--- trunk/COonPt/firstTry.tex	2013/03/11 22:37:32	3872
+++ trunk/COonPt/firstTry.tex	2013/03/12 21:33:15	3873
@@ -378,8 +378,8 @@ phase.  These systems were allowed to reach thermal eq
 Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while
 the Au surfaces often had a significant CO population in the gas
 phase.  These systems were allowed to reach thermal equilibrium (over
-5 ns) before being run in the microcanonical (NVE) ensemble for
-data collection. All of the systems examined had at least 40 ns in the
+5~ns) before being run in the microcanonical (NVE) ensemble for
+data collection. All of the systems examined had at least 40~ns in the
 data collection stage, although simulation times for some Pt of the
 systems exceeded 200~ns.  Simulations were carried out using the open
 source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE}
@@ -393,57 +393,68 @@ metal system. The surfaces to which no CO was exposed 
 \subsection{Structural remodeling}
 The surfaces of both systems, upon dosage of CO, began 
 to undergo remodeling that was not observed in the bare 
-metal system. The surfaces to which no CO was exposed 
-did experience minor roughening of the step-edge, but the 
+metal system. The surfaces which were not exposed to CO 
+did experience 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 formed double layers at numerous spots upon its surface.
+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}
 
 
 \subsubsection{Step wandering}
-The 0\% coverage surfaces for both metals showed 
-minimal movement at their respective run temperatures. 
-As the coverage increased, the mobility of the surface 
-also increased. Additionally, at the higher coverages 
-on both metals, there was a large increase in the amount 
-of observed step-wandering. Previous work by 
-Williams\cite{Williams:1993} highlighted the entropic 
-contribution to the repulsion felt between step-edges, 
-and situations were that repulsion could be negated, or 
-overcome, to allow for step coalescence or facet formation.
+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, 
+adatoms and step-edges alike, also increased. Additionally, 
+at the higher coverages on both metals, there was more 
+step-wandering. 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. Previous work by Williams 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 exists because the entropy of the step-edges is constrained 
+since step-edge crossing is not allowed. 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} and others will not. The presence 
+of adsorbates can affect these step interactions, potentially 
+leading to a new surface structure as the thermodynamic minimum.
 
 \subsubsection{Double layers}
 Tao et al. have shown experimentally that the Pt(557) surface 
-undergoes two separate reconstructions upon CO 
-adsorption.\cite{Tao:2010} The first involves a doubling of 
-the step height and plateau length. Similar behavior has been 
-seen to occur on numerous surfaces at varying conditions: Ni(977), 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. The amount 
-of reconstruction is correlated to the amount of CO 
+undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} 
+The first involves a doubling of the step height and plateau length. 
+Similar behavior has been seen to occur on numerous surfaces 
+at varying conditions: Ni(977), 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 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 Pt surface underwent the doubling seen by 
-Tao et al. within the time scales studied here.  
-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 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.
+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. 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 
+50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at 
+various times along the simulation showing the evolution of a 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 40~ns time scale, experienced this reconstruction.
+the 40~ns time scale or the extended simulation time of 150~ns for 
+the 50\% Pt system, experienced this reconstruction.
 
 \subsection{Dynamics}
 Previous atomistic simulations of stepped surfaces dealt largely
@@ -451,8 +462,8 @@ of ignoring the dynamics of the system. Previous work 
 \cite{Williams:1991,Williams:1994}. Consequently, the most common 
 technique utilized to date has been Monte Carlo sampling. 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 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. In this section we give data on dynamic and 
@@ -462,19 +473,18 @@ arising from the individual movements, primarily throu
 \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 steps. An ideal metal surface 
+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 
-on higher-index surfaces provide a source for mobile metal atoms. 
+be overcome to lift an atom out of the surface. The presence of step-edges and other surface features
+on higher-index facets provide a lower energy source for mobile metal atoms. 
 Breaking away from the step-edge on a clean surface still imposes an 
 energetic penalty around $\sim$~40 kcal/mol, but this is significantly 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, the penalty can fall 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 
+diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are 
 able to explore the terrace before rejoining either the original step-edge or 
 becoming a part of a different edge. It is a more difficult process for an atom 
 to traverse to a separate terrace although the presence of CO can lower the 
@@ -490,26 +500,53 @@ movement of buried atoms. Diffusion on  a surface is s
 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 used to prevent swamping the diffusion data with the in-place vibrational 
-movement of buried atoms. Diffusion on  a surface is strongly affected by 
+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. Parallel and perpendicular
 diffusion constants are shown in Figure \ref{fig:diff}.
 
+The lack of a definite trend in the Au diffusion data is likely due 
+to the weaker bonding between Au and CO. This leads to a lower 
+coverage ({\it x}-axis) when compared to dosage amount, which 
+then further limits the affects of the 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 is no longer a good source for adatoms. By 
+performing the same diffusion calculation but on a shorter run time 
+(20~ns), only including data before the formation of the double layer, 
+provides a $\mathbf{D}_{\perp}$ diffusion constant of $1.69~\pm~0.08$ 
+and a $\mathbf{D}_{\parallel}$ diffusion constant of $6.30~\pm~0.08$. 
+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 show the affect 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 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.
+
 \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. On the 
-50\%~Pt system, three separate layers were formed over 
-150~ns of simulation time. Previous experimental 
+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 run for an additional
+110~ns (150~ns total). Previous experimental 
 work gives insight into the upper bounds of the 
 time required for step coalescence.\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 
+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 
@@ -526,8 +563,8 @@ take longer at lower temperatures.
 \begin{figure}[H]
 \includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
 \caption{The Pt(557) / 50\% CO system at a sequence of times after
-  initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and
-  (d) 86.1 ns. Disruption of the (557) step-edges occurs quickly.  The
+  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.}
@@ -574,7 +611,7 @@ From simulations which exhibit a double layer, the tim
 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.
+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 
@@ -605,7 +642,7 @@ are displayed in Table \ref{tab:energies}. These value
 of Pt atoms was then examined to determine possible barriers. Because
 the movement was forced along a pre-defined reaction coordinate that may differ
 from the true minimum of this path, only the beginning and ending energies
-are displayed in Table \ref{tab:energies}. These values suggest that the presence of CO at suitable
+are displayed in Table \ref{tab:energies} with the corresponding beginning and ending reaction coordinates in Figure \ref{fig:lambdaTable}. These values suggest that the presence of CO at suitable
 locations can lead to lowered barriers for Pt breaking apart from the step-edge.
 Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the
 burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral
@@ -613,7 +650,7 @@ in terms of energetics.
 
 %lambda progression of Pt -> shoving its way into the step
 \begin{figure}[H]
-\includegraphics[width=\linewidth]{lambdaProgression_atopCO.png}
+\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png}
 \caption{A model system of the Pt(557) surface was used as the framework
  for exploring energy barriers along a reaction coordinate. Various numbers,
  placements, and rotations of CO were examined as they affect Pt movement.
@@ -624,6 +661,11 @@ in terms of energetics.
 \label{fig:lambda}
 \end{figure}
 
+\begin{figure}[H]
+\includegraphics[totalheight=0.9\textheight]{lambdaTable.png}
+\caption{}
+\label{fig:lambdaTable}
+\end{figure}
 
 
 \subsection{Diffusion}
@@ -644,8 +686,7 @@ more likely a growth point is to be formed. 
 %breaking of the double layer upon removal of CO
 \begin{figure}[H]
 \includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png}
-%:
-\caption{(A)  0 ps, (B) 100 ps, (C) 1 ns, after the removal of CO. The presence of the CO
+\caption{(A)  0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO
  helped maintain the stability of the double layer and upon removal the two layers break
  and begin separating. The separation is not a simple pulling apart however, rather 
  there is a mixing of the lower and upper atoms at the edge.}