--- trunk/COonPt/firstTry.tex	2012/12/13 22:42:37	3811
+++ trunk/COonPt/firstTry.tex	2012/12/17 16:50:21	3818
@@ -1,9 +1,12 @@
 \documentclass[11pt]{article}
 \usepackage{amsmath}
 \usepackage{amssymb}
+\usepackage{times}
+\usepackage{mathptm}
 \usepackage{setspace}
-\usepackage{endfloat}
+\usepackage{float}
 \usepackage{caption}
+
 %\usepackage{tabularx}
 \usepackage{graphicx}
 \usepackage{multirow}
@@ -18,7 +21,7 @@
 9.0in \textwidth 6.5in \brokenpenalty=10000
 
 % double space list of tables and figures
-\AtBeginDelayedFloats{\renewcommand{\baselinestretch}{1.66}}
+%\AtBeginDelayedFloats{\renewcommand{\baselinestretch}{1.66}}
 \setlength{\abovecaptionskip}{20 pt}
 \setlength{\belowcaptionskip}{30 pt}
 
@@ -48,15 +51,18 @@
 %%
 
 %Title
-\title{Investigation of the Pt and Au 557 Surface Reconstructions
-  under a CO Atmosphere}
-\author{Joseph R. Michalka, Patrick W. MacIntyre and J. Daniel
+\title{Molecular Dynamics simulations of the surface reconstructions
+  of Pt(557) and Au(557) under exposure to CO}
+
+\author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel
 Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\
 Department of Chemistry and Biochemistry,\\
 University of Notre Dame\\
 Notre Dame, Indiana 46556}
+
 %Date
-\date{Dec 15,  2012}
+\date{Dec 15, 2012}
+
 %authors
 
 % make the title
@@ -109,17 +115,13 @@ reconstruct under certain conditions. The Au(557) surf
 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 will provide a
-useful counterpoint
-
+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.
 %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
@@ -200,23 +202,27 @@ site at the center of mass along the CO bond.  The geo
 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 along with the interaction
-parameters are reproduced in Table 1. The effective dipole moment is still
+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 mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
+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, $\sigma$, $\epsilon$ and charges for CO geometry 
+and self-interactions\cite{Straub}. Distances are in \AA~, energies are 
+in kcal/mol, and charges are in $e$.}
 \centering
 \begin{tabular}{| c | c | ccc |}
 \hline
 \multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\
 \hline
-&  r & $\sigma$ & $\epsilon$ & q\\
+&  {\it z} & $\sigma$ & $\epsilon$ & q\\
 \hline
-\textbf{C} & 0.0 &  0.0262  & 3.83   &   -0.75 \\
-\textbf{O} &  1.13 &   0.1591 &   3.12 &   -0.85 \\
-\textbf{M} & 0.6457 & -  &  -  &    1.6 \\
+\textbf{C} & -0.6457 &  0.0262  & 3.83   &   -0.75 \\
+\textbf{O} &  0.4843 &   0.1591 &   3.12 &   -0.85 \\
+\textbf{M} & 0.0 & -  &  -  &    1.6 \\
 \hline
 \end{tabular}
 \end{table}
@@ -224,31 +230,83 @@ is the proper parameterization of all of the potential
 \subsection{Cross-Interactions}
 
 One hurdle that must be overcome in classical molecular simulations 
-is the proper parameterization of all of the potential interactions present
-in the system. CO adsorbed on 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} 
-We started with parameters reported by Korzeniewski et al. \cite{Pons:1986} and then
+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. 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. The resultant potential-energy
-surface suitably recovers the calculated Pt-CO bond length (1.1 \AA)\cite{Deshlahra:2012} and affinity
+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}
 
-The Au-C and Au-O interaction parameters were fit to a Lennard-Jones and Morse potential respectively. The binding energies were obtained from quantum calculations carried out using <functional> for gold. 
+%where did you actually get the functionals for citation?
+%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think
+%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there...
+The Au-C and Au-O cross-interactions were fit using Lennard-Jones and
+Morse potentials, respectively, to reproduce Au-CO binding energies.
 
-Numerous single point calculations were performed at various distances of the CO
+The fits were refined against gas-surface calculations using DFT 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
+included to an energy cutoff of 20 Ry. Electronic energies are
+computed with the PBE implementation of the generalized gradient
+approximation (GGA) for gold, carbon, and oxygen that was constructed
+by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP}
+Ionic relaxations were performed until the energy difference between
+subsequent steps was less than 0.0001 eV.  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. 
+
+%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. The bare crystals were initially run in the Canonical ensemble at 1000K and 800K respectively for Pt and Au. The difference in temperature is necessary because of the two metals different melting points. Various amounts of CO were added to the simulation box and allowed to absorb to the metal surfaces over a short period of 100 ps. After further thermal relaxation the simulations were all run for at least 40 ns. A subset of the runs that showed interesting effects were allowed to run longer. The system
+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}
 
 
-Our model systems are composed of approximately 4000 metal atoms cut along the 557 plane. This cut creates a stepped surface of 6x(111) surface plateaus separated by a single (100) atomic step height. The abundance of low-coordination atoms along the step edges acts as a suitable model for industrial catalysts which tend to have a high concentration of high-index sites. Experimental work has shown that such surfaces are notable for reconstructing upon adsorption\cite{}. Reconstructions have been seen for the Pt 557 surface that involve doubling of the step height and further formation of nano clusters with a triangular motif \cite{doi:10.1126/science.1182122}. To shed insight on whether this reconstruction is limited to the platinum surface, simulations of gold under similar conditions will also be examined. To properly observe these changes, our system size needs to be greater than the periodic phenomena we are examining. The large size and the long time scales needed precluded us from using quantum approaches. Thus, a forcefield describing the Metal-Metal, CO-CO, and CO-Metal interactions was parameterized and the simulations were run using OpenMD\cite{} an open-source molecular dynamics package.
 
 
 
@@ -285,7 +343,7 @@ Our model systems are composed of approximately 4000 m
  & Calc. & Exp. \\
 \hline
 \textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\
-\textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\
+\textbf{Au-CO} & -0.39 & -0.40~\cite{TPD_Gold} \\
 \hline
 \end{tabular}
 \end{table}
@@ -298,28 +356,53 @@ While an ideal metallic surface is unlikely to experie
 % Just results, leave discussion for discussion section
 \section{Results}
 \subsection{Diffusion}
-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 been running continuously. The lowered diffusion constant at longer run times will be examined in-depth in the discussion section.
+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. 
 
+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.
+
+%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. }
+\end{figure}
+
 %Table of Diffusion Constants
 %Add gold?M
 \begin{table}[H]
-\caption{Platinum 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. There were two approaches of analysis. One looking at the surface atoms that had moved more than a prescribed amount over the run time and the other looking at all surface atoms. Units are \AA\textsuperscript{2}/ns}
+\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 | ccc | ccc | c |}
+\begin{tabular}{| c | cc | cc | c |}
 \hline
-\textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & \textbf{Time (ns)}\\
+\textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  & \textbf{Time (ns)}\\
 \hline
-&\multicolumn{3}{c|}{\textbf{Mobile}}&\multicolumn{3}{c|}{\textbf{Surface Atoms}} & \\
+&\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} & \\
 \hline
-50\% & 3.74 & 0.89 & 497 & 2.05 & 0.49 & 912 & 116 \\
-50\% & 5.81 & 1.59 & 365 & 2.41 & 0.68 & 912 & 46   \\
-33\% & 6.73 & 2.47 & 332 & 2.51 & 0.93 & 912 & 46   \\
-25\% & 5.38 & 2.04 & 361 & 2.18 & 0.84 & 912 & 46  \\
-5\% & 5.54 & 0.63 & 230 & 1.44 & 0.19 & 912 & 46  \\
-0\% & 3.53 & 0.61 & 282 & 1.11 & 0.22 & 912 & 56  \\
-\hline
-50\%-r & 6.91 & 2.00 & 198 & 2.23 & 0.68  & 925 & 25\\
-0\%-r  & 4.73 & 0.27 & 128 & 0.72 & 0.05 & 925 & 43\\
+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}
@@ -328,7 +411,7 @@ Comparing the results from simulation to those reporte
 
 %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.
+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.
 
 \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?)
@@ -337,14 +420,17 @@ As shown in the results section, the diffusion paralle
 %Evolution of surface
 \begin{figure}[H]
 \includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
-\caption{Four snapshots at various times a) 258 ps b) 19 ns c) 31.2 ns 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.}
+\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.}
 \end{figure}
 
 
 
 
 %Peaks!
+\begin{figure}[H]
 \includegraphics[scale=0.25]{doublePeaks_noCO.png}
+\caption{}
+\end{figure}
 \section{Conclusion}
 
 
