| 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 |
| 130 |
|
%gold molecular dynamics |
| 131 |
|
|
| 132 |
|
\section{Simulation Methods} |
| 133 |
< |
The challenge in modeling any solid/gas interface problem is the |
| 133 |
> |
The challenge in modeling any solid/gas interface is the |
| 134 |
|
development of a sufficiently general yet computationally tractable |
| 135 |
|
model of the chemical interactions between the surface atoms and |
| 136 |
|
adsorbates. Since the interfaces involved are quite large (10$^3$ - |
| 146 |
|
Coulomb potential. For this work, we have used classical molecular |
| 147 |
|
dynamics with potential energy surfaces that are specifically tuned |
| 148 |
|
for transition metals. In particular, we used the EAM potential for |
| 149 |
< |
Au-Au and Pt-Pt interactions\cite{EAM}, while modeling the CO using a rigid |
| 149 |
> |
Au-Au and Pt-Pt interactions\cite{EAM}. The CO was modeled using a rigid |
| 150 |
|
three-site model developed by Straub and Karplus for studying |
| 151 |
|
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 152 |
|
Pt-CO cross interactions were parameterized as part of this work. |
| 197 |
|
fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack |
| 198 |
|
propagation,\cite{BECQUART:1993rg} and alloying |
| 199 |
|
dynamics.\cite{Shibata:2002hh} All of these potentials have their |
| 200 |
< |
strengths and weaknesses. One of the strengths common to all of the |
| 201 |
< |
methods is the relatively large library of metals for which these |
| 202 |
< |
potentials have been |
| 203 |
< |
parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 200 |
> |
strengths and weaknesses. \cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 201 |
|
|
| 202 |
|
\subsection{Carbon Monoxide model} |
| 203 |
|
Previous explanations for the surface rearrangements center on |
| 204 |
< |
the large linear quadrupole moment of carbon monoxide. |
| 204 |
> |
the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} |
| 205 |
|
We used a model first proposed by Karplus and Straub to study |
| 206 |
|
the photodissociation of CO from myoglobin because it reproduces |
| 207 |
|
the quadrupole moment well.\cite{Straub} The Straub and |
| 208 |
< |
Karplus model, treats CO as a rigid three site molecule which places a massless M |
| 209 |
< |
site at the center of mass position along the CO bond. The geometry used along |
| 210 |
< |
with the interaction parameters are reproduced in Table~\ref{tab:CO}. The effective |
| 208 |
> |
Karplus model, treats CO as a rigid three site molecule with a massless M |
| 209 |
> |
site at the molecular center of mass. The geometry and interaction |
| 210 |
> |
parameters are reproduced in Table~\ref{tab:CO}. The effective |
| 211 |
|
dipole moment, calculated from the assigned charges, is still |
| 212 |
|
small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
| 213 |
|
to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
| 216 |
|
\begin{table}[H] |
| 217 |
|
\caption{Positions, Lennard-Jones parameters ($\sigma$ and |
| 218 |
|
$\epsilon$), and charges for the CO-CO |
| 219 |
< |
interactions borrowed from Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are |
| 219 |
> |
interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are |
| 220 |
|
in kcal/mol, and charges are in atomic units.} |
| 221 |
|
\centering |
| 222 |
|
\begin{tabular}{| c | c | ccc |} |
| 223 |
|
\hline |
| 224 |
|
& {\it z} & $\sigma$ & $\epsilon$ & q\\ |
| 225 |
|
\hline |
| 226 |
< |
\textbf{C} & -0.6457 & 0.0262 & 3.83 & -0.75 \\ |
| 227 |
< |
\textbf{O} & 0.4843 & 0.1591 & 3.12 & -0.85 \\ |
| 226 |
> |
\textbf{C} & -0.6457 & 3.83 & 0.0262 & -0.75 \\ |
| 227 |
> |
\textbf{O} & 0.4843 & 3.12 & 0.1591 & -0.85 \\ |
| 228 |
|
\textbf{M} & 0.0 & - & - & 1.6 \\ |
| 229 |
|
\hline |
| 230 |
|
\end{tabular} |
| 238 |
|
and theoretical work |
| 239 |
|
\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
| 240 |
|
there is a significant amount of data on adsorption energies for CO on |
| 241 |
< |
clean metal surfaces. Parameters reported by Korzeniewski {\it et |
| 242 |
< |
al.}\cite{Pons:1986} were a starting point for our fits, which were |
| 241 |
> |
clean metal surfaces. An earlier model by Korzeniewski {\it et |
| 242 |
> |
al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were |
| 243 |
|
modified to ensure that the Pt-CO interaction favored the atop binding |
| 244 |
< |
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters} |
| 245 |
< |
This resulted in binding energies that are slightly higher |
| 244 |
> |
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}. |
| 245 |
> |
The modified parameters yield binding energies that are slightly higher |
| 246 |
|
than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
| 247 |
|
et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 248 |
|
Lennard-Jones interaction to mimic strong, but short-ranged partial |
| 249 |
|
binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
| 250 |
< |
Pt-O interaction was parameterized to a Morse potential at a larger |
| 251 |
< |
minimum distance, ($r_o$). This was chosen so that the C would be preferred |
| 252 |
< |
over O as the binder to the surface. In most cases, this parameterization contributes a weak |
| 250 |
> |
Pt-O interaction was modeled with a Morse potential with a large |
| 251 |
> |
equilibrium distance, ($r_o$). These choices ensure that the C is preferred |
| 252 |
> |
over O as the surface-binding atom. In most cases, the Pt-O parameterization contributes a weak |
| 253 |
|
repulsion which favors the atop site. The resulting potential-energy |
| 254 |
|
surface suitably recovers the calculated Pt-C separation length |
| 255 |
|
(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
| 260 |
|
%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
| 261 |
|
The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and |
| 262 |
|
Morse potentials, respectively, to reproduce Au-CO binding energies. |
| 263 |
< |
The limited experimental data for CO adsorption on Au lead us to refine our fits against DFT. |
| 263 |
> |
The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations. |
| 264 |
|
Adsorption energies were obtained from gas-surface DFT calculations with a |
| 265 |
|
periodic supercell plane-wave basis approach, as implemented in the |
| 266 |
< |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are |
| 266 |
> |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were |
| 267 |
|
described with the projector augmented-wave (PAW) |
| 268 |
|
method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
| 269 |
|
included to an energy cutoff of 20 Ry. Electronic energies are |
| 284 |
|
|
| 285 |
|
%Hint at future work |
| 286 |
|
The parameters employed for the metal-CO cross-interactions in this work |
| 287 |
< |
are shown in Table~\ref{co_parameters} and the binding energies on the |
| 288 |
< |
(111) surfaces are displayed in Table~\ref{co_energies}. Charge transfer |
| 287 |
> |
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
| 288 |
> |
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
| 289 |
|
and polarization are neglected in this model, although these effects are likely to |
| 290 |
< |
affect binding energies and binding site preferences, and will be added in |
| 290 |
> |
affect binding energies and binding site preferences, and will be addressed in |
| 291 |
|
a future work.\cite{Deshlahra:2012,StreitzMintmire:1994} |
| 292 |
|
|
| 293 |
|
%Table of Parameters |
| 295 |
|
%Au Parameter Set 35 |
| 296 |
|
\begin{table}[H] |
| 297 |
|
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
| 298 |
< |
interactions are modeled with Lennard-Jones potential, while the |
| 298 |
> |
interactions are modeled with Lennard-Jones potentials. While the |
| 299 |
|
metal-O interactions were fit to Morse |
| 300 |
|
potentials. Distances are given in \AA~and energies in kcal/mol. } |
| 301 |
|
\centering |
| 313 |
|
|
| 314 |
|
%Table of energies |
| 315 |
|
\begin{table}[H] |
| 316 |
< |
\caption{Adsorption energies for CO on M(111) at the atop site using the potentials |
| 316 |
> |
\caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials |
| 317 |
|
described in this work. All values are in eV.} |
| 318 |
|
\centering |
| 319 |
|
\begin{tabular}{| c | cc |} |
| 339 |
|
ranging from 300~K to 1200~K were performed to observe the relative |
| 340 |
|
stability of the surfaces without a CO overlayer. |
| 341 |
|
|
| 342 |
< |
The different bulk (and surface) melting temperatures (1337~K for Au |
| 343 |
< |
and 2045~K for Pt) suggest that any possible reconstruction may happen at |
| 342 |
> |
The different bulk melting temperatures (1337~K for Au |
| 343 |
> |
and 2045~K for Pt) suggest that any possible reconstruction should happen at |
| 344 |
|
different temperatures for the two metals. The bare Au and Pt surfaces were |
| 345 |
|
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
| 346 |
< |
respectively for 100 ps. These temperatures were chosen because the |
| 347 |
< |
surfaces were relatively stable at these temperatures when no CO was |
| 348 |
< |
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 |
| 346 |
> |
respectively for 100 ps. The two surfaces were relatively stable at these |
| 347 |
> |
temperatures when no CO was present, but experienced increased surface |
| 348 |
> |
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
| 349 |
|
that was initially placed in the vacuum region. Upon full adsorption, |
| 350 |
< |
these amounts correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 351 |
< |
coverage. Higher coverages were tried, but the CO-CO repulsion was preventing |
| 352 |
< |
a higher amount of adsorption. Because of the difference in binding energies, the Pt |
| 357 |
< |
systems very rarely had CO that was not bound to the surface, while |
| 350 |
> |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 351 |
> |
coverage. Higher coverages resulted in CO double layer formation, which introduces artifacts that are not relevant to (557) reconstruction. |
| 352 |
> |
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
| 353 |
|
the Au surfaces often had a significant CO population in the gas |
| 354 |
|
phase. These systems were allowed to reach thermal equilibrium (over |
| 355 |
|
5 ns) before being run in the microcanonical (NVE) ensemble for |
| 356 |
|
data collection. All of the systems examined had at least 40 ns in the |
| 357 |
|
data collection stage, although simulation times for some of the |
| 358 |
< |
systems exceeded 200ns. All simulations were run using the open |
| 358 |
> |
systems exceeded 200~ns. Simulations were run using the open |
| 359 |
|
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} |
| 360 |
|
|
| 361 |
|
% Just results, leave discussion for discussion section |
| 367 |
|
% time scale, formation, breakage |
| 368 |
|
\section{Results} |
| 369 |
|
\subsection{Structural remodeling} |
| 370 |
< |
Tao et al. showed experimentally that the Pt(557) surface |
| 370 |
> |
Tao et al. have shown experimentally that the Pt(557) surface |
| 371 |
|
undergoes two separate reconstructions upon CO |
| 372 |
|
adsorption.\cite{Tao:2010} The first involves a doubling of |
| 373 |
|
the step height and plateau length. Similar behavior has been |
| 374 |
< |
seen to occur on numerous surfaces at varying conditions (Ni 977, Si 111, etc). |
| 374 |
> |
seen to occur on numerous surfaces at varying conditions: Ni(977), Si(111). |
| 375 |
|
\cite{Williams:1994,Williams:1991,Pearl} Of the two systems |
| 376 |
|
we examined, the Pt system showed a larger amount of |
| 377 |
|
reconstruction when compared to the Au system. The amount |
| 378 |
< |
of reconstruction appears to be correlated to the amount of CO |
| 379 |
< |
adsorbed upon the surface. We believe this is related to the |
| 380 |
< |
effect that adsorbate coverage has on edge breakup and surface |
| 381 |
< |
diffusion of adatoms. While both systems displayed step-edge |
| 378 |
> |
of reconstruction is correlated to the amount of CO |
| 379 |
> |
adsorbed upon the surface. This appears to be related to the |
| 380 |
> |
effect that adsorbate coverage has on edge breakup and on the surface |
| 381 |
> |
diffusion of metal adatoms. While both systems displayed step-edge |
| 382 |
|
wandering, only the Pt surface underwent the doubling seen by |
| 383 |
< |
Tao et al., within the time scales we were modeling. Specifically, |
| 384 |
< |
only the 50~\% coverage Pt system was observed to have a |
| 385 |
< |
step-edge undergo a complete doubling in the time scales we |
| 386 |
< |
were able to monitor. This event encouraged us to allow that |
| 387 |
< |
specific system to run for much longer periods during which two |
| 388 |
< |
more double layers were created. The other systems, not displaying |
| 394 |
< |
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 |
| 383 |
> |
Tao et al. within the time scales studied here. |
| 384 |
> |
Only the 50~\% coverage Pt system exhibited |
| 385 |
> |
a complete doubling in the time scales we |
| 386 |
> |
were able to monitor. Over longer periods (150~ns) two more double layers formed on this interface. |
| 387 |
> |
Although double layer formation did not occur in the other Pt systems, they show |
| 388 |
> |
more lateral movement of the step-edges |
| 389 |
|
compared to the Au systems. The 50\% Pt system is highlighted |
| 390 |
|
in Figure \ref{fig:reconstruct} at various times along the simulation |
| 391 |
< |
showing the evolution of the system. |
| 391 |
> |
showing the evolution of a step-edge. |
| 392 |
|
|
| 393 |
|
The second reconstruction on the Pt(557) surface observed by |
| 394 |
|
Tao involved the formation of triangular clusters that stretched |
| 395 |
|
across the plateau between two step-edges. Neither system, within |
| 396 |
< |
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. |
| 396 |
> |
the 40~ns time scale, experienced this reconstruction. |
| 397 |
|
|
| 398 |
|
\subsection{Dynamics} |
| 399 |
|
While atomistic-like simulations of stepped surfaces have been |
