| 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] |
| 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 |
| 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{} |
| 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. |
| 369 |
|
|
| 370 |
< |
The primary observation and results of our simulation is that the |
| 371 |
< |
presence of CO overlayer on Pt(557) causes the same kind of |
| 372 |
< |
reconstruction observed experimentally. The 6-atom 111 facets |
| 373 |
< |
initially become disordered, and after 20-40 ns, a double-layer (with |
| 374 |
< |
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. |
| 370 |
> |
The second reconstruction on the Pt(557) surface observed by Tao involved the |
| 371 |
> |
formation of triangular clusters that stretched across the plateau between two step edges. |
| 372 |
> |
Neither system, within our simulated time scales, experiences this reconstruction. A constructed |
| 373 |
> |
system in which the triangular motifs were constructed on the surface will be explored in future |
| 374 |
> |
work and is shown in the supporting information. |
| 375 |
|
|
| 376 |
< |
In these simulations, the Au(557) surface did not exhibit any |
| 377 |
< |
significant restructuring either with or without the presence of a CO |
| 378 |
< |
overlayer. |
| 376 |
> |
\subsection{Dynamics} |
| 377 |
> |
While atomistic simulations of stepped surfaces have been performed before \cite{}, they tend to be |
| 378 |
> |
performed using Monte Carlo techniques\cite{}. This allows them to efficiently sample the thermodynamic |
| 379 |
> |
landscape but at the expense of ignoring the dynamics of the system. Previous work, using STM (?)\cite{}, |
| 380 |
> |
has been able to visualize the coalescing of steps of (system). The time scale of the image acquisition |
| 381 |
> |
provides an upper bounds for the time required for the doubling to actually occur. While statistical treatments |
| 382 |
> |
of step edges are adept at analyzing such systems, it is important to remember that the edges are made |
| 383 |
> |
up of individual atoms and thus can be examined in numerous ways. |
| 384 |
|
|
| 385 |
< |
\subsection{Transport of surface metal atoms} |
| 386 |
< |
An ideal metal surface displaying a low energy (111) face is unlikely |
| 387 |
< |
to experience much surface diffusion because of the large vacancy |
| 388 |
< |
formation energy for atoms at the surface. This implies that |
| 389 |
< |
significant energy must be expended to lift an atom out of the flat |
| 390 |
< |
face so it can migrate on the surface. Rougher surfaces and those |
| 391 |
< |
that already contain numerous adatoms, step edges, and kinks, are |
| 392 |
< |
expected to have higher surface diffusion rates. Metal atoms that are |
| 393 |
< |
mobile on the surface were observed to leave and then rejoin step |
| 394 |
< |
edges or other formations. They may travel together or as isolated |
| 395 |
< |
atoms. The primary challenge of quantifying the overall surface |
| 396 |
< |
mobility is in defining ``mobile'' vs. ``static'' atoms. |
| 385 |
> |
\subsubsection{Transport of surface metal atoms} |
| 386 |
> |
The movement of a step edge is a cooperative effect arising from the individual movements of the atoms |
| 387 |
> |
making up the step. An ideal metal surface displaying a low index facet (111, 100, 110) is unlikely to |
| 388 |
> |
experience much surface diffusion because of the large energetic barrier to lift an atom out of the surface. |
| 389 |
> |
For our surfaces, the presence of step edges provide a source for mobile metal atoms. Breaking away |
| 390 |
> |
from the step edge is still an energetic penalty around (value) but is much less than lifting the same metal |
| 391 |
> |
atom out from the surface and the penalty lowers even further when CO is present in sufficient quantities |
| 392 |
> |
on the surface. Once an adatom exists on the surface, its barrier for diffusion is negligible ( < 4 kcal/mole) |
| 393 |
> |
and is well able to explore its terrace because both steps act as barriers constraining the area in which |
| 394 |
> |
diffusion is allowed. By tracking the mobility of individual metal atoms on the surface we were able to determine |
| 395 |
> |
the relative diffusion rates and how varying coverages of CO affected the diffusion constants. Close |
| 396 |
> |
observation of the mobile metal atoms showed that they were typically in equilibrium with the |
| 397 |
> |
step edges, constantly breaking apart and rejoining. Additionally, at times their motion was concerted and |
| 398 |
> |
two or more atoms would be observed moving together across the surfaces. The primary challenge in quantifying |
| 399 |
> |
the overall surface mobility is in defining ``mobile" vs. ``static" atoms. |
| 400 |
|
|
| 401 |
< |
A particle was considered mobile once it had traveled more than 2~\AA~ |
| 402 |
< |
between saved configurations (XX ps). Restricting the transport |
| 403 |
< |
calculations to only mobile atoms eliminates all of the bulk metal as |
| 404 |
< |
well as any surface atoms that remain fixed for a significant length |
| 405 |
< |
of time. Since diffusion on a surface is strongly affected by local |
| 406 |
< |
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}. |
| 401 |
> |
A particle was considered mobile once it had traveled more than 2~\AA~ between saved configurations |
| 402 |
> |
of the system (10-100 ps). An atom that was truly mobile would typically travel much greater than this, but |
| 403 |
> |
the 2~\AA~ cutoff was to prevent the in place vibrational movement of atoms from being included in the analysis. |
| 404 |
> |
Since diffusion on a surface is strongly affected by local structures, in this case the presence of single and double |
| 405 |
> |
layer step edges, the diffusion parallel to the step edges was determined separately from the diffusion perpendicular |
| 406 |
> |
to these edges. The parallel and perpendicular diffusion constants are shown in figure \ref{fig:diff}. |
| 407 |
|
|
| 408 |
< |
%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. |
| 408 |
> |
\subsubsection{Double layer formation} |
| 409 |
> |
The increased amounts of diffusion on Pt at the higher CO coverages appears to play a role in the |
| 410 |
> |
formation of double layers. Seeing as how that was the only system within our observed simulation time |
| 411 |
> |
that showed the formation. As mentioned earlier, previous experimental work has given some insight into |
| 412 |
> |
the upper bounds of the time required for enough atoms to move around to allow two steps to coalesce\cite{}. |
| 413 |
> |
As seen in figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into |
| 414 |
> |
the simulation. Within 10 ns, nearly half of the step has formed the double layer and by 86 ns, the complete |
| 415 |
> |
layer has formed. From the appearance of the first node to the complete doubling of the layers, only ~65 ns |
| 416 |
> |
have elapsed. The other two layers in this simulation form over a period of ---- and ---- ns respectively. |
| 417 |
|
|
| 418 |
|
\begin{figure}[H] |
| 419 |
< |
\includegraphics[scale=0.6]{DiffusionComparison_error.png} |
| 419 |
> |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
| 420 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
| 421 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 422 |
|
($\mathbf{D}_{\perp}$) to the 557 step edges as a function of CO |
| 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 $\pm$ 0.008 & 1.72 $\pm$ 0.02 & 0.455 $\pm$ 0.006 \\ |
| 446 |
< |
% 33\% & 5.18 $\pm$ 0.03 & 1.999 $\pm$ 0.005 & 1.95 $\pm$ 0.02 & 0.337 $\pm$ 0.004 \\ |
| 447 |
< |
% 25\% & 5.01 $\pm$ 0.02 & 1.574 $\pm$ 0.004 & 1.26 $\pm$ 0.03 & 0.377 $\pm$ 0.006 \\ |
| 448 |
< |
% 5\% & 3.61 $\pm$ 0.02 & 0.355 $\pm$ 0.002 & 1.84 $\pm$ 0.03 & 0.169 $\pm$ 0.004 \\ |
| 449 |
< |
% 0\% & 3.27 $\pm$ 0.02 & 0.147 $\pm$ 0.004 & 1.50 $\pm$ 0.02 & 0.194 $\pm$ 0.002 \\ |
| 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} |
| 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} |
| 504 |
|
\end{figure} |
| 505 |
|
|
| 506 |
|
|
| 509 |
|
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 510 |
|
\caption{} |
| 511 |
|
\end{figure} |
| 512 |
+ |
\begin{figure}[H] |
| 513 |
+ |
\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
| 514 |
+ |
\caption{} |
| 515 |
+ |
\end{figure} |
| 516 |
|
\section{Conclusion} |
| 517 |
|
|
| 518 |
|
|
