| 68 |
|
\begin{doublespace} |
| 69 |
|
|
| 70 |
|
\begin{abstract} |
| 71 |
< |
We examine potential surface reconstructions of Pt and Au(557) |
| 72 |
< |
under various CO coverages using molecular dynamics in order |
| 73 |
< |
to explore possible mechanisms for any observed reconstructions and their dynamics. |
| 74 |
< |
The metal-CO interactions were parameterized as part of this |
| 75 |
< |
work so that an efficient large-scale treatment of this system could be |
| 76 |
< |
undertaken. The large difference in binding strengths of the metal-CO |
| 77 |
< |
interactions was found to play a significant role with regards to |
| 78 |
< |
step-edge stability and adatom diffusion. A small correlation |
| 79 |
< |
between coverage and the magnitude of the diffusion constant was |
| 80 |
< |
also determined. An in-depth examination of the energetics of CO |
| 81 |
< |
adsorbed to the surface provides results that appear sufficient to explain the |
| 82 |
< |
reconstructions observed on the Pt systems and the corresponding lack |
| 83 |
< |
on the Au systems. |
| 71 |
> |
We examine surface reconstructions of Pt and Au(557) under |
| 72 |
> |
various CO coverages using molecular dynamics in order to |
| 73 |
> |
explore possible mechanisms for any observed reconstructions |
| 74 |
> |
and their dynamics. The metal-CO interactions were parameterized |
| 75 |
> |
as part of this work so that an efficient large-scale treatment of |
| 76 |
> |
this system could be undertaken. The large difference in binding |
| 77 |
> |
strengths of the metal-CO interactions was found to play a significant |
| 78 |
> |
role with regards to step-edge stability and adatom diffusion. A |
| 79 |
> |
small correlation between coverage and the diffusion constant |
| 80 |
> |
was also determined. The energetics of CO adsorbed to the surface |
| 81 |
> |
is sufficient to explain the reconstructions observed on the Pt |
| 82 |
> |
systems and the lack of reconstruction of the Au systems. |
| 83 |
> |
|
| 84 |
|
\end{abstract} |
| 85 |
|
|
| 86 |
|
\newpage |
| 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. |
| 120 |
|
Since restructuring typically occurs as a result of specific interactions of the |
| 121 |
|
catalyst with adsorbates, in this work, two metal systems exposed |
| 122 |
|
to carbon monoxide were examined. The Pt(557) surface has already been shown |
| 123 |
< |
to reconstruct under certain conditions. The Au(557) surface, because |
| 124 |
< |
of a weaker interaction with CO, is less likely to undergo this kind |
| 125 |
< |
of reconstruction. |
| 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 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 |
| 134 |
> |
surface. Both groups suggested that the preference CO shows for |
| 135 |
> |
low-coordinated Au atoms was the primary driving force for the reconstruction. |
| 136 |
|
|
| 137 |
|
|
| 138 |
|
|
| 140 |
|
%gold molecular dynamics |
| 141 |
|
|
| 142 |
|
\section{Simulation Methods} |
| 143 |
< |
The challenge in modeling any solid/gas interface problem is the |
| 143 |
> |
The challenge in modeling any solid/gas interface is the |
| 144 |
|
development of a sufficiently general yet computationally tractable |
| 145 |
|
model of the chemical interactions between the surface atoms and |
| 146 |
|
adsorbates. Since the interfaces involved are quite large (10$^3$ - |
| 156 |
|
Coulomb potential. For this work, we have used classical molecular |
| 157 |
|
dynamics with potential energy surfaces that are specifically tuned |
| 158 |
|
for transition metals. In particular, we used the EAM potential for |
| 159 |
< |
Au-Au and Pt-Pt interactions\cite{EAM}, while modeling the CO using a rigid |
| 159 |
> |
Au-Au and Pt-Pt interactions\cite{EAM}. The CO was modeled using a rigid |
| 160 |
|
three-site model developed by Straub and Karplus for studying |
| 161 |
|
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 162 |
|
Pt-CO cross interactions were parameterized as part of this work. |
| 206 |
|
melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr} |
| 207 |
|
fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack |
| 208 |
|
propagation,\cite{BECQUART:1993rg} and alloying |
| 209 |
< |
dynamics.\cite{Shibata:2002hh} All of these potentials have their |
| 210 |
< |
strengths and weaknesses. One of the strengths common to all of the |
| 211 |
< |
methods is the relatively large library of metals for which these |
| 212 |
< |
potentials have been |
| 213 |
< |
parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 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} |
| 213 |
> |
Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88} |
| 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) 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 |
+ |
|
| 223 |
+ |
|
| 224 |
+ |
|
| 225 |
|
\subsection{Carbon Monoxide model} |
| 226 |
|
Previous explanations for the surface rearrangements center on |
| 227 |
< |
the large linear quadrupole moment of carbon monoxide. |
| 227 |
> |
the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} |
| 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 which places a massless M |
| 232 |
< |
site at the center of mass position along the CO bond. The geometry used along |
| 233 |
< |
with the interaction parameters are reproduced in Table~\ref{tab:CO}. The effective |
| 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 |
| 235 |
|
small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
| 236 |
|
to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
| 239 |
|
\begin{table}[H] |
| 240 |
|
\caption{Positions, Lennard-Jones parameters ($\sigma$ and |
| 241 |
|
$\epsilon$), and charges for the CO-CO |
| 242 |
< |
interactions borrowed from Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are |
| 242 |
> |
interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are |
| 243 |
|
in kcal/mol, and charges are in atomic units.} |
| 244 |
|
\centering |
| 245 |
|
\begin{tabular}{| c | c | ccc |} |
| 246 |
|
\hline |
| 247 |
|
& {\it z} & $\sigma$ & $\epsilon$ & q\\ |
| 248 |
|
\hline |
| 249 |
< |
\textbf{C} & -0.6457 & 0.0262 & 3.83 & -0.75 \\ |
| 250 |
< |
\textbf{O} & 0.4843 & 0.1591 & 3.12 & -0.85 \\ |
| 249 |
> |
\textbf{C} & -0.6457 & 3.83 & 0.0262 & -0.75 \\ |
| 250 |
> |
\textbf{O} & 0.4843 & 3.12 & 0.1591 & -0.85 \\ |
| 251 |
|
\textbf{M} & 0.0 & - & - & 1.6 \\ |
| 252 |
|
\hline |
| 253 |
|
\end{tabular} |
| 261 |
|
and theoretical work |
| 262 |
|
\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
| 263 |
|
there is a significant amount of data on adsorption energies for CO on |
| 264 |
< |
clean metal surfaces. Parameters reported by Korzeniewski {\it et |
| 265 |
< |
al.}\cite{Pons:1986} were a starting point for our fits, which were |
| 264 |
> |
clean metal surfaces. An earlier model by Korzeniewski {\it et |
| 265 |
> |
al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were |
| 266 |
|
modified to ensure that the Pt-CO interaction favored the atop binding |
| 267 |
< |
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters} |
| 268 |
< |
This resulted in binding energies that are slightly higher |
| 267 |
> |
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}. |
| 268 |
> |
The modified parameters yield binding energies that are slightly higher |
| 269 |
|
than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
| 270 |
|
et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 271 |
|
Lennard-Jones interaction to mimic strong, but short-ranged partial |
| 272 |
|
binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
| 273 |
< |
Pt-O interaction was parameterized to a Morse potential at a larger |
| 274 |
< |
minimum distance, ($r_o$). This was chosen so that the C would be preferred |
| 275 |
< |
over O as the binder to the surface. In most cases, this parameterization contributes a weak |
| 273 |
> |
Pt-O interaction was modeled with a Morse potential with a large |
| 274 |
> |
equilibrium distance, ($r_o$). These choices ensure that the C is preferred |
| 275 |
> |
over O as the surface-binding atom. In most cases, the Pt-O parameterization contributes a weak |
| 276 |
|
repulsion which favors the atop site. The resulting potential-energy |
| 277 |
|
surface suitably recovers the calculated Pt-C separation length |
| 278 |
|
(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
| 283 |
|
%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
| 284 |
|
The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and |
| 285 |
|
Morse potentials, respectively, to reproduce Au-CO binding energies. |
| 286 |
< |
The limited experimental data for CO adsorption on Au lead us to refine our fits against DFT. |
| 286 |
> |
The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations. |
| 287 |
|
Adsorption energies were obtained from gas-surface DFT calculations with a |
| 288 |
|
periodic supercell plane-wave basis approach, as implemented in the |
| 289 |
< |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are |
| 289 |
> |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were |
| 290 |
|
described with the projector augmented-wave (PAW) |
| 291 |
|
method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
| 292 |
|
included to an energy cutoff of 20 Ry. Electronic energies are |
| 307 |
|
|
| 308 |
|
%Hint at future work |
| 309 |
|
The parameters employed for the metal-CO cross-interactions in this work |
| 310 |
< |
are shown in Table~\ref{co_parameters} and the binding energies on the |
| 311 |
< |
(111) surfaces are displayed in Table~\ref{co_energies}. Charge transfer |
| 310 |
> |
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
| 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 added in |
| 314 |
< |
a future work.\cite{Deshlahra:2012,StreitzMintmire:1994} |
| 313 |
> |
affect binding energies and binding site preferences, and will be addressed in |
| 314 |
> |
future work. |
| 315 |
|
|
| 316 |
|
%Table of Parameters |
| 317 |
|
%Pt Parameter Set 9 |
| 318 |
|
%Au Parameter Set 35 |
| 319 |
|
\begin{table}[H] |
| 320 |
|
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
| 321 |
< |
interactions are modeled with Lennard-Jones potential, while the |
| 321 |
> |
interactions are modeled with Lennard-Jones potentials. While the |
| 322 |
|
metal-O interactions were fit to Morse |
| 323 |
|
potentials. Distances are given in \AA~and energies in kcal/mol. } |
| 324 |
|
\centering |
| 336 |
|
|
| 337 |
|
%Table of energies |
| 338 |
|
\begin{table}[H] |
| 339 |
< |
\caption{Adsorption energies for CO on M(111) at the atop site using the potentials |
| 339 |
> |
\caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials |
| 340 |
|
described in this work. All values are in eV.} |
| 341 |
|
\centering |
| 342 |
|
\begin{tabular}{| c | cc |} |
| 353 |
|
\end{table} |
| 354 |
|
|
| 355 |
|
\subsection{Pt(557) and Au(557) metal interfaces} |
| 356 |
< |
|
| 357 |
< |
Our model systems are composed of 3888 Pt atoms and 3384 Au atoms in a |
| 358 |
< |
FCC crystal that have been cut along the (557) plane so that they are |
| 359 |
< |
periodic in the {\it x} and {\it y} directions, and have been oriented |
| 360 |
< |
to expose two aligned (557) cuts along the extended {\it |
| 361 |
< |
z}-axis. Simulations of the bare metal interfaces at temperatures |
| 362 |
< |
ranging from 300~K to 1200~K were performed to observe the relative |
| 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 confirm the relative |
| 365 |
|
stability of the surfaces without a CO overlayer. |
| 366 |
|
|
| 367 |
< |
The different bulk (and surface) melting temperatures (1337~K for Au |
| 368 |
< |
and 2045~K for Pt) suggest that any possible reconstruction may happen at |
| 367 |
> |
The different bulk melting temperatures (1337~K for Au |
| 368 |
> |
and 2045~K for Pt) 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. These temperatures were chosen because the |
| 372 |
< |
surfaces were relatively stable at these temperatures when no CO was |
| 373 |
< |
present, but experienced additional instability upon addition of CO in the time |
| 352 |
< |
frames we were examining. Each surface was exposed to a range of CO |
| 371 |
> |
respectively for 100 ps. The two surfaces were relatively stable at these |
| 372 |
> |
temperatures when no CO was present, but experienced increased surface |
| 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 amounts correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 376 |
< |
coverage. Higher coverages were tried, but the CO-CO repulsion was preventing |
| 377 |
< |
a higher amount of adsorption. Because of the difference in binding energies, the Pt |
| 378 |
< |
systems very rarely had CO that was not bound to the surface, while |
| 375 |
> |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 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 200ns. All simulations were run using the open |
| 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 |
| 371 |
< |
% diffusion |
| 372 |
< |
% time scale, formation, breakage |
| 387 |
> |
|
| 388 |
> |
|
| 389 |
> |
|
| 390 |
> |
% RESULTS |
| 391 |
> |
% |
| 392 |
|
\section{Results} |
| 393 |
|
\subsection{Structural remodeling} |
| 394 |
< |
Tao et al. showed experimentally that the Pt(557) surface |
| 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 to which no CO was exposed |
| 397 |
> |
did experience minor roughening of the step-edge, but the |
| 398 |
> |
(557) lattice was well-maintained throughout the simulation |
| 399 |
> |
time. The Au systems were limited to greater amounts of |
| 400 |
> |
roughening, i.e. breakup of the step-edge, and some step |
| 401 |
> |
wandering. The lower coverage Pt systems experienced |
| 402 |
> |
similar restructuring but to a greater extent when |
| 403 |
> |
compared to the Au systems. The 50\% coverage |
| 404 |
> |
Pt system formed double layers at numerous spots upon its surface. |
| 405 |
> |
|
| 406 |
> |
|
| 407 |
> |
\subsubsection{Step wandering} |
| 408 |
> |
The 0\% coverage surfaces for both metals showed |
| 409 |
> |
minimal movement at their respective run temperatures. |
| 410 |
> |
As the coverage increased, the mobility of the surface |
| 411 |
> |
also increased. Additionally, at the higher coverages |
| 412 |
> |
on both metals, there was a large increase in the amount |
| 413 |
> |
of observed step-wandering. Previous work by |
| 414 |
> |
Williams\cite{Williams:1993} highlighted the entropic |
| 415 |
> |
contribution to the repulsion felt between step-edges, |
| 416 |
> |
and situations were that repulsion could be negated, or |
| 417 |
> |
overcome, to allow for step coalescence or facet formation. |
| 418 |
> |
|
| 419 |
> |
\subsubsection{Double layers} |
| 420 |
> |
Tao et al. have shown experimentally that the Pt(557) surface |
| 421 |
|
undergoes two separate reconstructions upon CO |
| 422 |
|
adsorption.\cite{Tao:2010} The first involves a doubling of |
| 423 |
|
the step height and plateau length. Similar behavior has been |
| 424 |
< |
seen to occur on numerous surfaces at varying conditions (Ni 977, Si 111, etc). |
| 424 |
> |
seen to occur on numerous surfaces at varying conditions: Ni(977), Si(111). |
| 425 |
|
\cite{Williams:1994,Williams:1991,Pearl} Of the two systems |
| 426 |
< |
we examined, the Pt system showed a larger amount of |
| 426 |
> |
we examined, the Pt system showed a greater propensity for |
| 427 |
|
reconstruction when compared to the Au system. The amount |
| 428 |
< |
of reconstruction appears to be correlated to the amount of CO |
| 429 |
< |
adsorbed upon the surface. We believe this is related to the |
| 430 |
< |
effect that adsorbate coverage has on edge breakup and surface |
| 431 |
< |
diffusion of adatoms. While both systems displayed step-edge |
| 428 |
> |
of reconstruction is correlated to the amount of CO |
| 429 |
> |
adsorbed upon the surface. This appears to be related to the |
| 430 |
> |
effect that adsorbate coverage has on edge breakup and on the surface |
| 431 |
> |
diffusion of metal adatoms. While both systems displayed step-edge |
| 432 |
|
wandering, only the Pt surface underwent the doubling seen by |
| 433 |
< |
Tao et al., within the time scales we were modeling. Specifically, |
| 434 |
< |
only the 50~\% coverage Pt system was observed to have a |
| 435 |
< |
step-edge undergo a complete doubling in the time scales we |
| 436 |
< |
were able to monitor. This event encouraged us to allow that |
| 437 |
< |
specific system to run for much longer periods during which two |
| 438 |
< |
more double layers were created. The other systems, not displaying |
| 439 |
< |
any large scale changes of interest, were all stopped after running |
| 395 |
< |
for 40 ns in the microcanonical ensemble. Despite no observation |
| 396 |
< |
of double layer formation, the other Pt systems tended to show |
| 397 |
< |
more cumulative lateral movement of the step-edges when |
| 398 |
< |
compared to the Au systems. The 50\% Pt system is highlighted |
| 433 |
> |
Tao et al. within the time scales studied here. |
| 434 |
> |
Only the 50\% coverage Pt system exhibited |
| 435 |
> |
a complete doubling in the time scales we |
| 436 |
> |
were able to monitor. Over longer periods (150~ns) two more double layers formed on this interface. |
| 437 |
> |
Although double layer formation did not occur in the other Pt systems, they show |
| 438 |
> |
more lateral movement of the step-edges |
| 439 |
> |
compared to their Au counterparts. The 50\% Pt system is highlighted |
| 440 |
|
in Figure \ref{fig:reconstruct} at various times along the simulation |
| 441 |
< |
showing the evolution of the system. |
| 441 |
> |
showing the evolution of a step-edge. |
| 442 |
|
|
| 443 |
|
The second reconstruction on the Pt(557) surface observed by |
| 444 |
|
Tao involved the formation of triangular clusters that stretched |
| 445 |
|
across the plateau between two step-edges. Neither system, within |
| 446 |
< |
our simulated time scales, experiences this reconstruction. A constructed |
| 406 |
< |
system in which the triangular motifs were constructed on the surface |
| 407 |
< |
will be explored in future work and is shown in the supporting information. |
| 446 |
> |
the 40~ns time scale, experienced this reconstruction. |
| 447 |
|
|
| 448 |
|
\subsection{Dynamics} |
| 449 |
< |
While atomistic-like simulations of stepped surfaces have been |
| 450 |
< |
performed before, they tend to be performed using Monte Carlo |
| 451 |
< |
techniques\cite{Williams:1991,Williams:1994}. This allows them |
| 452 |
< |
to efficiently sample the equilibrium thermodynamic landscape |
| 453 |
< |
but at the expense of ignoring the dynamics of the system. Previous |
| 454 |
< |
work by Pearl and Sibener\cite{Pearl}, using STM, has been able to |
| 455 |
< |
visualize the coalescing of steps of Ni(977). The time scale of the image |
| 456 |
< |
acquisition, $\sim$70 s/image provides an upper bounds for the time |
| 457 |
< |
required for the doubling to actually occur. Statistical treatments of step-edges |
| 458 |
< |
are adept at analyzing such systems. However, in a system where |
| 459 |
< |
the number of steps is limited, examining the individual atoms that make |
| 421 |
< |
up the steps can provide useful information as well. |
| 449 |
> |
Previous atomistic simulations of stepped surfaces dealt largely |
| 450 |
> |
with the energetics and structures at different conditions |
| 451 |
> |
\cite{Williams:1991,Williams:1994}. Consequently, the most common |
| 452 |
> |
technique utilized to date has been Monte Carlo sampling. Monte Carlo gives an efficient |
| 453 |
> |
sampling of the equilibrium thermodynamic landscape at the expense |
| 454 |
> |
of ignoring the dynamics of the system. Previous work by Pearl and |
| 455 |
> |
Sibener\cite{Pearl}, using STM, has been able to show the coalescing |
| 456 |
> |
of steps on Ni(977). The time scale of the image acquisition, |
| 457 |
> |
$\sim$70 s/image provides an upper bound for the time required for |
| 458 |
> |
the doubling to occur. In this section we give data on dynamic and |
| 459 |
> |
transport properties, e.g. diffusion, layer formation time, etc. |
| 460 |
|
|
| 461 |
|
|
| 462 |
|
\subsubsection{Transport of surface metal atoms} |
| 463 |
|
%forcedSystems/stepSeparation |
| 464 |
|
The movement or wandering of a step-edge is a cooperative effect |
| 465 |
|
arising from the individual movements, primarily through surface |
| 466 |
< |
diffusion, of the atoms making up the step. An ideal metal surface |
| 467 |
< |
displaying a low index facet, (111) or (100) is unlikely to experience |
| 466 |
> |
diffusion, of the atoms making up the steps. An ideal metal surface |
| 467 |
> |
displaying a low index facet, (111) or (100), is unlikely to experience |
| 468 |
|
much surface diffusion because of the large energetic barrier that must |
| 469 |
|
be overcome to lift an atom out of the surface. The presence of step-edges |
| 470 |
|
on higher-index surfaces provide a source for mobile metal atoms. |
| 471 |
|
Breaking away from the step-edge on a clean surface still imposes an |
| 472 |
< |
energetic penalty around $\sim$~40 kcal/mole, but is much less than lifting |
| 473 |
< |
the same metal atom out from the surface, \textgreater~60 kcal/mole, and |
| 474 |
< |
the penalty lowers even further when CO is present in sufficient quantities |
| 475 |
< |
on the surface. For certain tested distributions of CO, the penalty was lowered |
| 476 |
< |
to $\sim$~20 kcal/mole. Once an adatom exists on the surface, its barrier for |
| 477 |
< |
diffusion is negligible ( \textless~4 kcal/mole) and is well able to explore the |
| 478 |
< |
terrace before potentially rejoining its original step-edge or becoming a part |
| 479 |
< |
of a different edge. Atoms traversing separate terraces is a more difficult |
| 480 |
< |
process, but can be overcome through a joining and lifting stage which is |
| 481 |
< |
examined in the discussion section. By tracking the mobility of individual |
| 472 |
> |
energetic penalty around $\sim$~40 kcal/mol, but this is significantly easier than lifting |
| 473 |
> |
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 474 |
> |
The penalty lowers significantly when CO is present in sufficient quantities |
| 475 |
> |
on the surface. For certain distributions of CO, the penalty can fall as low as |
| 476 |
> |
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 477 |
> |
diffusion is negligible ( \textless~4 kcal/mol) and these adatoms are |
| 478 |
> |
able to explore the terrace before rejoining either the original step-edge or |
| 479 |
> |
becoming a part of a different edge. It is a more difficult process for an atom |
| 480 |
> |
to traverse to a separate terrace although the presence of CO can lower the |
| 481 |
> |
energy barrier required to lift or lower the adatom. By tracking the mobility of individual |
| 482 |
|
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 483 |
< |
diffusion rates and how varying coverages of CO affected the rates. Close |
| 483 |
> |
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 484 |
|
observation of the mobile metal atoms showed that they were typically in |
| 485 |
< |
equilibrium with the step-edges, constantly breaking apart and rejoining. |
| 486 |
< |
At times their motion was concerted and two or more adatoms would be |
| 487 |
< |
observed moving together across the surfaces. The primary challenge in |
| 450 |
< |
quantifying the overall surface mobility was in defining ``mobile" vs. ``static" atoms. |
| 485 |
> |
equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. |
| 486 |
> |
At times, their motion was concerted and two or more adatoms would be |
| 487 |
> |
observed moving together across the surfaces. |
| 488 |
|
|
| 489 |
< |
A particle was considered mobile once it had traveled more than 2~\AA~ |
| 490 |
< |
between saved configurations of the system (10-100 ps). An atom that was |
| 491 |
< |
truly mobile would typically travel much greater than this, but the 2~\AA~ cutoff |
| 492 |
< |
was to prevent the in-place vibrational movement of non-surface atoms from |
| 493 |
< |
being included in the analysis. Diffusion on a surface is strongly affected by |
| 494 |
< |
local structures and in this work the presence of single and double layer |
| 489 |
> |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 490 |
> |
between saved configurations of the system (typically 10-100 ps). An atom that was |
| 491 |
> |
truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 492 |
> |
was used to prevent swamping the diffusion data with the in-place vibrational |
| 493 |
> |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 494 |
> |
local structures and in this work, the presence of single and double layer |
| 495 |
|
step-edges causes the diffusion parallel to the step-edges to be different |
| 496 |
< |
from the diffusion perpendicular to these edges. This led us to compute |
| 497 |
< |
those diffusions separately as seen in Figure \ref{fig:diff}. |
| 496 |
> |
from the diffusion perpendicular to these edges. Parallel and perpendicular |
| 497 |
> |
diffusion constants are shown in Figure \ref{fig:diff}. |
| 498 |
|
|
| 499 |
< |
\subsubsection{Double layer formation} |
| 500 |
< |
The increased amounts of diffusion on Pt at the higher CO coverages appears |
| 501 |
< |
to play a primary role in the formation of double layers, although this conclusion |
| 502 |
< |
does not explain the 33\% coverage Pt system. On the 50\% system, three |
| 503 |
< |
separate layers were formed over the extended run time of this system. As |
| 504 |
< |
mentioned earlier, previous experimental work has given some insight into the |
| 505 |
< |
upper bounds of the time required for enough atoms to move around to allow two |
| 506 |
< |
steps to coalesce\cite{Williams:1991,Pearl}. As seen in Figure \ref{fig:reconstruct}, |
| 507 |
< |
the first appearance of a double layer, a nodal site, appears at 19 ns into the |
| 508 |
< |
simulation. Within 12 ns, nearly half of the step has formed the double layer and |
| 509 |
< |
by 86 ns, a smooth complete layer has formed. The double layer is ``complete" by |
| 510 |
< |
37 ns but is a bit rough. From the appearance of the first node to the initial doubling |
| 511 |
< |
of the layers ignoring their roughness took $\sim$~20 ns. Another ~40 ns was |
| 512 |
< |
necessary for the layer to completely straighten. The other two layers in this |
| 513 |
< |
simulation form over a period of 22 ns and 42 ns respectively. Comparing this to |
| 514 |
< |
the upper bounds of the image scan, it is likely that aspects of this reconstruction |
| 515 |
< |
occur very quickly. |
| 499 |
> |
\subsubsection{Dynamics of double layer formation} |
| 500 |
> |
The increased diffusion on Pt at the higher |
| 501 |
> |
CO coverages plays a primary role in double layer formation. However, this is not |
| 502 |
> |
a complete explanation -- the 33\%~Pt system |
| 503 |
> |
has higher diffusion constants but did not show |
| 504 |
> |
any signs of edge doubling. On the |
| 505 |
> |
50\%~Pt system, three separate layers were formed over |
| 506 |
> |
150~ns of simulation time. Previous experimental |
| 507 |
> |
work gives insight into the upper bounds of the |
| 508 |
> |
time required for step coalescence.\cite{Williams:1991,Pearl} |
| 509 |
> |
In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 510 |
> |
appearance of a double layer, appears at 19~ns |
| 511 |
> |
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
| 512 |
> |
formed the double layer and by 86 ns, the complete layer |
| 513 |
> |
has been flattened out. The double layer could be considered |
| 514 |
> |
``complete" by 37~ns but remains a bit rough. From the |
| 515 |
> |
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
| 516 |
> |
$\sim$40~ns was necessary for the layer to completely straighten. |
| 517 |
> |
The other two layers in this simulation formed over periods of |
| 518 |
> |
22~ns and 42~ns respectively. Comparing this to the upper |
| 519 |
> |
bounds of the image scan, it is likely that most aspects of this |
| 520 |
> |
reconstruction occur very rapidly. A possible explanation |
| 521 |
> |
for this rapid reconstruction is the elevated temperatures |
| 522 |
> |
under which our systems were simulated. It is probable that the process would |
| 523 |
> |
take longer at lower temperatures. |
| 524 |
|
|
| 525 |
|
%Evolution of surface |
| 526 |
|
\begin{figure}[H] |
| 554 |
|
|
| 555 |
|
%Discussion |
| 556 |
|
\section{Discussion} |
| 557 |
< |
In this paper we have shown that we were able to accurately model the initial reconstruction of the |
| 557 |
> |
We have shown that the classical potential models are able to model the initial reconstruction of the |
| 558 |
|
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 559 |
< |
were able to observe the dynamic processes necessary for this reconstruction. |
| 559 |
> |
were able to observe features of the dynamic processes necessary for this reconstruction. |
| 560 |
|
|
| 561 |
|
\subsection{Mechanism for restructuring} |
| 562 |
< |
Comparing the results from simulation to those reported previously by |
| 563 |
< |
Tao et al.\cite{Tao:2010} the similarities in the Pt-CO system are quite |
| 564 |
< |
strong. As shown in Figure \ref{fig:reconstruct}, the simulated Pt |
| 565 |
< |
system under a CO atmosphere will restructure by doubling the terrace |
| 566 |
< |
heights. The restructuring occurs slowly, one to two Pt atoms at a time. |
| 567 |
< |
Looking at individual configurations of the system, the adatoms either |
| 562 |
> |
Since the Au surface showed no large scale restructuring throughout |
| 563 |
> |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 564 |
> |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 565 |
> |
Similarities of our results to those reported previously by |
| 566 |
> |
Tao et al.\cite{Tao:2010} are quite |
| 567 |
> |
strong. The simulated Pt |
| 568 |
> |
system exposed to a large dosage of CO readily restructures by doubling the terrace |
| 569 |
> |
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. |
| 570 |
> |
The adatoms either |
| 571 |
|
break away from the step-edge and stay on the lower terrace or they lift |
| 572 |
< |
up onto the higher terrace. Once ``free'' they will diffuse on the terrace |
| 573 |
< |
until reaching another step-edge or coming back to their original edge. |
| 572 |
> |
up onto a higher terrace. Once ``free'', they diffuse on the terrace |
| 573 |
> |
until reaching another step-edge or rejoining their original edge. |
| 574 |
|
This combination of growth and decay of the step-edges is in a state of |
| 575 |
|
dynamic equilibrium. However, once two previously separated edges |
| 576 |
< |
meet as shown in Figure 1.B, this meeting point tends to act as a focus |
| 577 |
< |
or growth point for the rest of the edge to meet up, akin to that of a zipper. |
| 530 |
< |
From the handful of cases where a double layer was formed during the |
| 531 |
< |
simulation, measuring from the initial appearance of a growth point, the |
| 532 |
< |
double layer tends to be fully formed within $\sim$~35 ns. |
| 576 |
> |
meet as shown in Figure 1.B, this nucleates the rest of the edge to meet up, forming a double layer. |
| 577 |
> |
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. |
| 578 |
|
|
| 579 |
|
A number of possible mechanisms exist to explain the role of adsorbed |
| 580 |
|
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 581 |
< |
CO molecules adsorbed on the surface is one likely possibility. However, |
| 581 |
> |
CO molecules adsorbed on the surface is one possibility. However, |
| 582 |
|
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 583 |
|
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 584 |
< |
relative to each other, through atop adsorption perhaps, this explanation |
| 585 |
< |
gains some weight. The energetic repulsion between two CO located a |
| 586 |
< |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in |
| 587 |
< |
a vertical orientation is 8.62 kcal/mole. Moving the CO apart to the second |
| 584 |
> |
relative to each other, through atop adsorption for example, this explanation |
| 585 |
> |
gains some credence. The energetic repulsion between two CO located a |
| 586 |
> |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in |
| 587 |
> |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 588 |
|
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 589 |
< |
nearly 0 kcal/mole. Allowing the CO's to leave a purely vertical orientation |
| 590 |
< |
also quickly drops the repulsion, a minimum is reached at $\sim$24 degrees |
| 591 |
< |
of 6.2 kcal/mole. As mentioned above, the energy barrier for surface diffusion |
| 592 |
< |
of a Pt adatom is only 4 kcal/mole. So this repulsion between CO can help |
| 593 |
< |
increase the surface diffusion. However, the residence time of CO was |
| 589 |
> |
nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation |
| 590 |
> |
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. |
| 591 |
> |
As mentioned above, the energy barrier for surface diffusion |
| 592 |
> |
of a Pt adatom is only 4 kcal/mol. So this repulsion between neighboring CO molecules can |
| 593 |
> |
increase the surface diffusion. However, the residence time of CO on Pt was |
| 594 |
|
examined and while the majority of the CO is on or near the surface throughout |
| 595 |
< |
the run, it is extremely mobile. This mobility suggests that the CO are more |
| 596 |
< |
likely to shift their positions without necessarily dragging the Pt along with them. |
| 595 |
> |
the run, most molecules are mobile. This mobility suggests that the CO are more |
| 596 |
> |
likely to shift their positions without necessarily the Pt along with them. |
| 597 |
|
|
| 598 |
|
Another possible and more likely mechanism for the restructuring is in the |
| 599 |
|
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 627 |
|
|
| 628 |
|
|
| 629 |
|
\subsection{Diffusion} |
| 630 |
< |
As shown in the results section, the diffusion parallel to the step-edge tends to be |
| 631 |
< |
much larger than that perpendicular to the step-edge, likely because of the dynamic |
| 630 |
> |
The diffusion parallel to the step-edge tends to be |
| 631 |
> |
much larger than that perpendicular to the step-edge. The dynamic |
| 632 |
|
equilibrium that is established between the step-edge and adatom interface. The coverage |
| 633 |
|
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}. |
| 634 |
|
The |
| 656 |
|
|
| 657 |
|
|
| 658 |
|
%Peaks! |
| 659 |
< |
\begin{figure}[H] |
| 660 |
< |
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 661 |
< |
\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 662 |
< |
of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 663 |
< |
aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 664 |
< |
\label{fig:peaks} |
| 665 |
< |
\end{figure} |
| 659 |
> |
%\begin{figure}[H] |
| 660 |
> |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 661 |
> |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 662 |
> |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 663 |
> |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 664 |
> |
%\label{fig:peaks} |
| 665 |
> |
%\end{figure} |
| 666 |
|
|
| 667 |
|
|
| 668 |
|
%Don't think I need this |
| 676 |
|
|
| 677 |
|
|
| 678 |
|
\section{Conclusion} |
| 679 |
< |
In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in < $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems. |
| 679 |
> |
In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in less than a $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems. |
| 680 |
|
|
| 681 |
|
%Things I am not ready to remove yet |
| 682 |
|
|
