| 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{} |
| 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 doubling in the time scales we were able to monitor. |
| 365 |
< |
Although, the other Platinum systems tended to show more cumulative lateral movement of |
| 366 |
< |
the step edges when compared to the Gold systems. The 50 \% Pt system is highlighted |
| 367 |
< |
in figure \ref{fig:reconstruct} at various times along the simulation showing |
| 368 |
< |
the evolution of the 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 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. |
| 376 |
|
work and is shown in the supporting information. |
| 377 |
|
|
| 378 |
|
\subsection{Dynamics} |
| 379 |
< |
While atomistic simulations of stepped surfaces have been performed before \cite{}, they tend to be |
| 380 |
< |
performed using Monte Carlo techniques\cite{}. 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{}, |
| 382 |
< |
has been able to visualize the coalescing of steps of (system). The time scale of the image acquisition |
| 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 |
|
\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, the presence of step edges provide a source for mobile metal atoms. Breaking away |
| 393 |
< |
from the step edge is still an energetic penalty around (value) but is much less than lifting the same metal |
| 394 |
< |
atom out from the surface and the penalty lowers even further when CO is present in sufficient quantities |
| 395 |
< |
on the surface. 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 because both steps act as barriers constraining the area in which |
| 397 |
< |
diffusion is allowed. By tracking the mobility of individual metal atoms on the surface we were able to determine |
| 398 |
< |
the relative diffusion rates and how varying coverages of CO affected the diffusion constants. Close |
| 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 is in defining ``mobile" vs. ``static" atoms. |
| 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~ 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. |
| 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 |
|
\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. As mentioned earlier, previous experimental work has given some insight into |
| 415 |
< |
the upper bounds of the time required for enough atoms to move around to allow two steps to coalesce\cite{}. |
| 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 10 ns, nearly half of the step has formed the double layer and by 86 ns, the complete |
| 419 |
< |
layer has formed. From the appearance of the first node to the complete doubling of the layers, only ~65 ns |
| 420 |
< |
have elapsed. The other two layers in this simulation form over a period of ---- and ---- ns respectively. |
| 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[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 |
| 449 |
|
\label{fig:diff} |
| 450 |
|
\end{figure} |
| 451 |
|
|
| 434 |
– |
%Table of Diffusion Constants |
| 435 |
– |
%Add gold?M |
| 436 |
– |
% \begin{table}[H] |
| 437 |
– |
% \caption{} |
| 438 |
– |
% \centering |
| 439 |
– |
% \begin{tabular}{| c | cc | cc | } |
| 440 |
– |
% \hline |
| 441 |
– |
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
| 442 |
– |
% \hline |
| 443 |
– |
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
| 444 |
– |
% \hline |
| 445 |
– |
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
| 446 |
– |
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
| 447 |
– |
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
| 448 |
– |
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
| 449 |
– |
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
| 450 |
– |
% \hline |
| 451 |
– |
% \end{tabular} |
| 452 |
– |
% \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 |
| 462 |
< |
|
| 463 |
< |
There are a number of possible mechanisms to explain the role of |
| 464 |
< |
adsorbed CO in restructuring the Pt surface. Quadrupolar repulsion |
| 465 |
< |
between adjacent CO molecules adsorbed on the surface is one |
| 462 |
< |
possibility. However, the quadrupole-quadrupole interaction is |
| 463 |
< |
short-ranged and is attractive for some orientations. If the CO |
| 464 |
< |
molecules are locked in a specific orientation relative to each other, |
| 465 |
< |
this explanation gains some weight. |
| 466 |
< |
|
| 467 |
< |
Another possible mechanism for the restructuring is in the |
| 468 |
< |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 469 |
< |
Pt atoms. This could have the effect of increasing surface mobility |
| 470 |
< |
of these atoms. |
| 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 |
|
|
| 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 |
| 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 |
| 499 |
< |
(d) 86.1 ns. Disruption of the 557 step edges occurs quickly. The |
| 500 |
< |
doubling of the layers appears only after two adjacent step edges |
| 501 |
< |
touch. The circled spot in (b) nucleated the growth of the double |
| 502 |
< |
step observed in the later configurations.} |
| 503 |
< |
\label{fig:reconstruct} |
| 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 |
