| 68 |
|
\begin{doublespace} |
| 69 |
|
|
| 70 |
|
\begin{abstract} |
| 71 |
< |
|
| 71 |
> |
We examine potential surface reconstructions of Pt and Au (557) under various CO coverages using molecular dynamics in order to find possible mechanisms and dynamics for the restructuring. The metal-CO interactions were parameterized as part of this work so that a large scale treatment of this system could be undertaken. The relative binding strengths of the metal-CO interactions were found to play a large role with regards to step edge stability and adatom diffusion. A small correlation between coverage and the size of the diffusion constant was also determined. These results appear sufficient to explain the reconstructions observed on the Pt systems and the lack of reconstructions on the Au systems. |
| 72 |
|
\end{abstract} |
| 73 |
|
|
| 74 |
|
\newpage |
| 100 |
|
reversible restructuring under exposure to moderate pressures of |
| 101 |
|
carbon monoxide.\cite{Tao:2010} |
| 102 |
|
|
| 103 |
< |
This work an effort to understand the mechanism and timescale for |
| 103 |
> |
This work is an attempt to understand the mechanism and timescale for |
| 104 |
|
surface restructuring using molecular simulations. Since the dynamics |
| 105 |
< |
of the process is of particular interest, we utilize classical force |
| 105 |
> |
of the process are of particular interest, we employ classical force |
| 106 |
|
fields that represent a compromise between chemical accuracy and the |
| 107 |
< |
computational efficiency necessary to observe the process of interest. |
| 107 |
> |
computational efficiency necessary to simulate the process of interest. |
| 108 |
|
|
| 109 |
< |
Since restructuring occurs as a result of specific interactions of the |
| 110 |
< |
catalyst with adsorbates, two metal systems exposed to carbon monoxide |
| 111 |
< |
were examined in this work. The Pt(557) surface has already been shown |
| 109 |
> |
Restructuring can occur as a result of specific interactions of the |
| 110 |
> |
catalyst with adsorbates. In this work, two metal systems exposed |
| 111 |
> |
to carbon monoxide were examined. The Pt(557) surface has already been shown |
| 112 |
|
to reconstruct under certain conditions. The Au(557) surface, because |
| 113 |
|
of a weaker interaction with CO, is less likely to undergo this kind |
| 114 |
|
of reconstruction. MORE HERE ON PT AND AU PREVIOUS WORK. |
| 133 |
|
Coulomb potential. For this work, we have used classical molecular |
| 134 |
|
dynamics with potential energy surfaces that are specifically tuned |
| 135 |
|
for transition metals. In particular, we used the EAM potential for |
| 136 |
< |
Au-Au and Pt-Pt interactions, while modeling the CO using a rigid |
| 136 |
> |
Au-Au and Pt-Pt interactions\cite{EAM}, while modeling the CO using a rigid |
| 137 |
|
three-site model developed by Straub and Karplus for studying |
| 138 |
|
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 139 |
|
Pt-CO cross interactions were parameterized as part of this work. |
| 164 |
|
V_i = F[ \bar{\rho}_i ] + \sum_{j \neq i} \phi_{ij}(r_{ij}) |
| 165 |
|
\end{equation*} |
| 166 |
|
where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and |
| 167 |
< |
$\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the |
| 168 |
< |
overlap of the two positively charged cores. |
| 167 |
> |
$\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the |
| 168 |
> |
repulsive overlap of the two positively charged cores. |
| 169 |
|
|
| 170 |
|
% The {\it modified} embedded atom method (MEAM) adds angular terms to |
| 171 |
|
% the electron density functions and an angular screening factor to the |
| 176 |
|
% metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys}) |
| 177 |
|
% MEAM presents significant additional computational costs, however. |
| 178 |
|
|
| 179 |
< |
The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen potentials |
| 179 |
> |
The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials |
| 180 |
|
have all been widely used by the materials simulation community for |
| 181 |
|
simulations of bulk and nanoparticle |
| 182 |
|
properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq} |
| 190 |
|
parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 191 |
|
|
| 192 |
|
\subsection{Carbon Monoxide model} |
| 193 |
< |
Since previous explanations for the surface rearrangements center on |
| 194 |
< |
the large linear quadrupole moment of carbon monoxide, the model |
| 195 |
< |
chosen for this molecule exhibits this property in an efficient |
| 196 |
< |
manner. We used a model first proposed by Karplus and Straub to study |
| 197 |
< |
the photodissociation of CO from myoglobin.\cite{Straub} The Straub and |
| 198 |
< |
Karplus model is a rigid three site model which places a massless M |
| 199 |
< |
site at the center of mass along the CO bond. The geometry used along |
| 200 |
< |
with the interaction parameters are reproduced in Table~1. The effective |
| 193 |
> |
Previous explanations for the surface rearrangements center on |
| 194 |
> |
the large linear quadrupole moment of carbon monoxide. |
| 195 |
> |
We used a model first proposed by Karplus and Straub to study |
| 196 |
> |
the photodissociation of CO from myoglobin because it reproduces |
| 197 |
> |
the quadrupole moment well.\cite{Straub} The Straub and |
| 198 |
> |
Karplus model, treats CO as a rigid three site molecule which places a massless M |
| 199 |
> |
site at the center of mass position along the CO bond. The geometry used along |
| 200 |
> |
with the interaction parameters are reproduced in Table~\ref{tab:CO}. The effective |
| 201 |
|
dipole moment, calculated from the assigned charges, is still |
| 202 |
|
small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
| 203 |
|
to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
| 218 |
|
\textbf{M} & 0.0 & - & - & 1.6 \\ |
| 219 |
|
\hline |
| 220 |
|
\end{tabular} |
| 221 |
+ |
\label{tab:CO} |
| 222 |
|
\end{table} |
| 223 |
|
|
| 224 |
|
\subsection{Cross-Interactions between the metals and carbon monoxide} |
| 231 |
|
clean metal surfaces. Parameters reported by Korzeniewski {\it et |
| 232 |
|
al.}\cite{Pons:1986} were a starting point for our fits, which were |
| 233 |
|
modified to ensure that the Pt-CO interaction favored the atop binding |
| 234 |
< |
position on Pt(111). This resulting binding energies are on the higher |
| 235 |
< |
side of the experimentally-reported values. Following Korzeniewski |
| 234 |
> |
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters} |
| 235 |
> |
This resulted in binding energies that are slightly higher |
| 236 |
> |
than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
| 237 |
|
{\it et al.},\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 238 |
|
Lennard-Jones interaction to mimic strong, but short-ranged partial |
| 239 |
|
binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
| 240 |
< |
Pt-O interaction was parameterized to a Morse potential with a large |
| 241 |
< |
range parameter ($r_o$). In most cases, this contributes a weak |
| 240 |
> |
Pt-O interaction was parameterized to a Morse potential at a larger |
| 241 |
> |
minimum distance, ($r_o$). This was chosen so that the C would be preferred |
| 242 |
> |
over O as the binder to the surface. In most cases, this parameterization contributes a weak |
| 243 |
|
repulsion which favors the atop site. The resulting potential-energy |
| 244 |
|
surface suitably recovers the calculated Pt-C separation length |
| 245 |
|
(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
| 248 |
|
%where did you actually get the functionals for citation? |
| 249 |
|
%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
| 250 |
|
%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
| 251 |
< |
The Au-C and Au-O cross-interactions were fit using Lennard-Jones and |
| 251 |
> |
The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and |
| 252 |
|
Morse potentials, respectively, to reproduce Au-CO binding energies. |
| 253 |
< |
|
| 254 |
< |
The fits were refined against gas-surface DFT calculations with a |
| 253 |
> |
The limited experimental data for CO adsorption on Au lead us to refine our fits against DFT. |
| 254 |
> |
Adsorption energies were obtained from gas-surface DFT calculations with a |
| 255 |
|
periodic supercell plane-wave basis approach, as implemented in the |
| 256 |
|
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are |
| 257 |
|
described with the projector augmented-wave (PAW) |
| 260 |
|
computed with the PBE implementation of the generalized gradient |
| 261 |
|
approximation (GGA) for gold, carbon, and oxygen that was constructed |
| 262 |
|
by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP} |
| 263 |
< |
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 |
| 263 |
> |
In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4 |
| 264 |
|
Au x 2 Au surface planes and separated from vertical images by six |
| 265 |
< |
layers of vacuum space. The surface atoms were all allowed to relax. |
| 266 |
< |
Supercell calculations were performed nonspin-polarized with a 4 x 4 x |
| 267 |
< |
4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
| 265 |
> |
layers of vacuum space. The surface atoms were all allowed to relax |
| 266 |
> |
before CO was added to the system. Electronic relaxations were |
| 267 |
> |
performed until the energy difference between subsequent steps |
| 268 |
> |
was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
| 269 |
> |
were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
| 270 |
|
zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was |
| 271 |
|
then used in numerous single point calculations with CO at various |
| 272 |
|
heights (and angles relative to the surface) to allow fitting of the |
| 273 |
|
empirical force field. |
| 274 |
|
|
| 275 |
|
%Hint at future work |
| 276 |
< |
The parameters employed in this work are shown in Table 2 and the |
| 277 |
< |
binding energies on the 111 surfaces are displayed in Table 3. To |
| 278 |
< |
speed up the computations, charge transfer and polarization are not |
| 279 |
< |
being treated in this model, although these effects are likely to |
| 280 |
< |
affect binding energies and binding site |
| 281 |
< |
preferences.\cite{Deshlahra:2012} |
| 276 |
> |
The parameters employed for the metal-CO cross-interactions in this work |
| 277 |
> |
are shown in Table~\ref{co_parameters} and the binding energies on the |
| 278 |
> |
(111) surfaces are displayed in Table~\ref{co_energies}. Charge transfer |
| 279 |
> |
and polarization are neglected in this model, although these effects are likely to |
| 280 |
> |
affect binding energies and binding site preferences, and will be added in |
| 281 |
> |
a future work.\cite{Deshlahra:2012,StreitzMintmire} |
| 282 |
|
|
| 283 |
|
%Table of Parameters |
| 284 |
|
%Pt Parameter Set 9 |
| 298 |
|
|
| 299 |
|
\hline |
| 300 |
|
\end{tabular} |
| 301 |
+ |
\label{tab:co_parameters} |
| 302 |
|
\end{table} |
| 303 |
|
|
| 304 |
|
%Table of energies |
| 316 |
|
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPD_Gold}) \\ |
| 317 |
|
\hline |
| 318 |
|
\end{tabular} |
| 319 |
+ |
\label{tab:co_energies} |
| 320 |
|
\end{table} |
| 321 |
|
|
| 322 |
|
\subsection{Pt(557) and Au(557) metal interfaces} |
| 348 |
|
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,OpenMD} |
| 349 |
|
|
| 350 |
|
% Just results, leave discussion for discussion section |
| 351 |
< |
\section{Results} |
| 352 |
< |
Tao {\it et al.} showed experimentally that the Pt(557) surface |
| 353 |
< |
undergoes two separate reconstructions upon CO |
| 354 |
< |
adsorption.\cite{Tao:2010} The first reconstruction involves a |
| 355 |
< |
doubling of the step edge height which is accomplished by a doubling |
| 356 |
< |
of the plateau length. The second reconstruction led to the formation |
| 357 |
< |
of triangular clusters that arrange themselves along the lengthened |
| 358 |
< |
plateaus. |
| 351 |
> |
% structure |
| 352 |
> |
% Pt: step wandering, double layers, no triangular motifs |
| 353 |
> |
% Au: step wandering, no double layers |
| 354 |
> |
% dynamics |
| 355 |
> |
% diffusion |
| 356 |
> |
% time scale, formation, breakage |
| 357 |
> |
\section{Results} |
| 358 |
> |
\subsection{Structural remodeling} |
| 359 |
> |
Tao {\it et al.} showed experimentally that the Pt(557) surface undergoes |
| 360 |
> |
two separate reconstructions upon CO adsorption.\cite{Tao:2010} The first |
| 361 |
> |
reconstruction involves a doubling of the step height and plateau length. Similar |
| 362 |
> |
behavior has been seen to occur on numerous surfaces at varying conditions.\cite{Williams:1994,Williams:1991,Pearl} |
| 363 |
> |
Of the two systems we examined, the Platinum system showed the most surface |
| 364 |
> |
reconstruction. Additionally, the amount of reconstruction appears to be |
| 365 |
> |
dependent on the amount of CO adsorbed upon the surface. This result is likely |
| 366 |
> |
related to the effect that coverage has on surface diffusion. While both systems |
| 367 |
> |
displayed step edge wandering, only the Pt surface underwent doubling within |
| 368 |
> |
the time scales we were modeling. Specifically only the 50 \% coverage Pt system |
| 369 |
> |
was observed to undergo a complete doubling in the time scales we were able to monitor. |
| 370 |
> |
This event encouraged us to allow that specific system to run continuously during which two |
| 371 |
> |
more double layers were created. The other systems, not displaying any large scale changes |
| 372 |
> |
of interest, were all stopped after 40 ns of simulation. Neverthless, the other Platinum systems tended to show |
| 373 |
> |
more cumulative lateral movement of the step edges when compared to the Gold systems. |
| 374 |
> |
The 50 \% Pt system is highlighted in figure \ref{fig:reconstruct} at various times along the |
| 375 |
> |
simulation showing the evolution of the system. |
| 376 |
|
|
| 377 |
< |
The primary observation and results of our simulation is that the |
| 378 |
< |
presence of CO overlayer on Pt(557) causes the same kind of |
| 379 |
< |
reconstruction observed experimentally. The 6-atom 111 facets |
| 380 |
< |
initially become disordered, and after 20-40 ns, a double-layer (with |
| 381 |
< |
a 2-atom step between terraces) forms. However, we did not observe |
| 360 |
< |
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. |
| 377 |
> |
The second reconstruction on the Pt(557) surface observed by Tao involved the |
| 378 |
> |
formation of triangular clusters that stretched across the plateau between two step edges. |
| 379 |
> |
Neither system, within our simulated time scales, experiences this reconstruction. A constructed |
| 380 |
> |
system in which the triangular motifs were constructed on the surface will be explored in future |
| 381 |
> |
work and is shown in the supporting information. |
| 382 |
|
|
| 383 |
< |
In these simulations, the Au(557) surface did not exhibit any |
| 384 |
< |
significant restructuring either with or without the presence of a CO |
| 385 |
< |
overlayer. |
| 383 |
> |
\subsection{Dynamics} |
| 384 |
> |
While atomistic-like simulations of stepped surfaces have been performed before \cite{}, they tend to be |
| 385 |
> |
performed using Monte Carlo techniques\cite{Williams:1991,Williams:1994}. This allows them to efficiently sample the thermodynamic |
| 386 |
> |
landscape but at the expense of ignoring the dynamics of the system. Previous work, using STM \cite{Pearl}, |
| 387 |
> |
has been able to visualize the coalescing of steps of (system). The time scale of the image acquisition, ~ 70 s/image |
| 388 |
> |
provides an upper bounds for the time required for the doubling to actually occur. While statistical treatments |
| 389 |
> |
of step edges are adept at analyzing such systems, it is important to remember that the edges are made |
| 390 |
> |
up of individual atoms and thus can be examined in numerous ways. |
| 391 |
|
|
| 392 |
< |
\subsection{Transport of surface metal atoms} |
| 393 |
< |
An ideal metal surface displaying a low energy (111) face is unlikely |
| 394 |
< |
to experience much surface diffusion because of the large vacancy |
| 395 |
< |
formation energy for atoms at the surface. This implies that |
| 396 |
< |
significant energy must be expended to lift an atom out of the flat |
| 397 |
< |
face so it can migrate on the surface. Rougher surfaces and those |
| 398 |
< |
that already contain numerous adatoms, step edges, and kinks, are |
| 399 |
< |
expected to have higher surface diffusion rates. Metal atoms that are |
| 400 |
< |
mobile on the surface were observed to leave and then rejoin step |
| 401 |
< |
edges or other formations. They may travel together or as isolated |
| 402 |
< |
atoms. The primary challenge of quantifying the overall surface |
| 403 |
< |
mobility is in defining ``mobile'' vs. ``static'' atoms. |
| 392 |
> |
\subsubsection{Transport of surface metal atoms} |
| 393 |
> |
%forcedSystems/stepSeparation |
| 394 |
> |
The movement of a step edge is a cooperative effect arising from the individual movements of the atoms |
| 395 |
> |
making up the step. An ideal metal surface displaying a low index facet (111, 100, 110) is unlikely to |
| 396 |
> |
experience much surface diffusion because of the large energetic barrier to lift an atom out of the surface. |
| 397 |
> |
For our surfaces however, the presence of step edges provide a source for mobile metal atoms. Breaking away |
| 398 |
> |
from the step edge still imposes an energetic penalty around 40 kcal/mole, but is much less than lifting the same metal |
| 399 |
> |
atom out from the surface, > 60 kcal/mole, and the penalty lowers even further when CO is present in sufficient quantities |
| 400 |
> |
on the surface, ~20 kcal/mole. Once an adatom exists on the surface, its barrier for diffusion is negligible ( < 4 kcal/mole) |
| 401 |
> |
and is well able to explore its terrace. Atoms traversing terraces is more difficult, but can be overcome through a joining and lifting stage. |
| 402 |
> |
By tracking the mobility of individual metal atoms on the Platinum and Gold surfaces we were able to determine |
| 403 |
> |
the relative diffusion rates and how varying coverages of CO affected the rates. Close |
| 404 |
> |
observation of the mobile metal atoms showed that they were typically in equilibrium with the |
| 405 |
> |
step edges, constantly breaking apart and rejoining. Additionally, at times their motion was concerted and |
| 406 |
> |
two or more atoms would be observed moving together across the surfaces. The primary challenge in quantifying |
| 407 |
> |
the overall surface mobility was in defining ``mobile" vs. ``static" atoms. |
| 408 |
|
|
| 409 |
< |
A particle was considered mobile once it had traveled more than 2~\AA~ |
| 410 |
< |
between saved configurations (10-100 ps). Restricting the transport |
| 411 |
< |
calculations to only mobile atoms eliminates all of the bulk metal as |
| 412 |
< |
well as any surface atoms that remain fixed for a significant length |
| 413 |
< |
of time. Since diffusion on a surface is strongly affected by local |
| 414 |
< |
structures, the diffusion parallel to the step edges was determined |
| 388 |
< |
separately from the diffusion perpendicular to these edges. The |
| 389 |
< |
parallel and perpendicular diffusion constants (determined using |
| 390 |
< |
linear fits to the mean squared displacement) are shown in figure \ref{fig:diff}. |
| 409 |
> |
A particle was considered mobile once it had traveled more than 2~\AA~ between saved configurations |
| 410 |
> |
of the system (10-100 ps). An atom that was truly mobile would typically travel much greater than this, but |
| 411 |
> |
the 2~\AA~ cutoff was to prevent the in-place vibrational movement of atoms from being included in the analysis. |
| 412 |
> |
Since diffusion on a surface is strongly affected by local structures, in this case the presence of single and double |
| 413 |
> |
layer step edges, the diffusion parallel to the step edges was determined separately from the diffusion perpendicular |
| 414 |
> |
to these edges. The parallel and perpendicular diffusion constants are shown in figure \ref{fig:diff}. |
| 415 |
|
|
| 416 |
< |
%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. |
| 416 |
> |
\subsubsection{Double layer formation} |
| 417 |
> |
The increased amounts of diffusion on Pt at the higher CO coverages appears to play a role in the |
| 418 |
> |
formation of double layers, seeing as how that was the only system within our observed simulation time |
| 419 |
> |
that showed the formation. Despite this being the only system where this reconstruction occurs, three separate layers |
| 420 |
> |
were formed over the extended run time of this system. As mentioned earlier, previous experimental work has given some insight into |
| 421 |
> |
the upper bounds of the time required for enough atoms to move around to allow two steps to coalesce\cite{Williams:1991,Pearl}. |
| 422 |
> |
As seen in figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into |
| 423 |
> |
the simulation. Within 12 ns, nearly half of the step has formed the double layer and by 86 ns, a smooth complete |
| 424 |
> |
layer has formed. The double layer is complete by 37 ns but is a bit rough. |
| 425 |
> |
From the appearance of the first node to the initial doubling of the layers ignoring their roughness took ~20 ns. |
| 426 |
> |
Another ~40 ns was necessary for the layer to completely straighten. The other two layers in this simulation form |
| 427 |
> |
over a period of 22 ns and 42 ns respectively. |
| 428 |
|
|
| 429 |
+ |
%Evolution of surface |
| 430 |
|
\begin{figure}[H] |
| 431 |
+ |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 432 |
+ |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 433 |
+ |
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
| 434 |
+ |
(d) 86.1 ns. Disruption of the 557 step edges occurs quickly. The |
| 435 |
+ |
doubling of the layers appears only after two adjacent step edges |
| 436 |
+ |
touch. The circled spot in (b) nucleated the growth of the double |
| 437 |
+ |
step observed in the later configurations.} |
| 438 |
+ |
\label{fig:reconstruct} |
| 439 |
+ |
\end{figure} |
| 440 |
+ |
|
| 441 |
+ |
\begin{figure}[H] |
| 442 |
|
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
| 443 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
| 444 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 454 |
|
\label{fig:diff} |
| 455 |
|
\end{figure} |
| 456 |
|
|
| 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} |
| 457 |
|
|
| 458 |
+ |
|
| 459 |
+ |
|
| 460 |
|
%Discussion |
| 461 |
|
\section{Discussion} |
| 462 |
+ |
In this paper we have shown that we were able to accurately model the initial reconstruction of the |
| 463 |
+ |
Pt (557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 464 |
+ |
were able to capture the dynamic processes inherent within this reconstruction. |
| 465 |
|
|
| 466 |
< |
Mechanism for restructuring |
| 466 |
> |
\subsection{Mechanism for restructuring} |
| 467 |
> |
The increased computational cost to examine this system using molecular dynamics rather than |
| 468 |
> |
a Monte Carlo based approach was necessary so that our predictions on possible mechanisms |
| 469 |
> |
and driving forces would have support not only from thermodynamic arguments but also from the |
| 470 |
> |
actual dynamics of the system. |
| 471 |
|
|
| 435 |
– |
There are a number of possible mechanisms to explain the role of |
| 436 |
– |
adsorbed CO in restructuring the Pt surface. Quadrupolar repulsion |
| 437 |
– |
between adjacent CO molecules adsorbed on the surface is one |
| 438 |
– |
possibility. However, the quadrupole-quadrupole interaction is |
| 439 |
– |
short-ranged and is attractive for some orientations. If the CO |
| 440 |
– |
molecules are locked in a specific orientation relative to each other, |
| 441 |
– |
this explanation gains some weight. |
| 442 |
– |
|
| 443 |
– |
Another possible mechanism for the restructuring is in the |
| 444 |
– |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 445 |
– |
Pt atoms. This could have the effect of increasing surface mobility |
| 446 |
– |
of these atoms. |
| 447 |
– |
|
| 472 |
|
Comparing the results from simulation to those reported previously by |
| 473 |
|
Tao et al. the similarities in the platinum and CO system are quite |
| 474 |
< |
strong. As shown in figure, the simulated platinum system under a CO |
| 474 |
> |
strong. As shown in figure \ref{fig:reconstruct}, the simulated platinum system under a CO |
| 475 |
|
atmosphere will restructure slightly by doubling the terrace |
| 476 |
|
heights. The restructuring appears to occur slowly, one to two |
| 477 |
|
platinum atoms at a time. Looking at individual snapshots, these |
| 487 |
|
growth point, the double layer tends to be fully formed within |
| 488 |
|
$\sim$~35 ns. |
| 489 |
|
|
| 490 |
+ |
There are a number of possible mechanisms to explain the role of |
| 491 |
+ |
adsorbed CO in restructuring the Pt surface. Quadrupolar repulsion |
| 492 |
+ |
between adjacent CO molecules adsorbed on the surface is one |
| 493 |
+ |
possibility. However, the quadrupole-quadrupole interaction is |
| 494 |
+ |
short-ranged and is attractive for some orientations. If the CO |
| 495 |
+ |
molecules are ``locked'' in a specific orientation relative to each other however, |
| 496 |
+ |
this explanation gains some weight. The energetic repulsion between two CO |
| 497 |
+ |
located a distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in a |
| 498 |
+ |
vertical orientation is 8.62 kcal/mole. Moving the CO apart to the second nearest-neighbor |
| 499 |
+ |
distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to nearly 0 kcal/mole. SHOW A NUMBER FOR ROTATION. |
| 500 |
+ |
As mentioned above, the energy barrier for surface diffusion of a platinum adatom is only 4 kcal/mole. So this |
| 501 |
+ |
repulsion between CO can help increase the surface diffusion. However, the residence time of CO was examined |
| 502 |
+ |
and while the majority of the CO is on or near the surface throughout the run, it is extremely mobile. This mobility |
| 503 |
+ |
suggests that the CO are more likely to shift their positions without necessarily dragging the platinum along |
| 504 |
+ |
with them. |
| 505 |
+ |
|
| 506 |
+ |
Another possible and more likely mechanism for the restructuring is in the |
| 507 |
+ |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 508 |
+ |
Pt atoms. This could have the effect of increasing surface mobility |
| 509 |
+ |
of these atoms. To test this hypothesis, numerous configurations of |
| 510 |
+ |
CO in varying quantities were arranged on the higher and lower plateaus |
| 511 |
+ |
around a step on a otherwise clean Pt (557) surface. One representative |
| 512 |
+ |
configuration is displayed in figure \ref{fig:lambda}. Single or concerted movement |
| 513 |
+ |
of platinum atoms was then examined to determine possible barriers. Because |
| 514 |
+ |
of the forced movement along a pre-defined reaction coordinate that may differ |
| 515 |
+ |
from the true minimum of this path, only the beginning and ending energies |
| 516 |
+ |
are displayed in table \ref{tab:energies}. The presence of CO at suitable |
| 517 |
+ |
sites can lead to lowered barriers for platinum breaking apart from the step edge. |
| 518 |
+ |
Additionally, as highlighted in figure \ref{fig:lambda}, the presence of CO makes the |
| 519 |
+ |
burrowing and lifting nature favorable, whereas without CO, the process is neutral |
| 520 |
+ |
in terms of energetics. |
| 521 |
+ |
|
| 522 |
+ |
%lambda progression of Pt -> shoving its way into the step |
| 523 |
+ |
\begin{figure}[H] |
| 524 |
+ |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO.png} |
| 525 |
+ |
\caption{A model system of the Pt 557 surface was used as the framework for a reaction coordinate. |
| 526 |
+ |
Various numbers, placements, and rotations of CO were examined. The one displayed was a |
| 527 |
+ |
representative sample. As shown in Table , relative to the energy at 0\% there is a slight decrease |
| 528 |
+ |
upon insertion of the platinum atom into the step edge along with the resultant lifting of the other |
| 529 |
+ |
platinum atom.} |
| 530 |
+ |
\label{fig:lambda} |
| 531 |
+ |
\end{figure} |
| 532 |
+ |
|
| 533 |
+ |
|
| 534 |
+ |
|
| 535 |
|
\subsection{Diffusion} |
| 536 |
< |
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?) |
| 536 |
> |
As shown in the results section, the diffusion parallel to the step edge tends to be |
| 537 |
> |
much faster than that perpendicular to the step edge. Additionally, the coverage |
| 538 |
> |
of CO appears to play a slight role in relative rates of diffusion, as shown in figure \ref{fig:diff} |
| 539 |
> |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
| 540 |
> |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
| 541 |
> |
appears, parallel diffusion, along the now slightly angled step edge, will allow for |
| 542 |
> |
a faster formation of the double layer than if the entire process were dependent on |
| 543 |
> |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
| 544 |
> |
more likely a growth point is to be formed. |
| 545 |
|
\\ |
| 546 |
< |
\\ |
| 547 |
< |
%Evolution of surface |
| 546 |
> |
|
| 547 |
> |
|
| 548 |
> |
%breaking of the double layer upon removal of CO |
| 549 |
|
\begin{figure}[H] |
| 550 |
< |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 551 |
< |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 552 |
< |
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
| 475 |
< |
(d) 86.1 ns. Disruption of the 557 step edges occurs quickly. The |
| 476 |
< |
doubling of the layers appears only after two adjacent step edges |
| 477 |
< |
touch. The circled spot in (b) nucleated the growth of the double |
| 478 |
< |
step observed in the later configurations.} |
| 550 |
> |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 551 |
> |
\caption{Hi} |
| 552 |
> |
\label{fig:breaking} |
| 553 |
|
\end{figure} |
| 554 |
|
|
| 555 |
|
|
| 556 |
+ |
|
| 557 |
+ |
|
| 558 |
|
%Peaks! |
| 559 |
|
\begin{figure}[H] |
| 560 |
|
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 561 |
|
\caption{} |
| 562 |
+ |
\label{fig:peaks} |
| 563 |
|
\end{figure} |
| 564 |
+ |
|
| 565 |
+ |
%clean surface... |
| 566 |
|
\begin{figure}[H] |
| 567 |
|
\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
| 568 |
|
\caption{} |
| 569 |
+ |
|
| 570 |
|
\end{figure} |
| 571 |
+ |
\label{fig:clean} |
| 572 |
|
\section{Conclusion} |
| 573 |
|
|
| 574 |
|
|
| 575 |
+ |
%Things I am not ready to remove yet |
| 576 |
+ |
|
| 577 |
+ |
%Table of Diffusion Constants |
| 578 |
+ |
%Add gold?M |
| 579 |
+ |
% \begin{table}[H] |
| 580 |
+ |
% \caption{} |
| 581 |
+ |
% \centering |
| 582 |
+ |
% \begin{tabular}{| c | cc | cc | } |
| 583 |
+ |
% \hline |
| 584 |
+ |
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
| 585 |
+ |
% \hline |
| 586 |
+ |
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
| 587 |
+ |
% \hline |
| 588 |
+ |
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
| 589 |
+ |
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
| 590 |
+ |
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
| 591 |
+ |
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
| 592 |
+ |
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
| 593 |
+ |
% \hline |
| 594 |
+ |
% \end{tabular} |
| 595 |
+ |
% \end{table} |
| 596 |
+ |
|
| 597 |
|
\section{Acknowledgments} |
| 598 |
|
Support for this project was provided by the National Science |
| 599 |
|
Foundation under grant CHE-0848243 and by the Center for Sustainable |
