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Revision 3826 by gezelter, Wed Dec 19 21:37:51 2012 UTC vs.
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# Line 193 | Line 193 | manner. We used a model first proposed by Karplus and
193   Since previous explanations for the surface rearrangements center on
194   the large linear quadrupole moment of carbon monoxide, the model
195   chosen for this molecule exhibits this property in an efficient
196 < manner. We used a model first proposed by Karplus and Straub to study
197 < the photodissociation of CO from myoglobin.\cite{Straub} The Straub
198 < and Karplus model is a rigid linear three site model which places a
199 < massless (M) site at the center of mass along the CO bond.  The
200 < geometry and interaction parameters are reproduced in Table 1. The
201 < effective dipole moment, calculated from the assigned charges, is
202 < still small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is
203 < close to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
196 > manner.  We used a model first proposed by Karplus and Straub to study
197 > the photodissociation of CO from myoglobin.\cite{Straub} The Straub and
198 > Karplus model is a rigid three site model which places a massless M
199 > site at the center of mass along the CO bond.  The geometry used along
200 > with the interaction parameters are reproduced in Table~1. The effective
201 > dipole moment, calculated from the assigned charges, is still
202 > small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close
203 > to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum
204   mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}.
205   %CO Table
206   \begin{table}[H]
# Line 316 | Line 316 | Our model systems are composed of 3888 Pt atoms and XX
316  
317   \subsection{Pt(557) and Au(557) metal interfaces}
318  
319 < Our model systems are composed of 3888 Pt atoms and XXXX Au atoms in a
319 > Our model systems are composed of 3888 Pt atoms and 3384 Au atoms in a
320   FCC crystal that have been cut along the 557 plane so that they are
321   periodic in the {\it x} and {\it y} directions, and have been rotated
322   to expose two parallel 557 cuts along the positive and negative {\it
# Line 343 | Line 343 | source molecular dynamics package, OpenMD.\cite{Ewald,
343   source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,OpenMD}
344  
345   % Just results, leave discussion for discussion section
346 + % structure
347 + %       Pt: step wandering, double layers, no triangular motifs
348 + %       Au: step wandering, no double layers
349 + % dynamics
350 + %       diffusion
351 + %       time scale, formation, breakage
352   \section{Results}
353 < Tao {\it et al.} showed experimentally that the Pt(557) surface
354 < undergoes two separate reconstructions upon CO
355 < adsorption.\cite{Tao:2010} The first reconstruction involves a
356 < doubling of the step edge height which is accomplished by a doubling
357 < of the plateau length. The second reconstruction led to the formation
358 < of triangular clusters that arrange themselves along the lengthened
359 < plateaus.
353 > \subsection{Structural remodeling}
354 > Tao {\it et al.} showed experimentally that the Pt(557) surface undergoes
355 > two separate reconstructions upon CO adsorption.\cite{Tao:2010} The first
356 > reconstruction involves a doubling of the step height and plateau length. Similar
357 > behavior has been seen to occur on numerous surfaces at varying conditions.\cite{Williams:1994,Williams:1991,Pearl}
358 > Of the two systems we examined, the Platinum system showed the most surface
359 > reconstruction. Additionally, the amount of reconstruction appears to be
360 > dependent on the amount of CO adsorbed upon the surface. This result is likely
361 > related to the effect that coverage has on surface diffusion. While both systems
362 > displayed step edge wandering, only the Pt surface underwent doubling within
363 > the time scales we were modeling. Specifically only the 50 \% coverage Pt system
364 > was observed to undergo a complete doubling in the time scales we were able to monitor.
365 > This event encouraged us to allow that specific system to run continuously during which two
366 > more double layers were created. The other systems, not displaying any large scale changes
367 > of interest, were all stopped after 40 ns of simulation. Neverthless, the other Platinum systems tended to show
368 > more cumulative lateral movement of the step edges when compared to the Gold systems.
369 > The 50 \% Pt system is highlighted in figure \ref{fig:reconstruct} at various times along the
370 > simulation showing the evolution of the system.
371  
372 < The primary observation and results of our simulation is that the
373 < presence of CO overlayer on Pt(557) causes the same kind of
374 < reconstruction observed experimentally. The 6-atom 111 facets
375 < initially become disordered, and after 20-40 ns, a double-layer (with
376 < a 2-atom step between terraces) forms.  However, we did not observe
360 < the triangular cluster formation that was observed at longer times in
361 < the experiments.  Without the CO present on the Pt(557) surface, there
362 < was some disorder at the step edges, but no significant restructuring
363 < was observed.
372 > The second reconstruction on the Pt(557) surface observed by Tao involved the
373 > formation of triangular clusters that stretched across the plateau between two step edges.
374 > Neither system, within our simulated time scales, experiences this reconstruction. A constructed
375 > system in which the triangular motifs were constructed on the surface will be explored in future
376 > work and is shown in the supporting information.
377  
378 < In these simulations, the Au(557) surface did not exhibit any
379 < significant restructuring either with or without the presence of a CO
380 < overlayer.
378 > \subsection{Dynamics}
379 > While atomistic-like simulations of stepped surfaces have been performed before \cite{}, they tend to be
380 > performed using Monte Carlo techniques\cite{Williams:1991,Williams:1994}. This allows them to efficiently sample the thermodynamic
381 > landscape but at the expense of ignoring the dynamics of the system. Previous work, using STM \cite{Pearl},
382 > has been able to visualize the coalescing of steps of (system). The time scale of the image acquisition, ~ 70 s/image
383 > provides an upper bounds for the time required for the doubling to actually occur. While statistical treatments
384 > of step edges are adept at analyzing such systems, it is important to remember that the edges are made
385 > up of individual atoms and thus can be examined in numerous ways.
386  
387 < \subsection{Transport of surface metal atoms}
388 < An ideal metal surface displaying a low energy (111) face is unlikely
389 < to experience much surface diffusion because of the large vacancy
390 < formation energy for atoms at the surface.  This implies that
391 < significant energy must be expended to lift an atom out of the flat
392 < face so it can migrate on the surface.  Rougher surfaces and those
393 < that already contain numerous adatoms, step edges, and kinks, are
394 < expected to have higher surface diffusion rates.  Metal atoms that are
395 < mobile on the surface were observed to leave and then rejoin step
396 < edges or other formations. They may travel together or as isolated
397 < atoms.  The primary challenge of quantifying the overall surface
398 < mobility is in defining ``mobile'' vs. ``static'' atoms.
387 > \subsubsection{Transport of surface metal atoms}
388 > %forcedSystems/stepSeparation
389 > The movement of a step edge is a cooperative effect arising from the individual movements of the atoms
390 > making up the step. An ideal metal surface displaying a low index facet (111, 100, 110) is unlikely to
391 > experience much surface diffusion because of the large energetic barrier to lift an atom out of the surface.
392 > For our surfaces however, the presence of step edges provide a source for mobile metal atoms. Breaking away
393 > from the step edge still imposes an energetic penalty around 40 kcal/mole, but is much less than lifting the same metal
394 > atom out from the surface,  > 60 kcal/mole, and the penalty lowers even further when CO is present in sufficient quantities
395 > on the surface, ~20 kcal/mole. Once an adatom exists on the surface, its barrier for diffusion is negligible ( < 4 kcal/mole)
396 > and is well able to explore its terrace. Atoms traversing terraces is more difficult, but can be overcome through a joining and lifting stage.
397 > By tracking the mobility of individual metal atoms on the Platinum and Gold surfaces we were able to determine
398 > the relative diffusion rates and how varying coverages of CO affected the rates. Close
399 > observation of the mobile metal atoms showed that they were typically in equilibrium with the
400 > step edges, constantly breaking apart and rejoining. Additionally, at times their motion was concerted and
401 > two or more atoms would be observed moving together across the surfaces. The primary challenge in quantifying
402 > the overall surface mobility was in defining ``mobile" vs. ``static" atoms.
403  
404 < A particle was considered mobile once it had traveled more than 2~\AA~
405 < between saved configurations (XX ps). Restricting the transport
406 < calculations to only mobile atoms eliminates all of the bulk metal as
407 < well as any surface atoms that remain fixed for a significant length
408 < of time.  Since diffusion on a surface is strongly affected by local
409 < structures, the diffusion parallel to the step edges was determined
388 < separately from the diffusion perpendicular to these edges.  The
389 < parallel and perpendicular diffusion constants (determined using
390 < linear fits to the mean squared displacement) are shown in figure \ref{fig:diff}.
404 > A particle was considered mobile once it had traveled more than 2~\AA~ between saved configurations
405 > of the system (10-100 ps). An atom that was truly mobile would typically travel much greater than this, but
406 > the 2~\AA~ cutoff was to prevent the in-place vibrational movement of atoms from being included in the analysis.
407 > Since diffusion on  a surface is strongly affected by local structures, in this case the presence of single and double
408 > layer step edges, the diffusion parallel to the step edges was determined separately from the diffusion perpendicular
409 > to these edges. The parallel and perpendicular diffusion constants are shown in figure \ref{fig:diff}.
410  
411 < %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.
411 > \subsubsection{Double layer formation}
412 > The increased amounts of diffusion on Pt at the higher CO coverages appears to play a role in the
413 > formation of double layers, seeing as how that was the only system within our observed simulation time
414 > that showed the formation. Despite this being the only system where this reconstruction occurs, three separate layers
415 > were formed over the extended run time of this system. As mentioned earlier, previous experimental work has given some insight into
416 > the upper bounds of the time required for enough atoms to move around to allow two steps to coalesce\cite{Williams:1991,Pearl}.
417 > As seen in figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into
418 > the simulation. Within 12 ns, nearly half of the step has formed the double layer and by 86 ns, a smooth complete
419 > layer has formed. The double layer is complete by 37 ns but is a bit rough.
420 > From the appearance of the first node to the initial doubling of the layers ignoring their roughness took ~20 ns.
421 > Another ~40 ns was necessary for the layer to completely straighten. The other two layers in this simulation form
422 > over a period of 22 ns and 42 ns respectively.
423  
424 + %Evolution of surface
425   \begin{figure}[H]
426 < \includegraphics[scale=0.6]{DiffusionComparison_error.png}
426 > \includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
427 > \caption{The Pt(557) / 50\% CO system at a sequence of times after
428 >  initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and
429 >  (d) 86.1 ns. Disruption of the 557 step edges occurs quickly.  The
430 >  doubling of the layers appears only after two adjacent step edges
431 >  touch.  The circled spot in (b) nucleated the growth of the double
432 >  step observed in the later configurations.}
433 >  \label{fig:reconstruct}
434 > \end{figure}
435 >
436 > \begin{figure}[H]
437 > \includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf}
438   \caption{Diffusion constants for mobile surface atoms along directions
439    parallel ($\mathbf{D}_{\parallel}$) and perpendicular
440    ($\mathbf{D}_{\perp}$) to the 557 step edges as a function of CO
# Line 407 | Line 449 | linear fits to the mean squared displacement) are show
449   \label{fig:diff}
450   \end{figure}
451  
452 < %Table of Diffusion Constants
411 < %Add gold?M
412 < % \begin{table}[H]
413 < %   \caption{}
414 < %   \centering
415 < % \begin{tabular}{| c | cc | cc | }
416 < %   \hline
417 < %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
418 < %   \hline
419 < %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
420 < %   \hline
421 < %   50\% & 4.32(2) & 1.185 $\pm$ 0.008 & 1.72 $\pm$ 0.02 & 0.455 $\pm$ 0.006 \\
422 < %   33\% & 5.18 $\pm$ 0.03 & 1.999 $\pm$ 0.005 & 1.95 $\pm$ 0.02 & 0.337 $\pm$ 0.004  \\
423 < %   25\% & 5.01 $\pm$ 0.02 & 1.574 $\pm$ 0.004 & 1.26 $\pm$ 0.03 & 0.377 $\pm$ 0.006 \\
424 < %   5\%   & 3.61 $\pm$ 0.02 & 0.355 $\pm$ 0.002 & 1.84 $\pm$ 0.03 & 0.169 $\pm$ 0.004 \\
425 < %   0\%   & 3.27 $\pm$ 0.02 & 0.147 $\pm$ 0.004 & 1.50 $\pm$ 0.02 & 0.194 $\pm$ 0.002  \\
426 < %   \hline
427 < % \end{tabular}
428 < % \end{table}
452 >
453  
454 +
455   %Discussion
456   \section{Discussion}
457 + In this paper we have shown that we were able to accurately model the initial reconstruction of the
458 + Pt (557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we
459 + were able to capture the dynamic processes inherent within this reconstruction.
460  
461 < Mechanism for restructuring
461 > \subsection{Mechanism for restructuring}
462 > The increased computational cost to examine this system using molecular dynamics rather than
463 > a Monte Carlo based approach was necessary so that our predictions on possible mechanisms
464 > and driving forces would have support not only from thermodynamic arguments but also from the
465 > actual dynamics of the system.
466  
435 There are a number of possible mechanisms to explain the role of
436 adsorbed CO in restructuring the Pt surface. Quadrupolar repulsion
437 between adjacent CO molecules adsorbed on the surface is one
438 possibility.  However, the quadrupole-quadrupole interaction is
439 short-ranged and is attractive for some orientations.  If the CO
440 molecules are locked in a specific orientation relative to each other,
441 this explanation gains some weight.  
442
443 Another possible mechanism for the restructuring is in the
444 destabilization of strong Pt-Pt interactions by CO adsorbed on surface
445 Pt atoms.  This could have the effect of increasing surface mobility
446 of these atoms.  
447
467   Comparing the results from simulation to those reported previously by
468   Tao et al. the similarities in the platinum and CO system are quite
469 < strong. As shown in figure, the simulated platinum system under a CO
469 > strong. As shown in figure \ref{fig:reconstruct}, the simulated platinum system under a CO
470   atmosphere will restructure slightly by doubling the terrace
471   heights. The restructuring appears to occur slowly, one to two
472   platinum atoms at a time. Looking at individual snapshots, these
# Line 463 | Line 482 | $\sim$~35 ns.
482   growth point, the double layer tends to be fully formed within
483   $\sim$~35 ns.
484  
485 + There are a number of possible mechanisms to explain the role of
486 + adsorbed CO in restructuring the Pt surface. Quadrupolar repulsion
487 + between adjacent CO molecules adsorbed on the surface is one
488 + possibility.  However, the quadrupole-quadrupole interaction is
489 + short-ranged and is attractive for some orientations.  If the CO
490 + molecules are ``locked'' in a specific orientation relative to each other however,
491 + this explanation gains some weight.  The energetic repulsion between two CO
492 + located a distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in a
493 + vertical orientation is 8.62 kcal/mole. Moving the CO apart to the second nearest-neighbor
494 + distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to nearly 0 kcal/mole. SHOW A NUMBER FOR ROTATION.
495 + As mentioned above, the energy barrier for surface diffusion of a platinum adatom is only 4 kcal/mole. So this
496 + repulsion between CO can help increase the surface diffusion. However, the residence time of CO was examined
497 + and while the majority of the CO is on or near the surface throughout the run, it is extremely mobile. This mobility
498 + suggests that the CO are more likely to shift their positions without necessarily dragging the platinum along
499 + with them.
500 +
501 + Another possible and more likely mechanism for the restructuring is in the
502 + destabilization of strong Pt-Pt interactions by CO adsorbed on surface
503 + Pt atoms.  This could have the effect of increasing surface mobility
504 + of these atoms.  To test this hypothesis, numerous configurations of
505 + CO in varying quantities were arranged on the higher and lower plateaus
506 + around a step on a otherwise clean Pt (557) surface. One representative
507 + configuration is displayed in figure \ref{fig:lambda}. Single or concerted movement
508 + of platinum atoms was then examined to determine possible barriers. Because
509 + of the forced movement along a pre-defined reaction coordinate that may differ
510 + from the true minimum of this path, only the beginning and ending energies
511 + are displayed in table \ref{tab:energies}. The presence of CO at suitable
512 + sites can lead to lowered barriers for platinum breaking apart from the step edge.
513 + Additionally, as highlighted in figure \ref{fig:lambda}, the presence of CO makes the
514 + burrowing and lifting nature favorable, whereas without CO, the process is neutral
515 + in terms of energetics.
516 +
517 + %lambda progression of Pt -> shoving its way into the step
518 + \begin{figure}[H]
519 + \includegraphics[width=\linewidth]{lambdaProgression_atopCO.png}
520 + \caption{A model system of the Pt 557 surface was used as the framework for a reaction coordinate.
521 + Various numbers, placements, and rotations of CO were examined. The one displayed was a
522 + representative sample. As shown in Table , relative to the energy at 0\% there is a slight decrease
523 + upon insertion of the platinum atom into the step edge along with the resultant lifting of the other
524 + platinum atom.}
525 + \label{fig:lambda}
526 + \end{figure}
527 +
528 +
529 +
530   \subsection{Diffusion}
531 < 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?)
531 > As shown in the results section, the diffusion parallel to the step edge tends to be
532 > much faster than that perpendicular to the step edge. Additionally, the coverage
533 > of CO appears to play a slight role in relative rates of diffusion, as shown in figure \ref{fig:diff}
534 > Thus, the bottleneck of the double layer formation appears to be the initial formation
535 > of this growth point, which seems to be somewhat of a stochastic event. Once it
536 > appears, parallel diffusion, along the now slightly angled step edge, will allow for
537 > a faster formation of the double layer than if the entire process were dependent on
538 > only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the
539 > more likely a growth point is to be formed.
540   \\
541 < \\
542 < %Evolution of surface
541 >
542 >
543 > %breaking of the double layer upon removal of CO
544   \begin{figure}[H]
545 < \includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png}
546 < \caption{The Pt(557) / 50\% CO system at a sequence of times after
547 <  initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and
475 <  (d) 86.1 ns. Disruption of the 557 step edges occurs quickly.  The
476 <  doubling of the layers appears only after two adjacent step edges
477 <  touch.  The circled spot in (b) nucleated the growth of the double
478 <  step observed in the later configurations.}
545 > \includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png}
546 > \caption{Hi}
547 > \label{fig:breaking}
548   \end{figure}
549  
550  
551 +
552 +
553   %Peaks!
554   \begin{figure}[H]
555   \includegraphics[width=\linewidth]{doublePeaks_noCO.png}
556   \caption{}
557 + \label{fig:peaks}
558   \end{figure}
559 +
560 + %clean surface...
561 + \begin{figure}[H]
562 + \includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf}
563 + \caption{}
564 +
565 + \end{figure}
566 + \label{fig:clean}
567   \section{Conclusion}
568  
569  
570 + %Things I am not ready to remove yet
571 +
572 + %Table of Diffusion Constants
573 + %Add gold?M
574 + % \begin{table}[H]
575 + %   \caption{}
576 + %   \centering
577 + % \begin{tabular}{| c | cc | cc | }
578 + %   \hline
579 + %   &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\
580 + %   \hline
581 + %   \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$  \\
582 + %   \hline
583 + %   50\% & 4.32(2) & 1.185(8)  & 1.72(2) & 0.455(6) \\
584 + %   33\% & 5.18(3)  & 1.999(5)  & 1.95(2) & 0.337(4)   \\
585 + %   25\% & 5.01(2)  & 1.574(4)  & 1.26(3) & 0.377(6) \\
586 + %   5\%   & 3.61(2)  & 0.355(2)  & 1.84(3)  & 0.169(4)  \\
587 + %   0\%   & 3.27(2)  & 0.147(4)  & 1.50(2)  & 0.194(2)   \\
588 + %   \hline
589 + % \end{tabular}
590 + % \end{table}
591 +
592   \section{Acknowledgments}
593   Support for this project was provided by the National Science
594   Foundation under grant CHE-0848243 and by the Center for Sustainable

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