| 117 |
|
reversible restructuring under exposure to moderate pressures of |
| 118 |
|
carbon monoxide.\cite{Tao:2010} |
| 119 |
|
|
| 120 |
< |
This work is an investigation into the mechanism and timescale for |
| 120 |
> |
This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557) |
| 121 |
|
surface restructuring using molecular simulations. Since the dynamics |
| 122 |
|
of the process are of particular interest, we employ classical force |
| 123 |
|
fields that represent a compromise between chemical accuracy and the |
| 126 |
|
catalyst with adsorbates, in this work, two metal systems exposed |
| 127 |
|
to carbon monoxide were examined. The Pt(557) surface has already been shown |
| 128 |
|
to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010} |
| 129 |
< |
The Au(557) surface, because of a weaker interaction with CO, is seen as less |
| 130 |
< |
likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000} |
| 131 |
< |
and Piccolo et al.\cite{Piccolo:2004} have both observed CO-induced |
| 132 |
< |
reconstruction of a Au(111) surface. Peters et al. saw a relaxation to the |
| 129 |
> |
The Au(557) surface, because of a weaker interaction with CO, is less |
| 130 |
> |
likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000} |
| 131 |
> |
and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced |
| 132 |
> |
reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the |
| 133 |
|
22 x $\sqrt{3}$ cell. They argued that only a few Au atoms |
| 134 |
< |
become adatoms, limiting the stress of this reconstruction while |
| 134 |
> |
become adatoms, limiting the stress of this reconstruction, while |
| 135 |
|
allowing the rest to relax and approach the ideal (111) |
| 136 |
< |
configuration. They did not see the usual herringbone pattern being greatly |
| 137 |
< |
affected by this relaxation. Piccolo et al. on the other hand, did see a |
| 136 |
> |
configuration. They did not see the usual herringbone pattern on Au(111) being greatly |
| 137 |
> |
affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a |
| 138 |
|
disruption of the herringbone pattern as CO was adsorbed to the |
| 139 |
|
surface. Both groups suggested that the preference CO shows for |
| 140 |
|
low-coordinated Au atoms was the primary driving force for the reconstruction. |
| 149 |
|
development of a sufficiently general yet computationally tractable |
| 150 |
|
model of the chemical interactions between the surface atoms and |
| 151 |
|
adsorbates. Since the interfaces involved are quite large (10$^3$ - |
| 152 |
< |
10$^6$ atoms) and respond slowly to perturbations, {\it ab initio} |
| 152 |
> |
10$^4$ atoms) and respond slowly to perturbations, {\it ab initio} |
| 153 |
|
molecular dynamics |
| 154 |
|
(AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello |
| 155 |
|
methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum |
| 161 |
|
Coulomb potential. For this work, we have used classical molecular |
| 162 |
|
dynamics with potential energy surfaces that are specifically tuned |
| 163 |
|
for transition metals. In particular, we used the EAM potential for |
| 164 |
< |
Au-Au and Pt-Pt interactions\cite{EAM}. The CO was modeled using a rigid |
| 164 |
> |
Au-Au and Pt-Pt interactions.\cite{EAM} The CO was modeled using a rigid |
| 165 |
|
three-site model developed by Straub and Karplus for studying |
| 166 |
|
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 167 |
|
Pt-CO cross interactions were parameterized as part of this work. |
| 174 |
|
methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98} |
| 175 |
|
but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and |
| 176 |
|
the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
| 177 |
< |
parameter sets. The glue model of Ercolessi et al. is among the |
| 177 |
> |
parameter sets. The glue model of Ercolessi {\it et al}. is among the |
| 178 |
|
fastest of these density functional approaches.\cite{Ercolessi88} In |
| 179 |
< |
all of these models, atoms are conceptualized as a positively charged |
| 179 |
> |
all of these models, atoms are treated as a positively charged |
| 180 |
|
core with a radially-decaying valence electron distribution. To |
| 181 |
|
calculate the energy for embedding the core at a particular location, |
| 182 |
|
the electron density due to the valence electrons at all of the other |
| 213 |
|
propagation,\cite{BECQUART:1993rg} and alloying |
| 214 |
|
dynamics.\cite{Shibata:2002hh} One of EAM's strengths |
| 215 |
|
is its sensitivity to small changes in structure. This arises |
| 216 |
< |
from the original parameterization, where the interactions |
| 217 |
< |
up to the third nearest neighbor were taken into account.\cite{Voter95a} |
| 218 |
< |
Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88} |
| 216 |
> |
because interactions |
| 217 |
> |
up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a} |
| 218 |
> |
Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88} |
| 219 |
|
which is only parameterized up to the nearest-neighbor |
| 220 |
|
interactions, EAM is a suitable choice for systems where |
| 221 |
|
the bulk properties are of secondary importance to low-index |
| 222 |
< |
surface structures. Additionally, the similarity of EAMs functional |
| 222 |
> |
surface structures. Additionally, the similarity of EAM's functional |
| 223 |
|
treatment of the embedding energy to standard density functional |
| 224 |
|
theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier. |
| 225 |
|
\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 272 |
|
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}. |
| 273 |
|
The modified parameters yield binding energies that are slightly higher |
| 274 |
|
than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
| 275 |
< |
et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 276 |
< |
Lennard-Jones interaction to mimic strong, but short-ranged partial |
| 275 |
> |
{\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 276 |
> |
Lennard-Jones interaction to mimic strong, but short-ranged, partial |
| 277 |
|
binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
| 278 |
|
Pt-O interaction was modeled with a Morse potential with a large |
| 279 |
|
equilibrium distance, ($r_o$). These choices ensure that the C is preferred |
| 280 |
< |
over O as the surface-binding atom. In most cases, the Pt-O parameterization contributes a weak |
| 280 |
> |
over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak |
| 281 |
|
repulsion which favors the atop site. The resulting potential-energy |
| 282 |
|
surface suitably recovers the calculated Pt-C separation length |
| 283 |
|
(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
| 314 |
|
The parameters employed for the metal-CO cross-interactions in this work |
| 315 |
|
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
| 316 |
|
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
| 317 |
< |
and polarization are neglected in this model, although these effects are likely to |
| 318 |
< |
affect binding energies and binding site preferences, and will be addressed in |
| 319 |
< |
future work. |
| 317 |
> |
and polarization are neglected in this model, although these effects could have |
| 318 |
> |
an effect on binding energies and binding site preferences. |
| 319 |
|
|
| 320 |
|
%Table of Parameters |
| 321 |
|
%Pt Parameter Set 9 |
| 359 |
|
\subsection{Pt(557) and Au(557) metal interfaces} |
| 360 |
|
Our Pt system is an orthorhombic periodic box of dimensions |
| 361 |
|
54.482~x~50.046~x~120.88~\AA~while our Au system has |
| 362 |
< |
dimensions of 57.4~x~51.9285~x~100~\AA. |
| 362 |
> |
dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs |
| 363 |
> |
are 9 and 8 atoms deep respectively, corresponding to a slab |
| 364 |
> |
thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au. |
| 365 |
|
The systems are arranged in a FCC crystal that have been cut |
| 366 |
|
along the (557) plane so that they are periodic in the {\it x} and |
| 367 |
|
{\it y} directions, and have been oriented to expose two aligned |
| 370 |
|
1200~K were performed to confirm the relative |
| 371 |
|
stability of the surfaces without a CO overlayer. |
| 372 |
|
|
| 373 |
< |
The different bulk melting temperatures (1345~$\pm$~10~K for Au\cite{Au:melting} |
| 373 |
> |
The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting} |
| 374 |
|
and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
| 375 |
|
different temperatures for the two metals. The bare Au and Pt surfaces were |
| 376 |
|
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
| 397 |
|
% |
| 398 |
|
\section{Results} |
| 399 |
|
\subsection{Structural remodeling} |
| 400 |
< |
The surfaces of both systems, upon dosage of CO, began |
| 401 |
< |
to undergo extensive remodeling that was not observed in the bare |
| 402 |
< |
systems. The bare metal surfaces |
| 403 |
< |
experienced minor roughening of the step-edge because |
| 404 |
< |
of the elevated temperatures, but the |
| 405 |
< |
(557) lattice was well-maintained throughout the simulation |
| 406 |
< |
time. The Au systems were limited to greater amounts of |
| 407 |
< |
roughening, i.e. breakup of the step-edge, and some step |
| 408 |
< |
wandering. The lower coverage Pt systems experienced |
| 409 |
< |
similar restructuring but to a greater extent when |
| 410 |
< |
compared to the Au systems. The 50\% coverage |
| 410 |
< |
Pt system was unique among our simulations in that it |
| 411 |
< |
formed numerous double layers through step coalescence, |
| 412 |
< |
similar to results reported by Tao et al.\cite{Tao:2010} |
| 400 |
> |
The bare metal surfaces experienced minor roughening of the |
| 401 |
> |
step-edge because of the elevated temperatures, but the (557) |
| 402 |
> |
face was stable throughout the simulations. The surface of both |
| 403 |
> |
systems, upon dosage of CO, began to undergo extensive remodeling |
| 404 |
> |
that was not observed in the bare systems. Reconstructions of |
| 405 |
> |
the Au systems were limited to breakup of the step-edges and |
| 406 |
> |
some step wandering. The lower coverage Pt systems experienced |
| 407 |
> |
similar restructuring but to a greater extent. The 50\% coverage |
| 408 |
> |
Pt system was unique among our simulations in that it formed |
| 409 |
> |
well-defined and stable double layers through step coalescence, |
| 410 |
> |
similar to results reported by Tao {\it et al}.\cite{Tao:2010} |
| 411 |
|
|
| 412 |
|
|
| 413 |
|
\subsubsection{Step wandering} |
| 414 |
|
The 0\% coverage surfaces for both metals showed minimal |
| 415 |
< |
movement at their respective run temperatures. As the CO |
| 416 |
< |
coverage increased however, the mobility of the surface, |
| 415 |
> |
step-wandering at their respective temperatures. As the CO |
| 416 |
> |
coverage increased however, the mobility of the surface atoms, |
| 417 |
|
described through adatom diffusion and step-edge wandering, |
| 418 |
< |
also increased. Except for the 50\% Pt system, the step-edges |
| 419 |
< |
did not coalesce in any of the other simulations, instead |
| 420 |
< |
preferring to keep nearly the same distance between steps |
| 421 |
< |
as in the original (557) lattice, $\sim$13\AA for Pt and $\sim$14\AA for Au. |
| 422 |
< |
Previous work by Williams et al.\cite{Williams:1991, Williams:1994} |
| 418 |
> |
also increased. Except for the 50\% Pt system where step |
| 419 |
> |
coalescence occurred, the step-edges in the other simulations |
| 420 |
> |
preferred to keep nearly the same distance between steps as in |
| 421 |
> |
the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au. |
| 422 |
> |
Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994} |
| 423 |
|
highlights the repulsion that exists between step-edges even |
| 424 |
|
when no direct interactions are present in the system. This |
| 425 |
< |
repulsion arises because step-edge crossing is not allowed |
| 426 |
< |
which constrains the entropy. This entropic repulsion does |
| 427 |
< |
not completely define the interactions between steps, which |
| 428 |
< |
is why some surfaces will undergo step coalescence, where |
| 429 |
< |
additional attractive interactions can overcome the repulsion.\cite{Williams:1991} |
| 430 |
< |
The presence and concentration of adsorbates, as shown in |
| 431 |
< |
this work, can affect these step interactions, potentially leading |
| 432 |
< |
to a new surface structure as the thermodynamic minimum. |
| 425 |
> |
repulsion is caused by an entropic barrier that arises from |
| 426 |
> |
the fact that steps cannot cross over one another. This entropic |
| 427 |
> |
repulsion does not completely define the interactions between |
| 428 |
> |
steps, however, so it is possible to observe step coalescence |
| 429 |
> |
on some surfaces.\cite{Williams:1991} The presence and |
| 430 |
> |
concentration of adsorbates, as shown in this work, can |
| 431 |
> |
affect step-step interactions, potentially leading to a new |
| 432 |
> |
surface structure as the thermodynamic equilibrium. |
| 433 |
|
|
| 434 |
|
\subsubsection{Double layers} |
| 435 |
< |
Tao et al.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
| 436 |
< |
undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} |
| 435 |
> |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
| 436 |
> |
undergoes two separate reconstructions upon CO adsorption. |
| 437 |
|
The first involves a doubling of the step height and plateau length. |
| 438 |
< |
Similar behavior has been seen on numerous surfaces |
| 439 |
< |
at varying conditions: Ni(977), Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
| 438 |
> |
Similar behavior has been seen on a number of surfaces |
| 439 |
> |
at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
| 440 |
|
Of the two systems we examined, the Pt system showed a greater |
| 441 |
< |
propensity for reconstruction when compared to the Au system |
| 442 |
< |
because of the larger surface mobility and extent of step wandering. |
| 443 |
< |
The amount of reconstruction is strongly correlated to the amount of CO |
| 441 |
> |
propensity for reconstruction |
| 442 |
> |
because of the larger surface mobility and the greater extent of step wandering. |
| 443 |
> |
The amount of reconstruction was strongly correlated to the amount of CO |
| 444 |
|
adsorbed upon the surface. This appears to be related to the |
| 445 |
|
effect that adsorbate coverage has on edge breakup and on the |
| 446 |
< |
surface diffusion of metal adatoms. While both systems displayed |
| 447 |
< |
step-edge wandering, only the 50\% Pt surface underwent the |
| 448 |
< |
doubling seen by Tao et al.\cite{Tao:2010} within the time scales studied here. |
| 449 |
< |
Over longer periods, (150~ns) two more double layers formed |
| 450 |
< |
on this interface. Although double layer formation did not occur |
| 451 |
< |
in the other Pt systems, they show more step-wandering and |
| 454 |
< |
general roughening compared to their Au counterparts. The |
| 446 |
> |
surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
| 447 |
> |
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
| 448 |
> |
Over a longer time scale (150~ns) two more double layers formed |
| 449 |
> |
on this surface. Although double layer formation did not occur |
| 450 |
> |
in the other Pt systems, they exhibited more step-wandering and |
| 451 |
> |
roughening compared to their Au counterparts. The |
| 452 |
|
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
| 453 |
|
various times along the simulation showing the evolution of a double layer step-edge. |
| 454 |
|
|
| 455 |
< |
The second reconstruction on the Pt(557) surface observed by |
| 456 |
< |
Tao involved the formation of triangular clusters that stretched |
| 457 |
< |
across the plateau between two step-edges. Neither system, within |
| 455 |
> |
The second reconstruction observed by |
| 456 |
> |
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
| 457 |
> |
across the plateau between two step-edges. Neither metal, within |
| 458 |
|
the 40~ns time scale or the extended simulation time of 150~ns for |
| 459 |
|
the 50\% Pt system, experienced this reconstruction. |
| 460 |
|
|
| 471 |
|
\end{figure} |
| 472 |
|
|
| 473 |
|
\subsection{Dynamics} |
| 474 |
< |
Previous atomistic simulations of stepped surfaces dealt largely |
| 475 |
< |
with the energetics and structures at different conditions |
| 476 |
< |
\cite{Williams:1991,Williams:1994}. Consequently, the most common |
| 477 |
< |
technique utilized to date has been Monte Carlo sampling. Monte Carlo approaches give an efficient |
| 478 |
< |
sampling of the equilibrium thermodynamic landscape at the expense |
| 479 |
< |
of ignoring the dynamics of the system. Previous experimental work by Pearl and |
| 480 |
< |
Sibener\cite{Pearl}, using STM, has been able to capture the coalescing |
| 481 |
< |
of steps on Ni(977). The time scale of the image acquisition, |
| 485 |
< |
$\sim$70~s/image provides an upper bound for the time required for |
| 486 |
< |
the doubling to occur. By utilizing Molecular Dynamics we were able to probe the dynamics of these reconstructions and in this section we give data on dynamic and |
| 487 |
< |
transport properties, e.g. diffusion, layer formation time, etc. |
| 474 |
> |
Previous experimental work by Pearl and Sibener\cite{Pearl}, |
| 475 |
> |
using STM, has been able to capture the coalescence of steps |
| 476 |
> |
on Ni(977). The time scale of the image acquisition, $\sim$70~s/image, |
| 477 |
> |
provides an upper bound for the time required for the doubling |
| 478 |
> |
to occur. By utilizing Molecular Dynamics we are able to probe |
| 479 |
> |
the dynamics of these reconstructions at elevated temperatures |
| 480 |
> |
and in this section we provide data on the timescales for transport |
| 481 |
> |
properties, e.g. diffusion and layer formation time. |
| 482 |
|
|
| 483 |
|
|
| 484 |
|
\subsubsection{Transport of surface metal atoms} |
| 485 |
|
%forcedSystems/stepSeparation |
| 486 |
< |
The movement or wandering of a step-edge is a cooperative effect |
| 486 |
> |
The wandering of a step-edge is a cooperative effect |
| 487 |
|
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
| 488 |
|
displaying a low index facet, (111) or (100), is unlikely to experience |
| 489 |
|
much surface diffusion because of the large energetic barrier that must |
| 490 |
|
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
| 491 |
|
on higher-index facets provides a lower energy source for mobile metal atoms. |
| 492 |
< |
Breaking away from the step-edge on a clean surface still imposes an |
| 492 |
> |
Single-atom break-away from a step-edge on a clean surface still imposes an |
| 493 |
|
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
| 494 |
|
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 495 |
|
The penalty lowers significantly when CO is present in sufficient quantities |
| 496 |
< |
on the surface. For certain distributions of CO, see Figures \ref{fig:sketchGraphic} and \ref{fig:sketchEnergies}, the penalty can fall to as low as |
| 496 |
> |
on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as |
| 497 |
|
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 498 |
< |
diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are then |
| 498 |
> |
diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then |
| 499 |
|
able to explore the terrace before rejoining either their original step-edge or |
| 500 |
< |
becoming a part of a different edge. It is a difficult process for an atom |
| 500 |
> |
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom |
| 501 |
|
to traverse to a separate terrace although the presence of CO can lower the |
| 502 |
|
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
| 503 |
|
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 504 |
|
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 505 |
|
observation of the mobile metal atoms showed that they were typically in |
| 506 |
< |
equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. |
| 506 |
> |
equilibrium with the step-edges. |
| 507 |
|
At times, their motion was concerted and two or more adatoms would be |
| 508 |
|
observed moving together across the surfaces. |
| 509 |
|
|
| 510 |
|
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 511 |
< |
between saved configurations of the system (typically 10-100 ps). An atom that was |
| 512 |
< |
truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 511 |
> |
between saved configurations of the system (typically 10-100 ps). A mobile atom |
| 512 |
> |
would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 513 |
|
was used to prevent swamping the diffusion data with the in-place vibrational |
| 514 |
|
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 515 |
|
local structures and in this work, the presence of single and double layer |
| 533 |
|
\label{fig:diff} |
| 534 |
|
\end{figure} |
| 535 |
|
|
| 536 |
< |
The lack of a definite trend in the Au diffusion data in Figure \ref{fig:diff} is likely due |
| 537 |
< |
to the weaker bonding between Au and CO. This leads to a lower observed |
| 538 |
< |
coverage ({\it x}-axis) when compared to dosage amount, which |
| 539 |
< |
then further limits the effect the CO can have on surface diffusion. The correlation |
| 540 |
< |
between coverage and Pt diffusion rates conversely shows a |
| 541 |
< |
definite trend marred by the highest coverage surface. Two |
| 542 |
< |
explanations arise for this drop. First, upon a visual inspection of |
| 543 |
< |
the system, after a double layer has been formed, it maintains its |
| 544 |
< |
stability strongly and is no longer a good source for adatoms and so |
| 545 |
< |
atoms that had been tracked for mobility data have now been buried. By |
| 546 |
< |
performing the same diffusion calculation but on a shorter run time |
| 547 |
< |
(20~ns), only including data before the formation of the double layer, we obtain |
| 548 |
< |
the larger values for both $\mathbf{D}_{\parallel}$ and $\mathbf{D}_{\perp}$ at the 50\% coverage. |
| 549 |
< |
This places the parallel diffusion constant more closely in line with the |
| 556 |
< |
expected trend, while the perpendicular diffusion constant does not |
| 557 |
< |
drop as far. A secondary explanation arising from our analysis of the |
| 558 |
< |
mechanism of double layer formation focuses on the effect that CO on the |
| 559 |
< |
surface has with respect to overcoming surface diffusion of Pt. If the |
| 560 |
< |
coverage is too sparse, the Pt engages in minimal interactions and |
| 561 |
< |
thus minimal diffusion. As coverage increases, there are more favorable |
| 562 |
< |
arrangements of CO on the surface allowing the formation of a path, |
| 563 |
< |
a minimum energy trajectory, for the adatom to explore the surface. |
| 564 |
< |
As the CO is constantly moving on the surface, this path is constantly |
| 565 |
< |
changing. If the coverage becomes too great, the paths could |
| 566 |
< |
potentially be clogged leading to a decrease in diffusion despite |
| 567 |
< |
their being more adatoms and step-wandering. |
| 536 |
> |
The weaker Au-CO interaction is evident in the weak CO-coverage |
| 537 |
> |
dependance of Au diffusion. This weak interaction leads to lower |
| 538 |
> |
observed coverages when compared to dosage amounts. This further |
| 539 |
> |
limits the effect the CO can have on surface diffusion. The correlation |
| 540 |
> |
between coverage and Pt diffusion rates shows a near linear relationship |
| 541 |
> |
at the earliest times in the simulations. Following double layer formation, |
| 542 |
> |
however, there is a precipitous drop in adatom diffusion. As the double |
| 543 |
> |
layer forms, many atoms that had been tracked for mobility data have |
| 544 |
> |
now been buried resulting in a smaller reported diffusion constant. A |
| 545 |
> |
secondary effect of higher coverages is CO-CO cross interactions that |
| 546 |
> |
lower the effective mobility of the Pt adatoms that are bound to each CO. |
| 547 |
> |
This effect would become evident only at higher coverages. A detailed |
| 548 |
> |
account of Pt adatom energetics follows in the Discussion. |
| 549 |
> |
|
| 550 |
|
|
| 569 |
– |
|
| 570 |
– |
|
| 551 |
|
\subsubsection{Dynamics of double layer formation} |
| 552 |
< |
The increased diffusion on Pt at the higher |
| 553 |
< |
CO coverages plays a primary role in double layer formation. However, this is not |
| 554 |
< |
a complete explanation -- the 33\%~Pt system |
| 555 |
< |
has higher diffusion constants but did not show |
| 556 |
< |
any signs of edge doubling in the observed run time. On the |
| 557 |
< |
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 |
| 558 |
< |
110~ns (150~ns total). Previous experimental |
| 559 |
< |
work gives insight into the upper bounds of the |
| 560 |
< |
time required for step coalescence.\cite{Williams:1991,Pearl} |
| 561 |
< |
In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 562 |
< |
appearance of a double layer, appears at 19~ns |
| 563 |
< |
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
| 564 |
< |
formed the double layer and by 86~ns, the complete layer |
| 565 |
< |
has been flattened out. The double layer could be considered |
| 566 |
< |
``complete" by 37~ns but remains a bit rough. From the |
| 567 |
< |
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
| 568 |
< |
$\sim$40~ns was necessary for the layer to completely straighten. |
| 569 |
< |
The other two layers in this simulation formed over periods of |
| 570 |
< |
22~ns and 42~ns respectively. Comparing this to the upper |
| 571 |
< |
bounds of the image scan, it is likely that most aspects of this |
| 572 |
< |
reconstruction occur very rapidly. A possible explanation |
| 573 |
< |
for this rapid reconstruction is the elevated temperatures |
| 594 |
< |
under which our systems were simulated. It is probable that the process would |
| 595 |
< |
take longer at lower temperatures. |
| 552 |
> |
The increased diffusion on Pt at the higher CO coverages is the primary |
| 553 |
> |
contributor to double layer formation. However, this is not a complete |
| 554 |
> |
explanation -- the 33\%~Pt system has higher diffusion constants, but |
| 555 |
> |
did not show any signs of edge doubling in 40~ns. On the 50\%~Pt |
| 556 |
> |
system, one double layer formed within the first 40~ns of simulation time, |
| 557 |
> |
while two more were formed as the system was allowed to run for an |
| 558 |
> |
additional 110~ns (150~ns total). This suggests that this reconstruction |
| 559 |
> |
is a rapid process and that the previously mentioned upper bound is a |
| 560 |
> |
very large overestimate.\cite{Williams:1991,Pearl} In this system the first |
| 561 |
> |
appearance of a double layer appears at 19~ns into the simulation. |
| 562 |
> |
Within 12~ns of this nucleation event, nearly half of the step has formed |
| 563 |
> |
the double layer and by 86~ns the complete layer has flattened out. |
| 564 |
> |
From the appearance of the first nucleation event to the first observed |
| 565 |
> |
double layer, the process took $\sim$20~ns. Another $\sim$40~ns was |
| 566 |
> |
necessary for the layer to completely straighten. The other two layers in |
| 567 |
> |
this simulation formed over periods of 22~ns and 42~ns respectively. |
| 568 |
> |
A possible explanation for this rapid reconstruction is the elevated |
| 569 |
> |
temperatures under which our systems were simulated. The process |
| 570 |
> |
would almost certainly take longer at lower temperatures. Additionally, |
| 571 |
> |
our measured times for completion of the doubling after the appearance |
| 572 |
> |
of a nucleation site are likely affected by our periodic boxes. A longer |
| 573 |
> |
step-edge will likely take longer to ``zipper''. |
| 574 |
|
|
| 575 |
|
|
| 576 |
+ |
%Discussion |
| 577 |
+ |
\section{Discussion} |
| 578 |
+ |
We have shown that a classical potential model is able to model the |
| 579 |
+ |
initial reconstruction of the Pt(557) surface upon CO adsorption as |
| 580 |
+ |
shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were |
| 581 |
+ |
able to observe features of the dynamic processes necessary for |
| 582 |
+ |
this reconstruction. Here we discuss the features of the model that |
| 583 |
+ |
give rise to the observed dynamical properties of the (557) reconstruction. |
| 584 |
|
|
| 585 |
+ |
\subsection{Diffusion} |
| 586 |
+ |
The perpendicular diffusion constant |
| 587 |
+ |
appears to be the most important indicator of double layer |
| 588 |
+ |
formation. As highlighted in Figure \ref{fig:reconstruct}, the |
| 589 |
+ |
formation of the double layer did not begin until a nucleation |
| 590 |
+ |
site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994}, |
| 591 |
+ |
the inability for edges to cross leads to an effective edge-edge repulsion that |
| 592 |
+ |
must be overcome to allow step coalescence. |
| 593 |
+ |
A greater $\textbf{D}_\perp$ implies more step-wandering |
| 594 |
+ |
and a larger chance for the stochastic meeting of two edges |
| 595 |
+ |
to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double |
| 596 |
+ |
layer. This helps explain why the time scale for formation after |
| 597 |
+ |
the appearance of a nucleation site was rapid, while the initial |
| 598 |
+ |
appearance of the nucleation site was unpredictable. |
| 599 |
|
|
| 600 |
+ |
\subsection{Mechanism for restructuring} |
| 601 |
+ |
Since the Au surface showed no large scale restructuring in any of |
| 602 |
+ |
our simulations, our discussion will focus on the 50\% Pt-CO system |
| 603 |
+ |
which did exhibit doubling featured in Figure \ref{fig:reconstruct}. A |
| 604 |
+ |
number of possible mechanisms exist to explain the role of adsorbed |
| 605 |
+ |
CO in restructuring the Pt surface. Quadrupolar repulsion between |
| 606 |
+ |
adjacent CO molecules adsorbed on the surface is one possibility. |
| 607 |
+ |
However, the quadrupole-quadrupole interaction is short-ranged and |
| 608 |
+ |
is attractive for some orientations. If the CO molecules are ``locked'' in |
| 609 |
+ |
a specific orientation relative to each other, through atop adsorption for |
| 610 |
+ |
example, this explanation would gain credence. The energetic repulsion |
| 611 |
+ |
between two CO molecules located a distance of 2.77~\AA~apart |
| 612 |
+ |
(nearest-neighbor distance of Pt) and both in a vertical orientation, |
| 613 |
+ |
is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance |
| 614 |
+ |
of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away |
| 615 |
+ |
from a purely vertical orientation also lowers the repulsion. When the |
| 616 |
+ |
carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is |
| 617 |
+ |
reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}. |
| 618 |
+ |
The barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
| 619 |
+ |
repulsion between adjacent CO molecules bound to Pt could increase the surface |
| 620 |
+ |
diffusion. However, the residence time of CO on Pt suggests that these |
| 621 |
+ |
molecules are extremely mobile, with diffusion constants 40 to 2500 times |
| 622 |
+ |
larger than surface Pt atoms. This mobility suggests that the CO are more |
| 623 |
+ |
likely to shift their positions without dragging the Pt along with them. |
| 624 |
|
|
| 625 |
+ |
A different interpretation of the above mechanism, taking into account the large |
| 626 |
+ |
mobility of the CO, looks at how instantaneous and short-lived configurations of |
| 627 |
+ |
CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge |
| 628 |
+ |
breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach |
| 629 |
+ |
an edge atom is $\sim$~43~kcal/mol, as is shown in configuration (a) in Figures |
| 630 |
+ |
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases |
| 631 |
+ |
(e), (g), and (h), the barrier can be lowered to $\sim$~23~kcal/mole. In these instances, |
| 632 |
+ |
it becomes quite energetically favorable to roughen the edge by introducing a small |
| 633 |
+ |
separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in |
| 634 |
+ |
simulations with significant CO populations, although it is present to a lesser extent |
| 635 |
+ |
on lower coverage surfaces and even on the bare surfaces. In these cases it is likely |
| 636 |
+ |
due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism |
| 637 |
+ |
of step-edge breakup suggested by these energy curves is one the most difficult |
| 638 |
+ |
processes, a complete break-away from the step-edge in one unbroken movement. |
| 639 |
+ |
Easier multistep mechanisms likely exist where an adatom moves laterally on the surface |
| 640 |
+ |
after being ejected so it is sitting on the edge. This provides the atom with 5 nearest |
| 641 |
+ |
neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher |
| 642 |
+ |
than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO |
| 643 |
+ |
quadrupolar repulsion is still playing a primary role, but for its importance in roughening |
| 644 |
+ |
the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not |
| 645 |
+ |
born out by their mobility data. The requirement for a large density of CO on the surface |
| 646 |
+ |
for some of the more favorable suggested mechanisms in Figure \ref{fig:SketchGraphic} |
| 647 |
+ |
correspond well with the increased mobility seen on higher coverage surfaces. |
| 648 |
|
|
| 649 |
|
%Sketch graphic of different configurations |
| 650 |
|
\begin{figure}[H] |
| 670 |
|
\label{fig:SketchEnergies} |
| 671 |
|
\end{figure} |
| 672 |
|
|
| 673 |
< |
%Discussion |
| 674 |
< |
\section{Discussion} |
| 675 |
< |
We have shown that the classical potential models are able to model the initial reconstruction of the |
| 676 |
< |
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 677 |
< |
were able to observe features of the dynamic processes necessary for this reconstruction. |
| 673 |
> |
While configurations of CO on the surface are able to increase diffusion, |
| 674 |
> |
this does not immediately provide an explanation for the formation of double |
| 675 |
> |
layers. If adatoms were constrained to their terrace then doubling would be |
| 676 |
> |
much less likely to occur. Nucleation sites could still potentially form, but there |
| 677 |
> |
would not be enough atoms to finish the doubling. Real materials, where the |
| 678 |
> |
step lengths can be taken as infinite, local doubling would be possible, but in |
| 679 |
> |
our simulations with our periodic treatment of the system, this is not possible. |
| 680 |
> |
Thus, there must be a mechanism that explains how adatoms are able to move |
| 681 |
> |
amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate |
| 682 |
> |
where an adatom along the step-edge with an adsorbed CO ``burrows'' into the |
| 683 |
> |
edge displacing an atom onto the higher terrace. This mechanism was chosen |
| 684 |
> |
because of similar events that were observed during the simulations. The barrier |
| 685 |
> |
heights we obtained are only approximations because we constrained the movement |
| 686 |
> |
of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s |
| 687 |
> |
are the more interesting results from this investigation. When CO is not present and |
| 688 |
> |
this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown |
| 689 |
> |
in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol. |
| 690 |
> |
While the barrier height is comparable to the non-CO case, that is a nearly a 20~kcal/mol |
| 691 |
> |
difference in energies and moves the process from slightly unfavorable to energetically favorable. |
| 692 |
|
|
| 632 |
– |
\subsection{Diffusion} |
| 633 |
– |
As shown in Figure \ref{fig:diff}, for the Pt systems, there |
| 634 |
– |
is a strong trend toward higher diffusion constants as |
| 635 |
– |
surface coverage of CO increases. The drop for the 50\% |
| 636 |
– |
case being explained as double layer formation already |
| 637 |
– |
beginning to occur in the analyzed 40~ns, which lowered |
| 638 |
– |
the calculated diffusion rates. Between the parallel and |
| 639 |
– |
perpendicular rates, the perpendicular diffusion constant |
| 640 |
– |
appears to be the most important indicator of double layer |
| 641 |
– |
formation. As highlighted in Figure \ref{fig:reconstruct}, the |
| 642 |
– |
formation of the double layer did not begin until a nucleation |
| 643 |
– |
site appeared. And as mentioned by Williams et al.\cite{Williams:1991, Williams:1994}, |
| 644 |
– |
the inability for edges to cross leads to an effective repulsion. |
| 645 |
– |
This repulsion must be overcome to allow step coalescence. |
| 646 |
– |
A greater $\textbf{D}_\perp$ implies more step-wandering |
| 647 |
– |
and a larger chance for the stochastic meeting of two edges |
| 648 |
– |
to form the nucleation point. Upon that appearance, parallel |
| 649 |
– |
diffusion along the step-edge can help ``zipper'' up the double |
| 650 |
– |
layer. This helps explain why the time scale for formation after |
| 651 |
– |
the appearance of a nucleation site was rapid, while the initial |
| 652 |
– |
appearance of said site was unpredictable. |
| 653 |
– |
|
| 654 |
– |
\subsection{Mechanism for restructuring} |
| 655 |
– |
Since the Au surface showed no large scale restructuring throughout |
| 656 |
– |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 657 |
– |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 658 |
– |
Similarities of our results to those reported previously by Tao et al.\cite{Tao:2010} |
| 659 |
– |
are quite strong. The simulated Pt system exposed to a large dosage |
| 660 |
– |
of CO readily restructures by doubling the terrace widths and step heights. |
| 661 |
– |
The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a |
| 662 |
– |
time, but is rapid on experimental timescales. The adatoms either break |
| 663 |
– |
away from the step-edge and stay on the lower terrace or they lift up onto |
| 664 |
– |
a higher terrace. Once ``free'', they diffuse on the terrace until reaching |
| 665 |
– |
another step-edge or rejoining their original edge. This combination of |
| 666 |
– |
growth and decay of the step-edges is in a state of dynamic equilibrium. |
| 667 |
– |
However, once two previously separated edges meet as shown in Figure 1.B, |
| 668 |
– |
this nucleates the rest of the edge to meet up, forming a double layer. |
| 669 |
– |
From simulations which exhibit a double layer, the time delay from the |
| 670 |
– |
initial appearance of a nucleation point to a fully formed double layer is $\sim$35~ns. |
| 671 |
– |
|
| 672 |
– |
A number of possible mechanisms exist to explain the role of adsorbed |
| 673 |
– |
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 674 |
– |
CO molecules adsorbed on the surface is one possibility. However, |
| 675 |
– |
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 676 |
– |
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 677 |
– |
relative to each other, through atop adsorption for example, this explanation |
| 678 |
– |
gains some credence. The energetic repulsion between two CO located a |
| 679 |
– |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in |
| 680 |
– |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 681 |
– |
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 682 |
– |
nearly 0 kcal/mol. Allowing the CO to rotate away from a purely vertical orientation |
| 683 |
– |
also lowers the repulsion. A minimum of 6.2 kcal/mol is reached at when the |
| 684 |
– |
angle between the 2 CO is $\sim$24\textsuperscript{o}, when the carbons are |
| 685 |
– |
locked at a distance of 2.77 \AA apart. As mentioned above, the energy barrier |
| 686 |
– |
for surface diffusion of a Pt adatom is only 4 kcal/mol. So this repulsion between |
| 687 |
– |
neighboring CO molecules can increase the surface diffusion. However, the |
| 688 |
– |
residence time of CO on Pt was examined and while the majority of the CO is |
| 689 |
– |
on or near the surface throughout the run, the molecules are extremely mobile, |
| 690 |
– |
with diffusion constants 40 to 2500 times larger, depending on coverage. This |
| 691 |
– |
mobility suggests that the CO are more likely to shift their positions without |
| 692 |
– |
necessarily the Pt along with them. |
| 693 |
– |
|
| 694 |
– |
Another possible and more likely mechanism for the restructuring is in the |
| 695 |
– |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 696 |
– |
Pt atoms. To test this hypothesis, numerous configurations of |
| 697 |
– |
CO in varying quantities were arranged on the higher and lower plateaus |
| 698 |
– |
around a step on a otherwise clean Pt(557) surface. A few sample |
| 699 |
– |
configurations are displayed in Figure \ref{fig:lambdaTable}, with |
| 700 |
– |
energies at various positions along the path displayed in Table |
| 701 |
– |
\ref{tab:rxcoord}. Certain configurations of CO, cases B and D for |
| 702 |
– |
example, can have quite strong energetic reasons for breaking |
| 703 |
– |
away from the step-edge. Although the packing of these configurations |
| 704 |
– |
is unlikely until CO coverage has reached a high enough value. |
| 705 |
– |
These examples are showing the most difficult cases, immediate |
| 706 |
– |
adatom formation through breakage away from the step-edge, which |
| 707 |
– |
is why their energies at large distances are relatively high. There are |
| 708 |
– |
mechanistic paths where an edge atom could get shifted to onto the |
| 709 |
– |
step-edge to form a small peak before fully breaking away. And again, |
| 710 |
– |
once the adatom is formed, the barrier for diffusion on the surface is |
| 711 |
– |
negligible. These sample configurations help explain CO's effect on |
| 712 |
– |
general surface mobility and step wandering, but they are lacking in |
| 713 |
– |
providing a mechanism for the formation of double layers. One possible |
| 714 |
– |
mechanism is elucidated in Figure \ref{fig:lambda}, where a burrowing |
| 715 |
– |
and lifting process of an adatom and step-edge atom respectively is |
| 716 |
– |
examined. The system, without CO present, is nearly energetically |
| 717 |
– |
neutral, whereas with CO present there is a $\sim$ 15 kcal/mol drop |
| 718 |
– |
in the energy of the system. |
| 719 |
– |
|
| 693 |
|
%lambda progression of Pt -> shoving its way into the step |
| 694 |
|
\begin{figure}[H] |
| 695 |
|
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
| 702 |
|
\label{fig:lambda} |
| 703 |
|
\end{figure} |
| 704 |
|
|
| 705 |
+ |
The mechanism for doubling on this surface appears to be a convolution of at least |
| 706 |
+ |
these two described processes. For complete doubling of a layer to occur there must |
| 707 |
+ |
be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from |
| 708 |
+ |
that terrace they must either rise up on the ledge above them or drop to the ledge below |
| 709 |
+ |
them. The presence of CO helps with both of these situations. There must be sufficient |
| 710 |
+ |
breakage of the step-edge to increase the concentration of adatoms on the surface. |
| 711 |
+ |
These adatoms must then undergo the burrowing highlighted above or some comparable |
| 712 |
+ |
mechanism to traverse the step-edge. Over time, these mechanisms working in concert |
| 713 |
+ |
led to the formation of a double layer. |
| 714 |
|
|
| 715 |
+ |
\subsection{CO Removal and double layer stability} |
| 716 |
+ |
Once a double layer had formed on the 50\%~Pt system it |
| 717 |
+ |
remained for the rest of the simulation time with minimal |
| 718 |
+ |
movement. There were configurations that showed small |
| 719 |
+ |
wells or peaks forming, but typically within a few nanoseconds |
| 720 |
+ |
the feature would smooth away. Within our simulation time, |
| 721 |
+ |
the formation of the double layer was irreversible and a double |
| 722 |
+ |
layer was never observed to split back into two single layer |
| 723 |
+ |
step-edges while CO was present. To further gauge the effect |
| 724 |
+ |
CO had on this system, additional simulations were run starting |
| 725 |
+ |
from a late configuration of the 50\%~Pt system that had formed |
| 726 |
+ |
double layers. These simulations then had their CO removed. |
| 727 |
+ |
The double layer breaks rapidly in these simulations, already |
| 728 |
+ |
showing a well-defined splitting after 100~ps. Configurations of |
| 729 |
+ |
this system are shown in Figure \ref{fig:breaking}. The coloring |
| 730 |
+ |
of the top and bottom layers helps to exhibit how much mixing |
| 731 |
+ |
the edges experience as they split. These systems were only |
| 732 |
+ |
examined briefly, 10~ns, and within that time despite the initial |
| 733 |
+ |
rapid splitting, the edges only moved another few \AA~apart. |
| 734 |
+ |
It is possible with longer simulation times that the |
| 735 |
+ |
(557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010} |
| 736 |
|
|
| 737 |
|
|
| 738 |
|
|
