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\begin{doublespace} |
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|
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\begin{abstract} |
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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. |
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\end{abstract} |
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|
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\newpage |
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reversible restructuring under exposure to moderate pressures of |
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carbon monoxide.\cite{Tao:2010} |
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|
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This work an effort to understand the mechanism and timescale for |
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This work is an attempt to understand the mechanism and timescale for |
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surface restructuring using molecular simulations. Since the dynamics |
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of the process is of particular interest, we utilize classical force |
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of the process are of particular interest, we employ classical force |
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fields that represent a compromise between chemical accuracy and the |
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< |
computational efficiency necessary to observe the process of interest. |
| 107 |
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computational efficiency necessary to simulate the process of interest. |
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|
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Since restructuring occurs as a result of specific interactions of the |
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catalyst with adsorbates, two metal systems exposed to carbon monoxide |
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were examined in this work. The Pt(557) surface has already been shown |
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Restructuring can occur as a result of specific interactions of the |
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catalyst with adsorbates. In this work, two metal systems exposed |
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> |
to carbon monoxide were examined. The Pt(557) surface has already been shown |
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to reconstruct under certain conditions. The Au(557) surface, because |
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of a weaker interaction with CO, is less likely to undergo this kind |
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of reconstruction. MORE HERE ON PT AND AU PREVIOUS WORK. |
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Coulomb potential. For this work, we have used classical molecular |
| 134 |
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dynamics with potential energy surfaces that are specifically tuned |
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for transition metals. In particular, we used the EAM potential for |
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Au-Au and Pt-Pt interactions, while modeling the CO using a rigid |
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Au-Au and Pt-Pt interactions\cite{EAM}, while modeling the CO using a rigid |
| 137 |
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three-site model developed by Straub and Karplus for studying |
| 138 |
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photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 139 |
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Pt-CO cross interactions were parameterized as part of this work. |
| 164 |
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V_i = F[ \bar{\rho}_i ] + \sum_{j \neq i} \phi_{ij}(r_{ij}) |
| 165 |
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\end{equation*} |
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where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and |
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$\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the |
| 168 |
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overlap of the two positively charged cores. |
| 167 |
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$\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the |
| 168 |
> |
repulsive overlap of the two positively charged cores. |
| 169 |
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|
| 170 |
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% The {\it modified} embedded atom method (MEAM) adds angular terms to |
| 171 |
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% the electron density functions and an angular screening factor to the |
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% metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys}) |
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% MEAM presents significant additional computational costs, however. |
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|
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The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen potentials |
| 179 |
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The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials |
| 180 |
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have all been widely used by the materials simulation community for |
| 181 |
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simulations of bulk and nanoparticle |
| 182 |
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properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq} |
| 190 |
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parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 191 |
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|
| 192 |
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\subsection{Carbon Monoxide model} |
| 193 |
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Since previous explanations for the surface rearrangements center on |
| 194 |
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the large linear quadrupole moment of carbon monoxide, the model |
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chosen for this molecule exhibits this property in an efficient |
| 196 |
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manner. We used a model first proposed by Karplus and Straub to study |
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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 |
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Previous explanations for the surface rearrangements center on |
| 194 |
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the large linear quadrupole moment of carbon monoxide. |
| 195 |
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We used a model first proposed by Karplus and Straub to study |
| 196 |
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the photodissociation of CO from myoglobin because it reproduces |
| 197 |
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the quadrupole moment well.\cite{Straub} The Straub and |
| 198 |
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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 |
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small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
| 203 |
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to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
| 218 |
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\textbf{M} & 0.0 & - & - & 1.6 \\ |
| 219 |
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\hline |
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\end{tabular} |
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\label{tab:CO} |
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\end{table} |
| 223 |
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|
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\subsection{Cross-Interactions between the metals and carbon monoxide} |
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clean metal surfaces. Parameters reported by Korzeniewski {\it et |
| 232 |
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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 |
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{\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} |
