trunk/COonPt/COonPtAu.tex

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

\author{Joseph R. Michalka}
\author{Patrick W. McIntyre}
\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
%       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
%%


\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.


The mechanism and dynamics of surface reconstructions of Pt(557) 
and Au(557) exposed to various coverages of carbon monoxide (CO) 
were investigated using molecular dynamics simulations. Metal-CO 
interactions were parameterized from experimental data and plane-wave 
Density Functional Theory (DFT) calculations.  The large difference in 
binding strengths of the Pt-CO and Au-CO interactions was found to play 
a significant role in step-edge stability and adatom diffusion constants. 
The energetics of CO adsorbed to the surface is sufficient to explain the 
step-doubling reconstruction observed on Pt(557) and the lack of such 
a reconstruction on the Au(557) surface.
\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 the Pt(557) \& Au(557)
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 less 
likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000} 
and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced 
reconstruction of a Au(111) surface. Peters {\it 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 on Au(111) being greatly 
affected by this relaxation. Piccolo {\it 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$^4$ 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{Foiles86} 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 {\it et al}.\cite{Ercolessi88} is among the
fastest of these density functional approaches. In
all of these models, atoms are treated 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
because interactions
up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a}
Comparing that to the glue model of Ercolessi {\it 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 EAM's 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
{\it 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 geometries, 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} 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 could have 
an effect on  binding energies and binding site preferences.

%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{TPDGold}) \\
  \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 metal slabs 
are 9 and 8 atoms deep respectively, corresponding to a slab 
thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au.
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 predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting}
and $\sim$~2045~K for Pt\cite{Pt:melting}) 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 bare metal surfaces experienced minor roughening of the 
step-edge because of the elevated temperatures, but the (557) 
face was stable throughout the simulations. The surface of both 
systems, upon dosage of CO, began to undergo extensive remodeling 
that was not observed in the bare systems. Reconstructions of 
the Au systems were limited to breakup of the step-edges and 
some step wandering. The lower coverage Pt systems experienced 
similar restructuring but to a greater extent. The 50\% coverage 
Pt system was unique among our simulations in that it formed 
well-defined and stable double layers through step coalescence, 
similar to results reported by Tao {\it et al}.\cite{Tao:2010}


\subsubsection{Step wandering}
The 0\% coverage surfaces for both metals showed minimal 
step-wandering at their respective temperatures. As the CO 
coverage increased however, the mobility of the surface atoms, 
described through adatom diffusion and step-edge wandering, 
also increased.  Except for the 50\% Pt system where step 
coalescence occurred, the step-edges in the other simulations 
preferred to keep nearly the same distance between steps as in 
the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au. 
Previous work by Williams {\it 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 is caused by an entropic barrier that arises from 
the fact that steps cannot cross over one another. This entropic 
repulsion does not completely define the interactions between 
steps, however, so it is possible to observe step coalescence 
on some surfaces.\cite{Williams:1991} The presence and 
concentration of adsorbates, as shown in this work, can 
affect step-step interactions, potentially leading to a new 
surface structure as the thermodynamic equilibrium.

\subsubsection{Double layers}
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface 
undergoes two separate reconstructions upon CO adsorption.
The first involves a doubling of the step height and plateau length. 
Similar behavior has been seen on a number of surfaces 
at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl} 
Of the two systems we examined, the Pt system showed a greater 
propensity for reconstruction  
because of the larger surface mobility and the greater extent of step wandering. 
The amount of reconstruction was strongly 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. Only the 50\% Pt surface underwent the 
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. 
Over a longer time scale (150~ns) two more double layers formed 
on this surface. Although double layer formation did not occur 
in the other Pt systems, they exhibited more step-wandering and 
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 double layer step-edge.

The second reconstruction observed by 
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched 
across the plateau between two step-edges. Neither metal, within 
the 40~ns time scale or the extended simulation time of 150~ns for 
the 50\% Pt system, experienced this reconstruction.

%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}

\subsection{Dynamics}
Previous experimental work by Pearl and Sibener\cite{Pearl}, 
using STM, has been able to capture the coalescence 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. By utilizing Molecular Dynamics we are able to probe 
the dynamics of these reconstructions at elevated temperatures 
and in this section we provide data on the timescales for transport 
properties, e.g. diffusion and layer formation time.


\subsubsection{Transport of surface metal atoms}
%forcedSystems/stepSeparation
The 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 provides a lower energy source for mobile metal atoms. 
Single-atom break-away from a step-edge on a clean surface still imposes an 
energetic penalty around $\sim$~45 kcal/mol, but this is 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, see Discussion, the penalty can fall to 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 then
able to explore the terrace before rejoining either their original step-edge or 
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom 
to traverse to a separate terrace although the presence of CO can lower the 
energy barrier required to lift or lower an 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. 
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). A mobile atom 
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 larger than 
the diffusion perpendicular to these edges. Parallel and perpendicular
diffusion constants are shown in Figure \ref{fig:diff}.

%Diffusion graph
\begin{figure}[H]
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.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. The two reported diffusion constants for
  the 50\% Pt system arise from different sample sets. The lower values
  correspond to the same 40~ns amount that all of the other systems were
  examined at, while the larger values correspond to a 20~ns period }
\label{fig:diff}
\end{figure}

The weaker Au-CO interaction is evident in the weak CO-coverage 
dependance of Au diffusion. This weak interaction leads to lower 
observed coverages when compared to dosage amounts. This further 
limits the effect the CO can have on surface diffusion. The correlation 
between coverage and Pt diffusion rates shows a near linear relationship 
at the earliest times in the simulations. Following double layer formation, 
however, there is a precipitous drop in adatom diffusion. As the double 
layer forms, many atoms that had been tracked for mobility data have 
now been buried resulting in a smaller reported diffusion constant. A
secondary effect of higher coverages is CO-CO cross interactions that
lower the effective mobility of the Pt adatoms that are bound to each CO.
This effect would become evident only at higher coverages. A detailed
account of Pt adatom energetics follows in the Discussion.
 

\subsubsection{Dynamics of double layer formation}
The increased diffusion on Pt at the higher CO coverages is the primary 
contributor to 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 40~ns. On the 50\%~Pt 
system, one double layer formed within the first 40~ns of simulation time, 
while two more were formed as the system was allowed to run for an 
additional 110~ns (150~ns total). This suggests that this reconstruction 
is a rapid process and that the previously mentioned upper bound is a 
very large overestimate.\cite{Williams:1991,Pearl} In this system 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 flattened out. 
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. 
A possible explanation for this rapid reconstruction is the elevated 
temperatures under which our systems were simulated. The process 
would almost certainly take longer at lower temperatures. Additionally, 
our measured times for completion of the doubling after the appearance 
of a nucleation site are likely affected by our periodic boxes. A longer 
step-edge will likely take longer to ``zipper''. 


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

\subsection{Diffusion}
The perpendicular diffusion constant 
appears to be the most important indicator of double layer 
formation. As highlighted in Figure \ref{fig:reconstruct}, the 
formation of the double layer did not begin until a nucleation 
site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994}, 
the inability for edges to cross leads to an effective edge-edge repulsion that 
must be overcome to allow step coalescence. 
A greater $\textbf{D}_\perp$ implies more step-wandering 
and a larger chance for the stochastic meeting of two edges 
to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double 
layer. This helps explain why the time scale for formation after 
the appearance of a nucleation site was rapid, while the initial 
appearance of the nucleation site was unpredictable. 

\subsection{Mechanism for restructuring}
Since the Au surface showed no large scale restructuring in any of 
our simulations, our discussion will focus on the 50\% Pt-CO system 
which did exhibit doubling. 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 would gain credence. The calculated energetic repulsion 
between two CO molecules 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 to the second nearest-neighbor distance 
of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away 
from a purely vertical orientation also lowers the repulsion. When the 
carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is 
reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}. 
The calculated barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so 
repulsion between adjacent CO molecules bound to Pt could increase the surface 
diffusion. However, the residence time of CO on Pt suggests that these 
molecules are extremely mobile, with diffusion constants 40 to 2500 times 
larger than surface Pt atoms. This mobility suggests that the CO molecules jump
between different Pt atoms throughout the simulation, but will stay bound for 
significant periods of time. 

A different interpretation of the above mechanism, taking into account the large 
mobility of the CO, looks at how instantaneous and short-lived configurations of 
CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge 
breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach 
an edge atom is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures 
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases 
(e), (g), and (h), the barrier can be lowered to $\sim$23~kcal/mole. In these instances, 
it becomes quite energetically favorable to roughen the edge by introducing a small 
separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in 
simulations with significant CO populations. The roughening is present to a lesser extent 
on lower coverage surfaces and even on the bare surfaces, although in these cases it is likely 
due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism 
of step-edge breakup suggested by these energy curves is one of the most difficult 
processes, a complete break-away from the step-edge in one unbroken movement. 
Easier multistep mechanisms likely exist where an adatom moves laterally on the surface 
after being ejected so it ends up alongside the ledge. This provides the atom with 5 nearest 
neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher 
than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO 
quadrupolar repulsion is still playing a primary role, but for its importance in roughening 
the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not 
born out by their mobility data. The requirement for a large density of CO on the surface 
for some of the more favorable suggested configurations in Figure \ref{fig:SketchGraphic} 
correspond well with the increased mobility seen on higher coverage surfaces.

%Sketch graphic of different configurations
\begin{figure}[H]
\includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf}
\caption{The dark grey atoms refer to the upper ledge, while the white atoms are 
the lower terrace. The blue highlighted atoms had a CO in a vertical atop position 
upon them. These are a sampling of the configurations examined to gain a more 
complete understanding of the effects CO has on surface diffusion and edge breakup. 
Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.}
\label{fig:SketchGraphic}
\end{figure}

%energy graph corresponding to sketch graphic
\begin{figure}[H]
\includegraphics[width=\linewidth]{stepSeparationComparison.pdf}
\caption{The energy curves directly correspond to the labeled model 
surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative 
to their initial configuration so the energy of a and h do not have the 
same zero value. As is seen, certain arrangements of CO can lower 
the energetic barrier that must be overcome to create an adatom. 
However, it is the highest coverages where these higher-energy 
configurations of CO will be more likely. }
\label{fig:SketchEnergies}
\end{figure}

While configurations of CO on the surface are able to increase diffusion, 
this does not immediately provide an explanation for the formation of double 
layers. If adatoms were constrained to their terrace then doubling would be 
much less likely to occur. Nucleation sites could still potentially form, but there 
would not be enough atoms to finish the doubling. For a non-simulated metal surface, where the 
step lengths can be assumed to be infinite relative to atomic sizes, local doubling would be possible, but in 
our simulations with our periodic treatment of the system, the system is not large enough to experience this effect. 
Thus, there must be a mechanism that explains how adatoms are able to move 
amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate 
where an adatom along the step-edge with an adsorbed CO ``burrows'' into the 
edge displacing an atom onto the higher terrace. This mechanism was chosen 
because of similar events that were observed during the simulations. The barrier 
heights we obtained are only approximations because we constrained the movement 
of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s 
are provide a strong energetic support for this modeled lifting mechanism. When CO is not present and 
this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown 
in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol. 
While the barrier height is comparable for both cases, there is nearly a 20~kcal/mol 
difference in energies and makes the process energetically favorable.

%lambda progression of Pt -> shoving its way into the step
\begin{figure}[H]
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png}
\caption{ Various points along a reaction coordinate are displayed in the figure. 
The mechanism of edge traversal is examined in the presence of CO. The approximate
barrier for the displayed process is 20~kcal/mol. However, the $\Delta E$ of this process
is -15~kcal/mol making it an energetically favorable process.}
\label{fig:lambda}
\end{figure}

The mechanism for doubling on this surface appears to require the cooperation of at least 
these two described processes. For complete doubling of a layer to occur there must 
be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from 
that terrace they must either rise up on the ledge above them or drop to the ledge below 
them. The presence of CO helps with the energetics of both of these situations. There must be sufficient 
breakage of the step-edge to increase the concentration of adatoms on the surface and
these adatoms must then undergo the burrowing highlighted above or some comparable 
mechanism to traverse the step-edge. Over time, these mechanisms working in concert 
lead to the formation of a double layer.

\subsection{CO Removal and double layer stability}
Once a double layer had formed on the 50\%~Pt system it 
remained for the rest of the simulation time with minimal 
movement. There were configurations that showed small 
wells or peaks forming, but typically within a few nanoseconds 
the feature would smooth away. Within our simulation time, 
the formation of the double layer was irreversible and a double 
layer was never observed to split back into two single layer 
step-edges while CO was present. To further gauge the effect 
CO had on this system, additional simulations were run starting 
from a late configuration of the 50\%~Pt system that had formed 
double layers. These simulations then had their CO removed. 
The double layer breaks rapidly in these simulations, already 
showing a well-defined splitting after 100~ps. Configurations of 
this system are shown in Figure \ref{fig:breaking}. The coloring 
of the top and bottom layers helps to exhibit how much mixing 
the edges experience as they split. These systems were only 
examined briefly, 10~ns, and within that time despite the initial 
rapid splitting, the edges only moved another few \AA~apart.
It is possible with longer simulation times that the 
(557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010}


%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 its microfaceting of the double layer 
into a (111) configuration. This microfacet immediately reverts to the original (100) step 
edge which is a hallmark of the (557) surface. The separation is not a simple sliding apart, 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}
The strength of the Pt-CO binding interaction as well as the large 
quadrupolar repulsion between CO molecules are sufficient to 
explain the observed increase in surface mobility and the resultant 
reconstructions at the highest simulated coverage. The weaker 
Au-CO interaction results in lower diffusion constants, less step-wandering, 
and a lack of the double layer reconstruction. An in-depth examination 
of the energetics shows the important role CO plays in increasing 
step-breakup and in facilitating edge traversal which are both 
necessary for double layer formation.


%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}

\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
\bibliography{firstTryBibliography}
%\end{doublespace}

\begin{tocentry}
%\includegraphics[height=3.5cm]{timelapse}
\end{tocentry}

\end{document}
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