--- trunk/COonPt/firstTry.tex	2013/03/05 22:54:02	3869
+++ trunk/COonPt/firstTry.tex	2013/03/08 22:06:22	3870
@@ -120,9 +120,19 @@ to reconstruct under certain conditions. The Au(557) s
 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 reconstruct under certain conditions. The Au(557) surface, because
-of a weaker interaction with CO, is less likely to undergo this kind
-of reconstruction.  
+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 relaxing of the 
+22 x $\sqrt{3}$ cell. They argued that a very small number of Au atoms
+would become adatoms, limiting the stress of this reconstruction while 
+allowing the rest of the row to relax and approach the ideal (111) 
+configuration. They did not see the ``herringbone'' pattern being greatly 
+affected by this relaxation. Piccolo 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 particles was the primary driving force for these reconstructions.
 
 
 
@@ -196,9 +206,22 @@ dynamics.\cite{Shibata:2002hh} All of these potentials
 melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr}
 fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack
 propagation,\cite{BECQUART:1993rg} and alloying
-dynamics.\cite{Shibata:2002hh} All of these potentials have their
-strengths and weaknesses.  \cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  
+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}
+which 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 
+treatment of the embedding energy to standard density functional 
+theory (DFT) approaches gives EAM, and conclusions derived, a firm theoretical footing.
+\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni}  
 
+
+
+
 \subsection{Carbon Monoxide model}
 Previous explanations for the surface rearrangements center on
 the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010}  
@@ -330,13 +353,15 @@ a future work.\cite{Deshlahra:2012,StreitzMintmire:199
 \end{table}
 
 \subsection{Pt(557) and Au(557) metal interfaces}
-
-Our model systems are composed of 3888 Pt atoms and 3384 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 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 observe the relative
+Our Pt system has dimensions of 18~x~24~x~9 in a box of size
+54.482~x~50.046~x~120.88~\AA while our Au system has 
+dimensions of 18~x~24~x~8 in a box of size 57.4~x~51.9285~x~100~\AA.
+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 observe the relative
 stability of the surfaces without a CO overlayer.  
 
 The different bulk melting temperatures (1337~K for Au
@@ -381,12 +406,12 @@ Only the 50~\% coverage Pt system exhibited
 diffusion of metal adatoms. While both systems displayed step-edge 
 wandering, only the Pt surface underwent the doubling seen by 
 Tao et al. within the time scales studied here.  
-Only the 50~\% coverage Pt system exhibited
+Only the 50\% coverage Pt system exhibited
 a complete doubling in the time scales we 
 were able to monitor. 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 lateral movement of the step-edges
-compared to the Au systems. The 50\% Pt system is highlighted 
+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 step-edge.
 
@@ -396,75 +421,59 @@ While atomistic-like simulations of stepped surfaces h
 the 40~ns time scale, experienced this reconstruction.
 
 \subsection{Dynamics}
-While atomistic-like simulations of stepped surfaces have been 
-performed before, they tend to be performed using Monte Carlo 
-techniques\cite{Williams:1991,Williams:1994}. This allows them 
-to efficiently sample the equilibrium thermodynamic landscape 
-but at the expense of ignoring the dynamics of the system. Previous
-work by Pearl and Sibener\cite{Pearl}, using STM, has been able to 
-visualize the coalescing of steps of Ni(977). The time scale of the image 
-acquisition, $\sim$70 s/image provides an upper bounds for the time 
-required for the doubling to actually occur. Statistical treatments of step-edges
-are adept at analyzing such systems. However, in a system where 
-the number of steps is limited, examining the individual atoms that make 
-up the steps can provide useful information as well. 
+Previous atomistic simulations of stepped surfaces were largely 
+concerned with the energetics and structures at different conditions
+\cite{Williams:1991,Williams:1994}. Consequently, the most common 
+technique has been Monte Carlo. Monte Carlo gives an efficient 
+sampling of the equilibrium thermodynamic landscape at the expense 
+of ignoring the dynamics of the system. Previous work by Pearl and 
+Sibener\cite{Pearl}, using STM, has been able to show the coalescing 
+of steps on Ni(977). The time scale of the image acquisition, 
+$\sim$70 s/image provides an upper bound for the time required for 
+the doubling to occur. In this section we give data on dynamic and 
+transport properties, e.g. diffusion, layer formation time, etc.
 
 
 \subsubsection{Transport of surface metal atoms}
 %forcedSystems/stepSeparation
 The movement or wandering of a step-edge is a cooperative effect 
 arising from the individual movements, primarily through surface 
-diffusion, of the atoms making up the step. An ideal metal surface 
+diffusion, 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 
 on higher-index surfaces provide a source for mobile metal atoms. 
 Breaking away from the step-edge on a clean surface still imposes an 
-energetic penalty around $\sim$~40 kcal/mole, but is much less than lifting 
-the same metal atom out from the surface,  \textgreater~60 kcal/mole, and 
-the penalty lowers even further when CO is present in sufficient quantities 
-on the surface. For certain tested distributions of CO, the penalty was lowered 
-to $\sim$~20 kcal/mole. Once an adatom exists on the surface, its barrier for 
-diffusion is negligible ( \textless~4 kcal/mole) and is well able to explore the 
-terrace before potentially rejoining its original step-edge or becoming a part 
+energetic penalty around $\sim$~40 kcal/mol, but is much less 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, the penalty can be as low as 
+$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for 
+diffusion is negligible ( \textless~4 kcal/mol) and these adatoms are well 
+able to explore the terrace before rejoining either the original step-edge or becoming a part 
 of a different edge. Atoms traversing separate terraces is a more difficult 
 process, but can be overcome through a joining and lifting stage which is 
 examined in the discussion section. By tracking the mobility of individual 
 metal atoms on the Pt and Au surfaces we were able to determine the relative 
-diffusion rates and how varying coverages of CO affected the rates. Close 
+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, constantly breaking apart and rejoining. 
-At times their motion was concerted and two or more adatoms would be 
+equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. 
+At times, their motion was concerted and two or more adatoms would be 
 observed moving together across the surfaces. The primary challenge in 
 quantifying the overall surface mobility was in defining ``mobile" vs. ``static" atoms.
 
 A particle was considered mobile once it had traveled more than 2~\AA~
-between saved configurations of the system (10-100 ps). An atom that was 
-truly mobile would typically travel much greater than this, but the 2~\AA~ cutoff 
-was to prevent the in-place vibrational movement of non-surface atoms from 
-being included in the analysis. Diffusion on  a surface is strongly affected by 
-local structures and in this work the presence of single and double layer 
+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 
+was 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 different 
-from the diffusion perpendicular to these edges. This led us to compute 
-those diffusions separately as seen in Figure \ref{fig:diff}.
+from the diffusion perpendicular to these edges. Parallel and perpendicular
+diffusion constants are shown in Figure \ref{fig:diff}.
 
-\subsubsection{Double layer formation}
-The increased amounts of diffusion on Pt at the higher CO coverages appears
-to play a primary role in the formation of double layers, although this conclusion
-does not explain the 33\% coverage Pt system. On the 50\% system, three
-separate layers were formed over the extended run time of this system. As 
-mentioned earlier, previous experimental work has given some insight into the 
-upper bounds of the time required for enough atoms to move around to allow two 
-steps to coalesce\cite{Williams:1991,Pearl}. As seen in Figure \ref{fig:reconstruct},
-the first appearance of a double layer, a nodal site, appears at 19 ns into the 
-simulation. Within 12 ns, nearly half of the step has formed the double layer and 
-by 86 ns, a smooth complete layer has formed. The double layer is ``complete" by 
-37 ns but is a bit rough. From the appearance of the first node to the initial doubling 
-of the layers ignoring their roughness took $\sim$~20 ns. Another ~40 ns was 
-necessary for the layer to completely straighten. The other two layers in this 
-simulation form over a period of 22 ns and 42 ns respectively. Comparing this to 
-the upper bounds of the image scan, it is likely that aspects of this reconstruction 
-occur very quickly.
+\subsubsection{Double layer formation dynamics}
+The increased amounts of diffusion on Pt at the higher CO coverages plays a primary role in the formation of the double layers observed on Pt. However, this is not a complete explanation as seen by the 33\% Pt system which has higher diffusion constants but did not show any signs of undergoing the doubling. This difference will be explored more fully in the discussion. On the 50\% Pt system, three separate layers were formed over the extended run time of this system. Previous experimental work has given some insight into the upper bounds of the time required for step coalescing.\cite{Williams:1991,Pearl} In this system, as seen in Figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into the simulation. Within 12 ns, nearly half of the step has formed the double layer and by 86 ns, the complete layer has been smoothed. The double layer could be considered ``complete" by 37 ns but is a bit rough or wavy. From the appearance of the first node to the first observed double layer, ignoring roughening, 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 form over a period of 22 ns and 42 ns respectively. Comparing this to the upper bounds of the image scan, it is likely that aspects of this reconstruction occur very quickly. A possible explanation for this rapid reconstruction is the elevated temperatures our systems were run at. It is likely that the process would take longer at lower temperatures and is an area of exploration for future work.
 
 %Evolution of surface
 \begin{figure}[H]
@@ -503,38 +512,41 @@ Comparing the results from simulation to those reporte
 were able to observe the dynamic processes necessary for this reconstruction. 
 
 \subsection{Mechanism for restructuring}
-Comparing the results from simulation to those reported previously by 
+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}.
+Comparing the results from this simulation to those reported previously by 
 Tao et al.\cite{Tao:2010} the similarities in the Pt-CO system are quite 
 strong. As shown in Figure \ref{fig:reconstruct}, the simulated Pt 
-system under a CO atmosphere will restructure by doubling the terrace 
-heights. The restructuring occurs slowly, one to two Pt atoms at a time. 
+system exposed to a large dosage of CO will restructure by doubling the terrace 
+widths and step heights. The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a time and as such is a fairly stochastic event. 
 Looking at individual configurations of the system, the adatoms either 
 break away from the step-edge and stay on the lower terrace or they lift 
-up onto the higher terrace. Once ``free'' they will diffuse on the terrace 
-until reaching another step-edge or coming back to their original edge.  
+up onto the higher terrace. Once ``free'', they will 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 meeting 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.
+double layer tends to be fully formed within $\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 likely 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 perhaps, this explanation 
+relative to each other, through atop adsorption for example, this explanation 
 gains some weight.  The energetic repulsion between two CO located a 
 distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in 
-a  vertical orientation is 8.62 kcal/mole. Moving the CO apart to the second 
+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/mole. Allowing the CO's to leave a purely vertical orientation 
-also quickly drops the repulsion, a minimum is reached at $\sim$24 degrees 
-of 6.2 kcal/mole. As mentioned above, the energy barrier for surface diffusion 
-of a Pt adatom is only 4 kcal/mole. So this repulsion between CO can help 
-increase the surface diffusion. However, the residence time of CO was 
+nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation 
+also quickly drops the repulsion, a minimum of 6.2 kcal/mol is reached at $\sim$24 degrees between the 2 CO 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 CO can help 
+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, it is extremely mobile. This mobility suggests that the CO are more 
 likely to shift their positions without necessarily dragging the Pt along with them.
@@ -620,7 +632,7 @@ In this work we have shown the reconstruction of the P
 
 
 \section{Conclusion}
-In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in < $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems. 
+In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in less than a $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems. 
 
 %Things I am not ready to remove yet