safely
estimated.

However, there is significant movement of surface Pt in the subsurface
alloys, and the mobility of the surface Pt layer increases with
increasing \ce{CO} coverage. To estimate the surface diffusion, we define a
``mobile'' atom as one which moves at least 2~\AA~ in any 10 ps window
during the simulation. Once an atom has been labeled as mobile, we
analyze the entire simulation to find the planar ($xy$) diffusion
constant for the mobile atoms of a particular type. The calculated
diffusion constants of mobile Pt atoms from the subsurface alloys are
shown in Table \ref{tab:diffusion}. The absolute number of mobile Pt
atoms ($\sim 600$) was similar between all systems, independent of \ce{CO}
coverage. There is a correlation between increasing \ce{CO} coverage and Pt
diffusion rates of $\sim 1.6$ \AA\textsuperscript{2}/ns/ML.

\begin{table} \centering \begin{tabular}{| c | c |} \hline
    \ce{CO} Coverage & Diffusion Constant\footnotemark[1] (\AA\textsuperscript{2}/ns) \\
    \hline
    0    & 2.779(2) \\
    0.05 & 3.992(6) \\
    0.25 & 3.436(5) \\
    0.33 & 4.180(7) \\
    0.50 & 3.935(5) \\
    \hline \end{tabular}
\caption{Diffusion constants of mobile \ce{Pt}
    atoms for the subsurface alloys.\label{tab:diffusion}} 

  \footnotemark[1]{Uncertainties in the last digit
    are shown in parentheses.}
\end{table}

\subsection{Island Formation and Clustering in the Subsurface Alloy}

In a similar manner to the \ce{Pt}(557) surfaces, the structural
reconstructions that occur for the subsurface alloy are influenced by
the presence of the \ce{CO} adsorbate. In Figure
\ref{fig:domainAreasPd}, the area of exposed \ce{Pd} increases both
over time, and as a function of \ce{CO} coverage. The presence of
\ce{CO} leads to more exposure of the underlying \ce{Pd}, measured by
the increasing number and size of \ce{Pd} domains. Without \ce{CO}
exposure, the bare \ce{Pt/Pd} surface does undergo some restructuring,
although both the rate and extent is significantly smaller than in the
0.25 and 0.50 monolayer (ML) systems.

The appearance of \ce{Pd} from the bulk layers on the surface requires
a simultaneous reduction in the surface area of the outer \ce{Pt}
skin. Two scenarios could explain the reduction of exposed \ce{Pt}:
either the \ce{Pt} atoms are being buried under the \ce{Pd} bulk, or
islands of \ce{Pt} are forming on top of the \ce{Pd} surface.

Both mechanisms would explain the decreased \ce{Pt} surface area (see
Fig.  \ref{fig:domainAreasPt}).  To discern which of these mechanisms
is taking place, the identity of nearest metal atom neighbors can be
tabulated as a function of time of exposure to \ce{CO}. Single-layer
\ce{Pt} skins have atoms with 6 \ce{Pt} nearest neighbors. Islands of
\ce{Pt} require the presence of \ce{Pt} atoms with 7-9 \ce{Pt} nearest
neighbors. In figure \ref{fig:nearestNeighbors}, we see an increase in
\ce{Pt} population with 9 \ce{Pt} nearest neighbors along with the
simultaneous decrease in \ce{Pt} atoms with only 6 \ce{Pt} nearest
neighbors.  This is evidence for the formation of multi-layer \ce{Pt}
features since single layers of \ce{Pt} are restricted to having 6
\ce{Pt} nearest neighbors.

The presence of \ce{CO} therefore appears to facilitate the clustering
of \ce{Pt} into smaller domains by forming multilayer features which
leads to a reduction of \ce{Pt} surface coverage and concomitant
increased exposure of the \ce{Pd}.  We note that nearest-neighbor
population analysis provides information similar to the information
one might obtain from an XAFS experiment, which could make this
phenomenon experimentally observable.

\begin{figure}
\includegraphics[width=\linewidth]{../figures/domainAreas/domainSize_Pd_110ns_deCluttered_color.pdf}
%\includegraphics[width=\linewidth]{../figures/domainAreas/final_domain_Pd.pdf}
\caption{Distributions of \ce{Pd} domain sizes at different \ce{CO}
  coverages and at different times after exposure to \ce{CO}.}
\label{fig:domainAreasPd} 
\end{figure}

\begin{figure}
\includegraphics[width=\linewidth]{../figures/domainAreas/domainSize_Pt_110ns_deCluttered_color.pdf}
%\includegraphics[width=\linewidth]{../figures/domainAreas/final_domain_Pt.pdf}
\caption{Distributions of \ce{Pt} domain sizes at different \ce{CO}
  coverages and at different times after exposure to \ce{CO}.}
\label{fig:domainAreasPt}
\end{figure}

\begin{figure}
  \includegraphics[width=\linewidth]{../figures/nearestNeighbor/NearestNeighbor_110ns_color.pdf}
  \caption{Population of \ce{Pt} atoms with either 6 (solid) or 9
    (hollow) \ce{Pt} nearest neighbors averaged over 18 ns blocks of
    time.  At $t=0$, the majority ($\frac{2}{3}$) of \ce{Pt} is
    located in the (111) plateaus where the number of \ce{Pt} nearest
    neighbors is 6. The remaining \ce{Pt} is located at step edges,
    with a nearest neighbor \ce{Pt} count of 5.} \label{fig:nearestNeighbors}
\end{figure}

The small amount of restructuring observed in the bare metal system
suggests that the relative surface energies of the two metals provides
some of the driving force for the restructuring, while the \ce{CO}
significantly speeds up the effects (and may help to drive the process
at lower temperatures).

\begin{table}
  \caption{\ce{Pd} surface coverage (in \% of total surface area)
    averaged over 18 ns blocks of time.}
  \begin{tabular}{| c || c | c | c | c | c | c |}
  \hline
 \ce{CO} coverage  & 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}

Explaining figure 1:  The minor restructuring in B is due to the energy benefit gained when
\ce{Pt} maximizes \ce{Pt\bond{-}Pt} bonds. (C) and (D) have undergone greater
remodeling because the presence of \ce{CO} helps speed up adatom mobility
and enables the vertical displacement of \ce{Pt} adatoms leading to more
clustering.

The stronger \ce{Pd\bond{-}CO} binding energy when compared to \ce{Pt\bond{-}CO} is hypothesized to
play a role in disrupting the surface and in the case of the shell system in
revealing the underlying \ce{Pd} by causing clustering and island formation of the
\ce{Pt} shell. 

\subsection{Diffusion}
As noted above, their is limited movement of \ce{Pd} in any of the systems we
examined. In a few instances, inversion is observed where a \ce{Pd} and a \ce{Pt} atom
are swapped in the shell systems. But on the whole the \ce{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 \ce{Pt} is acting as a protective layer. Even with significant
restructuring of the \ce{Pt} overlayer, the underlying \ce{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
\ce{Pd} systems and is an area for further exploration.

An analysis of \ce{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 \ce{CO} coverage. This correlation likely stems from the same mechanism
we reported previously, where the presence of \ce{CO}, coupled with its large
quadrupolar moment assists in the initial break-up of the step-edges allowing
for consistent adatom formation.  Once the \ce{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 \ce{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 \ce{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 \ce{CO} present. Rather, there appears to be two
factors that are both responsible for aspects of the restructuring. This other
driving force is that \ce{Pt\bond{-}Pt} interactions are stronger and thus more favored
when compared to \ce{Pt\bond{-}Pd} interactions, as established by the EAM forcefield.
Removing a \ce{Pt} surface atom from a (111) plateau on a pure \ce{Pt} (557) surface,
shows that the \ce{Pt} was contributing (-$\infty$ kcal/mol) to the energy of the
system, while a \ce{Pt} taken from a similar spot in our shell system was only
contributing (-$\infty$ kcal/mol).  In the first instance, the \ce{Pt} had 9
nearest neighbors, all \ce{Pt}, while in the second the three atoms underneath the
surface are now \ce{Pd}, which contribute a smaller electron density, leading to a
weaker binding between the \ce{Pt} and \ce{Pd}. As Figure \ref{fig:nearestNeighbors}
shows, over the 110 ns of the simulation, the number of \ce{Pt} with increasing
number of \ce{Pt\bond{-}Pt} nearest neighbors grows. Thus, the restructuring of the surface
for the 0\%~coverage system can be explained by the stronger \ce{Pt\bond{-}Pt} binding
interaction, while the presence of \ce{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, \ce{Pt} or \ce{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 \ce{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 \ce{Pd} domains.  The
presence of \ce{CO} in the system allows further clustering
of the \ce{Pt} domains, which requires a larger amount of exposed
\ce{Pd} of various domain sizes. For clarity purposes, there is a small peak in the
\ce{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 \ce{Pt} embedded in the \ce{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 \ce{CO} being present.
This is due to the stronger \ce{Pt\bond{-}Pt} compared to \ce{Pt\bond{-}Pd} binding energy.  Movement
of \ce{Pt} from one layer onto the top of another layer without vertical
displacement benefits both layers of \ce{Pt}, and the small energy barrier
preventing it is overcome by the increased thermal motion at elevated
temperatures. The now underlying \ce{Pt} has approximately 9 nearest neighbors of \ce{Pt}
and 3 of \ce{Pd} and is essentially in bulk.  The upper layer of \ce{Pt} also benefits
because it is now experiencing 9 nearest neighbor interactions, all with other
\ce{Pt}. The ideal case would involve the majority of \ce{Pt} maximizing their \ce{Pt\bond{-}Pt}
interactions which could lead to massive disruption without any need for \ce{CO},
but as seen in Figure \ref{fig:systems}.B, the (557) crystal facet is still
present, just with \ce{Pt} plateaus moved slightly forward and backward. Without the
presence of \ce{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 \ce{CO}: Presence and Absence} 
As shown in the previous sections, the presence of \ce{CO} plays a large role in the
restructuring of the \ce{Pt/Pd} shell systems. The small amount of restructuring due
to favorable \ce{Pt\bond{-}Pt} interactions is greatly enhanced when \ce{CO} is added to the
system. As concluded in our previous paper\cite{Michalka:2013}, \ce{CO} helps enable
vertical displacement of adatoms between layers, which is also seen here by
examining the degree of clustering that occurred for various \ce{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 \ce{Pt\bond{-}Pt} interactions, coupled with the stronger \ce{Pd\bond{-}CO} binding
energy help to explain the clustering seen on the \ce{Pt/Pd} (557) systems. The lack
of any surface disruption on the \ce{Pd} (557) surfaces at all coverages, suggests
that the presence of \ce{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}
\newpage
\bibstyle{achemso}
\bibliography{draft}
%\end{doublespace}

\begin{tocentry}
\begin{wrapfigure}{l}{0.5\textwidth}
\begin{center}
%\includegraphics[width=\linewidth]{}
\end{center}
\end{wrapfigure}
\end{tocentry}

\end{document}


% 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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