--- trunk/COonPt/firstTry.tex	2012/12/17 18:45:57	3820
+++ trunk/COonPt/firstTry.tex	2012/12/19 21:37:51	3826
@@ -4,9 +4,8 @@
 \usepackage{times}
 \usepackage{mathptm}
 \usepackage{setspace}
-\usepackage{float}
+\usepackage{endfloat}
 \usepackage{caption}
-
 %\usepackage{tabularx}
 \usepackage{graphicx}
 \usepackage{multirow}
@@ -83,43 +82,40 @@ Industrial catalysts usually consist of small particle
 %	Sub: Also, easier to observe what is going on and provide reasons and explanations
 %
 
-Industrial catalysts usually consist of small particles exposing
-different atomic terminations that exhibit a high concentration of
-step, kink sites, and vacancies at the edges of the facets.  These
-sites are thought to be the locations of catalytic
+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 to demonstrate that solid surfaces are often
-structurally, compositionally, and chemically {\it modified} by
-reactants under operating conditions.\cite{Tao2008,Tao:2010,Tao2011}
-The coupling between surface oxidation state 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 currently 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}
+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 part of an ongoing effort to understand the causes,
-mechanisms and timescales for surface restructuring using molecular
-simulation methods.  Since the dynamics of the process is of
-particular interest, we utilize classical molecular dynamic methods
-with force fields that represent a compromise between chemical
-accuracy and the computational efficiency necessary to observe the
-process of interest.
+This work an effort to understand the mechanism and timescale for
+surface restructuring using molecular simulations.  Since the dynamics
+of the process is of particular interest, we utilize classical force
+fields that represent a compromise between chemical accuracy and the
+computational efficiency necessary to observe the process of interest.
 
-Since restructuring occurs as a result of specific interactions of the catalyst
-with adsorbates, two metals systems exposed to the same adsorbate, CO,
-were examined in this work. The Pt(557) surface has already been shown to 
-reconstruct under certain conditions. The Au(557) surface, because of gold's
-weaker interaction with CO, is less likely to undergo such a large reconstruction.
+Since restructuring occurs as a result of specific interactions of the
+catalyst with adsorbates, two metal systems exposed to carbon monoxide
+were examined in this work. The Pt(557) surface has already been shown
+to reconstruct under certain conditions. The Au(557) surface, because
+of a weaker interaction with CO, is less likely to undergo this kind
+of reconstruction.  MORE HERE ON PT AND AU PREVIOUS WORK.
+
 %Platinum molecular dynamics
 %gold molecular dynamics
 
-
-
 \section{Simulation Methods}
 The challenge in modeling any solid/gas interface problem is the
 development of a sufficiently general yet computationally tractable
@@ -134,19 +130,19 @@ Coulomb potential.  For this work, we have been using 
 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 been using classical
-molecular dynamics with potential energy surfaces that are
-specifically tuned for transition metals.  In particular, we use the
-EAM potential for Au-Au and Pt-Pt interactions, while modeling the CO
-using a 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.
+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, while modeling the CO 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 classical simulation of 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
+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
@@ -156,7 +152,7 @@ atomic sites is computed at atom $i$'s location, 
 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, 
+atomic sites is computed at atom $i$'s location,
 \begin{equation*}
 \bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij})
 \end{equation*}
@@ -171,16 +167,16 @@ The {\it modified} embedded atom method (MEAM) adds an
 $\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the
 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 {\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, MEAM, and the Quantum Sutton-Chen potentials
+The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen 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}
@@ -191,31 +187,30 @@ parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin19
 strengths and weaknesses.  One of the strengths common to all of the
 methods is the relatively large library of metals for which these
 potentials have been
-parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} 
+parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  
 
-\subsection{CO}
-Since one explanation for the strong surface CO repulsion on metals is
+\subsection{Carbon Monoxide model}
+Since previous explanations for the surface rearrangements center on
 the large linear quadrupole moment of carbon monoxide, the model
 chosen for this molecule exhibits this property in an efficient
-manner.  We used a model first proposed by Karplus and Straub to study
-the photodissociation of CO from myoglobin.\cite{Straub} The Straub and
-Karplus model is a rigid three site model which places a massless M
-site at the center of mass along the CO bond.  The geometry used along
-with the interaction parameters are reproduced in Table 1. 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 
+manner. We used a model first proposed by Karplus and Straub to study
+the photodissociation of CO from myoglobin.\cite{Straub} The Straub
+and Karplus model is a rigid linear three site model which places a
+massless (M) site at the center of mass along the CO bond.  The
+geometry and interaction parameters are reproduced in Table 1. 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, $\sigma$, $\epsilon$ and charges for CO geometry 
-and self-interactions\cite{Straub}. Distances are in \AA~, energies are 
-in kcal/mol, and charges are in $e$.}
+  \caption{Positions, Lennard-Jones parameters ($\sigma$ and
+    $\epsilon$), and charges for the CO-CO 
+    interactions borrowed from 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
-\multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\
-\hline
 &  {\it z} & $\sigma$ & $\epsilon$ & q\\
 \hline
 \textbf{C} & -0.6457 &  0.0262  & 3.83   &   -0.75 \\
@@ -225,25 +220,27 @@ in kcal/mol, and charges are in $e$.}
 \end{tabular}
 \end{table}
 
-\subsection{Cross-Interactions}
+\subsection{Cross-Interactions between the metals and carbon monoxide}
 
-One hurdle that must be overcome in classical molecular simulations 
-is the proper parameterization of the potential interactions present
-in the system. Since the adsorption of CO onto a platinum surface has been 
-the focus of many experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979} 
-and theoretical studies \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004}
-there is a large amount of data in the literature to fit too. We started with parameters 
-reported by Korzeniewski et al. \cite{Pons:1986} and then
-modified them to ensure that the Pt-CO interaction favored 
-an atop binding position for the CO upon the Pt surface. This 
-constraint led to the binding energies being on the higher side 
-of reported values. Following the method laid out by Korzeniewski, 
-the Pt-C interaction was fit to a strong Lennard-Jones 12-6 
-interaction to mimic binding, while the Pt-O interaction
-was parameterized to a Morse potential with a large $r_o$ 
-to contribute a weak repulsion. The resultant potential-energy
-surface suitably recovers the calculated Pt-C bond length ( 1.6\AA)\cite{Beurden:2002ys} and affinity
-for the atop binding position.\cite{Deshlahra:2012, Hopster:1978}
+Since the adsorption of CO onto a platinum 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. Parameters reported by Korzeniewski {\it et
+  al.}\cite{Pons:1986} were a starting point for our fits, which were
+modified to ensure that the Pt-CO interaction favored the atop binding
+position on Pt(111). This resulting binding energies are on the higher
+side of the experimentally-reported values. 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 parameterized to a Morse potential with a large
+range parameter ($r_o$).  In most cases, this 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
@@ -251,8 +248,8 @@ The fits were refined against gas-surface calculations
 The Au-C and Au-O cross-interactions were fit using Lennard-Jones and
 Morse potentials, respectively, to reproduce Au-CO binding energies.
 
-The fits were refined against gas-surface calculations using DFT with
-a periodic supercell plane-wave basis approach, as implemented in the
+The fits were refined against 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 are
 described with the projector augmented-wave (PAW)
 method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves
@@ -261,70 +258,38 @@ subsequent steps was less than 0.0001 eV.  In testing 
 approximation (GGA) for gold, carbon, and oxygen that was constructed
 by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
 Ionic relaxations were performed until the energy difference between
-subsequent steps was less than 0.0001 eV.  In testing the CO-Au
+subsequent steps was less than $10^{-8}$ Ry.  In testing the CO-Au
 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.
-Supercell calculations were performed nonspin-polarized, and energies
-were converged to within 0.03 meV per Au atom with a 4 x 4 x 4
-Monkhorst-Pack\cite{Monkhorst:1976,PhysRevB.13.5188} {\bf k}-point
-sampling of the first Brillouin zone.  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. 
+Supercell calculations were performed nonspin-polarized with a 4 x 4 x
+4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin
+zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was
+then used in numerous single point calculations with CO at various
+heights (and angles relative to the surface) to allow fitting of the
+empirical force field.
 
 %Hint at future work
-The fit parameter sets employed in this work are shown in Table 2 and their
-reproduction of the binding energies are displayed in Table 3. Currently,
-charge transfer is not being treated in this system, however, that is a goal
-for future work as the effect has been seen to affect binding energies and 
-binding site preferences. \cite{Deshlahra:2012}
-
-
-
-
-\subsection{Construction and Equilibration of 557 Metal interfaces}
-
-Our model systems are composed of approximately 4000 metal atoms 
-cut along the 557 plane so that they are periodic in the {\it x} and {\it y} 
-directions exposing the 557 plane in the {\it z} direction. Runs at various
-temperatures ranging from 300~K to 1200~K were started with the intent
-of viewing relative stability of the surface when CO was not present in the
-system.  Owing to the different melting points (1337~K for Au and 2045~K for Pt),
-the bare crystal systems were initially run in the Canonical ensemble at
-800~K and 1000~K respectively for 100 ps. Various amounts of CO were
-placed in the vacuum region, which upon full adsorption to the surface
-corresponded to 5\%, 25\%, 33\%, and 50\% coverages. Because of the 
-high temperature and the difference in binding energies, the platinum systems
-very rarely had CO that was not adsorbed to the surface whereas the gold systems
-often had a substantial minority of CO away from the surface.
-These systems were again allowed to reach thermal equilibrium before being run in the
-microcanonical ensemble. All of the systems examined in this work were
-run for at least 40 ns. A subset that were undergoing interesting effects
-have been allowed to continue running with one system approaching 200 ns.
-All simulations were run using the open source molecular dynamics package, OpenMD. \cite{Ewald, OOPSE}
-
-
-
-
-
-
-%\subsection{System}
-%Once equilibration was reached, the systems were exposed to various sub-monolayer coverage of CO: $0, \frac{1}{10}, \frac{1}{4}, \frac{1}{3},\frac{1}{2}$. The CO was started many \AA~above the surface with random velocity and rotational velocity vectors sampling from a Gaussian distribution centered on the temperature of the equilibrated metal block.  Full adsorption occurred over the period of approximately 10 ps for Pt, while the binding energy between Au and CO is smaller and led to an incomplete adsorption. The metal-metal interactions were treated using the Embedded Atom Method while the Pt-CO and Au-CO interactions were fit to experimental data and quantum calculations. The raised temperature helped shorten the length of the simulations by allowing the activation barrier of reconstruction to be more easily overcome. A few runs at lower temperatures showed the very beginnings of reconstructions, but their simulation lengths limited their usefulness.
-
+The parameters employed in this work are shown in Table 2 and the
+binding energies on the 111 surfaces are displayed in Table 3.  To
+speed up the computations, charge transfer and polarization are not
+being treated in this model, although these effects are likely to
+affect binding energies and binding site
+preferences.\cite{Deshlahra:2012}
 
 %Table  of Parameters
 %Pt Parameter Set 9
 %Au Parameter Set 35
 \begin{table}[H]
-\caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol}
+  \caption{Best fit parameters for metal-CO cross-interactions.   Metal-C
+    interactions are modeled with Lennard-Jones potential, while the
+    (mostly-repulsive) 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
-\multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\
+ &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\
 \hline
- &  $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\
-\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\\
 
@@ -334,99 +299,189 @@ All simulations were run using the open source molecul
 
 %Table of energies
 \begin{table}[H]
-\caption{Adsorption energies in eV}
+  \caption{Adsorption energies for CO on M(111) using the potentials
+    described in this work.  All values are in eV}
 \centering
 \begin{tabular}{| c | cc |}
-\hline
- & Calc. & Exp. \\
-\hline
-\textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\
-\textbf{Au-CO} & -0.39 & -0.40~\cite{TPD_Gold} \\
-\hline
+  \hline
+  & Calculated & Experimental \\
+  \hline
+  \multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,}
+  (Ref. \protect\cite{Kelemen:1979}) \\
+ & &  -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline
+  \textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,}  (Ref. \protect\cite{TPD_Gold}) \\
+  \hline
 \end{tabular}
 \end{table}
 
+\subsection{Pt(557) and Au(557) metal interfaces}
 
+Our model systems are composed of 3888 Pt atoms and XXXX Au atoms 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 rotated
+to expose two parallel 557 cuts along the positive and negative {\it
+  z}-axis.  Simulations of the bare metal interfaces at temperatures
+ranging from 300~K to 1200~K were done to observe the relative
+stability of the surfaces without a CO overlayer.  
 
+The different bulk (and surface) melting temperatures (1337~K for Au
+and 2045~K for Pt) suggest that the reconstruction may happen at
+different temperatures for the two metals.  To copy experimental
+conditions for the CO-exposed surfaces, the bare surfaces were
+initially run in the canonical (NVT) ensemble at 800~K and 1000~K
+respectively for 100 ps.  Each surface was exposed to a range of CO
+that was initially placed in the vacuum region.  Upon full adsorption,
+these amounts correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface
+coverage.  Because of the difference in binding energies, the platinum
+systems very rarely had CO that was not bound to the surface, while
+the gold surfaces often had a significant CO population in the gas
+phase.  These systems were allowed to reach thermal equilibrium (over
+5 ns) before being shifted to 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 of the
+systems exceeded 200ns.  All simulations were run using the open
+source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,OpenMD}
 
-
-
 % Just results, leave discussion for discussion section
 \section{Results}
-\subsection{Diffusion}
-An ideal metal surface displaying a low-energy facet, a (111) face for 
-instance, is unlikely to experience much surface diffusion because of 
-the large energy barrier associated with atoms 'lifting' from the top 
-layer to then be able to explore the surface. Rougher surfaces, those 
-that already contain numerous adatoms, step edges, and kinks, should 
-have concomitantly higher surface diffusion rates. Tao et al. showed 
-that the platinum 557 surface undergoes two separate reconstructions 
-upon CO adsorption. \cite{Tao:2010} The first reconstruction involves a 
-doubling of the step edge height which is accomplished by a doubling 
-of the plateau length. The second reconstruction led to the formation of 
-triangular motifs stretching across the lengthened plateaus. 
+Tao {\it et al.} showed experimentally that the Pt(557) surface
+undergoes two separate reconstructions upon CO
+adsorption.\cite{Tao:2010} The first reconstruction involves a
+doubling of the step edge height which is accomplished by a doubling
+of the plateau length. The second reconstruction led to the formation
+of triangular clusters that arrange themselves along the lengthened
+plateaus.
 
-As shown in Figure 2, over a period of approximately 100 ns, the surface
-has reconstructed from a 557 surface by doubling the step height and 
-step length. Focusing on only the platinum, or gold, atoms that were 
-deemed mobile on the surface, an analysis of the surface diffusion was 
-performed. A particle was considered mobile once it had traveled more 
-than 2~\AA between snapshots. This immediately eliminates all of the 
-bulk metal and greatly limits the number of surface atoms examined. 
-Since diffusion on a surface is strongly affected by overcoming energy 
-barriers, the diffusion parallel to the step edge axis was determined 
-separately from the diffusion perpendicular to the step edge. The results 
-at various coverages on both platinum and gold are shown in Table 4.
+The primary observation and results of our simulation is that the
+presence of CO overlayer on Pt(557) causes the same kind of
+reconstruction observed experimentally. The 6-atom 111 facets
+initially become disordered, and after 20-40 ns, a double-layer (with
+a 2-atom step between terraces) forms.  However, we did not observe
+the triangular cluster formation that was observed at longer times in
+the experiments.  Without the CO present on the Pt(557) surface, there
+was some disorder at the step edges, but no significant restructuring
+was observed.
 
+In these simulations, the Au(557) surface did not exhibit any
+significant restructuring either with or without the presence of a CO
+overlayer.
+
+\subsection{Transport of surface metal atoms}
+An ideal metal surface displaying a low energy (111) face is unlikely
+to experience much surface diffusion because of the large vacancy
+formation energy for atoms at the surface.  This implies that
+significant energy must be expended to lift an atom out of the flat
+face so it can migrate on the surface.  Rougher surfaces and those
+that already contain numerous adatoms, step edges, and kinks, are
+expected to have higher surface diffusion rates.  Metal atoms that are
+mobile on the surface were observed to leave and then rejoin step
+edges or other formations. They may travel together or as isolated
+atoms.  The primary challenge of quantifying the overall surface
+mobility is in defining ``mobile'' vs. ``static'' atoms.
+
+A particle was considered mobile once it had traveled more than 2~\AA~
+between saved configurations (XX ps). Restricting the transport
+calculations to only mobile atoms eliminates all of the bulk metal as
+well as any surface atoms that remain fixed for a significant length
+of time.  Since diffusion on a surface is strongly affected by local
+structures, the diffusion parallel to the step edges was determined
+separately from the diffusion perpendicular to these edges.  The
+parallel and perpendicular diffusion constants (determined using
+linear fits to the mean squared displacement) are shown in figure \ref{fig:diff}.
+
 %While an ideal metallic surface is unlikely to experience much surface diffusion, high-index surfaces have large numbers of low-coordinated atoms which have a much easier time overcoming the energetic barriers limiting diffusion, leading to easier surface reconstructions. Surface movement was divided between the parallel ($\parallel$) and perpendicular ($\perp$) directions relative to the step edge. We were then able to calculate diffusion constants as a function of CO coverage. As can be seen in Table 4, the presence and amount of CO directly affects the diffusion constants of surface platinum atoms. The presence of two 50\% coverage systems is to show how the diffusion process is affected by time. The majority of the systems were run for approximately 50 ns while the half monolayer system has been running continuously. The lowered diffusion constant at longer run times will be examined in-depth in the discussion section.
 
 \begin{figure}[H]
 \includegraphics[scale=0.6]{DiffusionComparison_error.png}
-\caption{Diffusion parallel to the step edge will always be higher than that perpendicular to the edge because of the lower energy barrier associated with going from approximately 7 nearest neighbors to 5, as compared to the 3 of an adatom. Additionally, the observed maximum and subsequent decrease for the Pt system suggests that the CO self-interactions are playing a significant role with regards to movement of the platinum atoms around and more importantly across the surface. }
+\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 going from approximately 7 nearest neighbors
+  to 5, as compared to the 3 of an adatom. Additionally, the observed
+  maximum and subsequent decrease for the Pt system suggests that the
+  CO self-interactions are playing a significant role with regards to
+  movement of the platinum atoms around and more importantly across
+  the surface. }
+\label{fig:diff}
 \end{figure}
 
 %Table of Diffusion Constants
 %Add gold?M
-\begin{table}[H]
-\caption{Platinum and gold diffusion constants parallel and perpendicular to the 557 step edge. As the coverage increases, the diffusion constants parallel and  perpendicular to the step edge both initially increase and then decrease slightly. Units are \AA\textsuperscript{2}/ns}
-\centering
-\begin{tabular}{| c | cc | cc | c |}
-\hline
-\textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  & \textbf{Time (ns)}\\
-\hline
-&\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} & \\
-\hline
-50\% & 4.32 $\pm$ 0.02 & 1.185 $\pm$ 0.008 & 1.72 $\pm$ 0.02 & 0.455 $\pm$ 0.006 & 40 \\
-33\% & 5.18 $\pm$ 0.03 & 1.999 $\pm$ 0.005 & 1.95 $\pm$ 0.02 & 0.337 $\pm$ 0.004 & 40   \\
-25\% & 5.01 $\pm$ 0.02 & 1.574 $\pm$ 0.004 & 1.26 $\pm$ 0.03 & 0.377 $\pm$ 0.006 & 40  \\
-5\%   & 3.61 $\pm$ 0.02 & 0.355 $\pm$ 0.002 & 1.84 $\pm$ 0.03 & 0.169 $\pm$ 0.004 & 40  \\
-0\%   & 3.27 $\pm$ 0.02 & 0.147 $\pm$ 0.004 & 1.50 $\pm$ 0.02 & 0.194 $\pm$ 0.002  & 40  \\
-\hline 
-\end{tabular}
-\end{table}
+% \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 $\pm$ 0.008 & 1.72 $\pm$ 0.02 & 0.455 $\pm$ 0.006 \\
+%   33\% & 5.18 $\pm$ 0.03 & 1.999 $\pm$ 0.005 & 1.95 $\pm$ 0.02 & 0.337 $\pm$ 0.004  \\
+%   25\% & 5.01 $\pm$ 0.02 & 1.574 $\pm$ 0.004 & 1.26 $\pm$ 0.03 & 0.377 $\pm$ 0.006 \\
+%   5\%   & 3.61 $\pm$ 0.02 & 0.355 $\pm$ 0.002 & 1.84 $\pm$ 0.03 & 0.169 $\pm$ 0.004 \\
+%   0\%   & 3.27 $\pm$ 0.02 & 0.147 $\pm$ 0.004 & 1.50 $\pm$ 0.02 & 0.194 $\pm$ 0.002  \\
+%   \hline 
+% \end{tabular}
+% \end{table}
 
-
-
 %Discussion
 \section{Discussion}
-Comparing the results from simulation to those reported previously by Tao et al. the similarities in the platinum and CO system are quite strong. As shown in figure 1, the simulated platinum system under a CO atmosphere will restructure slightly by doubling the terrace heights. The restructuring appears to occur slowly, one to two platinum atoms at a time. Looking at individual snapshots, these adatoms tend to either rise on top of the plateau or break away from the step edge and then diffuse perpendicularly to the step direction until reaching another step edge. This combination of growth and decay of the step edges appears to be in somewhat of a state of dynamic equilibrium. However, once two previously separated edges meet as shown in figure 1.B, this point tends to act as a focus or growth point for the rest of the edge to meet up, akin to that of a zipper. From the handful of cases where a double layer was formed during the simulation, measuring from the initial appearance of a growth point, the double layer tends to be fully formed within $\sim$~35 ns.
 
+Mechanism for restructuring
+
+There are a number of possible mechanisms 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,
+this explanation gains some weight.  
+
+Another possible mechanism for the restructuring is in the
+destabilization of strong Pt-Pt interactions by CO adsorbed on surface
+Pt atoms.  This could have the effect of increasing surface mobility
+of these atoms.  
+
+Comparing the results from simulation to those reported previously by
+Tao et al. the similarities in the platinum and CO system are quite
+strong. As shown in figure, the simulated platinum system under a CO
+atmosphere will restructure slightly by doubling the terrace
+heights. The restructuring appears to occur slowly, one to two
+platinum atoms at a time. Looking at individual snapshots, these
+adatoms tend to either rise on top of the plateau or break away from
+the step edge and then diffuse perpendicularly to the step direction
+until reaching another step edge. This combination of growth and decay
+of the step edges appears to be in somewhat of a state of dynamic
+equilibrium. However, once two previously separated edges meet as
+shown in figure 1.B, this point tends to act as a focus or growth
+point for the rest of the edge to meet up, akin to that of a
+zipper. From the handful of cases where a double layer was formed
+during the simulation, measuring from the initial appearance of a
+growth point, the double layer tends to be fully formed within
+$\sim$~35 ns.
+
 \subsection{Diffusion}
 As shown in the results section, the diffusion parallel to the step edge tends to be much faster than that perpendicular to the step edge. Additionally, the coverage of CO appears to play a slight role in relative rates of diffusion, as shown in Table 4. Thus, the bottleneck of the double layer formation appears to be the initial formation of this growth point, which seems to be somewhat of a stochastic event. Once it appears, parallel diffusion, along the now slightly angled step edge, will allow for a faster formation of the double layer than if the entire process were dependent on only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the more likely a growth point is to be formed. One driving force behind this reconstruction appears to be the lowering of surface energy that occurs by doubling the terrace widths. (I'm not really proving this... I have the surface flatness to show it, but surface energy?)
 \\
 \\
 %Evolution of surface
 \begin{figure}[H]
-\includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
-\caption{Four snapshots of the $\frac{1}{2}$ monolayer system at various times a) 258 ps b) 19 ns c) 31.2 ns and d) 86.1 ns. Slight disruption of the surface occurs fairly quickly. However, the doubling of the layers seems to be very dependent on the initial linking of two separate step edges. The focal point in b, appears to be a growth spot for the rest of the double layer.}
+\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.}
 \end{figure}
 
 
-
-
 %Peaks!
 \begin{figure}[H]
-\includegraphics[scale=0.25]{doublePeaks_noCO.png}
+\includegraphics[width=\linewidth]{doublePeaks_noCO.png}
 \caption{}
 \end{figure}
 \section{Conclusion}
