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}
  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.  Various mechanisms for CO-mediated step
  wandering and step doubling were investigated on the Pt(557)
  surface.  We find that the energetics of CO adsorbed to the surface
  can 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,mishin99:_inter}
melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
fracture,\cite{Shastry:1996qg,Shastry:1998dx,mishin01:cu} crack
propagation,\cite{BECQUART:1993rg,Rifkin1992} and alloying
dynamics.\cite{Shibata:2002hh,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} 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.


\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,openmd}


% 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]{EPS_ProgressionOfDoubleLayerFormation}
\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]{Portrait_DiffusionComparison_1}
\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 is able to model the initial
reconstruction of the Pt(557) surface upon CO adsorption, and have
reproduced the double layer structure observed by Tao {\it et
  al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be
rapid -- occurring within 100 ns of the initial exposure to CO.  Here
we discuss the features of the classical potential that are
contributing to the stability and speed of the Pt(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.  Williams {\it et
  al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge
repulsion arising from the inability of edge crossing.  This repulsion
must be overcome to allow step coalescence.  A larger
$\textbf{D}_\perp$ value implies more step-wandering and a larger
chance for the stochastic meeting of two edges to create a nucleation
point.  Diffusion parallel to the step-edge can help ``zipper'' up a
nascent double layer. This helps explain the rapid time scale for
double layer completion after the appearance of a nucleation site, 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 vertical orientation, 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 the CO 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 can stay bound for significant periods of time.

A different interpretation of the above mechanism which takes the
large mobility of the CO into account, would be in the destabilization
of Pt-Pt interactions due to bound CO.  Destabilizing Pt-Pt bonds at
the edges could lead 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/mol by the presence of bound CO molecules. In these
instances, it becomes 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 surfaces
with lower CO coverage (and even on the bare surfaces), although in
these cases it is likely due to random fluctuations that squeeze out
step-edge atoms. Step-edge breakup by continuous single-atom
translations (as suggested by these energy curves) is probably a
worst-case scenario.  Multistep mechanisms in which an adatom moves
laterally on the surface after being ejected would be more
energetically favorable.  This would leave the adatom alongside the
ledge, providing it with 5 nearest neighbors.  While fewer than the 7
neighbors it had as part of the step-edge, it keeps more Pt neighbors
than the 3 an isolated adatom would have on the terrace. In this
proposed mechanism, the CO quadrupolar repulsion still plays a role in
the initial roughening of the step-edge, but not in any long-term
bonds with individual Pt atoms.  Higher CO coverages create more
opportunities for the crowded CO configurations shown in Figure
\ref{fig:SketchGraphic}, and this is likely to cause an increased
propensity for step-edge breakup.

%Sketch graphic of different configurations
\begin{figure}[H]
\includegraphics[width=\linewidth]{COpaths}
\caption{Configurations used to investigate the mechanism of step-edge
  breakup on Pt(557). In each case, the central (starred) atom is
  pulled directly across the surface away from the step edge.  The Pt
  atoms on the upper terrace are colored dark grey, while those on the
  lower terrace are in white.  In each of these configurations, some
  number of the atoms (highlighted in blue) had a CO molecule bound in
  a vertical atop position.  The energies of these configurations as a
  function of central atom displacement are displayed in Figure
  \ref{fig:SketchEnergies}.}
\label{fig:SketchGraphic}
\end{figure}

%energy graph corresponding to sketch graphic
\begin{figure}[H]
\includegraphics[width=\linewidth]{Portrait_SeparationComparison}
\caption{Energies for displacing a single edge atom perpendicular to
  the step edge as a function of atomic displacement. Each of the
  energy curves corresponds to one of the labeled configurations in
  Figure \ref{fig:SketchGraphic}, and are referenced to the
  unperturbed step-edge.  Certain arrangements of bound CO (notably
  configurations g and h) can lower the energetic barrier for creating
  an adatom relative to the bare surface (configuration a).}
\label{fig:SketchEnergies}
\end{figure}

While configurations of CO on the surface are able to increase
diffusion and the likelihood of edge wandering, this does not provide
a complete explanation for the formation of double layers. If adatoms
were constrained to their original terraces then doubling could not
occur.  A mechanism for vertical displacement of adatoms at the
step-edge is required to explain the doubling.

We have discovered one possible mechanism for a CO-mediated vertical
displacement of Pt atoms at the step edge. Figure \ref{fig:lambda}
shows four points along a reaction coordinate in which a CO-bound
adatom along the step-edge ``burrows'' into the edge and displaces the
original edge atom onto the higher terrace. A number of events similar
to this mechanism were observed during the simulations.  We predict an
energetic barrier of 20~kcal/mol for this process (in which the
displaced edge atom follows a curvilinear path into an adjacent 3-fold
hollow site).  The barrier heights we obtain for this reaction
coordinate are approximate because the exact path is unknown, but the
calculated energy barriers would be easily accessible at operating
conditions.  Additionally, this mechanism is exothermic, with a final
energy 15~kcal/mol below the original $\lambda = 0$ configuration.
When CO is not present and this reaction coordinate is followed, the
process is endothermic by 3~kcal/mol.  The difference in the relative 
energies for the $\lambda=0$ and $\lambda=1$ case when CO is present
provides strong support for CO-mediated Pt-Pt interactions giving rise
to the doubling reconstruction. 

%lambda progression of Pt -> shoving its way into the step
\begin{figure}[H]
\includegraphics[width=\linewidth]{EPS_rxnCoord}
\caption{Points along a possible reaction coordinate for CO-mediated
  edge doubling. Here, a CO-bound adatom burrows into an established
  step edge and displaces an edge atom onto the upper terrace along a
  curvilinear path.  The approximate barrier for the process is
  20~kcal/mol, and the complete process is exothermic by 15~kcal/mol
  in the presence of CO, but is endothermic by 3~kcal/mol without.}
\label{fig:lambda}
\end{figure}

The mechanism for doubling on the Pt(557) surface appears to require
the cooperation of at least two distinct processes. For complete
doubling of a layer to occur there must be a breakup of one
terrace. These atoms must then ``disappear'' from that terrace, either
by travelling to the terraces above of below their original levels.
The presence of CO helps explain mechanisms for 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 a comparable
mechanism) to create the double layer.  With sufficient 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.  Random
fluctuations that involved small clusters or divots were observed, but
these features typically healed within a few nanoseconds.  Within our
simulations, the formation of the double layer appeared to be
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 has on this surface, additional
simulations were run starting from a late configuration of the 50\%~Pt
system that had already formed double layers. These simulations then
had their CO forcibly removed.  The double layer broke apart rapidly
in these simulations, showing a well-defined edge-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 for 10~ns, and within that time despite the
initial rapid splitting, the edges only moved another few
\AA~apart. It is possible that with longer simulation times, the (557)
surface recovery observed by Tao {\it et al}.\cite{Tao:2010} could
also be recovered.

%breaking of the double layer upon removal of CO
\begin{figure}[H]
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking}
\caption{Dynamics of an established (111) double step after removal of
  the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the removal
  of CO. The presence of the CO helped maintain the stability of the
  double step.  Nearly immediately after the CO is removed, the step
  edge reforms in a (100) configuration, which is also the step type
  seen on clean (557) surfaces. The step separation involves
  significant 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}
%\caption{}

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


\section{Conclusion}
The strength and directionality of the Pt-CO binding interaction, as
well as the large quadrupolar repulsion between atop-bound CO
molecules, help to explain the observed increase in surface mobility
of Pt(557) and the resultant reconstruction into a double-layer
configuration at the highest simulated CO-coverages.  The weaker Au-CO
interaction results in significantly lower adataom diffusion
constants, less step-wandering, and a lack of the double layer
reconstruction on the Au(557) surface.

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}
  We gratefully acknowledge conversations with Dr. William
  F. Schneider and Dr. Feng Tao.  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}
A reconstructed Pt(557) surface after having been exposed to a dosage of CO equivalent to half a monolayer of coverage is observed to undergo a doubling of the step-edge height and terrace length.
\includegraphics[height=3.5cm]{TOC_doubleLayer}
\end{tocentry}

\end{document}
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