--- trunk/COonPt/firstTry.tex	2013/03/15 13:18:17	3877
+++ trunk/COonPt/firstTry.tex	2013/03/15 21:35:55	3878
@@ -117,7 +117,7 @@ This work is an investigation into the mechanism and t
 reversible restructuring under exposure to moderate pressures of
 carbon monoxide.\cite{Tao:2010}
 
-This work is an investigation into the mechanism and timescale for
+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
@@ -126,15 +126,15 @@ The Au(557) surface, because of a weaker interaction w
 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 seen as less 
-likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000} 
-and Piccolo et al.\cite{Piccolo:2004} have both observed CO-induced 
-reconstruction of a Au(111) surface. Peters et al. saw a relaxation to the 
+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 
+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 being greatly 
-affected by this relaxation. Piccolo et al. on the other hand, did see a 
+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.
@@ -149,7 +149,7 @@ adsorbates.  Since the interfaces involved are quite l
 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$^6$ atoms) and respond slowly to perturbations, {\it ab initio}
+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
@@ -174,9 +174,9 @@ parameter sets. The glue model of Ercolessi et al. is 
 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 et al. is among the
+parameter sets. The glue model of Ercolessi {\it et al}. is among the
 fastest of these density functional approaches.\cite{Ercolessi88} In
-all of these models, atoms are conceptualized as a positively charged
+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
@@ -213,13 +213,13 @@ from the original parameterization, where the interact
 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
-from the original parameterization, where the interactions
-up to the third nearest neighbor were taken into account.\cite{Voter95a}
-Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88}
+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 EAMs functional 
+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}  
@@ -272,12 +272,12 @@ et al.,\cite{Pons:1986} the Pt-C interaction was fit t
 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
-et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep
-Lennard-Jones interaction to mimic strong, but short-ranged partial
+{\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 cases, the Pt-O parameterization contributes a weak
+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
@@ -314,9 +314,8 @@ and polarization are neglected in this model, although
 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 are likely to
-affect binding energies and binding site preferences, and will be addressed in
-future work.
+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
@@ -360,7 +359,9 @@ dimensions of 57.4~x~51.9285~x~100~\AA.
 \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.
+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$19~\AA~for Au.
 The systems are arranged in a FCC crystal that have been cut
 along the (557) plane so that they are periodic in the {\it x} and
 {\it y} directions, and have been oriented to expose two aligned
@@ -369,7 +370,7 @@ The different bulk melting temperatures (1345~$\pm$~10
 1200~K were performed to confirm the relative
 stability of the surfaces without a CO overlayer.  
 
-The different bulk melting temperatures (1345~$\pm$~10~K for Au\cite{Au:melting}
+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
@@ -396,68 +397,64 @@ The surfaces of both systems, upon dosage of CO, began
 %
 \section{Results}
 \subsection{Structural remodeling}
-The surfaces of both systems, upon dosage of CO, began 
-to undergo extensive remodeling that was not observed in the bare 
-systems. The bare metal surfaces 
-experienced minor roughening of the step-edge because 
-of the elevated temperatures, but the 
-(557) lattice was well-maintained throughout the simulation 
-time. The Au systems were limited to greater amounts of 
-roughening, i.e. breakup of the step-edge, and some step 
-wandering. The lower coverage Pt systems experienced 
-similar restructuring but to a greater extent when 
-compared to the Au systems. The 50\% coverage 
-Pt system was unique among our simulations in that it 
-formed numerous double layers through step coalescence, 
-similar to results reported by Tao et al.\cite{Tao:2010}
+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 
-movement at their respective run temperatures. As the CO 
-coverage increased however, the mobility of the surface, 
+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, the step-edges 
-did not coalesce in any of the other simulations, instead 
-preferring 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 et al.\cite{Williams:1991, Williams:1994} 
+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 arises because step-edge crossing is not allowed 
-which constrains the entropy. This entropic repulsion does 
-not completely define the interactions between steps, which 
-is why some surfaces will undergo step coalescence, where 
-additional attractive interactions can overcome the repulsion.\cite{Williams:1991} 
-The presence and concentration of adsorbates, as shown in 
-this work, can affect these step interactions, potentially leading 
-to a new surface structure as the thermodynamic minimum.
+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 et al.\cite{Tao:2010} have shown experimentally that the Pt(557) surface 
-undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} 
+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 numerous surfaces 
-at varying conditions: Ni(977), Si(111).\cite{Williams:1994,Williams:1991,Pearl} 
+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 when compared to the Au system 
-because of the larger surface mobility and extent of step wandering. 
-The amount of reconstruction is strongly correlated to the amount of CO 
+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. While both systems displayed 
-step-edge wandering, only the 50\% Pt surface underwent the 
-doubling seen by Tao et al.\cite{Tao:2010} within the time scales studied here. 
-Over longer periods, (150~ns) two more double layers formed 
-on this interface. Although double layer formation did not occur 
-in the other Pt systems, they show more step-wandering and 
-general roughening compared to their Au counterparts. 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 on the Pt(557) surface observed by 
-Tao involved the formation of triangular clusters that stretched 
-across the plateau between two step-edges. Neither system, within 
+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.
 
@@ -474,48 +471,45 @@ Previous atomistic simulations of stepped surfaces dea
 \end{figure}
 
 \subsection{Dynamics}
-Previous atomistic simulations of stepped surfaces dealt largely
-with the energetics and structures at different conditions.
-\cite{Williams:1991,Williams:1994} Consequently, the most common 
-technique utilized to date has been Monte Carlo sampling. Monte Carlo approaches give an efficient 
-sampling of the equilibrium thermodynamic landscape at the expense 
-of ignoring the dynamics of the system. Previous experimental work by Pearl and 
-Sibener\cite{Pearl}, using STM, has been able to capture the coalescing 
-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 were able to probe the dynamics of these reconstructions and in this section we give data on dynamic and 
-transport properties, e.g. diffusion, layer formation time, etc.
+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 movement or wandering of a step-edge is a cooperative effect 
+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. 
-Breaking away from the step-edge on a clean surface still imposes an 
+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 Figures \ref{fig:SketchGraphic} and \ref{fig:SketchEnergies}, the penalty can fall to as low as 
+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
+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 a difficult process for an atom 
+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, dynamically breaking apart and rejoining the edges. 
+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). An atom that was 
-truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff 
+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 
@@ -539,70 +533,98 @@ The lack of a definite trend in the Au diffusion data 
 \label{fig:diff}
 \end{figure}
 
-The lack of a definite trend in the Au diffusion data in Figure \ref{fig:diff} is likely due 
-to the weaker bonding between Au and CO. This leads to a lower observed
-coverage ({\it x}-axis) when compared to dosage amount, which 
-then further limits the effect the CO can have on surface diffusion. The correlation 
-between coverage and Pt diffusion rates conversely shows a 
-definite trend marred by the highest coverage surface. Two 
-explanations arise for this drop. First, upon a visual inspection of 
-the system, after a double layer has been formed, it maintains its 
-stability strongly and many atoms that had been tracked for mobility 
-data have now been buried. By performing the same diffusion 
-calculation but on a shorter run time (20~ns), only including data 
-before the formation of the first double layer, we obtain the larger 
-values for both $\mathbf{D}_{\parallel}$ and $\mathbf{D}_{\perp}$ 
-at the 50\% coverage as seen in Figure \ref{fig:diff}.
-This places the parallel diffusion constant more closely in line with the 
-expected trend, while the perpendicular diffusion constant does not 
-drop as far. A secondary explanation arising from our analysis of the 
-mechanism of double layer formation focuses on the effect that CO on the 
-surface has with respect to overcoming surface diffusion of Pt. If the 
-coverage is too sparse, the Pt engages in minimal interactions and 
-thus minimal diffusion. As coverage increases, there are more favorable 
-arrangements of CO on the surface allowing for the formation of a path, 
-a minimum energy trajectory, for the adatom to explore the surface. 
-As the CO is constantly moving on the surface, this path is constantly 
-changing. If the coverage becomes too great, the paths could 
-potentially be clogged leading to a decrease in diffusion despite 
-their being more adatoms and step-wandering.
+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''. 
 
 
-\subsubsection{Dynamics of double layer formation}
-The increased diffusion on Pt at the higher CO coverages 
-plays a primary role in 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 the observed run time. On the 
-50\%~Pt system, one 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
-will be lowered as experimental techniques continue to improve.\cite{Williams:1991,Pearl} 
-In this system, as seen in Figure \ref{fig:reconstruct}, 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 been flattened out. The double layer could be considered 
-``complete" by 37~ns but remains a bit rough. 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. It is probable that the process would 
-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 
-constrained axes. A longer step-edge will likely take longer to ``zipper''. However, 
-the first appearance of a nucleation site will likely occur more quickly due to its stochastic nature.
+%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 featured in Figure \ref{fig:reconstruct}. 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 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 barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so 
+repulsion between adjacent CO molecules 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 are more 
+likely to shift their positions without dragging the Pt along with them.
 
+Another possible mechanism for the restructuring is in the destabilization of strong Pt-Pt interactions by CO adsorbed on surface Pt atoms. To test this hypothesis, a number of configurations of CO in varying quantities were arranged on the upper plateaus around a step on an otherwise clean Pt(557) surface. A few sample configurations are displayed in Figure \ref{fig:SketchGraphic}, with energy curves corresponding to each configuration in Figure \ref{fig:SketchEnergies}. Certain configurations of CO, cases (e), (g) and (h) for example, can provide significant energetic pushes for Pt atoms to break away from the step-edge.
 
 
-
 %Sketch graphic of different configurations
 \begin{figure}[H]
 \includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf}
@@ -627,100 +649,8 @@ configurations of CO will be more likely. }
 \label{fig:SketchEnergies}
 \end{figure}
 
-%Discussion
-\section{Discussion}
-We have shown that the classical potential models are able to model the initial reconstruction of the
-Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we
-were able to observe features of the dynamic processes necessary for this reconstruction. 
 
-\subsection{Diffusion}
-As shown in Figure \ref{fig:diff}, for the Pt systems, there 
-is a strong trend toward higher diffusion constants as 
-surface coverage of CO increases. The drop for the 50\% 
-case being explained as double layer formation already 
-beginning to occur in the analyzed 40~ns, which lowered 
-the calculated diffusion rates. Between the parallel and 
-perpendicular rates, 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 et al.\cite{Williams:1991, Williams:1994}, 
-the inability for edges to cross leads to an effective repulsion. 
-This repulsion 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 form the nucleation point. Upon that appearance, parallel 
-diffusion along the step-edge can help ``zipper'' up the 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 said site was unpredictable. 
 
-\subsection{Mechanism for restructuring}
-Since the Au surface showed no large scale restructuring throughout 
-our simulation time our discussion will focus on the 50\% Pt-CO system 
-which did undergo the doubling featured in Figure \ref{fig:reconstruct}. 
-Similarities of our results to those reported previously by Tao et al.\cite{Tao:2010} 
-are quite strong. The simulated Pt system exposed to a large dosage 
-of CO readily restructures by doubling the terrace widths and step heights. 
-The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a 
-time, but is rapid on experimental timescales. The adatoms either break 
-away from the step-edge and stay on the lower terrace or they lift up onto 
-a higher terrace. Once ``free'', they diffuse on the terrace until reaching 
-another step-edge or rejoining their original edge. This combination of 
-growth and decay of the step-edges is in a state of dynamic equilibrium. 
-However, once two previously separated edges meet as shown in Figure 1.B, 
-this nucleates the rest of the edge to meet up, forming a double layer. 
-From simulations which exhibit a double layer, the time delay from the 
-initial appearance of a nucleation point to a fully formed double layer is $\sim$35~ns.
-
-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 
-gains some credence. The energetic repulsion between two CO 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 apart to the second 
-nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to 
-nearly 0 kcal/mol. Allowing the CO to rotate away from a purely vertical orientation 
-also lowers the repulsion. A minimum of 6.2 kcal/mol is reached at when the 
-angle between the 2 CO is $\sim$24\textsuperscript{o}, when the carbons are 
-locked at a distance of 2.77 \AA apart. As mentioned above, the energy barrier 
-for surface diffusion of a Pt adatom is only 4 kcal/mol. So this repulsion between 
-neighboring CO molecules can increase the surface diffusion. However, the 
-residence time of CO on Pt was examined and while the majority of the CO is 
-on or near the surface throughout the run, the molecules are extremely mobile, 
-with diffusion constants 40 to 2500 times larger, depending on coverage. This 
-mobility suggests that the CO are more likely to shift their positions without 
-necessarily the Pt along with them.
-
-Another possible and more likely mechanism for the restructuring is in the
-destabilization of strong Pt-Pt interactions by CO adsorbed on surface
-Pt atoms. To test this hypothesis, numerous configurations of 
-CO in varying quantities were arranged on the higher and lower plateaus
-around a step on a otherwise clean Pt(557) surface. A few sample 
-configurations are displayed in Figure \ref{fig:SketchGraphic}, with 
-energies at various positions along the path displayed in Table 
-NO TABLE. Certain configurations of CO, cases B and D for 
-example, can have quite strong energetic reasons for breaking 
-away from the step-edge. Although the packing of these configurations 
-is unlikely until CO coverage has reached a high enough value. 
-These examples are showing the most difficult cases, immediate 
-adatom formation through breakage away from the step-edge, which 
-is why their energies at large distances are relatively high. There are 
-mechanistic paths where an edge atom could get shifted to onto the 
-step-edge to form a small peak before fully breaking away. And again, 
-once the adatom is formed, the barrier for diffusion on the surface is 
-negligible. These sample configurations help explain CO's effect on 
-general surface mobility and step wandering, but they are lacking in 
-providing a mechanism for the formation of double layers. One possible 
-mechanism is elucidated in Figure \ref{fig:lambda}, where a burrowing 
-and lifting process of an adatom and step-edge atom respectively is 
-examined. The system, without CO present, is nearly energetically 
-neutral, whereas with CO present there is a $\sim$ 15 kcal/mol drop 
-in the energy of the system.
-
 %lambda progression of Pt -> shoving its way into the step
 \begin{figure}[H]
 \includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png}
@@ -733,10 +663,33 @@ in the energy of the system.
 \label{fig:lambda}
 \end{figure}
 
+\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}