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Notre Dame, Indiana 46556} |
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|
| 60 |
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%Date |
| 61 |
< |
\date{Dec 15, 2012} |
| 61 |
> |
\date{Mar 5, 2013} |
| 62 |
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|
| 63 |
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%authors |
| 64 |
|
|
| 68 |
|
\begin{doublespace} |
| 69 |
|
|
| 70 |
|
\begin{abstract} |
| 71 |
+ |
We examine surface reconstructions of Pt and Au(557) under |
| 72 |
+ |
various CO coverages using molecular dynamics in order to |
| 73 |
+ |
explore possible mechanisms for any observed reconstructions |
| 74 |
+ |
and their dynamics. The metal-CO interactions were parameterized |
| 75 |
+ |
as part of this work so that an efficient large-scale treatment of |
| 76 |
+ |
this system could be undertaken. The large difference in binding |
| 77 |
+ |
strengths of the metal-CO interactions was found to play a significant |
| 78 |
+ |
role with regards to step-edge stability and adatom diffusion. A |
| 79 |
+ |
small correlation between coverage and the diffusion constant |
| 80 |
+ |
was also determined. The energetics of CO adsorbed to the surface |
| 81 |
+ |
is sufficient to explain the reconstructions observed on the Pt |
| 82 |
+ |
systems and the lack of reconstruction of the Au systems. |
| 83 |
|
|
| 84 |
|
\end{abstract} |
| 85 |
|
|
| 94 |
|
% Sub: Also, easier to observe what is going on and provide reasons and explanations |
| 95 |
|
% |
| 96 |
|
|
| 97 |
< |
Industrial catalysts usually consist of small particles exposing |
| 98 |
< |
different atomic terminations that exhibit a high concentration of |
| 99 |
< |
step, kink sites, and vacancies at the edges of the facets. These |
| 89 |
< |
sites are thought to be the locations of catalytic |
| 97 |
> |
Industrial catalysts usually consist of small particles that exhibit a |
| 98 |
> |
high concentration of steps, kink sites, and vacancies at the edges of |
| 99 |
> |
the facets. These sites are thought to be the locations of catalytic |
| 100 |
|
activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now |
| 101 |
< |
significant evidence to demonstrate that solid surfaces are often |
| 102 |
< |
structurally, compositionally, and chemically {\it modified} by |
| 103 |
< |
reactants under operating conditions.\cite{Tao2008,Tao:2010,Tao2011} |
| 104 |
< |
The coupling between surface oxidation state and catalytic activity |
| 105 |
< |
for CO oxidation on Pt, for instance, is widely |
| 106 |
< |
documented.\cite{Ertl08,Hendriksen:2002} Despite the well-documented |
| 107 |
< |
role of these effects on reactivity, the ability to capture or predict |
| 108 |
< |
them in atomistic models is currently somewhat limited. While these |
| 109 |
< |
effects are perhaps unsurprising on the highly disperse, multi-faceted |
| 110 |
< |
nanoscale particles that characterize industrial catalysts, they are |
| 111 |
< |
manifest even on ordered, well-defined surfaces. The Pt(557) surface, |
| 112 |
< |
for example, exhibits substantial and reversible restructuring under |
| 113 |
< |
exposure to moderate pressures of carbon monoxide.\cite{Tao:2010} |
| 101 |
> |
significant evidence that solid surfaces are often structurally, |
| 102 |
> |
compositionally, and chemically modified by reactants under operating |
| 103 |
> |
conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between |
| 104 |
> |
surface oxidation states and catalytic activity for CO oxidation on |
| 105 |
> |
Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002} |
| 106 |
> |
Despite the well-documented role of these effects on reactivity, the |
| 107 |
> |
ability to capture or predict them in atomistic models is somewhat |
| 108 |
> |
limited. While these effects are perhaps unsurprising on the highly |
| 109 |
> |
disperse, multi-faceted nanoscale particles that characterize |
| 110 |
> |
industrial catalysts, they are manifest even on ordered, well-defined |
| 111 |
> |
surfaces. The Pt(557) surface, for example, exhibits substantial and |
| 112 |
> |
reversible restructuring under exposure to moderate pressures of |
| 113 |
> |
carbon monoxide.\cite{Tao:2010} |
| 114 |
|
|
| 115 |
< |
This work is part of an ongoing effort to understand the causes, |
| 116 |
< |
mechanisms and timescales for surface restructuring using molecular |
| 117 |
< |
simulation methods. Since the dynamics of the process is of |
| 118 |
< |
particular interest, we utilize classical molecular dynamic methods |
| 119 |
< |
with force fields that represent a compromise between chemical |
| 120 |
< |
accuracy and the computational efficiency necessary to observe the |
| 121 |
< |
process of interest. |
| 115 |
> |
This work is an investigation into the mechanism and timescale for |
| 116 |
> |
surface restructuring using molecular simulations. Since the dynamics |
| 117 |
> |
of the process are of particular interest, we employ classical force |
| 118 |
> |
fields that represent a compromise between chemical accuracy and the |
| 119 |
> |
computational efficiency necessary to simulate the process of interest. |
| 120 |
> |
Since restructuring typically occurs as a result of specific interactions of the |
| 121 |
> |
catalyst with adsorbates, in this work, two metal systems exposed |
| 122 |
> |
to carbon monoxide were examined. The Pt(557) surface has already been shown |
| 123 |
> |
to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010} |
| 124 |
> |
The Au(557) surface, because of a weaker interaction with CO, is seen as less |
| 125 |
> |
likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000} |
| 126 |
> |
and Piccolo et al.\cite{Piccolo:2004} have both observed CO-induced |
| 127 |
> |
reconstruction of a Au(111) surface. Peters et al. saw a relaxation to the |
| 128 |
> |
22 x $\sqrt{3}$ cell. They argued that only a few Au atoms |
| 129 |
> |
become adatoms, limiting the stress of this reconstruction while |
| 130 |
> |
allowing the rest to relax and approach the ideal (111) |
| 131 |
> |
configuration. They did not see the usual herringbone pattern being greatly |
| 132 |
> |
affected by this relaxation. Piccolo et al. on the other hand, did see a |
| 133 |
> |
disruption of the herringbone pattern as CO was adsorbed to the |
| 134 |
> |
surface. Both groups suggested that the preference CO shows for |
| 135 |
> |
low-coordinated Au atoms was the primary driving force for the reconstruction. |
| 136 |
|
|
| 137 |
< |
Since restructuring occurs as a result of specific interactions of the catalyst |
| 138 |
< |
with adsorbates, two metals systems exposed to the same adsorbate, CO, |
| 115 |
< |
were examined in this work. The Pt(557) surface has already been shown to |
| 116 |
< |
reconstruct under certain conditions. The Au(557) surface, because of gold's |
| 117 |
< |
weaker interaction with CO, is less likely to undergo such a large reconstruction. |
| 137 |
> |
|
| 138 |
> |
|
| 139 |
|
%Platinum molecular dynamics |
| 140 |
|
%gold molecular dynamics |
| 141 |
|
|
| 121 |
– |
|
| 122 |
– |
|
| 142 |
|
\section{Simulation Methods} |
| 143 |
< |
The challenge in modeling any solid/gas interface problem is the |
| 143 |
> |
The challenge in modeling any solid/gas interface is the |
| 144 |
|
development of a sufficiently general yet computationally tractable |
| 145 |
|
model of the chemical interactions between the surface atoms and |
| 146 |
|
adsorbates. Since the interfaces involved are quite large (10$^3$ - |
| 153 |
|
typically not well represented in terms of classical pairwise |
| 154 |
|
interactions in the same way that bonds in a molecular material are, |
| 155 |
|
nor are they captured by simple non-directional interactions like the |
| 156 |
< |
Coulomb potential. For this work, we have been using classical |
| 157 |
< |
molecular dynamics with potential energy surfaces that are |
| 158 |
< |
specifically tuned for transition metals. In particular, we use the |
| 159 |
< |
EAM potential for Au-Au and Pt-Pt interactions, while modeling the CO |
| 160 |
< |
using a model developed by Straub and Karplus for studying |
| 161 |
< |
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and Pt-CO |
| 162 |
< |
cross interactions were parameterized as part of this work. |
| 156 |
> |
Coulomb potential. For this work, we have used classical molecular |
| 157 |
> |
dynamics with potential energy surfaces that are specifically tuned |
| 158 |
> |
for transition metals. In particular, we used the EAM potential for |
| 159 |
> |
Au-Au and Pt-Pt interactions\cite{EAM}. The CO was modeled using a rigid |
| 160 |
> |
three-site model developed by Straub and Karplus for studying |
| 161 |
> |
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 162 |
> |
Pt-CO cross interactions were parameterized as part of this work. |
| 163 |
|
|
| 164 |
|
\subsection{Metal-metal interactions} |
| 165 |
< |
Many of the potentials used for classical simulation of transition |
| 166 |
< |
metals are based on a non-pairwise additive functional of the local |
| 167 |
< |
electron density. The embedded atom method (EAM) is perhaps the best |
| 168 |
< |
known of these |
| 165 |
> |
Many of the potentials used for modeling transition metals are based |
| 166 |
> |
on a non-pairwise additive functional of the local electron |
| 167 |
> |
density. The embedded atom method (EAM) is perhaps the best known of |
| 168 |
> |
these |
| 169 |
|
methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98} |
| 170 |
|
but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and |
| 171 |
|
the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
| 172 |
< |
parameter sets. The glue model of Ercolessi {\it et al.} is among the |
| 172 |
> |
parameter sets. The glue model of Ercolessi et al. is among the |
| 173 |
|
fastest of these density functional approaches.\cite{Ercolessi88} In |
| 174 |
|
all of these models, atoms are conceptualized as a positively charged |
| 175 |
|
core with a radially-decaying valence electron distribution. To |
| 176 |
|
calculate the energy for embedding the core at a particular location, |
| 177 |
|
the electron density due to the valence electrons at all of the other |
| 178 |
< |
atomic sites is computed at atom $i$'s location, |
| 178 |
> |
atomic sites is computed at atom $i$'s location, |
| 179 |
|
\begin{equation*} |
| 180 |
|
\bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij}) |
| 181 |
|
\end{equation*} |
| 187 |
|
V_i = F[ \bar{\rho}_i ] + \sum_{j \neq i} \phi_{ij}(r_{ij}) |
| 188 |
|
\end{equation*} |
| 189 |
|
where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and |
| 190 |
< |
$\phi_{ij}(r_{ij})$ is an pairwise term that is meant to represent the |
| 191 |
< |
overlap of the two positively charged cores. |
| 190 |
> |
$\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the |
| 191 |
> |
repulsive overlap of the two positively charged cores. |
| 192 |
|
|
| 193 |
< |
The {\it modified} embedded atom method (MEAM) adds angular terms to |
| 194 |
< |
the electron density functions and an angular screening factor to the |
| 195 |
< |
pairwise interaction between two |
| 196 |
< |
atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve} |
| 197 |
< |
MEAM has become widely used to simulate systems in which angular |
| 198 |
< |
interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc |
| 199 |
< |
metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys}) |
| 200 |
< |
MEAM presents significant additional computational costs, however. |
| 193 |
> |
% The {\it modified} embedded atom method (MEAM) adds angular terms to |
| 194 |
> |
% the electron density functions and an angular screening factor to the |
| 195 |
> |
% pairwise interaction between two |
| 196 |
> |
% atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve} |
| 197 |
> |
% MEAM has become widely used to simulate systems in which angular |
| 198 |
> |
% interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc |
| 199 |
> |
% metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys}) |
| 200 |
> |
% MEAM presents significant additional computational costs, however. |
| 201 |
|
|
| 202 |
< |
The EAM, Finnis-Sinclair, MEAM, and the Quantum Sutton-Chen potentials |
| 202 |
> |
The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials |
| 203 |
|
have all been widely used by the materials simulation community for |
| 204 |
|
simulations of bulk and nanoparticle |
| 205 |
|
properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq} |
| 206 |
|
melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr} |
| 207 |
|
fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack |
| 208 |
|
propagation,\cite{BECQUART:1993rg} and alloying |
| 209 |
< |
dynamics.\cite{Shibata:2002hh} All of these potentials have their |
| 210 |
< |
strengths and weaknesses. One of the strengths common to all of the |
| 211 |
< |
methods is the relatively large library of metals for which these |
| 212 |
< |
potentials have been |
| 213 |
< |
parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 209 |
> |
dynamics.\cite{Shibata:2002hh} One of EAM's strengths |
| 210 |
> |
is its sensitivity to small changes in structure. This arises |
| 211 |
> |
from the original parameterization, where the interactions |
| 212 |
> |
up to the third nearest neighbor were taken into account.\cite{Voter95a} |
| 213 |
> |
Comparing that to the glue model of Ercolessi et al.\cite{Ercolessi88} |
| 214 |
> |
which is only parameterized up to the nearest-neighbor |
| 215 |
> |
interactions, EAM is a suitable choice for systems where |
| 216 |
> |
the bulk properties are of secondary importance to low-index |
| 217 |
> |
surface structures. Additionally, the similarity of EAMs functional |
| 218 |
> |
treatment of the embedding energy to standard density functional |
| 219 |
> |
theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier. |
| 220 |
> |
\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 221 |
|
|
| 222 |
< |
\subsection{CO} |
| 223 |
< |
Since one explanation for the strong surface CO repulsion on metals is |
| 224 |
< |
the large linear quadrupole moment of carbon monoxide, the model |
| 225 |
< |
chosen for this molecule exhibits this property in an efficient |
| 226 |
< |
manner. We used a model first proposed by Karplus and Straub to study |
| 227 |
< |
the photodissociation of CO from myoglobin.\cite{Straub} The Straub and |
| 228 |
< |
Karplus model is a rigid three site model which places a massless M |
| 229 |
< |
site at the center of mass along the CO bond. The geometry used along |
| 230 |
< |
with the interaction parameters are reproduced in Table 1. The effective |
| 222 |
> |
|
| 223 |
> |
|
| 224 |
> |
|
| 225 |
> |
\subsection{Carbon Monoxide model} |
| 226 |
> |
Previous explanations for the surface rearrangements center on |
| 227 |
> |
the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} |
| 228 |
> |
We used a model first proposed by Karplus and Straub to study |
| 229 |
> |
the photodissociation of CO from myoglobin because it reproduces |
| 230 |
> |
the quadrupole moment well.\cite{Straub} The Straub and |
| 231 |
> |
Karplus model treats CO as a rigid three site molecule with a massless M |
| 232 |
> |
site at the molecular center of mass. The geometry and interaction |
| 233 |
> |
parameters are reproduced in Table~\ref{tab:CO}. The effective |
| 234 |
|
dipole moment, calculated from the assigned charges, is still |
| 235 |
|
small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
| 236 |
|
to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
| 237 |
|
mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}. |
| 238 |
|
%CO Table |
| 239 |
|
\begin{table}[H] |
| 240 |
< |
\caption{Positions, $\sigma$, $\epsilon$ and charges for CO geometry |
| 241 |
< |
and self-interactions\cite{Straub}. Distances are in \AA~, energies are |
| 242 |
< |
in kcal/mol, and charges are in $e$.} |
| 240 |
> |
\caption{Positions, Lennard-Jones parameters ($\sigma$ and |
| 241 |
> |
$\epsilon$), and charges for the CO-CO |
| 242 |
> |
interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are |
| 243 |
> |
in kcal/mol, and charges are in atomic units.} |
| 244 |
|
\centering |
| 245 |
|
\begin{tabular}{| c | c | ccc |} |
| 246 |
|
\hline |
| 217 |
– |
\multicolumn{5}{|c|}{\textbf{Self-Interactions}}\\ |
| 218 |
– |
\hline |
| 247 |
|
& {\it z} & $\sigma$ & $\epsilon$ & q\\ |
| 248 |
|
\hline |
| 249 |
< |
\textbf{C} & -0.6457 & 0.0262 & 3.83 & -0.75 \\ |
| 250 |
< |
\textbf{O} & 0.4843 & 0.1591 & 3.12 & -0.85 \\ |
| 249 |
> |
\textbf{C} & -0.6457 & 3.83 & 0.0262 & -0.75 \\ |
| 250 |
> |
\textbf{O} & 0.4843 & 3.12 & 0.1591 & -0.85 \\ |
| 251 |
|
\textbf{M} & 0.0 & - & - & 1.6 \\ |
| 252 |
|
\hline |
| 253 |
|
\end{tabular} |
| 254 |
+ |
\label{tab:CO} |
| 255 |
|
\end{table} |
| 256 |
|
|
| 257 |
< |
\subsection{Cross-Interactions} |
| 257 |
> |
\subsection{Cross-Interactions between the metals and carbon monoxide} |
| 258 |
|
|
| 259 |
< |
One hurdle that must be overcome in classical molecular simulations |
| 260 |
< |
is the proper parameterization of the potential interactions present |
| 261 |
< |
in the system. Since the adsorption of CO onto a platinum surface has been |
| 262 |
< |
the focus of many experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979} |
| 263 |
< |
and theoretical studies \cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
| 264 |
< |
there is a large amount of data in the literature to fit too. We started with parameters |
| 265 |
< |
reported by Korzeniewski et al. \cite{Pons:1986} and then |
| 266 |
< |
modified them to ensure that the Pt-CO interaction favored |
| 267 |
< |
an atop binding position for the CO upon the Pt surface. This |
| 268 |
< |
constraint led to the binding energies being on the higher side |
| 269 |
< |
of reported values. Following the method laid out by Korzeniewski, |
| 270 |
< |
the Pt-C interaction was fit to a strong Lennard-Jones 12-6 |
| 271 |
< |
interaction to mimic binding, while the Pt-O interaction |
| 272 |
< |
was parameterized to a Morse potential with a large $r_o$ |
| 273 |
< |
to contribute a weak repulsion. The resultant potential-energy |
| 274 |
< |
surface suitably recovers the calculated Pt-C bond length ( 1.6\AA)\cite{Beurden:2002ys} and affinity |
| 275 |
< |
for the atop binding position.\cite{Deshlahra:2012, Hopster:1978} |
| 259 |
> |
Since the adsorption of CO onto a Pt surface has been the focus |
| 260 |
> |
of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979} |
| 261 |
> |
and theoretical work |
| 262 |
> |
\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
| 263 |
> |
there is a significant amount of data on adsorption energies for CO on |
| 264 |
> |
clean metal surfaces. An earlier model by Korzeniewski {\it et |
| 265 |
> |
al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were |
| 266 |
> |
modified to ensure that the Pt-CO interaction favored the atop binding |
| 267 |
> |
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}. |
| 268 |
> |
The modified parameters yield binding energies that are slightly higher |
| 269 |
> |
than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
| 270 |
> |
et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 271 |
> |
Lennard-Jones interaction to mimic strong, but short-ranged partial |
| 272 |
> |
binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
| 273 |
> |
Pt-O interaction was modeled with a Morse potential with a large |
| 274 |
> |
equilibrium distance, ($r_o$). These choices ensure that the C is preferred |
| 275 |
> |
over O as the surface-binding atom. In most cases, the Pt-O parameterization contributes a weak |
| 276 |
> |
repulsion which favors the atop site. The resulting potential-energy |
| 277 |
> |
surface suitably recovers the calculated Pt-C separation length |
| 278 |
> |
(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
| 279 |
> |
position.\cite{Deshlahra:2012, Hopster:1978} |
| 280 |
|
|
| 281 |
|
%where did you actually get the functionals for citation? |
| 282 |
|
%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
| 283 |
|
%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
| 284 |
< |
The Au-C and Au-O cross-interactions were fit using Lennard-Jones and |
| 284 |
> |
The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and |
| 285 |
|
Morse potentials, respectively, to reproduce Au-CO binding energies. |
| 286 |
< |
|
| 287 |
< |
The fits were refined against gas-surface calculations using DFT with |
| 288 |
< |
a periodic supercell plane-wave basis approach, as implemented in the |
| 289 |
< |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are |
| 286 |
> |
The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations. |
| 287 |
> |
Adsorption energies were obtained from gas-surface DFT calculations with a |
| 288 |
> |
periodic supercell plane-wave basis approach, as implemented in the |
| 289 |
> |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were |
| 290 |
|
described with the projector augmented-wave (PAW) |
| 291 |
|
method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
| 292 |
|
included to an energy cutoff of 20 Ry. Electronic energies are |
| 293 |
|
computed with the PBE implementation of the generalized gradient |
| 294 |
|
approximation (GGA) for gold, carbon, and oxygen that was constructed |
| 295 |
|
by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP} |
| 296 |
< |
Ionic relaxations were performed until the energy difference between |
| 264 |
< |
subsequent steps was less than 0.0001 eV. In testing the CO-Au |
| 265 |
< |
interaction, Au(111) supercells were constructed of four layers of 4 |
| 296 |
> |
In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4 |
| 297 |
|
Au x 2 Au surface planes and separated from vertical images by six |
| 298 |
< |
layers of vacuum space. The surface atoms were all allowed to relax. |
| 299 |
< |
Supercell calculations were performed nonspin-polarized, and energies |
| 300 |
< |
were converged to within 0.03 meV per Au atom with a 4 x 4 x 4 |
| 301 |
< |
Monkhorst-Pack\cite{Monkhorst:1976,PhysRevB.13.5188} {\bf k}-point |
| 302 |
< |
sampling of the first Brillouin zone. The relaxed gold slab was then |
| 303 |
< |
used in numerous single point calculations with CO at various heights |
| 304 |
< |
(and angles relative to the surface) to allow fitting of the empirical |
| 305 |
< |
force field. |
| 298 |
> |
layers of vacuum space. The surface atoms were all allowed to relax |
| 299 |
> |
before CO was added to the system. Electronic relaxations were |
| 300 |
> |
performed until the energy difference between subsequent steps |
| 301 |
> |
was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
| 302 |
> |
were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
| 303 |
> |
zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was |
| 304 |
> |
then used in numerous single point calculations with CO at various |
| 305 |
> |
heights (and angles relative to the surface) to allow fitting of the |
| 306 |
> |
empirical force field. |
| 307 |
|
|
| 308 |
|
%Hint at future work |
| 309 |
< |
The fit parameter sets employed in this work are shown in Table 2 and their |
| 310 |
< |
reproduction of the binding energies are displayed in Table 3. Currently, |
| 311 |
< |
charge transfer is not being treated in this system, however, that is a goal |
| 312 |
< |
for future work as the effect has been seen to affect binding energies and |
| 313 |
< |
binding site preferences. \cite{Deshlahra:2012} |
| 309 |
> |
The parameters employed for the metal-CO cross-interactions in this work |
| 310 |
> |
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
| 311 |
> |
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
| 312 |
> |
and polarization are neglected in this model, although these effects are likely to |
| 313 |
> |
affect binding energies and binding site preferences, and will be addressed in |
| 314 |
> |
future work. |
| 315 |
|
|
| 283 |
– |
|
| 284 |
– |
|
| 285 |
– |
|
| 286 |
– |
\subsection{Construction and Equilibration of 557 Metal interfaces} |
| 287 |
– |
|
| 288 |
– |
Our model systems are composed of approximately 4000 metal atoms |
| 289 |
– |
cut along the 557 plane so that they are periodic in the {\it x} and {\it y} |
| 290 |
– |
directions exposing the 557 plane in the {\it z} direction. Runs at various |
| 291 |
– |
temperatures ranging from 300~K to 1200~K were started with the intent |
| 292 |
– |
of viewing relative stability of the surface when CO was not present in the |
| 293 |
– |
system. Owing to the different melting points (1337~K for Au and 2045~K for Pt), |
| 294 |
– |
the bare crystal systems were initially run in the Canonical ensemble at |
| 295 |
– |
800~K and 1000~K respectively for 100 ps. Various amounts of CO were |
| 296 |
– |
placed in the vacuum region, which upon full adsorption to the surface |
| 297 |
– |
corresponded to 5\%, 25\%, 33\%, and 50\% coverages. Because of the |
| 298 |
– |
high temperature and the difference in binding energies, the platinum systems |
| 299 |
– |
very rarely had CO that was not adsorbed to the surface whereas the gold systems |
| 300 |
– |
often had a substantial minority of CO away from the surface. |
| 301 |
– |
These systems were again allowed to reach thermal equilibrium before being run in the |
| 302 |
– |
microcanonical ensemble. All of the systems examined in this work were |
| 303 |
– |
run for at least 40 ns. A subset that were undergoing interesting effects |
| 304 |
– |
have been allowed to continue running with one system approaching 200 ns. |
| 305 |
– |
All simulations were run using the open source molecular dynamics package, OpenMD. \cite{Ewald, OOPSE} |
| 306 |
– |
|
| 307 |
– |
|
| 308 |
– |
|
| 309 |
– |
|
| 310 |
– |
|
| 311 |
– |
|
| 312 |
– |
%\subsection{System} |
| 313 |
– |
%Once equilibration was reached, the systems were exposed to various sub-monolayer coverage of CO: $0, \frac{1}{10}, \frac{1}{4}, \frac{1}{3},\frac{1}{2}$. The CO was started many \AA~above the surface with random velocity and rotational velocity vectors sampling from a Gaussian distribution centered on the temperature of the equilibrated metal block. Full adsorption occurred over the period of approximately 10 ps for Pt, while the binding energy between Au and CO is smaller and led to an incomplete adsorption. The metal-metal interactions were treated using the Embedded Atom Method while the Pt-CO and Au-CO interactions were fit to experimental data and quantum calculations. The raised temperature helped shorten the length of the simulations by allowing the activation barrier of reconstruction to be more easily overcome. A few runs at lower temperatures showed the very beginnings of reconstructions, but their simulation lengths limited their usefulness. |
| 314 |
– |
|
| 315 |
– |
|
| 316 |
|
%Table of Parameters |
| 317 |
|
%Pt Parameter Set 9 |
| 318 |
|
%Au Parameter Set 35 |
| 319 |
|
\begin{table}[H] |
| 320 |
< |
\caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol} |
| 320 |
> |
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
| 321 |
> |
interactions are modeled with Lennard-Jones potentials. While the |
| 322 |
> |
metal-O interactions were fit to Morse |
| 323 |
> |
potentials. Distances are given in \AA~and energies in kcal/mol. } |
| 324 |
|
\centering |
| 325 |
|
\begin{tabular}{| c | cc | c | ccc |} |
| 326 |
|
\hline |
| 327 |
< |
\multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\ |
| 327 |
> |
& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\ |
| 328 |
|
\hline |
| 326 |
– |
& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\ |
| 327 |
– |
\hline |
| 329 |
|
\textbf{Pt-C} & 1.3 & 15 & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\ |
| 330 |
|
\textbf{Au-C} & 1.9 & 6.5 & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\ |
| 331 |
|
|
| 332 |
|
\hline |
| 333 |
|
\end{tabular} |
| 334 |
+ |
\label{tab:co_parameters} |
| 335 |
|
\end{table} |
| 336 |
|
|
| 337 |
|
%Table of energies |
| 338 |
|
\begin{table}[H] |
| 339 |
< |
\caption{Adsorption energies in eV} |
| 339 |
> |
\caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials |
| 340 |
> |
described in this work. All values are in eV.} |
| 341 |
|
\centering |
| 342 |
|
\begin{tabular}{| c | cc |} |
| 343 |
< |
\hline |
| 344 |
< |
& Calc. & Exp. \\ |
| 345 |
< |
\hline |
| 346 |
< |
\textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen:1979}-- -1.9~\cite{Yeo} \\ |
| 347 |
< |
\textbf{Au-CO} & -0.39 & -0.40~\cite{TPD_Gold} \\ |
| 348 |
< |
\hline |
| 343 |
> |
\hline |
| 344 |
> |
& Calculated & Experimental \\ |
| 345 |
> |
\hline |
| 346 |
> |
\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
| 347 |
> |
(Ref. \protect\cite{Kelemen:1979}) \\ |
| 348 |
> |
& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
| 349 |
> |
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPD_Gold}) \\ |
| 350 |
> |
\hline |
| 351 |
|
\end{tabular} |
| 352 |
+ |
\label{tab:co_energies} |
| 353 |
|
\end{table} |
| 354 |
|
|
| 355 |
+ |
\subsection{Pt(557) and Au(557) metal interfaces} |
| 356 |
+ |
Our Pt system is an orthorhombic periodic box of dimensions |
| 357 |
+ |
54.482~x~50.046~x~120.88~\AA~while our Au system has |
| 358 |
+ |
dimensions of 57.4~x~51.9285~x~100~\AA. |
| 359 |
+ |
The systems are arranged in a FCC crystal that have been cut |
| 360 |
+ |
along the (557) plane so that they are periodic in the {\it x} and |
| 361 |
+ |
{\it y} directions, and have been oriented to expose two aligned |
| 362 |
+ |
(557) cuts along the extended {\it z}-axis. Simulations of the |
| 363 |
+ |
bare metal interfaces at temperatures ranging from 300~K to |
| 364 |
+ |
1200~K were performed to confirm the relative |
| 365 |
+ |
stability of the surfaces without a CO overlayer. |
| 366 |
|
|
| 367 |
+ |
The different bulk melting temperatures (1337~K for Au\cite{Au:melting} |
| 368 |
+ |
and 2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
| 369 |
+ |
different temperatures for the two metals. The bare Au and Pt surfaces were |
| 370 |
+ |
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
| 371 |
+ |
respectively for 100 ps. The two surfaces were relatively stable at these |
| 372 |
+ |
temperatures when no CO was present, but experienced increased surface |
| 373 |
+ |
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
| 374 |
+ |
that was initially placed in the vacuum region. Upon full adsorption, |
| 375 |
+ |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 376 |
+ |
coverage. Higher coverages resulted in the formation of a double layer of CO, |
| 377 |
+ |
which introduces artifacts that are not relevant to (557) reconstruction. |
| 378 |
+ |
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
| 379 |
+ |
the Au surfaces often had a significant CO population in the gas |
| 380 |
+ |
phase. These systems were allowed to reach thermal equilibrium (over |
| 381 |
+ |
5~ns) before being run in the microcanonical (NVE) ensemble for |
| 382 |
+ |
data collection. All of the systems examined had at least 40~ns in the |
| 383 |
+ |
data collection stage, although simulation times for some Pt of the |
| 384 |
+ |
systems exceeded 200~ns. Simulations were carried out using the open |
| 385 |
+ |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} |
| 386 |
|
|
| 387 |
|
|
| 388 |
|
|
| 389 |
|
|
| 390 |
< |
% Just results, leave discussion for discussion section |
| 390 |
> |
% RESULTS |
| 391 |
> |
% |
| 392 |
|
\section{Results} |
| 393 |
< |
\subsection{Diffusion} |
| 394 |
< |
An ideal metal surface displaying a low-energy facet, a (111) face for |
| 395 |
< |
instance, is unlikely to experience much surface diffusion because of |
| 396 |
< |
the large energy barrier associated with atoms 'lifting' from the top |
| 397 |
< |
layer to then be able to explore the surface. Rougher surfaces, those |
| 398 |
< |
that already contain numerous adatoms, step edges, and kinks, should |
| 399 |
< |
have concomitantly higher surface diffusion rates. Tao et al. showed |
| 400 |
< |
that the platinum 557 surface undergoes two separate reconstructions |
| 401 |
< |
upon CO adsorption. \cite{Tao:2010} The first reconstruction involves a |
| 402 |
< |
doubling of the step edge height which is accomplished by a doubling |
| 403 |
< |
of the plateau length. The second reconstruction led to the formation of |
| 404 |
< |
triangular motifs stretching across the lengthened plateaus. |
| 393 |
> |
\subsection{Structural remodeling} |
| 394 |
> |
The surfaces of both systems, upon dosage of CO, began |
| 395 |
> |
to undergo remodeling that was not observed in the bare |
| 396 |
> |
metal system. The surfaces which were not exposed to CO |
| 397 |
> |
did experience minor roughening of the step-edge because |
| 398 |
> |
of the elevated temperatures, but the |
| 399 |
> |
(557) lattice was well-maintained throughout the simulation |
| 400 |
> |
time. The Au systems were limited to greater amounts of |
| 401 |
> |
roughening, i.e. breakup of the step-edge, and some step |
| 402 |
> |
wandering. The lower coverage Pt systems experienced |
| 403 |
> |
similar restructuring but to a greater extent when |
| 404 |
> |
compared to the Au systems. The 50\% coverage |
| 405 |
> |
Pt system was unique among our simulations in that it |
| 406 |
> |
formed numerous double layers through step coalescence, |
| 407 |
> |
similar to results reported by Tao et al.\cite{Tao:2010} |
| 408 |
|
|
| 369 |
– |
As shown in Figure 2, over a period of approximately 100 ns, the surface |
| 370 |
– |
has reconstructed from a 557 surface by doubling the step height and |
| 371 |
– |
step length. Focusing on only the platinum, or gold, atoms that were |
| 372 |
– |
deemed mobile on the surface, an analysis of the surface diffusion was |
| 373 |
– |
performed. A particle was considered mobile once it had traveled more |
| 374 |
– |
than 2~\AA between snapshots. This immediately eliminates all of the |
| 375 |
– |
bulk metal and greatly limits the number of surface atoms examined. |
| 376 |
– |
Since diffusion on a surface is strongly affected by overcoming energy |
| 377 |
– |
barriers, the diffusion parallel to the step edge axis was determined |
| 378 |
– |
separately from the diffusion perpendicular to the step edge. The results |
| 379 |
– |
at various coverages on both platinum and gold are shown in Table 4. |
| 409 |
|
|
| 410 |
< |
%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. |
| 410 |
> |
\subsubsection{Step wandering} |
| 411 |
> |
The 0\% coverage surfaces for both metals showed minimal |
| 412 |
> |
movement at their respective run temperatures. As the CO |
| 413 |
> |
coverage increased however, the mobility of the surface, |
| 414 |
> |
adatoms and step-edges alike, also increased. Additionally, |
| 415 |
> |
at the higher coverages on both metals, there was more |
| 416 |
> |
step-wandering. Except for the 50\% Pt system, the step-edges |
| 417 |
> |
did not coalesce in any of the other simulations, instead preferring |
| 418 |
> |
to keep nearly the same distance between steps as in the |
| 419 |
> |
original (557) lattice. Previous work by Williams et al.\cite{Williams:1991, Williams:1994} |
| 420 |
> |
highlights the repulsion that exists between step-edges even |
| 421 |
> |
when no direct interactions are present in the system. This |
| 422 |
> |
repulsion arises because the entropy of the step-edges is constrained, |
| 423 |
> |
since step-edge crossing is not allowed. This entropic repulsion |
| 424 |
> |
does not completely define the interactions between steps, |
| 425 |
> |
which is why some surfaces will undergo step coalescence, |
| 426 |
> |
where additional attractive interactions can overcome the |
| 427 |
> |
repulsion\cite{Williams:1991} and others will not. The presence and concentration |
| 428 |
> |
of adsorbates, as shown in this work, can affect these step interactions, potentially |
| 429 |
> |
leading to a new surface structure as the thermodynamic minimum. |
| 430 |
|
|
| 431 |
+ |
\subsubsection{Double layers} |
| 432 |
+ |
Tao et al. have shown experimentally that the Pt(557) surface |
| 433 |
+ |
undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} |
| 434 |
+ |
The first involves a doubling of the step height and plateau length. |
| 435 |
+ |
Similar behavior has been seen to occur on numerous surfaces |
| 436 |
+ |
at varying conditions: Ni(977), Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
| 437 |
+ |
Of the two systems we examined, the Pt system showed a greater |
| 438 |
+ |
propensity for reconstruction when compared to the Au system |
| 439 |
+ |
because of the larger surface mobility and extent of step wandering. |
| 440 |
+ |
The amount of reconstruction is correlated to the amount of CO |
| 441 |
+ |
adsorbed upon the surface. This appears to be related to the |
| 442 |
+ |
effect that adsorbate coverage has on edge breakup and on the |
| 443 |
+ |
surface diffusion of metal adatoms. While both systems displayed |
| 444 |
+ |
step-edge wandering, only the 50\% Pt surface underwent the |
| 445 |
+ |
doubling seen by Tao et al.\cite{Tao:2010} within the time scales studied here. |
| 446 |
+ |
Over longer periods, (150~ns) two more double layers formed |
| 447 |
+ |
on this interface. Although double layer formation did not occur |
| 448 |
+ |
in the other Pt systems, they show more step-wandering and |
| 449 |
+ |
general roughening compared to their Au counterparts. The |
| 450 |
+ |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
| 451 |
+ |
various times along the simulation showing the evolution of a step-edge. |
| 452 |
+ |
|
| 453 |
+ |
The second reconstruction on the Pt(557) surface observed by |
| 454 |
+ |
Tao involved the formation of triangular clusters that stretched |
| 455 |
+ |
across the plateau between two step-edges. Neither system, within |
| 456 |
+ |
the 40~ns time scale or the extended simulation time of 150~ns for |
| 457 |
+ |
the 50\% Pt system, experienced this reconstruction. |
| 458 |
+ |
|
| 459 |
+ |
\subsection{Dynamics} |
| 460 |
+ |
Previous atomistic simulations of stepped surfaces dealt largely |
| 461 |
+ |
with the energetics and structures at different conditions |
| 462 |
+ |
\cite{Williams:1991,Williams:1994}. Consequently, the most common |
| 463 |
+ |
technique utilized to date has been Monte Carlo sampling. Monte Carlo gives an efficient |
| 464 |
+ |
sampling of the equilibrium thermodynamic landscape at the expense |
| 465 |
+ |
of ignoring the dynamics of the system. Previous experimental work by Pearl and |
| 466 |
+ |
Sibener\cite{Pearl}, using STM, has been able to capture the coalescing |
| 467 |
+ |
of steps on Ni(977). The time scale of the image acquisition, |
| 468 |
+ |
$\sim$70~s/image provides an upper bound for the time required for |
| 469 |
+ |
the doubling to occur. In this section we give data on dynamic and |
| 470 |
+ |
transport properties, e.g. diffusion, layer formation time, etc. |
| 471 |
+ |
|
| 472 |
+ |
|
| 473 |
+ |
\subsubsection{Transport of surface metal atoms} |
| 474 |
+ |
%forcedSystems/stepSeparation |
| 475 |
+ |
The movement or wandering of a step-edge is a cooperative effect |
| 476 |
+ |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
| 477 |
+ |
displaying a low index facet, (111) or (100), is unlikely to experience |
| 478 |
+ |
much surface diffusion because of the large energetic barrier that must |
| 479 |
+ |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
| 480 |
+ |
on higher-index facets provide a lower energy source for mobile metal atoms. |
| 481 |
+ |
Breaking away from the step-edge on a clean surface still imposes an |
| 482 |
+ |
energetic penalty around $\sim$~40 kcal/mol, but this is significantly easier than lifting |
| 483 |
+ |
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 484 |
+ |
The penalty lowers significantly when CO is present in sufficient quantities |
| 485 |
+ |
on the surface. For certain distributions of CO, the penalty can fall as low as |
| 486 |
+ |
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 487 |
+ |
diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are |
| 488 |
+ |
able to explore the terrace before rejoining either the original step-edge or |
| 489 |
+ |
becoming a part of a different edge. It is a more difficult process for an atom |
| 490 |
+ |
to traverse to a separate terrace although the presence of CO can lower the |
| 491 |
+ |
energy barrier required to lift or lower the adatom. By tracking the mobility of individual |
| 492 |
+ |
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 493 |
+ |
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 494 |
+ |
observation of the mobile metal atoms showed that they were typically in |
| 495 |
+ |
equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. |
| 496 |
+ |
At times, their motion was concerted and two or more adatoms would be |
| 497 |
+ |
observed moving together across the surfaces. |
| 498 |
+ |
|
| 499 |
+ |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 500 |
+ |
between saved configurations of the system (typically 10-100 ps). An atom that was |
| 501 |
+ |
truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 502 |
+ |
was used to prevent swamping the diffusion data with the in-place vibrational |
| 503 |
+ |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 504 |
+ |
local structures and in this work, the presence of single and double layer |
| 505 |
+ |
step-edges causes the diffusion parallel to the step-edges to be different |
| 506 |
+ |
from the diffusion perpendicular to these edges. Parallel and perpendicular |
| 507 |
+ |
diffusion constants are shown in Figure \ref{fig:diff}. |
| 508 |
+ |
|
| 509 |
+ |
The lack of a definite trend in the Au diffusion data is likely due |
| 510 |
+ |
to the weaker bonding between Au and CO. This leads to a lower |
| 511 |
+ |
coverage ({\it x}-axis) when compared to dosage amount, which |
| 512 |
+ |
then further limits the affects of the surface diffusion. The correlation |
| 513 |
+ |
between coverage and Pt diffusion rates conversely shows a |
| 514 |
+ |
definite trend marred by the highest coverage surface. Two |
| 515 |
+ |
explanations arise for this drop. First, upon a visual inspection of |
| 516 |
+ |
the system, after a double layer has been formed, it maintains its |
| 517 |
+ |
stability strongly and is no longer a good source for adatoms. By |
| 518 |
+ |
performing the same diffusion calculation but on a shorter run time |
| 519 |
+ |
(20~ns), only including data before the formation of the double layer, |
| 520 |
+ |
provides a $\mathbf{D}_{\perp}$ diffusion constant of $1.69~\pm~0.08$ |
| 521 |
+ |
and a $\mathbf{D}_{\parallel}$ diffusion constant of $6.30~\pm~0.08$. |
| 522 |
+ |
This places the parallel diffusion constant more closely in line with the |
| 523 |
+ |
expected trend, while the perpendicular diffusion constant does not |
| 524 |
+ |
drop as far. A secondary explanation arising from our analysis of the |
| 525 |
+ |
mechanism of double layer formation show the affect that CO on the |
| 526 |
+ |
surface has with respect to overcoming surface diffusion of Pt. If the |
| 527 |
+ |
coverage is too sparse, the Pt engages in minimal interactions and |
| 528 |
+ |
thus minimal diffusion. As coverage increases, there are more favorable |
| 529 |
+ |
arrangements of CO on the surface allowing the formation of a path, |
| 530 |
+ |
a minimum energy trajectory, for the adatom to explore the surface. |
| 531 |
+ |
As the CO is constantly moving on the surface, this path is constantly |
| 532 |
+ |
changing. If the coverage becomes too great, the paths could |
| 533 |
+ |
potentially be clogged leading to a decrease in diffusion despite |
| 534 |
+ |
their being more adatoms and step-wandering. |
| 535 |
+ |
|
| 536 |
+ |
\subsubsection{Dynamics of double layer formation} |
| 537 |
+ |
The increased diffusion on Pt at the higher |
| 538 |
+ |
CO coverages plays a primary role in double layer formation. However, this is not |
| 539 |
+ |
a complete explanation -- the 33\%~Pt system |
| 540 |
+ |
has higher diffusion constants but did not show |
| 541 |
+ |
any signs of edge doubling in the observed run time. On the |
| 542 |
+ |
50\%~Pt system, one layer formed within the first 40~ns of simulation time, while two more were formed as the system was run for an additional |
| 543 |
+ |
110~ns (150~ns total). Previous experimental |
| 544 |
+ |
work gives insight into the upper bounds of the |
| 545 |
+ |
time required for step coalescence.\cite{Williams:1991,Pearl} |
| 546 |
+ |
In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 547 |
+ |
appearance of a double layer, appears at 19~ns |
| 548 |
+ |
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
| 549 |
+ |
formed the double layer and by 86~ns, the complete layer |
| 550 |
+ |
has been flattened out. The double layer could be considered |
| 551 |
+ |
``complete" by 37~ns but remains a bit rough. From the |
| 552 |
+ |
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
| 553 |
+ |
$\sim$40~ns was necessary for the layer to completely straighten. |
| 554 |
+ |
The other two layers in this simulation formed over periods of |
| 555 |
+ |
22~ns and 42~ns respectively. Comparing this to the upper |
| 556 |
+ |
bounds of the image scan, it is likely that most aspects of this |
| 557 |
+ |
reconstruction occur very rapidly. A possible explanation |
| 558 |
+ |
for this rapid reconstruction is the elevated temperatures |
| 559 |
+ |
under which our systems were simulated. It is probable that the process would |
| 560 |
+ |
take longer at lower temperatures. |
| 561 |
+ |
|
| 562 |
+ |
%Evolution of surface |
| 563 |
|
\begin{figure}[H] |
| 564 |
< |
\includegraphics[scale=0.6]{DiffusionComparison_error.png} |
| 565 |
< |
\caption{Diffusion parallel to the step edge will always be higher than that perpendicular to the edge because of the lower energy barrier associated with going from approximately 7 nearest neighbors to 5, as compared to the 3 of an adatom. Additionally, the observed maximum and subsequent decrease for the Pt system suggests that the CO self-interactions are playing a significant role with regards to movement of the platinum atoms around and more importantly across the surface. } |
| 564 |
> |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 565 |
> |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 566 |
> |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 567 |
> |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 568 |
> |
doubling of the layers appears only after two adjacent step-edges |
| 569 |
> |
touch. The circled spot in (b) nucleated the growth of the double |
| 570 |
> |
step observed in the later configurations.} |
| 571 |
> |
\label{fig:reconstruct} |
| 572 |
|
\end{figure} |
| 573 |
|
|
| 574 |
< |
%Table of Diffusion Constants |
| 575 |
< |
%Add gold?M |
| 574 |
> |
\begin{figure}[H] |
| 575 |
> |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
| 576 |
> |
\caption{Diffusion constants for mobile surface atoms along directions |
| 577 |
> |
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 578 |
> |
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 579 |
> |
surface coverage. Diffusion parallel to the step-edge is higher |
| 580 |
> |
than that perpendicular to the edge because of the lower energy |
| 581 |
> |
barrier associated with traversing along the edge as compared to |
| 582 |
> |
completely breaking away. Additionally, the observed |
| 583 |
> |
maximum and subsequent decrease for the Pt system suggests that the |
| 584 |
> |
CO self-interactions are playing a significant role with regards to |
| 585 |
> |
movement of the Pt atoms around and across the surface. } |
| 586 |
> |
\label{fig:diff} |
| 587 |
> |
\end{figure} |
| 588 |
> |
|
| 589 |
> |
|
| 590 |
> |
|
| 591 |
> |
|
| 592 |
> |
%Discussion |
| 593 |
> |
\section{Discussion} |
| 594 |
> |
We have shown that the classical potential models are able to model the initial reconstruction of the |
| 595 |
> |
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 596 |
> |
were able to observe features of the dynamic processes necessary for this reconstruction. |
| 597 |
> |
|
| 598 |
> |
\subsection{Mechanism for restructuring} |
| 599 |
> |
Since the Au surface showed no large scale restructuring throughout |
| 600 |
> |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 601 |
> |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 602 |
> |
Similarities of our results to those reported previously by |
| 603 |
> |
Tao et al.\cite{Tao:2010} are quite |
| 604 |
> |
strong. The simulated Pt |
| 605 |
> |
system exposed to a large dosage of CO readily restructures by doubling the terrace |
| 606 |
> |
widths and step heights. The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a time, but is rapid on experimental timescales. |
| 607 |
> |
The adatoms either |
| 608 |
> |
break away from the step-edge and stay on the lower terrace or they lift |
| 609 |
> |
up onto a higher terrace. Once ``free'', they diffuse on the terrace |
| 610 |
> |
until reaching another step-edge or rejoining their original edge. |
| 611 |
> |
This combination of growth and decay of the step-edges is in a state of |
| 612 |
> |
dynamic equilibrium. However, once two previously separated edges |
| 613 |
> |
meet as shown in Figure 1.B, this nucleates the rest of the edge to meet up, forming a double layer. |
| 614 |
> |
From simulations which exhibit a double layer, the time delay from the initial appearance of a nucleation point to a fully formed double layer is $\sim$35~ns. |
| 615 |
> |
|
| 616 |
> |
A number of possible mechanisms exist to explain the role of adsorbed |
| 617 |
> |
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 618 |
> |
CO molecules adsorbed on the surface is one possibility. However, |
| 619 |
> |
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 620 |
> |
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 621 |
> |
relative to each other, through atop adsorption for example, this explanation |
| 622 |
> |
gains some credence. The energetic repulsion between two CO located a |
| 623 |
> |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in |
| 624 |
> |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 625 |
> |
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 626 |
> |
nearly 0 kcal/mol. Allowing the CO's to leave a purely vertical orientation |
| 627 |
> |
also quickly drops the repulsion, a minimum of 6.2 kcal/mol is reached at $\sim$24 degrees between the 2 CO when the carbons are locked at a distance of 2.77 \AA apart. |
| 628 |
> |
As mentioned above, the energy barrier for surface diffusion |
| 629 |
> |
of a Pt adatom is only 4 kcal/mol. So this repulsion between neighboring CO molecules can |
| 630 |
> |
increase the surface diffusion. However, the residence time of CO on Pt was |
| 631 |
> |
examined and while the majority of the CO is on or near the surface throughout |
| 632 |
> |
the run, most molecules are mobile. This mobility suggests that the CO are more |
| 633 |
> |
likely to shift their positions without necessarily the Pt along with them. |
| 634 |
> |
|
| 635 |
> |
Another possible and more likely mechanism for the restructuring is in the |
| 636 |
> |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 637 |
> |
Pt atoms. This would then have the effect of increasing surface mobility |
| 638 |
> |
of these atoms. To test this hypothesis, numerous configurations of |
| 639 |
> |
CO in varying quantities were arranged on the higher and lower plateaus |
| 640 |
> |
around a step on a otherwise clean Pt(557) surface. One representative |
| 641 |
> |
configuration is displayed in Figure \ref{fig:lambda}. Single or concerted movement |
| 642 |
> |
of Pt atoms was then examined to determine possible barriers. Because |
| 643 |
> |
the movement was forced along a pre-defined reaction coordinate that may differ |
| 644 |
> |
from the true minimum of this path, only the beginning and ending energies |
| 645 |
> |
are displayed in Table \ref{tab:rxcoord} with the corresponding beginning and ending reaction coordinates in Figure \ref{fig:lambdaTable}. These values suggest that the presence of CO at suitable |
| 646 |
> |
locations can lead to lowered barriers for Pt breaking apart from the step-edge. |
| 647 |
> |
Additionally, as highlighted in Figure \ref{fig:lambda}, the presence of CO makes the |
| 648 |
> |
burrowing and lifting of adatoms favorable, whereas without CO, the process is neutral |
| 649 |
> |
in terms of energetics. |
| 650 |
> |
|
| 651 |
> |
%lambda progression of Pt -> shoving its way into the step |
| 652 |
> |
\begin{figure}[H] |
| 653 |
> |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
| 654 |
> |
\caption{A model system of the Pt(557) surface was used as the framework |
| 655 |
> |
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 656 |
> |
placements, and rotations of CO were examined as they affect Pt movement. |
| 657 |
> |
The coordinate displayed in this Figure was a representative run. As shown |
| 658 |
> |
in Table \ref{tab:rxcoord}, relative to the energy of the system at 0\%, there |
| 659 |
> |
is a slight decrease upon insertion of the Pt atom into the step-edge along |
| 660 |
> |
with the resultant lifting of the other Pt atom when CO is present at certain positions.} |
| 661 |
> |
\label{fig:lambda} |
| 662 |
> |
\end{figure} |
| 663 |
> |
|
| 664 |
> |
\begin{figure}[H] |
| 665 |
> |
\includegraphics[totalheight=0.9\textheight]{lambdaTable.png} |
| 666 |
> |
\caption{} |
| 667 |
> |
\label{fig:lambdaTable} |
| 668 |
> |
\end{figure} |
| 669 |
> |
|
| 670 |
> |
|
| 671 |
> |
|
| 672 |
|
\begin{table}[H] |
| 673 |
< |
\caption{Platinum and gold diffusion constants parallel and perpendicular to the 557 step edge. As the coverage increases, the diffusion constants parallel and perpendicular to the step edge both initially increase and then decrease slightly. Units are \AA\textsuperscript{2}/ns} |
| 673 |
> |
\caption{} |
| 674 |
|
\centering |
| 675 |
< |
\begin{tabular}{| c | cc | cc | c |} |
| 675 |
> |
\begin{tabular}{| c || c | c | c | c |} |
| 676 |
|
\hline |
| 677 |
< |
\textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Time (ns)}\\ |
| 677 |
> |
\textbf{System} & 0.5~\AA & 2~\AA & 4~\AA & 6~\AA \\ |
| 678 |
|
\hline |
| 679 |
< |
&\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} & \\ |
| 680 |
< |
\hline |
| 681 |
< |
50\% & 4.32 $\pm$ 0.02 & 1.185 $\pm$ 0.008 & 1.72 $\pm$ 0.02 & 0.455 $\pm$ 0.006 & 40 \\ |
| 682 |
< |
33\% & 5.18 $\pm$ 0.03 & 1.999 $\pm$ 0.005 & 1.95 $\pm$ 0.02 & 0.337 $\pm$ 0.004 & 40 \\ |
| 683 |
< |
25\% & 5.01 $\pm$ 0.02 & 1.574 $\pm$ 0.004 & 1.26 $\pm$ 0.03 & 0.377 $\pm$ 0.006 & 40 \\ |
| 684 |
< |
5\% & 3.61 $\pm$ 0.02 & 0.355 $\pm$ 0.002 & 1.84 $\pm$ 0.03 & 0.169 $\pm$ 0.004 & 40 \\ |
| 403 |
< |
0\% & 3.27 $\pm$ 0.02 & 0.147 $\pm$ 0.004 & 1.50 $\pm$ 0.02 & 0.194 $\pm$ 0.002 & 40 \\ |
| 679 |
> |
A & 6.38 & 38.34 & 44.65 & 47.60 \\ |
| 680 |
> |
B & -20.72 & 0.67 & 17.33 & 24.28 \\ |
| 681 |
> |
C & 4.92 & 27.02 & 41.05 & 47.43 \\ |
| 682 |
> |
D & -16.97 & 21.21 & 35.87 & 40.93 \\ |
| 683 |
> |
E & 5.92 & 30.96 & 43.69 & 49.23 \\ |
| 684 |
> |
F & 8.53 & 46.23 & 53.98 & 65.55 \\ |
| 685 |
|
\hline |
| 686 |
|
\end{tabular} |
| 687 |
+ |
\label{tab:rxcoord} |
| 688 |
|
\end{table} |
| 689 |
|
|
| 690 |
|
|
| 409 |
– |
|
| 410 |
– |
%Discussion |
| 411 |
– |
\section{Discussion} |
| 412 |
– |
Comparing the results from simulation to those reported previously by Tao et al. the similarities in the platinum and CO system are quite strong. As shown in figure 1, the simulated platinum system under a CO atmosphere will restructure slightly by doubling the terrace heights. The restructuring appears to occur slowly, one to two platinum atoms at a time. Looking at individual snapshots, these adatoms tend to either rise on top of the plateau or break away from the step edge and then diffuse perpendicularly to the step direction until reaching another step edge. This combination of growth and decay of the step edges appears to be in somewhat of a state of dynamic equilibrium. However, once two previously separated edges meet as shown in figure 1.B, this point tends to act as a focus or growth point for the rest of the edge to meet up, akin to that of a zipper. From the handful of cases where a double layer was formed during the simulation, measuring from the initial appearance of a growth point, the double layer tends to be fully formed within $\sim$~35 ns. |
| 413 |
– |
|
| 691 |
|
\subsection{Diffusion} |
| 692 |
< |
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?) |
| 692 |
> |
The diffusion parallel to the step-edge tends to be |
| 693 |
> |
much larger than that perpendicular to the step-edge. The dynamic |
| 694 |
> |
equilibrium that is established between the step-edge and adatom interface. The coverage |
| 695 |
> |
of CO also appears to play a slight role in relative rates of diffusion, as shown in Figure \ref{fig:diff}. |
| 696 |
> |
The |
| 697 |
> |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
| 698 |
> |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
| 699 |
> |
appears, parallel diffusion, along the now slightly angled step-edge, will allow for |
| 700 |
> |
a faster formation of the double layer than if the entire process were dependent on |
| 701 |
> |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
| 702 |
> |
more likely a growth point is to be formed. |
| 703 |
|
\\ |
| 704 |
< |
\\ |
| 705 |
< |
%Evolution of surface |
| 704 |
> |
|
| 705 |
> |
|
| 706 |
> |
%breaking of the double layer upon removal of CO |
| 707 |
|
\begin{figure}[H] |
| 708 |
< |
\includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 709 |
< |
\caption{Four snapshots of the $\frac{1}{2}$ monolayer system at various times a) 258 ps b) 19 ns c) 31.2 ns and d) 86.1 ns. Slight disruption of the surface occurs fairly quickly. However, the doubling of the layers seems to be very dependent on the initial linking of two separate step edges. The focal point in b, appears to be a growth spot for the rest of the double layer.} |
| 708 |
> |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 709 |
> |
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
| 710 |
> |
helped maintain the stability of the double layer and upon removal the two layers break |
| 711 |
> |
and begin separating. The separation is not a simple pulling apart however, rather |
| 712 |
> |
there is a mixing of the lower and upper atoms at the edge.} |
| 713 |
> |
\label{fig:breaking} |
| 714 |
|
\end{figure} |
| 715 |
|
|
| 716 |
|
|
| 717 |
|
|
| 718 |
|
|
| 719 |
|
%Peaks! |
| 720 |
< |
\begin{figure}[H] |
| 721 |
< |
\includegraphics[scale=0.25]{doublePeaks_noCO.png} |
| 722 |
< |
\caption{} |
| 723 |
< |
\end{figure} |
| 720 |
> |
%\begin{figure}[H] |
| 721 |
> |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 722 |
> |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 723 |
> |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 724 |
> |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 725 |
> |
%\label{fig:peaks} |
| 726 |
> |
%\end{figure} |
| 727 |
> |
|
| 728 |
> |
|
| 729 |
> |
%Don't think I need this |
| 730 |
> |
%clean surface... |
| 731 |
> |
%\begin{figure}[H] |
| 732 |
> |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
| 733 |
> |
%\caption{} |
| 734 |
> |
|
| 735 |
> |
%\end{figure} |
| 736 |
> |
%\label{fig:clean} |
| 737 |
> |
|
| 738 |
> |
|
| 739 |
|
\section{Conclusion} |
| 740 |
+ |
In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in less than a $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems. |
| 741 |
|
|
| 742 |
+ |
%Things I am not ready to remove yet |
| 743 |
|
|
| 744 |
+ |
%Table of Diffusion Constants |
| 745 |
+ |
%Add gold?M |
| 746 |
+ |
% \begin{table}[H] |
| 747 |
+ |
% \caption{} |
| 748 |
+ |
% \centering |
| 749 |
+ |
% \begin{tabular}{| c | cc | cc | } |
| 750 |
+ |
% \hline |
| 751 |
+ |
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
| 752 |
+ |
% \hline |
| 753 |
+ |
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
| 754 |
+ |
% \hline |
| 755 |
+ |
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
| 756 |
+ |
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
| 757 |
+ |
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
| 758 |
+ |
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
| 759 |
+ |
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
| 760 |
+ |
% \hline |
| 761 |
+ |
% \end{tabular} |
| 762 |
+ |
% \end{table} |
| 763 |
+ |
|
| 764 |
|
\section{Acknowledgments} |
| 765 |
|
Support for this project was provided by the National Science |
| 766 |
|
Foundation under grant CHE-0848243 and by the Center for Sustainable |
