| 58 |
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Notre Dame, Indiana 46556} |
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|
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%Date |
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\date{Dec 15, 2012} |
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\date{Mar 4, 2013} |
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|
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%authors |
| 64 |
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|
| 68 |
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\begin{doublespace} |
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|
| 70 |
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\begin{abstract} |
| 71 |
< |
|
| 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 relative binding strengths of the metal-CO |
| 77 |
> |
interactions were found to play a large role with regards to |
| 78 |
> |
step-edge stability and adatom diffusion. A small correlation |
| 79 |
> |
between coverage and the size 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 |
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reconstructions observed on the Pt systems and the corresponding lack |
| 83 |
> |
on the Au systems. |
| 84 |
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\end{abstract} |
| 85 |
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|
| 86 |
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\newpage |
| 112 |
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reversible restructuring under exposure to moderate pressures of |
| 113 |
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carbon monoxide.\cite{Tao:2010} |
| 114 |
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|
| 115 |
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This work an effort to understand the mechanism and timescale for |
| 115 |
> |
This work is an attempt to understand the mechanism and timescale for |
| 116 |
|
surface restructuring using molecular simulations. Since the dynamics |
| 117 |
< |
of the process is of particular interest, we utilize classical force |
| 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 observe the process of interest. |
| 120 |
< |
|
| 121 |
< |
Since restructuring occurs as a result of specific interactions of the |
| 122 |
< |
catalyst with adsorbates, two metal systems exposed to carbon monoxide |
| 111 |
< |
were examined in this work. The Pt(557) surface has already been shown |
| 119 |
> |
computational efficiency necessary to simulate the process of interest. |
| 120 |
> |
Restructuring can occur as a result of specific interactions of the |
| 121 |
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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 |
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of a weaker interaction with CO, is less likely to undergo this kind |
| 125 |
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of reconstruction. MORE HERE ON PT AND AU PREVIOUS WORK. |
| 144 |
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Coulomb potential. For this work, we have used classical molecular |
| 145 |
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dynamics with potential energy surfaces that are specifically tuned |
| 146 |
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for transition metals. In particular, we used the EAM potential for |
| 147 |
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Au-Au and Pt-Pt interactions, while modeling the CO using a rigid |
| 147 |
> |
Au-Au and Pt-Pt interactions\cite{EAM}, while modeling the CO using a rigid |
| 148 |
|
three-site model developed by Straub and Karplus for studying |
| 149 |
|
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 150 |
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Pt-CO cross interactions were parameterized as part of this work. |
| 157 |
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methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98} |
| 158 |
|
but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and |
| 159 |
|
the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
| 160 |
< |
parameter sets. The glue model of Ercolessi {\it et al.} is among the |
| 160 |
> |
parameter sets. The glue model of Ercolessi et al. is among the |
| 161 |
|
fastest of these density functional approaches.\cite{Ercolessi88} In |
| 162 |
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all of these models, atoms are conceptualized as a positively charged |
| 163 |
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core with a radially-decaying valence electron distribution. To |
| 175 |
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V_i = F[ \bar{\rho}_i ] + \sum_{j \neq i} \phi_{ij}(r_{ij}) |
| 176 |
|
\end{equation*} |
| 177 |
|
where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and |
| 178 |
< |
$\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the |
| 179 |
< |
overlap of the two positively charged cores. |
| 178 |
> |
$\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the |
| 179 |
> |
repulsive overlap of the two positively charged cores. |
| 180 |
|
|
| 181 |
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% The {\it modified} embedded atom method (MEAM) adds angular terms to |
| 182 |
|
% the electron density functions and an angular screening factor to the |
| 187 |
|
% metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys}) |
| 188 |
|
% MEAM presents significant additional computational costs, however. |
| 189 |
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|
| 190 |
< |
The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen potentials |
| 190 |
> |
The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials |
| 191 |
|
have all been widely used by the materials simulation community for |
| 192 |
|
simulations of bulk and nanoparticle |
| 193 |
|
properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq} |
| 201 |
|
parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 202 |
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|
| 203 |
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\subsection{Carbon Monoxide model} |
| 204 |
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Since previous explanations for the surface rearrangements center on |
| 205 |
< |
the large linear quadrupole moment of carbon monoxide, the model |
| 206 |
< |
chosen for this molecule exhibits this property in an efficient |
| 207 |
< |
manner. We used a model first proposed by Karplus and Straub to study |
| 208 |
< |
the photodissociation of CO from myoglobin.\cite{Straub} The Straub and |
| 209 |
< |
Karplus model is a rigid three site model which places a massless M |
| 210 |
< |
site at the center of mass along the CO bond. The geometry used along |
| 211 |
< |
with the interaction parameters are reproduced in Table~1. The effective |
| 204 |
> |
Previous explanations for the surface rearrangements center on |
| 205 |
> |
the large linear quadrupole moment of carbon monoxide. |
| 206 |
> |
We used a model first proposed by Karplus and Straub to study |
| 207 |
> |
the photodissociation of CO from myoglobin because it reproduces |
| 208 |
> |
the quadrupole moment well.\cite{Straub} The Straub and |
| 209 |
> |
Karplus model, treats CO as a rigid three site molecule which places a massless M |
| 210 |
> |
site at the center of mass position along the CO bond. The geometry used along |
| 211 |
> |
with the interaction parameters are reproduced in Table~\ref{tab:CO}. The effective |
| 212 |
|
dipole moment, calculated from the assigned charges, is still |
| 213 |
|
small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
| 214 |
|
to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
| 217 |
|
\begin{table}[H] |
| 218 |
|
\caption{Positions, Lennard-Jones parameters ($\sigma$ and |
| 219 |
|
$\epsilon$), and charges for the CO-CO |
| 220 |
< |
interactions borrowed from Ref. \bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA~, energies are |
| 220 |
> |
interactions borrowed from Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are |
| 221 |
|
in kcal/mol, and charges are in atomic units.} |
| 222 |
|
\centering |
| 223 |
|
\begin{tabular}{| c | c | ccc |} |
| 229 |
|
\textbf{M} & 0.0 & - & - & 1.6 \\ |
| 230 |
|
\hline |
| 231 |
|
\end{tabular} |
| 232 |
+ |
\label{tab:CO} |
| 233 |
|
\end{table} |
| 234 |
|
|
| 235 |
|
\subsection{Cross-Interactions between the metals and carbon monoxide} |
| 236 |
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|
| 237 |
< |
Since the adsorption of CO onto a platinum surface has been the focus |
| 237 |
> |
Since the adsorption of CO onto a Pt surface has been the focus |
| 238 |
|
of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979} |
| 239 |
|
and theoretical work |
| 240 |
|
\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
| 242 |
|
clean metal surfaces. Parameters reported by Korzeniewski {\it et |
| 243 |
|
al.}\cite{Pons:1986} were a starting point for our fits, which were |
| 244 |
|
modified to ensure that the Pt-CO interaction favored the atop binding |
| 245 |
< |
position on Pt(111). This resulting binding energies are on the higher |
| 246 |
< |
side of the experimentally-reported values. Following Korzeniewski |
| 247 |
< |
{\it et al.},\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 245 |
> |
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters} |
| 246 |
> |
This resulted in binding energies that are slightly higher |
| 247 |
> |
than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
| 248 |
> |
et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 249 |
|
Lennard-Jones interaction to mimic strong, but short-ranged partial |
| 250 |
|
binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
| 251 |
< |
Pt-O interaction was parameterized to a Morse potential with a large |
| 252 |
< |
range parameter ($r_o$). In most cases, this contributes a weak |
| 251 |
> |
Pt-O interaction was parameterized to a Morse potential at a larger |
| 252 |
> |
minimum distance, ($r_o$). This was chosen so that the C would be preferred |
| 253 |
> |
over O as the binder to the surface. In most cases, this parameterization contributes a weak |
| 254 |
|
repulsion which favors the atop site. The resulting potential-energy |
| 255 |
|
surface suitably recovers the calculated Pt-C separation length |
| 256 |
|
(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
| 259 |
|
%where did you actually get the functionals for citation? |
| 260 |
|
%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
| 261 |
|
%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
| 262 |
< |
The Au-C and Au-O cross-interactions were fit using Lennard-Jones and |
| 262 |
> |
The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and |
| 263 |
|
Morse potentials, respectively, to reproduce Au-CO binding energies. |
| 264 |
< |
|
| 265 |
< |
The fits were refined against gas-surface DFT calculations with a |
| 264 |
> |
The limited experimental data for CO adsorption on Au lead us to refine our fits against DFT. |
| 265 |
> |
Adsorption energies were obtained from gas-surface DFT calculations with a |
| 266 |
|
periodic supercell plane-wave basis approach, as implemented in the |
| 267 |
|
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are |
| 268 |
|
described with the projector augmented-wave (PAW) |
| 271 |
|
computed with the PBE implementation of the generalized gradient |
| 272 |
|
approximation (GGA) for gold, carbon, and oxygen that was constructed |
| 273 |
|
by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP} |
| 274 |
< |
Ionic relaxations were performed until the energy difference between |
| 261 |
< |
subsequent steps was less than $10^{-8}$ Ry. In testing the CO-Au |
| 262 |
< |
interaction, Au(111) supercells were constructed of four layers of 4 |
| 274 |
> |
In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4 |
| 275 |
|
Au x 2 Au surface planes and separated from vertical images by six |
| 276 |
< |
layers of vacuum space. The surface atoms were all allowed to relax. |
| 277 |
< |
Supercell calculations were performed nonspin-polarized with a 4 x 4 x |
| 278 |
< |
4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
| 276 |
> |
layers of vacuum space. The surface atoms were all allowed to relax |
| 277 |
> |
before CO was added to the system. Electronic relaxations were |
| 278 |
> |
performed until the energy difference between subsequent steps |
| 279 |
> |
was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
| 280 |
> |
were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
| 281 |
|
zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was |
| 282 |
|
then used in numerous single point calculations with CO at various |
| 283 |
|
heights (and angles relative to the surface) to allow fitting of the |
| 284 |
|
empirical force field. |
| 285 |
|
|
| 286 |
|
%Hint at future work |
| 287 |
< |
The parameters employed in this work are shown in Table 2 and the |
| 288 |
< |
binding energies on the 111 surfaces are displayed in Table 3. To |
| 289 |
< |
speed up the computations, charge transfer and polarization are not |
| 290 |
< |
being treated in this model, although these effects are likely to |
| 291 |
< |
affect binding energies and binding site |
| 292 |
< |
preferences.\cite{Deshlahra:2012} |
| 287 |
> |
The parameters employed for the metal-CO cross-interactions in this work |
| 288 |
> |
are shown in Table~\ref{co_parameters} and the binding energies on the |
| 289 |
> |
(111) surfaces are displayed in Table~\ref{co_energies}. Charge transfer |
| 290 |
> |
and polarization are neglected in this model, although these effects are likely to |
| 291 |
> |
affect binding energies and binding site preferences, and will be added in |
| 292 |
> |
a future work.\cite{Deshlahra:2012,StreitzMintmire:1994} |
| 293 |
|
|
| 294 |
|
%Table of Parameters |
| 295 |
|
%Pt Parameter Set 9 |
| 296 |
|
%Au Parameter Set 35 |
| 297 |
|
\begin{table}[H] |
| 298 |
< |
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
| 298 |
> |
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
| 299 |
|
interactions are modeled with Lennard-Jones potential, while the |
| 300 |
< |
(mostly-repulsive) metal-O interactions were fit to Morse |
| 300 |
> |
metal-O interactions were fit to Morse |
| 301 |
|
potentials. Distances are given in \AA~and energies in kcal/mol. } |
| 302 |
|
\centering |
| 303 |
|
\begin{tabular}{| c | cc | c | ccc |} |
| 309 |
|
|
| 310 |
|
\hline |
| 311 |
|
\end{tabular} |
| 312 |
+ |
\label{tab:co_parameters} |
| 313 |
|
\end{table} |
| 314 |
|
|
| 315 |
|
%Table of energies |
| 316 |
|
\begin{table}[H] |
| 317 |
< |
\caption{Adsorption energies for CO on M(111) using the potentials |
| 318 |
< |
described in this work. All values are in eV} |
| 317 |
> |
\caption{Adsorption energies for CO on M(111) at the atop site using the potentials |
| 318 |
> |
described in this work. All values are in eV.} |
| 319 |
|
\centering |
| 320 |
|
\begin{tabular}{| c | cc |} |
| 321 |
|
\hline |
| 327 |
|
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPD_Gold}) \\ |
| 328 |
|
\hline |
| 329 |
|
\end{tabular} |
| 330 |
+ |
\label{tab:co_energies} |
| 331 |
|
\end{table} |
| 332 |
|
|
| 333 |
|
\subsection{Pt(557) and Au(557) metal interfaces} |
| 334 |
|
|
| 335 |
|
Our model systems are composed of 3888 Pt atoms and 3384 Au atoms in a |
| 336 |
< |
FCC crystal that have been cut along the 557 plane so that they are |
| 337 |
< |
periodic in the {\it x} and {\it y} directions, and have been rotated |
| 338 |
< |
to expose two parallel 557 cuts along the positive and negative {\it |
| 336 |
> |
FCC crystal that have been cut along the (557) plane so that they are |
| 337 |
> |
periodic in the {\it x} and {\it y} directions, and have been oriented |
| 338 |
> |
to expose two aligned (557) cuts along the extended {\it |
| 339 |
|
z}-axis. Simulations of the bare metal interfaces at temperatures |
| 340 |
< |
ranging from 300~K to 1200~K were done to observe the relative |
| 340 |
> |
ranging from 300~K to 1200~K were performed to observe the relative |
| 341 |
|
stability of the surfaces without a CO overlayer. |
| 342 |
|
|
| 343 |
|
The different bulk (and surface) melting temperatures (1337~K for Au |
| 344 |
< |
and 2045~K for Pt) suggest that the reconstruction may happen at |
| 345 |
< |
different temperatures for the two metals. To copy experimental |
| 330 |
< |
conditions for the CO-exposed surfaces, the bare surfaces were |
| 344 |
> |
and 2045~K for Pt) suggest that any possible reconstruction may happen at |
| 345 |
> |
different temperatures for the two metals. The bare Au and Pt surfaces were |
| 346 |
|
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
| 347 |
< |
respectively for 100 ps. Each surface was exposed to a range of CO |
| 347 |
> |
respectively for 100 ps. These temperatures were chosen because the |
| 348 |
> |
surfaces were relatively stable at these temperatures when no CO was |
| 349 |
> |
present, but experienced additional instability upon addition of CO in the time |
| 350 |
> |
frames we were examining. Each surface was exposed to a range of CO |
| 351 |
|
that was initially placed in the vacuum region. Upon full adsorption, |
| 352 |
|
these amounts correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 353 |
< |
coverage. Because of the difference in binding energies, the platinum |
| 353 |
> |
coverage. Higher coverages were tried, but the CO-CO repulsion was preventing |
| 354 |
> |
a higher amount of adsorption. Because of the difference in binding energies, the Pt |
| 355 |
|
systems very rarely had CO that was not bound to the surface, while |
| 356 |
< |
the gold surfaces often had a significant CO population in the gas |
| 356 |
> |
the Au surfaces often had a significant CO population in the gas |
| 357 |
|
phase. These systems were allowed to reach thermal equilibrium (over |
| 358 |
< |
5 ns) before being shifted to the microcanonical (NVE) ensemble for |
| 358 |
> |
5 ns) before being run in the microcanonical (NVE) ensemble for |
| 359 |
|
data collection. All of the systems examined had at least 40 ns in the |
| 360 |
|
data collection stage, although simulation times for some of the |
| 361 |
|
systems exceeded 200ns. All simulations were run using the open |
| 362 |
< |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,OpenMD} |
| 362 |
> |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} |
| 363 |
|
|
| 364 |
|
% Just results, leave discussion for discussion section |
| 365 |
+ |
% structure |
| 366 |
+ |
% Pt: step wandering, double layers, no triangular motifs |
| 367 |
+ |
% Au: step wandering, no double layers |
| 368 |
+ |
% dynamics |
| 369 |
+ |
% diffusion |
| 370 |
+ |
% time scale, formation, breakage |
| 371 |
|
\section{Results} |
| 372 |
< |
Tao {\it et al.} showed experimentally that the Pt(557) surface |
| 373 |
< |
undergoes two separate reconstructions upon CO |
| 374 |
< |
adsorption.\cite{Tao:2010} The first reconstruction involves a |
| 375 |
< |
doubling of the step edge height which is accomplished by a doubling |
| 376 |
< |
of the plateau length. The second reconstruction led to the formation |
| 377 |
< |
of triangular clusters that arrange themselves along the lengthened |
| 378 |
< |
plateaus. |
| 372 |
> |
\subsection{Structural remodeling} |
| 373 |
> |
Tao et al. showed experimentally that the Pt(557) surface |
| 374 |
> |
undergoes two separate reconstructions upon CO |
| 375 |
> |
adsorption.\cite{Tao:2010} The first involves a doubling of |
| 376 |
> |
the step height and plateau length. Similar behavior has been |
| 377 |
> |
seen to occur on numerous surfaces at varying conditions (Ni 977, Si 111, etc). |
| 378 |
> |
\cite{Williams:1994,Williams:1991,Pearl} Of the two systems |
| 379 |
> |
we examined, the Pt system showed a larger amount of |
| 380 |
> |
reconstruction when compared to the Au system. The amount |
| 381 |
> |
of reconstruction appears to be correlated to the amount of CO |
| 382 |
> |
adsorbed upon the surface. We believe this is related to the |
| 383 |
> |
effect that adsorbate coverage has on edge breakup and surface |
| 384 |
> |
diffusion of adatoms. While both systems displayed step-edge |
| 385 |
> |
wandering, only the Pt surface underwent the doubling seen by |
| 386 |
> |
Tao et al., within the time scales we were modeling. Specifically, |
| 387 |
> |
only the 50~\% coverage Pt system was observed to have a |
| 388 |
> |
step-edge undergo a complete doubling in the time scales we |
| 389 |
> |
were able to monitor. This event encouraged us to allow that |
| 390 |
> |
specific system to run for much longer periods during which two |
| 391 |
> |
more double layers were created. The other systems, not displaying |
| 392 |
> |
any large scale changes of interest, were all stopped after running |
| 393 |
> |
for 40 ns in the microcanonical ensemble. Despite no observation |
| 394 |
> |
of double layer formation, the other Pt systems tended to show |
| 395 |
> |
more cumulative lateral movement of the step-edges when |
| 396 |
> |
compared to the Au systems. The 50\% Pt system is highlighted |
| 397 |
> |
in Figure \ref{fig:reconstruct} at various times along the simulation |
| 398 |
> |
showing the evolution of the system. |
| 399 |
|
|
| 400 |
< |
The primary observation and results of our simulation is that the |
| 401 |
< |
presence of CO overlayer on Pt(557) causes the same kind of |
| 402 |
< |
reconstruction observed experimentally. The 6-atom 111 facets |
| 403 |
< |
initially become disordered, and after 20-40 ns, a double-layer (with |
| 404 |
< |
a 2-atom step between terraces) forms. However, we did not observe |
| 405 |
< |
the triangular cluster formation that was observed at longer times in |
| 361 |
< |
the experiments. Without the CO present on the Pt(557) surface, there |
| 362 |
< |
was some disorder at the step edges, but no significant restructuring |
| 363 |
< |
was observed. |
| 400 |
> |
The second reconstruction on the Pt(557) surface observed by |
| 401 |
> |
Tao involved the formation of triangular clusters that stretched |
| 402 |
> |
across the plateau between two step-edges. Neither system, within |
| 403 |
> |
our simulated time scales, experiences this reconstruction. A constructed |
| 404 |
> |
system in which the triangular motifs were constructed on the surface |
| 405 |
> |
will be explored in future work and is shown in the supporting information. |
| 406 |
|
|
| 407 |
< |
In these simulations, the Au(557) surface did not exhibit any |
| 408 |
< |
significant restructuring either with or without the presence of a CO |
| 409 |
< |
overlayer. |
| 407 |
> |
\subsection{Dynamics} |
| 408 |
> |
While atomistic-like simulations of stepped surfaces have been |
| 409 |
> |
performed before, they tend to be performed using Monte Carlo |
| 410 |
> |
techniques\cite{Williams:1991,Williams:1994}. This allows them |
| 411 |
> |
to efficiently sample the equilibrium thermodynamic landscape |
| 412 |
> |
but at the expense of ignoring the dynamics of the system. Previous |
| 413 |
> |
work by Pearl and Sibener\cite{Pearl}, using STM, has been able to |
| 414 |
> |
visualize the coalescing of steps of Ni(977). The time scale of the image |
| 415 |
> |
acquisition, $\sim$70 s/image provides an upper bounds for the time |
| 416 |
> |
required for the doubling to actually occur. Statistical treatments of step-edges |
| 417 |
> |
are adept at analyzing such systems. However, in a system where |
| 418 |
> |
the number of steps is limited, examining the individual atoms that make |
| 419 |
> |
up the steps can provide useful information as well. |
| 420 |
|
|
| 369 |
– |
\subsection{Transport of surface metal atoms} |
| 370 |
– |
An ideal metal surface displaying a low energy (111) face is unlikely |
| 371 |
– |
to experience much surface diffusion because of the large vacancy |
| 372 |
– |
formation energy for atoms at the surface. This implies that |
| 373 |
– |
significant energy must be expended to lift an atom out of the flat |
| 374 |
– |
face so it can migrate on the surface. Rougher surfaces and those |
| 375 |
– |
that already contain numerous adatoms, step edges, and kinks, are |
| 376 |
– |
expected to have higher surface diffusion rates. Metal atoms that are |
| 377 |
– |
mobile on the surface were observed to leave and then rejoin step |
| 378 |
– |
edges or other formations. They may travel together or as isolated |
| 379 |
– |
atoms. The primary challenge of quantifying the overall surface |
| 380 |
– |
mobility is in defining ``mobile'' vs. ``static'' atoms. |
| 421 |
|
|
| 422 |
< |
A particle was considered mobile once it had traveled more than 2~\AA~ |
| 423 |
< |
between saved configurations (10-100 ps). Restricting the transport |
| 424 |
< |
calculations to only mobile atoms eliminates all of the bulk metal as |
| 425 |
< |
well as any surface atoms that remain fixed for a significant length |
| 426 |
< |
of time. Since diffusion on a surface is strongly affected by local |
| 427 |
< |
structures, the diffusion parallel to the step edges was determined |
| 428 |
< |
separately from the diffusion perpendicular to these edges. The |
| 429 |
< |
parallel and perpendicular diffusion constants (determined using |
| 430 |
< |
linear fits to the mean squared displacement) are shown in figure \ref{fig:diff}. |
| 422 |
> |
\subsubsection{Transport of surface metal atoms} |
| 423 |
> |
%forcedSystems/stepSeparation |
| 424 |
> |
The movement or wandering of a step-edge is a cooperative effect |
| 425 |
> |
arising from the individual movements, primarily through surface |
| 426 |
> |
diffusion, of the atoms making up the step. An ideal metal surface |
| 427 |
> |
displaying a low index facet, (111) or (100) is unlikely to experience |
| 428 |
> |
much surface diffusion because of the large energetic barrier that must |
| 429 |
> |
be overcome to lift an atom out of the surface. The presence of step-edges |
| 430 |
> |
on higher-index surfaces provide a source for mobile metal atoms. |
| 431 |
> |
Breaking away from the step-edge on a clean surface still imposes an |
| 432 |
> |
energetic penalty around $\sim$~40 kcal/mole, but is much less than lifting |
| 433 |
> |
the same metal atom out from the surface, \textgreater~60 kcal/mole, and |
| 434 |
> |
the penalty lowers even further when CO is present in sufficient quantities |
| 435 |
> |
on the surface. For certain tested distributions of CO, the penalty was lowered |
| 436 |
> |
to $\sim$~20 kcal/mole. Once an adatom exists on the surface, its barrier for |
| 437 |
> |
diffusion is negligible ( \textless~4 kcal/mole) and is well able to explore the |
| 438 |
> |
terrace before potentially rejoining its original step-edge or becoming a part |
| 439 |
> |
of a different edge. Atoms traversing separate terraces is a more difficult |
| 440 |
> |
process, but can be overcome through a joining and lifting stage which is |
| 441 |
> |
examined in the discussion section. By tracking the mobility of individual |
| 442 |
> |
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 443 |
> |
diffusion rates and how varying coverages of CO affected the rates. Close |
| 444 |
> |
observation of the mobile metal atoms showed that they were typically in |
| 445 |
> |
equilibrium with the step-edges, constantly breaking apart and rejoining. |
| 446 |
> |
At times their motion was concerted and two or more adatoms would be |
| 447 |
> |
observed moving together across the surfaces. The primary challenge in |
| 448 |
> |
quantifying the overall surface mobility was in defining ``mobile" vs. ``static" atoms. |
| 449 |
|
|
| 450 |
< |
%While an ideal metallic surface is unlikely to experience much surface diffusion, high-index surfaces have large numbers of low-coordinated atoms which have a much easier time overcoming the energetic barriers limiting diffusion, leading to easier surface reconstructions. Surface movement was divided between the parallel ($\parallel$) and perpendicular ($\perp$) directions relative to the step edge. We were then able to calculate diffusion constants as a function of CO coverage. As can be seen in Table 4, the presence and amount of CO directly affects the diffusion constants of surface platinum atoms. The presence of two 50\% coverage systems is to show how the diffusion process is affected by time. The majority of the systems were run for approximately 50 ns while the half monolayer system has been running continuously. The lowered diffusion constant at longer run times will be examined in-depth in the discussion section. |
| 450 |
> |
A particle was considered mobile once it had traveled more than 2~\AA~ |
| 451 |
> |
between saved configurations of the system (10-100 ps). An atom that was |
| 452 |
> |
truly mobile would typically travel much greater than this, but the 2~\AA~ cutoff |
| 453 |
> |
was to prevent the in-place vibrational movement of non-surface atoms from |
| 454 |
> |
being included in the analysis. Diffusion on a surface is strongly affected by |
| 455 |
> |
local structures and in this work the presence of single and double layer |
| 456 |
> |
step-edges causes the diffusion parallel to the step-edges to be different |
| 457 |
> |
from the diffusion perpendicular to these edges. This led us to compute |
| 458 |
> |
those diffusions separately as seen in Figure \ref{fig:diff}. |
| 459 |
|
|
| 460 |
+ |
\subsubsection{Double layer formation} |
| 461 |
+ |
The increased amounts of diffusion on Pt at the higher CO coverages appears |
| 462 |
+ |
to play a primary role in the formation of double layers, although this conclusion |
| 463 |
+ |
does not explain the 33\% coverage Pt system. On the 50\% system, three |
| 464 |
+ |
separate layers were formed over the extended run time of this system. As |
| 465 |
+ |
mentioned earlier, previous experimental work has given some insight into the |
| 466 |
+ |
upper bounds of the time required for enough atoms to move around to allow two |
| 467 |
+ |
steps to coalesce\cite{Williams:1991,Pearl}. As seen in Figure \ref{fig:reconstruct}, |
| 468 |
+ |
the first appearance of a double layer, a nodal site, appears at 19 ns into the |
| 469 |
+ |
simulation. Within 12 ns, nearly half of the step has formed the double layer and |
| 470 |
+ |
by 86 ns, a smooth complete layer has formed. The double layer is ``complete" by |
| 471 |
+ |
37 ns but is a bit rough. From the appearance of the first node to the initial doubling |
| 472 |
+ |
of the layers ignoring their roughness took $\sim$~20 ns. Another ~40 ns was |
| 473 |
+ |
necessary for the layer to completely straighten. The other two layers in this |
| 474 |
+ |
simulation form over a period of 22 ns and 42 ns respectively. Comparing this to |
| 475 |
+ |
the upper bounds of the image scan, it is likely that aspects of this reconstruction |
| 476 |
+ |
occur very quickly. |
| 477 |
+ |
|
| 478 |
+ |
%Evolution of surface |
| 479 |
|
\begin{figure}[H] |
| 480 |
+ |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 481 |
+ |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 482 |
+ |
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
| 483 |
+ |
(d) 86.1 ns. Disruption of the (557) step-edges occurs quickly. The |
| 484 |
+ |
doubling of the layers appears only after two adjacent step-edges |
| 485 |
+ |
touch. The circled spot in (b) nucleated the growth of the double |
| 486 |
+ |
step observed in the later configurations.} |
| 487 |
+ |
\label{fig:reconstruct} |
| 488 |
+ |
\end{figure} |
| 489 |
+ |
|
| 490 |
+ |
\begin{figure}[H] |
| 491 |
|
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
| 492 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
| 493 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 494 |
< |
($\mathbf{D}_{\perp}$) to the 557 step edges as a function of CO |
| 495 |
< |
surface coverage. Diffusion parallel to the step edge is higher |
| 494 |
> |
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 495 |
> |
surface coverage. Diffusion parallel to the step-edge is higher |
| 496 |
|
than that perpendicular to the edge because of the lower energy |
| 497 |
< |
barrier associated with going from approximately 7 nearest neighbors |
| 498 |
< |
to 5, as compared to the 3 of an adatom. Additionally, the observed |
| 497 |
> |
barrier associated with traversing along the edge as compared to |
| 498 |
> |
completely breaking away. Additionally, the observed |
| 499 |
|
maximum and subsequent decrease for the Pt system suggests that the |
| 500 |
|
CO self-interactions are playing a significant role with regards to |
| 501 |
< |
movement of the platinum atoms around and more importantly across |
| 406 |
< |
the surface. } |
| 501 |
> |
movement of the Pt atoms around and across the surface. } |
| 502 |
|
\label{fig:diff} |
| 503 |
|
\end{figure} |
| 504 |
|
|
| 410 |
– |
%Table of Diffusion Constants |
| 411 |
– |
%Add gold?M |
| 412 |
– |
% \begin{table}[H] |
| 413 |
– |
% \caption{} |
| 414 |
– |
% \centering |
| 415 |
– |
% \begin{tabular}{| c | cc | cc | } |
| 416 |
– |
% \hline |
| 417 |
– |
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
| 418 |
– |
% \hline |
| 419 |
– |
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
| 420 |
– |
% \hline |
| 421 |
– |
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
| 422 |
– |
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
| 423 |
– |
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
| 424 |
– |
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
| 425 |
– |
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
| 426 |
– |
% \hline |
| 427 |
– |
% \end{tabular} |
| 428 |
– |
% \end{table} |
| 505 |
|
|
| 506 |
+ |
|
| 507 |
+ |
|
| 508 |
|
%Discussion |
| 509 |
|
\section{Discussion} |
| 510 |
+ |
In this paper we have shown that we were able to accurately model the initial reconstruction of the |
| 511 |
+ |
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 512 |
+ |
were able to observe the dynamic processes necessary for this reconstruction. |
| 513 |
|
|
| 514 |
< |
Mechanism for restructuring |
| 514 |
> |
\subsection{Mechanism for restructuring} |
| 515 |
> |
Comparing the results from simulation to those reported previously by |
| 516 |
> |
Tao et al.\cite{Tao:2010} the similarities in the Pt-CO system are quite |
| 517 |
> |
strong. As shown in Figure \ref{fig:reconstruct}, the simulated Pt |
| 518 |
> |
system under a CO atmosphere will restructure by doubling the terrace |
| 519 |
> |
heights. The restructuring occurs slowly, one to two Pt atoms at a time. |
| 520 |
> |
Looking at individual configurations of the system, the adatoms either |
| 521 |
> |
break away from the step-edge and stay on the lower terrace or they lift |
| 522 |
> |
up onto the higher terrace. Once ``free'' they will diffuse on the terrace |
| 523 |
> |
until reaching another step-edge or coming back to their original edge. |
| 524 |
> |
This combination of growth and decay of the step-edges is in a state of |
| 525 |
> |
dynamic equilibrium. However, once two previously separated edges |
| 526 |
> |
meet as shown in Figure 1.B, this meeting point tends to act as a focus |
| 527 |
> |
or growth point for the rest of the edge to meet up, akin to that of a zipper. |
| 528 |
> |
From the handful of cases where a double layer was formed during the |
| 529 |
> |
simulation, measuring from the initial appearance of a growth point, the |
| 530 |
> |
double layer tends to be fully formed within $\sim$~35 ns. |
| 531 |
|
|
| 532 |
< |
There are a number of possible mechanisms to explain the role of |
| 533 |
< |
adsorbed CO in restructuring the Pt surface. Quadrupolar repulsion |
| 534 |
< |
between adjacent CO molecules adsorbed on the surface is one |
| 535 |
< |
possibility. However, the quadrupole-quadrupole interaction is |
| 536 |
< |
short-ranged and is attractive for some orientations. If the CO |
| 537 |
< |
molecules are locked in a specific orientation relative to each other, |
| 538 |
< |
this explanation gains some weight. |
| 532 |
> |
A number of possible mechanisms exist to explain the role of adsorbed |
| 533 |
> |
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 534 |
> |
CO molecules adsorbed on the surface is one likely possibility. However, |
| 535 |
> |
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 536 |
> |
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 537 |
> |
relative to each other, through atop adsorption perhaps, this explanation |
| 538 |
> |
gains some weight. The energetic repulsion between two CO located a |
| 539 |
> |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in |
| 540 |
> |
a vertical orientation is 8.62 kcal/mole. Moving the CO apart to the second |
| 541 |
> |
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 542 |
> |
nearly 0 kcal/mole. Allowing the CO's to leave a purely vertical orientation |
| 543 |
> |
also quickly drops the repulsion, a minimum is reached at $\sim$24 degrees |
| 544 |
> |
of 6.2 kcal/mole. As mentioned above, the energy barrier for surface diffusion |
| 545 |
> |
of a Pt adatom is only 4 kcal/mole. So this repulsion between CO can help |
| 546 |
> |
increase the surface diffusion. However, the residence time of CO was |
| 547 |
> |
examined and while the majority of the CO is on or near the surface throughout |
| 548 |
> |
the run, it is extremely mobile. This mobility suggests that the CO are more |
| 549 |
> |
likely to shift their positions without necessarily dragging the Pt along with them. |
| 550 |
|
|
| 551 |
< |
Another possible mechanism for the restructuring is in the |
| 551 |
> |
Another possible and more likely mechanism for the restructuring is in the |
| 552 |
|
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 553 |
< |
Pt atoms. This could have the effect of increasing surface mobility |
| 554 |
< |
of these atoms. |
| 553 |
> |
Pt atoms. This would then have the effect of increasing surface mobility |
| 554 |
> |
of these atoms. To test this hypothesis, numerous configurations of |
| 555 |
> |
CO in varying quantities were arranged on the higher and lower plateaus |
| 556 |
> |
around a step on a otherwise clean Pt(557) surface. One representative |
| 557 |
> |
configuration is displayed in Figure \ref{fig:lambda}. Single or concerted movement |
| 558 |
> |
of Pt atoms was then examined to determine possible barriers. Because |
| 559 |
> |
the movement was forced along a pre-defined reaction coordinate that may differ |
| 560 |
> |
from the true minimum of this path, only the beginning and ending energies |
| 561 |
> |
are displayed in Table \ref{tab:energies}. These values suggest that the presence of CO at suitable |
| 562 |
> |
locations can lead to lowered barriers for Pt breaking apart from the step-edge. |
| 563 |
> |
Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the |
| 564 |
> |
burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral |
| 565 |
> |
in terms of energetics. |
| 566 |
|
|
| 567 |
< |
Comparing the results from simulation to those reported previously by |
| 568 |
< |
Tao et al. the similarities in the platinum and CO system are quite |
| 569 |
< |
strong. As shown in figure, the simulated platinum system under a CO |
| 570 |
< |
atmosphere will restructure slightly by doubling the terrace |
| 571 |
< |
heights. The restructuring appears to occur slowly, one to two |
| 572 |
< |
platinum atoms at a time. Looking at individual snapshots, these |
| 573 |
< |
adatoms tend to either rise on top of the plateau or break away from |
| 574 |
< |
the step edge and then diffuse perpendicularly to the step direction |
| 575 |
< |
until reaching another step edge. This combination of growth and decay |
| 576 |
< |
of the step edges appears to be in somewhat of a state of dynamic |
| 577 |
< |
equilibrium. However, once two previously separated edges meet as |
| 578 |
< |
shown in figure 1.B, this point tends to act as a focus or growth |
| 460 |
< |
point for the rest of the edge to meet up, akin to that of a |
| 461 |
< |
zipper. From the handful of cases where a double layer was formed |
| 462 |
< |
during the simulation, measuring from the initial appearance of a |
| 463 |
< |
growth point, the double layer tends to be fully formed within |
| 464 |
< |
$\sim$~35 ns. |
| 567 |
> |
%lambda progression of Pt -> shoving its way into the step |
| 568 |
> |
\begin{figure}[H] |
| 569 |
> |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO.png} |
| 570 |
> |
\caption{A model system of the Pt(557) surface was used as the framework |
| 571 |
> |
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 572 |
> |
placements, and rotations of CO were examined as they affect Pt movement. |
| 573 |
> |
The coordinate displayed in this Figure was a representative run. As shown |
| 574 |
> |
in Table \ref{tab:rxcoord}, relative to the energy of the system at 0\%, there |
| 575 |
> |
is a slight decrease upon insertion of the Pt atom into the step-edge along |
| 576 |
> |
with the resultant lifting of the other Pt atom when CO is present at certain positions.} |
| 577 |
> |
\label{fig:lambda} |
| 578 |
> |
\end{figure} |
| 579 |
|
|
| 580 |
+ |
|
| 581 |
+ |
|
| 582 |
|
\subsection{Diffusion} |
| 583 |
< |
As shown in the results section, the diffusion parallel to the step edge tends to be much faster than that perpendicular to the step edge. Additionally, the coverage of CO appears to play a slight role in relative rates of diffusion, as shown in Table 4. Thus, the bottleneck of the double layer formation appears to be the initial formation of this growth point, which seems to be somewhat of a stochastic event. Once it appears, parallel diffusion, along the now slightly angled step edge, will allow for a faster formation of the double layer than if the entire process were dependent on only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the more likely a growth point is to be formed. One driving force behind this reconstruction appears to be the lowering of surface energy that occurs by doubling the terrace widths. (I'm not really proving this... I have the surface flatness to show it, but surface energy?) |
| 583 |
> |
As shown in the results section, the diffusion parallel to the step-edge tends to be |
| 584 |
> |
much larger than that perpendicular to the step-edge, likely because of the dynamic |
| 585 |
> |
equilibrium that is established between the step-edge and adatom interface. The coverage |
| 586 |
> |
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}. |
| 587 |
> |
The |
| 588 |
> |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
| 589 |
> |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
| 590 |
> |
appears, parallel diffusion, along the now slightly angled step-edge, will allow for |
| 591 |
> |
a faster formation of the double layer than if the entire process were dependent on |
| 592 |
> |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
| 593 |
> |
more likely a growth point is to be formed. |
| 594 |
|
\\ |
| 595 |
< |
\\ |
| 596 |
< |
%Evolution of surface |
| 595 |
> |
|
| 596 |
> |
|
| 597 |
> |
%breaking of the double layer upon removal of CO |
| 598 |
|
\begin{figure}[H] |
| 599 |
< |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 600 |
< |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 601 |
< |
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
| 602 |
< |
(d) 86.1 ns. Disruption of the 557 step edges occurs quickly. The |
| 603 |
< |
doubling of the layers appears only after two adjacent step edges |
| 604 |
< |
touch. The circled spot in (b) nucleated the growth of the double |
| 605 |
< |
step observed in the later configurations.} |
| 599 |
> |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 600 |
> |
%: |
| 601 |
> |
\caption{(A) 0 ps, (B) 100 ps, (C) 1 ns, after the removal of CO. The presence of the CO |
| 602 |
> |
helped maintain the stability of the double layer and upon removal the two layers break |
| 603 |
> |
and begin separating. The separation is not a simple pulling apart however, rather |
| 604 |
> |
there is a mixing of the lower and upper atoms at the edge.} |
| 605 |
> |
\label{fig:breaking} |
| 606 |
|
\end{figure} |
| 607 |
|
|
| 608 |
|
|
| 609 |
+ |
|
| 610 |
+ |
|
| 611 |
|
%Peaks! |
| 612 |
|
\begin{figure}[H] |
| 613 |
|
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 614 |
< |
\caption{} |
| 614 |
> |
\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 615 |
> |
of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 616 |
> |
aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 617 |
> |
\label{fig:peaks} |
| 618 |
|
\end{figure} |
| 619 |
< |
\begin{figure}[H] |
| 620 |
< |
\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
| 621 |
< |
\caption{} |
| 622 |
< |
\end{figure} |
| 619 |
> |
|
| 620 |
> |
|
| 621 |
> |
%Don't think I need this |
| 622 |
> |
%clean surface... |
| 623 |
> |
%\begin{figure}[H] |
| 624 |
> |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
| 625 |
> |
%\caption{} |
| 626 |
> |
|
| 627 |
> |
%\end{figure} |
| 628 |
> |
%\label{fig:clean} |
| 629 |
> |
|
| 630 |
> |
|
| 631 |
|
\section{Conclusion} |
| 632 |
+ |
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. |
| 633 |
|
|
| 634 |
+ |
%Things I am not ready to remove yet |
| 635 |
|
|
| 636 |
+ |
%Table of Diffusion Constants |
| 637 |
+ |
%Add gold?M |
| 638 |
+ |
% \begin{table}[H] |
| 639 |
+ |
% \caption{} |
| 640 |
+ |
% \centering |
| 641 |
+ |
% \begin{tabular}{| c | cc | cc | } |
| 642 |
+ |
% \hline |
| 643 |
+ |
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
| 644 |
+ |
% \hline |
| 645 |
+ |
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
| 646 |
+ |
% \hline |
| 647 |
+ |
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
| 648 |
+ |
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
| 649 |
+ |
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
| 650 |
+ |
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
| 651 |
+ |
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
| 652 |
+ |
% \hline |
| 653 |
+ |
% \end{tabular} |
| 654 |
+ |
% \end{table} |
| 655 |
+ |
|
| 656 |
|
\section{Acknowledgments} |
| 657 |
|
Support for this project was provided by the National Science |
| 658 |
|
Foundation under grant CHE-0848243 and by the Center for Sustainable |
