| 112 |
|
reversible restructuring under exposure to moderate pressures of |
| 113 |
|
carbon monoxide.\cite{Tao:2010} |
| 114 |
|
|
| 115 |
< |
This work is an attempt to understand the mechanism and timescale for |
| 116 |
< |
surface restructuring by using molecular simulations. Since the dynamics |
| 115 |
> |
This work is an investigation into the mechanism and timescale for |
| 116 |
> |
surface restructuring using molecular simulations. Since the dynamics |
| 117 |
|
of the process are of particular interest, we employ classical force |
| 118 |
|
fields that represent a compromise between chemical accuracy and the |
| 119 |
|
computational efficiency necessary to simulate the process of interest. |
| 123 |
|
to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010} |
| 124 |
|
The Au(557) surface, because of a weaker interaction with CO, is seen as less |
| 125 |
|
likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000} |
| 126 |
< |
and Piccolo et al.\cite{Piccolo:2004} have both observed CO induced |
| 127 |
< |
reconstruction of a Au(111) surface. Peters et al. saw a relaxing of the |
| 128 |
< |
22 x $\sqrt{3}$ cell. They argued that a very small number of Au atoms |
| 129 |
< |
would become adatoms, limiting the stress of this reconstruction while |
| 130 |
< |
allowing the rest of the row to relax and approach the ideal (111) |
| 131 |
< |
configuration. They did not see the ``herringbone'' pattern being greatly |
| 126 |
> |
and Piccolo et al.\cite{Piccolo:2004} have both observed CO-induced |
| 127 |
> |
reconstruction of a Au(111) surface. Peters et al. saw a relaxation to the |
| 128 |
> |
22 x $\sqrt{3}$ cell. They argued that only a few Au atoms |
| 129 |
> |
become adatoms, limiting the stress of this reconstruction while |
| 130 |
> |
allowing the rest to relax and approach the ideal (111) |
| 131 |
> |
configuration. They did not see the usual herringbone pattern being greatly |
| 132 |
|
affected by this relaxation. Piccolo et al. on the other hand, did see a |
| 133 |
< |
disruption of the ``herringbone'' pattern as CO was adsorbed to the |
| 133 |
> |
disruption of the herringbone pattern as CO was adsorbed to the |
| 134 |
|
surface. Both groups suggested that the preference CO shows for |
| 135 |
< |
low-coordinated Au particles was the primary driving force for these reconstructions. |
| 135 |
> |
low-coordinated Au atoms was the primary driving force for the reconstruction. |
| 136 |
|
|
| 137 |
|
|
| 138 |
|
|
| 209 |
|
dynamics.\cite{Shibata:2002hh} One of EAM's strengths |
| 210 |
|
is its sensitivity to small changes in structure. This arises |
| 211 |
|
from the original parameterization, where the interactions |
| 212 |
< |
up to the third nearest-neighbor were taken into account.\cite{Voter95a} |
| 212 |
> |
up to the third nearest neighbor were taken into account.\cite{Voter95a} |
| 213 |
|
Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88} |
| 214 |
< |
which only parameterized up to the nearest-neighbor |
| 214 |
> |
which is only parameterized up to the nearest-neighbor |
| 215 |
|
interactions, EAM is a suitable choice for systems where |
| 216 |
|
the bulk properties are of secondary importance to low-index |
| 217 |
|
surface structures. Additionally, the similarity of EAMs functional |
| 218 |
|
treatment of the embedding energy to standard density functional |
| 219 |
< |
theory (DFT) approaches gives EAM, and conclusions derived, a firm theoretical footing. |
| 219 |
> |
theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier. |
| 220 |
|
\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 221 |
|
|
| 222 |
|
|
| 228 |
|
We used a model first proposed by Karplus and Straub to study |
| 229 |
|
the photodissociation of CO from myoglobin because it reproduces |
| 230 |
|
the quadrupole moment well.\cite{Straub} The Straub and |
| 231 |
< |
Karplus model, treats CO as a rigid three site molecule with a massless M |
| 231 |
> |
Karplus model treats CO as a rigid three site molecule with a massless M |
| 232 |
|
site at the molecular center of mass. The geometry and interaction |
| 233 |
|
parameters are reproduced in Table~\ref{tab:CO}. The effective |
| 234 |
|
dipole moment, calculated from the assigned charges, is still |
| 311 |
|
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
| 312 |
|
and polarization are neglected in this model, although these effects are likely to |
| 313 |
|
affect binding energies and binding site preferences, and will be addressed in |
| 314 |
< |
a future work.\cite{Deshlahra:2012,StreitzMintmire:1994} |
| 314 |
> |
future work. |
| 315 |
|
|
| 316 |
|
%Table of Parameters |
| 317 |
|
%Pt Parameter Set 9 |
| 353 |
|
\end{table} |
| 354 |
|
|
| 355 |
|
\subsection{Pt(557) and Au(557) metal interfaces} |
| 356 |
< |
Our Pt system has dimensions of 18~x~24~x~9 in a box of size |
| 357 |
< |
54.482~x~50.046~x~120.88~\AA while our Au system has |
| 358 |
< |
dimensions of 18~x~24~x~8 in a box of size 57.4~x~51.9285~x~100~\AA. |
| 356 |
> |
Our Pt system is an orthorhombic periodic box of dimensions |
| 357 |
> |
54.482~x~50.046~x~120.88~\AA~while our Au system has |
| 358 |
> |
dimensions of 57.4~x~51.9285~x~100~\AA. |
| 359 |
|
The systems are arranged in a FCC crystal that have been cut |
| 360 |
|
along the (557) plane so that they are periodic in the {\it x} and |
| 361 |
|
{\it y} directions, and have been oriented to expose two aligned |
| 362 |
|
(557) cuts along the extended {\it z}-axis. Simulations of the |
| 363 |
|
bare metal interfaces at temperatures ranging from 300~K to |
| 364 |
< |
1200~K were performed to observe the relative |
| 364 |
> |
1200~K were performed to confirm the relative |
| 365 |
|
stability of the surfaces without a CO overlayer. |
| 366 |
|
|
| 367 |
< |
The different bulk melting temperatures (1337~K for Au |
| 368 |
< |
and 2045~K for Pt) suggest that any possible reconstruction should happen at |
| 367 |
> |
The different bulk melting temperatures (1337~K for Au\cite{Au:melting} |
| 368 |
> |
and 2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
| 369 |
|
different temperatures for the two metals. The bare Au and Pt surfaces were |
| 370 |
|
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
| 371 |
|
respectively for 100 ps. The two surfaces were relatively stable at these |
| 373 |
|
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
| 374 |
|
that was initially placed in the vacuum region. Upon full adsorption, |
| 375 |
|
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 376 |
< |
coverage. Higher coverages resulted in CO double layer formation, which introduces artifacts that are not relevant to (557) reconstruction. |
| 376 |
> |
coverage. Higher coverages resulted in the formation of a double layer of CO, |
| 377 |
> |
which introduces artifacts that are not relevant to (557) reconstruction. |
| 378 |
|
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
| 379 |
|
the Au surfaces often had a significant CO population in the gas |
| 380 |
|
phase. These systems were allowed to reach thermal equilibrium (over |
| 381 |
< |
5 ns) before being run in the microcanonical (NVE) ensemble for |
| 382 |
< |
data collection. All of the systems examined had at least 40 ns in the |
| 383 |
< |
data collection stage, although simulation times for some of the |
| 384 |
< |
systems exceeded 200~ns. Simulations were run using the open |
| 381 |
> |
5~ns) before being run in the microcanonical (NVE) ensemble for |
| 382 |
> |
data collection. All of the systems examined had at least 40~ns in the |
| 383 |
> |
data collection stage, although simulation times for some Pt of the |
| 384 |
> |
systems exceeded 200~ns. Simulations were carried out using the open |
| 385 |
|
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} |
| 386 |
|
|
| 387 |
< |
% Just results, leave discussion for discussion section |
| 388 |
< |
% structure |
| 389 |
< |
% Pt: step wandering, double layers, no triangular motifs |
| 390 |
< |
% Au: step wandering, no double layers |
| 391 |
< |
% dynamics |
| 391 |
< |
% diffusion |
| 392 |
< |
% time scale, formation, breakage |
| 387 |
> |
|
| 388 |
> |
|
| 389 |
> |
|
| 390 |
> |
% RESULTS |
| 391 |
> |
% |
| 392 |
|
\section{Results} |
| 393 |
|
\subsection{Structural remodeling} |
| 394 |
+ |
The surfaces of both systems, upon dosage of CO, began |
| 395 |
+ |
to undergo remodeling that was not observed in the bare |
| 396 |
+ |
metal system. The surfaces which were not exposed to CO |
| 397 |
+ |
did experience minor roughening of the step-edge because |
| 398 |
+ |
of the elevated temperatures, but the |
| 399 |
+ |
(557) lattice was well-maintained throughout the simulation |
| 400 |
+ |
time. The Au systems were limited to greater amounts of |
| 401 |
+ |
roughening, i.e. breakup of the step-edge, and some step |
| 402 |
+ |
wandering. The lower coverage Pt systems experienced |
| 403 |
+ |
similar restructuring but to a greater extent when |
| 404 |
+ |
compared to the Au systems. The 50\% coverage |
| 405 |
+ |
Pt system was unique among our simulations in that it |
| 406 |
+ |
formed numerous double layers through step coalescence, |
| 407 |
+ |
similar to results reported by Tao et al.\cite{Tao:2010} |
| 408 |
+ |
|
| 409 |
+ |
|
| 410 |
|
\subsubsection{Step wandering} |
| 411 |
+ |
The 0\% coverage surfaces for both metals showed minimal |
| 412 |
+ |
movement at their respective run temperatures. As the CO |
| 413 |
+ |
coverage increased however, the mobility of the surface, |
| 414 |
+ |
adatoms and step-edges alike, also increased. Additionally, |
| 415 |
+ |
at the higher coverages on both metals, there was more |
| 416 |
+ |
step-wandering. Except for the 50\% Pt system, the step-edges |
| 417 |
+ |
did not coalesce in any of the other simulations, instead preferring |
| 418 |
+ |
to keep nearly the same distance between steps as in the |
| 419 |
+ |
original (557) lattice. Previous work by Williams et al.\cite{Williams:1991, Williams:1994} |
| 420 |
+ |
highlights the repulsion that exists between step-edges even |
| 421 |
+ |
when no direct interactions are present in the system. This |
| 422 |
+ |
repulsion arises because the entropy of the step-edges is constrained, |
| 423 |
+ |
since step-edge crossing is not allowed. This entropic repulsion |
| 424 |
+ |
does not completely define the interactions between steps, |
| 425 |
+ |
which is why some surfaces will undergo step coalescence, |
| 426 |
+ |
where additional attractive interactions can overcome the |
| 427 |
+ |
repulsion\cite{Williams:1991} and others will not. The presence and concentration |
| 428 |
+ |
of adsorbates, as shown in this work, can affect these step interactions, potentially |
| 429 |
+ |
leading to a new surface structure as the thermodynamic minimum. |
| 430 |
+ |
|
| 431 |
|
\subsubsection{Double layers} |
| 432 |
|
Tao et al. have shown experimentally that the Pt(557) surface |
| 433 |
< |
undergoes two separate reconstructions upon CO |
| 434 |
< |
adsorption.\cite{Tao:2010} The first involves a doubling of |
| 435 |
< |
the step height and plateau length. Similar behavior has been |
| 436 |
< |
seen to occur on numerous surfaces at varying conditions: Ni(977), Si(111). |
| 437 |
< |
\cite{Williams:1994,Williams:1991,Pearl} Of the two systems |
| 438 |
< |
we examined, the Pt system showed a larger amount of |
| 439 |
< |
reconstruction when compared to the Au system. The amount |
| 440 |
< |
of reconstruction is correlated to the amount of CO |
| 433 |
> |
undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} |
| 434 |
> |
The first involves a doubling of the step height and plateau length. |
| 435 |
> |
Similar behavior has been seen to occur on numerous surfaces |
| 436 |
> |
at varying conditions: Ni(977), Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
| 437 |
> |
Of the two systems we examined, the Pt system showed a greater |
| 438 |
> |
propensity for reconstruction when compared to the Au system |
| 439 |
> |
because of the larger surface mobility and extent of step wandering. |
| 440 |
> |
The amount of reconstruction is correlated to the amount of CO |
| 441 |
|
adsorbed upon the surface. This appears to be related to the |
| 442 |
< |
effect that adsorbate coverage has on edge breakup and on the surface |
| 443 |
< |
diffusion of metal adatoms. While both systems displayed step-edge |
| 444 |
< |
wandering, only the Pt surface underwent the doubling seen by |
| 445 |
< |
Tao et al. within the time scales studied here. |
| 446 |
< |
Only the 50\% coverage Pt system exhibited |
| 447 |
< |
a complete doubling in the time scales we |
| 448 |
< |
were able to monitor. Over longer periods (150~ns) two more double layers formed on this interface. |
| 449 |
< |
Although double layer formation did not occur in the other Pt systems, they show |
| 450 |
< |
more lateral movement of the step-edges |
| 451 |
< |
compared to their Au counterparts. The 50\% Pt system is highlighted |
| 417 |
< |
in Figure \ref{fig:reconstruct} at various times along the simulation |
| 418 |
< |
showing the evolution of a step-edge. |
| 442 |
> |
effect that adsorbate coverage has on edge breakup and on the |
| 443 |
> |
surface diffusion of metal adatoms. While both systems displayed |
| 444 |
> |
step-edge wandering, only the 50\% Pt surface underwent the |
| 445 |
> |
doubling seen by Tao et al.\cite{Tao:2010} within the time scales studied here. |
| 446 |
> |
Over longer periods, (150~ns) two more double layers formed |
| 447 |
> |
on this interface. Although double layer formation did not occur |
| 448 |
> |
in the other Pt systems, they show more step-wandering and |
| 449 |
> |
general roughening compared to their Au counterparts. The |
| 450 |
> |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
| 451 |
> |
various times along the simulation showing the evolution of a step-edge. |
| 452 |
|
|
| 453 |
|
The second reconstruction on the Pt(557) surface observed by |
| 454 |
|
Tao involved the formation of triangular clusters that stretched |
| 455 |
|
across the plateau between two step-edges. Neither system, within |
| 456 |
< |
the 40~ns time scale, experienced this reconstruction. |
| 456 |
> |
the 40~ns time scale or the extended simulation time of 150~ns for |
| 457 |
> |
the 50\% Pt system, experienced this reconstruction. |
| 458 |
|
|
| 459 |
|
\subsection{Dynamics} |
| 460 |
< |
Previous atomistic simulations of stepped surfaces were largely |
| 461 |
< |
concerned with the energetics and structures at different conditions |
| 460 |
> |
Previous atomistic simulations of stepped surfaces dealt largely |
| 461 |
> |
with the energetics and structures at different conditions |
| 462 |
|
\cite{Williams:1991,Williams:1994}. Consequently, the most common |
| 463 |
< |
technique has been Monte Carlo. Monte Carlo gives an efficient |
| 463 |
> |
technique utilized to date has been Monte Carlo sampling. Monte Carlo gives an efficient |
| 464 |
|
sampling of the equilibrium thermodynamic landscape at the expense |
| 465 |
< |
of ignoring the dynamics of the system. Previous work by Pearl and |
| 466 |
< |
Sibener\cite{Pearl}, using STM, has been able to show the coalescing |
| 465 |
> |
of ignoring the dynamics of the system. Previous experimental work by Pearl and |
| 466 |
> |
Sibener\cite{Pearl}, using STM, has been able to capture the coalescing |
| 467 |
|
of steps on Ni(977). The time scale of the image acquisition, |
| 468 |
< |
$\sim$70 s/image provides an upper bound for the time required for |
| 468 |
> |
$\sim$70~s/image provides an upper bound for the time required for |
| 469 |
|
the doubling to occur. In this section we give data on dynamic and |
| 470 |
|
transport properties, e.g. diffusion, layer formation time, etc. |
| 471 |
|
|
| 473 |
|
\subsubsection{Transport of surface metal atoms} |
| 474 |
|
%forcedSystems/stepSeparation |
| 475 |
|
The movement or wandering of a step-edge is a cooperative effect |
| 476 |
< |
arising from the individual movements, primarily through surface |
| 477 |
< |
diffusion, of the atoms making up the steps An ideal metal surface |
| 444 |
< |
displaying a low index facet, (111) or (100) is unlikely to experience |
| 476 |
> |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
| 477 |
> |
displaying a low index facet, (111) or (100), is unlikely to experience |
| 478 |
|
much surface diffusion because of the large energetic barrier that must |
| 479 |
< |
be overcome to lift an atom out of the surface. The presence of step-edges |
| 480 |
< |
on higher-index surfaces provide a source for mobile metal atoms. |
| 479 |
> |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
| 480 |
> |
on higher-index facets provide a lower energy source for mobile metal atoms. |
| 481 |
|
Breaking away from the step-edge on a clean surface still imposes an |
| 482 |
< |
energetic penalty around $\sim$~40 kcal/mol, but is much less than lifting |
| 482 |
> |
energetic penalty around $\sim$~40 kcal/mol, but this is significantly easier than lifting |
| 483 |
|
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 484 |
|
The penalty lowers significantly when CO is present in sufficient quantities |
| 485 |
< |
on the surface. For certain distributions of CO, the penalty can be as low as |
| 485 |
> |
on the surface. For certain distributions of CO, the penalty can fall as low as |
| 486 |
|
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 487 |
< |
diffusion is negligible ( \textless~4 kcal/mol) and these adatoms are well |
| 488 |
< |
able to explore the terrace before rejoining either the original step-edge or becoming a part |
| 489 |
< |
of a different edge. Atoms traversing separate terraces is a more difficult |
| 490 |
< |
process, but can be overcome through a joining and lifting stage which is |
| 491 |
< |
examined in the discussion section. By tracking the mobility of individual |
| 487 |
> |
diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are |
| 488 |
> |
able to explore the terrace before rejoining either the original step-edge or |
| 489 |
> |
becoming a part of a different edge. It is a more difficult process for an atom |
| 490 |
> |
to traverse to a separate terrace although the presence of CO can lower the |
| 491 |
> |
energy barrier required to lift or lower the adatom. By tracking the mobility of individual |
| 492 |
|
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 493 |
|
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 494 |
|
observation of the mobile metal atoms showed that they were typically in |
| 495 |
|
equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. |
| 496 |
|
At times, their motion was concerted and two or more adatoms would be |
| 497 |
< |
observed moving together across the surfaces. The primary challenge in |
| 465 |
< |
quantifying the overall surface mobility was in defining ``mobile" vs. ``static" atoms. |
| 497 |
> |
observed moving together across the surfaces. |
| 498 |
|
|
| 499 |
< |
A particle was considered mobile once it had traveled more than 2~\AA~ |
| 499 |
> |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 500 |
|
between saved configurations of the system (typically 10-100 ps). An atom that was |
| 501 |
< |
truly mobile would typically travel much greater distances than this, but the 2~\AA~ cutoff |
| 502 |
< |
was to prevent swamping the diffusion data with the in-place vibrational |
| 503 |
< |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 501 |
> |
truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 502 |
> |
was used to prevent swamping the diffusion data with the in-place vibrational |
| 503 |
> |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 504 |
|
local structures and in this work, the presence of single and double layer |
| 505 |
|
step-edges causes the diffusion parallel to the step-edges to be different |
| 506 |
|
from the diffusion perpendicular to these edges. Parallel and perpendicular |
| 507 |
|
diffusion constants are shown in Figure \ref{fig:diff}. |
| 508 |
|
|
| 509 |
+ |
The lack of a definite trend in the Au diffusion data is likely due |
| 510 |
+ |
to the weaker bonding between Au and CO. This leads to a lower |
| 511 |
+ |
coverage ({\it x}-axis) when compared to dosage amount, which |
| 512 |
+ |
then further limits the affects of the surface diffusion. The correlation |
| 513 |
+ |
between coverage and Pt diffusion rates conversely shows a |
| 514 |
+ |
definite trend marred by the highest coverage surface. Two |
| 515 |
+ |
explanations arise for this drop. First, upon a visual inspection of |
| 516 |
+ |
the system, after a double layer has been formed, it maintains its |
| 517 |
+ |
stability strongly and is no longer a good source for adatoms. By |
| 518 |
+ |
performing the same diffusion calculation but on a shorter run time |
| 519 |
+ |
(20~ns), only including data before the formation of the double layer, |
| 520 |
+ |
provides a $\mathbf{D}_{\perp}$ diffusion constant of $1.69~\pm~0.08$ |
| 521 |
+ |
and a $\mathbf{D}_{\parallel}$ diffusion constant of $6.30~\pm~0.08$. |
| 522 |
+ |
This places the parallel diffusion constant more closely in line with the |
| 523 |
+ |
expected trend, while the perpendicular diffusion constant does not |
| 524 |
+ |
drop as far. A secondary explanation arising from our analysis of the |
| 525 |
+ |
mechanism of double layer formation show the affect that CO on the |
| 526 |
+ |
surface has with respect to overcoming surface diffusion of Pt. If the |
| 527 |
+ |
coverage is too sparse, the Pt engages in minimal interactions and |
| 528 |
+ |
thus minimal diffusion. As coverage increases, there are more favorable |
| 529 |
+ |
arrangements of CO on the surface allowing the formation of a path, |
| 530 |
+ |
a minimum energy trajectory, for the adatom to explore the surface. |
| 531 |
+ |
As the CO is constantly moving on the surface, this path is constantly |
| 532 |
+ |
changing. If the coverage becomes too great, the paths could |
| 533 |
+ |
potentially be clogged leading to a decrease in diffusion despite |
| 534 |
+ |
their being more adatoms and step-wandering. |
| 535 |
+ |
|
| 536 |
|
\subsubsection{Dynamics of double layer formation} |
| 537 |
< |
The increased amounts of diffusion on Pt at the higher CO coverages plays a primary role in the formation of the double layers observed on Pt. However, this is not a complete explanation as seen by the 33\% Pt system which has higher diffusion constants but did not show any signs of undergoing the doubling. This difference will be explored more fully in the discussion. On the 50\% Pt system, three separate layers were formed over the extended run time of this system. Previous experimental work has given some insight into the upper bounds of the time required for step coalescing.\cite{Williams:1991,Pearl} In this system, as seen in Figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into the simulation. Within 12 ns, nearly half of the step has formed the double layer and by 86 ns, the complete layer has been smoothed. The double layer could be considered ``complete" by 37 ns but is a bit rough or wavy. From the appearance of the first node to the first observed double layer, ignoring roughening, the process took $\sim$20 ns. Another $\sim$40 ns was necessary for the layer to completely straighten. The other two layers in this simulation form over a period of 22 ns and 42 ns respectively. Comparing this to the upper bounds of the image scan, it is likely that aspects of this reconstruction occur very quickly. A possible explanation for this rapid reconstruction is the elevated temperatures our systems were run at. It is likely that the process would take longer at lower temperatures and is an area of exploration for future work. |
| 537 |
> |
The increased diffusion on Pt at the higher |
| 538 |
> |
CO coverages plays a primary role in double layer formation. However, this is not |
| 539 |
> |
a complete explanation -- the 33\%~Pt system |
| 540 |
> |
has higher diffusion constants but did not show |
| 541 |
> |
any signs of edge doubling in the observed run time. On the |
| 542 |
> |
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 |
| 543 |
> |
110~ns (150~ns total). Previous experimental |
| 544 |
> |
work gives insight into the upper bounds of the |
| 545 |
> |
time required for step coalescence.\cite{Williams:1991,Pearl} |
| 546 |
> |
In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 547 |
> |
appearance of a double layer, appears at 19~ns |
| 548 |
> |
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
| 549 |
> |
formed the double layer and by 86~ns, the complete layer |
| 550 |
> |
has been flattened out. The double layer could be considered |
| 551 |
> |
``complete" by 37~ns but remains a bit rough. From the |
| 552 |
> |
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
| 553 |
> |
$\sim$40~ns was necessary for the layer to completely straighten. |
| 554 |
> |
The other two layers in this simulation formed over periods of |
| 555 |
> |
22~ns and 42~ns respectively. Comparing this to the upper |
| 556 |
> |
bounds of the image scan, it is likely that most aspects of this |
| 557 |
> |
reconstruction occur very rapidly. A possible explanation |
| 558 |
> |
for this rapid reconstruction is the elevated temperatures |
| 559 |
> |
under which our systems were simulated. It is probable that the process would |
| 560 |
> |
take longer at lower temperatures. |
| 561 |
|
|
| 562 |
|
%Evolution of surface |
| 563 |
|
\begin{figure}[H] |
| 564 |
|
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 565 |
|
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 566 |
< |
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
| 567 |
< |
(d) 86.1 ns. Disruption of the (557) step-edges occurs quickly. The |
| 566 |
> |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 567 |
> |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 568 |
|
doubling of the layers appears only after two adjacent step-edges |
| 569 |
|
touch. The circled spot in (b) nucleated the growth of the double |
| 570 |
|
step observed in the later configurations.} |
| 591 |
|
|
| 592 |
|
%Discussion |
| 593 |
|
\section{Discussion} |
| 594 |
< |
In this paper we have shown that we were able to accurately model the initial reconstruction of the |
| 594 |
> |
We have shown that the classical potential models are able to model the initial reconstruction of the |
| 595 |
|
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 596 |
< |
were able to observe the dynamic processes necessary for this reconstruction. |
| 596 |
> |
were able to observe features of the dynamic processes necessary for this reconstruction. |
| 597 |
|
|
| 598 |
|
\subsection{Mechanism for restructuring} |
| 599 |
|
Since the Au surface showed no large scale restructuring throughout |
| 600 |
|
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 601 |
|
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 602 |
< |
Comparing the results from this simulation to those reported previously by |
| 603 |
< |
Tao et al.\cite{Tao:2010} the similarities in the Pt-CO system are quite |
| 604 |
< |
strong. As shown in Figure \ref{fig:reconstruct}, the simulated Pt |
| 605 |
< |
system exposed to a large dosage of CO will restructure by doubling the terrace |
| 606 |
< |
widths and step heights. The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a time and as such is a fairly stochastic event. |
| 607 |
< |
Looking at individual configurations of the system, the adatoms either |
| 602 |
> |
Similarities of our results to those reported previously by |
| 603 |
> |
Tao et al.\cite{Tao:2010} are quite |
| 604 |
> |
strong. The simulated Pt |
| 605 |
> |
system exposed to a large dosage of CO readily restructures by doubling the terrace |
| 606 |
> |
widths and step heights. The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a time, but is rapid on experimental timescales. |
| 607 |
> |
The adatoms either |
| 608 |
|
break away from the step-edge and stay on the lower terrace or they lift |
| 609 |
< |
up onto the higher terrace. Once ``free'', they will diffuse on the terrace |
| 609 |
> |
up onto a higher terrace. Once ``free'', they diffuse on the terrace |
| 610 |
|
until reaching another step-edge or rejoining their original edge. |
| 611 |
|
This combination of growth and decay of the step-edges is in a state of |
| 612 |
|
dynamic equilibrium. However, once two previously separated edges |
| 613 |
< |
meet as shown in Figure 1.B, this meeting point tends to act as a focus |
| 614 |
< |
or growth point for the rest of the edge to meet up, akin to that of a zipper. |
| 533 |
< |
From the handful of cases where a double layer was formed during the |
| 534 |
< |
simulation, measuring from the initial appearance of a growth point, the |
| 535 |
< |
double layer tends to be fully formed within $\sim$35 ns. |
| 613 |
> |
meet as shown in Figure 1.B, this nucleates the rest of the edge to meet up, forming a double layer. |
| 614 |
> |
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. |
| 615 |
|
|
| 616 |
|
A number of possible mechanisms exist to explain the role of adsorbed |
| 617 |
|
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 618 |
< |
CO molecules adsorbed on the surface is one likely possibility. However, |
| 618 |
> |
CO molecules adsorbed on the surface is one possibility. However, |
| 619 |
|
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 620 |
|
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 621 |
|
relative to each other, through atop adsorption for example, this explanation |
| 622 |
< |
gains some weight. The energetic repulsion between two CO located a |
| 623 |
< |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in |
| 624 |
< |
a vertical orientation is 8.62 kcal/mol. Moving the CO apart to the second |
| 622 |
> |
gains some credence. The energetic repulsion between two CO located a |
| 623 |
> |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in |
| 624 |
> |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 625 |
|
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 626 |
|
nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation |
| 627 |
|
also quickly drops the repulsion, a minimum of 6.2 kcal/mol is reached at $\sim$24 degrees between the 2 CO when the carbons are locked at a distance of 2.77 \AA apart. |
| 628 |
|
As mentioned above, the energy barrier for surface diffusion |
| 629 |
< |
of a Pt adatom is only 4 kcal/mol. So this repulsion between CO can help |
| 629 |
> |
of a Pt adatom is only 4 kcal/mol. So this repulsion between neighboring CO molecules can |
| 630 |
|
increase the surface diffusion. However, the residence time of CO on Pt was |
| 631 |
|
examined and while the majority of the CO is on or near the surface throughout |
| 632 |
< |
the run, it is extremely mobile. This mobility suggests that the CO are more |
| 633 |
< |
likely to shift their positions without necessarily dragging the Pt along with them. |
| 632 |
> |
the run, most molecules are mobile. This mobility suggests that the CO are more |
| 633 |
> |
likely to shift their positions without necessarily the Pt along with them. |
| 634 |
|
|
| 635 |
|
Another possible and more likely mechanism for the restructuring is in the |
| 636 |
|
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 642 |
|
of Pt atoms was then examined to determine possible barriers. Because |
| 643 |
|
the movement was forced along a pre-defined reaction coordinate that may differ |
| 644 |
|
from the true minimum of this path, only the beginning and ending energies |
| 645 |
< |
are displayed in Table \ref{tab:energies}. These values suggest that the presence of CO at suitable |
| 645 |
> |
are displayed in Table \ref{tab:rxcoord} with the corresponding beginning and ending reaction coordinates in Figure \ref{fig:lambdaTable}. These values suggest that the presence of CO at suitable |
| 646 |
|
locations can lead to lowered barriers for Pt breaking apart from the step-edge. |
| 647 |
|
Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the |
| 648 |
|
burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral |
| 650 |
|
|
| 651 |
|
%lambda progression of Pt -> shoving its way into the step |
| 652 |
|
\begin{figure}[H] |
| 653 |
< |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO.png} |
| 653 |
> |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
| 654 |
|
\caption{A model system of the Pt(557) surface was used as the framework |
| 655 |
|
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 656 |
|
placements, and rotations of CO were examined as they affect Pt movement. |
| 661 |
|
\label{fig:lambda} |
| 662 |
|
\end{figure} |
| 663 |
|
|
| 664 |
+ |
\begin{figure}[H] |
| 665 |
+ |
\includegraphics[totalheight=0.9\textheight]{lambdaTable.png} |
| 666 |
+ |
\caption{} |
| 667 |
+ |
\label{fig:lambdaTable} |
| 668 |
+ |
\end{figure} |
| 669 |
|
|
| 670 |
|
|
| 671 |
+ |
|
| 672 |
+ |
\begin{table}[H] |
| 673 |
+ |
\caption{} |
| 674 |
+ |
\centering |
| 675 |
+ |
\begin{tabular}{| c || c | c | c | c |} |
| 676 |
+ |
\hline |
| 677 |
+ |
\textbf{System} & 0.5~\AA & 2~\AA & 4~\AA & 6~\AA \\ |
| 678 |
+ |
\hline |
| 679 |
+ |
A & 6.38 & 38.34 & 44.65 & 47.60 \\ |
| 680 |
+ |
B & -20.72 & 0.67 & 17.33 & 24.28 \\ |
| 681 |
+ |
C & 4.92 & 27.02 & 41.05 & 47.43 \\ |
| 682 |
+ |
D & -16.97 & 21.21 & 35.87 & 40.93 \\ |
| 683 |
+ |
E & 5.92 & 30.96 & 43.69 & 49.23 \\ |
| 684 |
+ |
F & 8.53 & 46.23 & 53.98 & 65.55 \\ |
| 685 |
+ |
\hline |
| 686 |
+ |
\end{tabular} |
| 687 |
+ |
\label{tab:rxcoord} |
| 688 |
+ |
\end{table} |
| 689 |
+ |
|
| 690 |
+ |
|
| 691 |
|
\subsection{Diffusion} |
| 692 |
< |
As shown in the results section, the diffusion parallel to the step-edge tends to be |
| 693 |
< |
much larger than that perpendicular to the step-edge, likely because of the dynamic |
| 692 |
> |
The diffusion parallel to the step-edge tends to be |
| 693 |
> |
much larger than that perpendicular to the step-edge. The dynamic |
| 694 |
|
equilibrium that is established between the step-edge and adatom interface. The coverage |
| 695 |
|
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}. |
| 696 |
|
The |
| 706 |
|
%breaking of the double layer upon removal of CO |
| 707 |
|
\begin{figure}[H] |
| 708 |
|
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 709 |
< |
%: |
| 606 |
< |
\caption{(A) 0 ps, (B) 100 ps, (C) 1 ns, after the removal of CO. The presence of the CO |
| 709 |
> |
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
| 710 |
|
helped maintain the stability of the double layer and upon removal the two layers break |
| 711 |
|
and begin separating. The separation is not a simple pulling apart however, rather |
| 712 |
|
there is a mixing of the lower and upper atoms at the edge.} |
| 717 |
|
|
| 718 |
|
|
| 719 |
|
%Peaks! |
| 720 |
< |
\begin{figure}[H] |
| 721 |
< |
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 722 |
< |
\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 723 |
< |
of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 724 |
< |
aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 725 |
< |
\label{fig:peaks} |
| 726 |
< |
\end{figure} |
| 720 |
> |
%\begin{figure}[H] |
| 721 |
> |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 722 |
> |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 723 |
> |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 724 |
> |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 725 |
> |
%\label{fig:peaks} |
| 726 |
> |
%\end{figure} |
| 727 |
|
|
| 728 |
|
|
| 729 |
|
%Don't think I need this |
